A STUDY ON PORE FORMATION AND EVOLUTION AND ITS … Uzzal Hossain_Joardder_Thesis.pdfA STUDY ON PORE FORMATION AND EVOLUTION, AND ITS EFFECT ON FOOD QUALITY DURING INTERMITTENT MICROWAVE-CONVECTIVE

A STUDY ON PORE FORMATION AND

EVOLUTION, AND ITS EFFECT ON FOOD

QUALITY DURING INTERMITTENT

MICROWAVE-CONVECTIVE DRYING

(IMCD)

Mohammad Uzzal Hossain Joardder

B. Sc. In Mechanical Engineering

Submitted in fulfilment of the requirements for the degree of

Doctor of Philosophy

Chemistry, Physics and Mechanical Engineering

Science and Engineering Faculty

Queensland University of Technology

February 2016

To those who serve humanity

throughout history

Pore Formation and Evolution, Food Quality and Intermittent Microwave Convective

Drying i

Keywords

Binary diffusion

Capillary diffusion

Case hardening

COMSOL Multiphysics

Dielectric properties

Diffusion coefficient

Effective diffusivity

Energy efficiency

Equilibrium vapour

Gas pressure

Evaporation rate

Food quality

Glass transition temperature

Heat and mass transfer

Intermittent microwave-convective drying

Lambert’s Law

Mathematical modelling

Microwave power distribution

Multicomponent transport

Multiphase porous media model

Microstructure

Nano- pores

Non-equilibrium evaporation

Non-uniform heating

Porosity

Pore evolution

Rehydration

Pore Formation and Evolution, Food Quality and Intermittent Microwave Convective Drying iii

Abstract

A number of factors including quality of raw material, internal microstructure,

method of preparation, pre-processing treatments and drying conditions affect the

quality of dried food. The structure of the food materials goes through deformations

due to the simultaneous effect of heat and mass transfer during the drying process.

Pore formation and evolution lead to changes in many quality attributes and directly

affects physical properties including the mass diffusion coefficient, thermal

conductivity, thermal diffusivity and microstructure. A considerable amount of

research work has been done to investigate the characteristics of pore during drying.

However, the research up to now has examined porosity formation during traditional

drying methods like convective drying and freeze-drying. Microwave assisted

convective drying is an advanced area of drying and research shows that intermittent

microwave-convective drying (IMCD) increases both energy efficiency and product

quality. However, researchers have not investigated pore formation and evolution in

IMCD yet.

Plant-based food materials are complex in nature as these have heterogeneous,

amorphous, hygroscopic and porous properties. During drying, water from

hygroscopic porous media is migrated in different phases (e.g. liquid water and

vapour). Only multiphase transport models consider transport of liquid water,

vapour, and the air inside the food materials separately and, therefore,, are more

realistic. However, currently, there is no multiphase model for IMCD process.

This research, therefore, first develops a pore formation and evolution model

and investigates the relationship between the porosity and mechanical and other

properties of food. The model takes both process parameters (e.g. drying

temperature) and sample properties (e.g. glass transition temperature) into

consideration. The model can predict dynamically the changes in porosity, shrinkage

and case hardening of food samples during drying. A multiphase model for IMWC

drying has been developed taking porosity evolution and shrinkage over the course

of drying into account. In this model, solid matrix, liquid water and gas (water

vapour and air) phases, pressure-driven flow as well as capillary diffusion, binary

diffusion, and evaporation are considered.

iv Pore Formation and Evolution, Food Quality and Intermittent Microwave Convective Drying

Thus, the model provides an in-depth understanding of IMCD drying enabling

investigation of moisture distribution, temperature distribution and redistribution,

evaporation, and fluxes due to different drying mechanisms, deformation, and pore

formation and evolution. Some selected properties including rehydration capacity,

microstructure and mechanical characteristics of IMCD treated samples have been

investigated and compared with that of convective drying. Uniform and higher open

porosity was found in the IMCD treated sample leading to better rehydration

capacity and texture. This study thus establishes that IMCD leads to an improvement

in the food quality and energy efficiency.

This research provides a method of porosity prediction taking process

conditions and sample properties into consideration. Eventually, more accurate

predictions of heat and mass transfer during IMCD were achieved because of

consideration of porosity evolution in these models. Some positive correlations were

found between pore development and the quality of IMCD treated samples. Finally, a

hypothesised relationship between process parameters, product quality attributes, and

porosity has been proposed. Therefore, the present study makes several noteworthy

contributions to the modelling of IMCD and its effect on food quality.

Pore Formation and Evolution, Food Quality and Intermittent Microwave Convective Drying v

List of Publications

Book (1)

M.U.H. Joardder, C. Kumar, M. A. Karim, and R. J. Brown (2015), 1.

Porosity: Establishing the Relationship between Drying Parameters and

Dried Food Quality. Springer (DOI 10.1007/978-3-319-23045-0)

Journal papers (12)

M. U. H. Joardder, C. Kumar, and M. A. Karim (2015) Food Structure: 2.

Its Formation and Relationships with Other Properties. Critical Reviews in

Food Science and Nutrition, (available online) [ I.F. 5.55]

M. U. H. Joardder; C. Kumar, R. J Brown, and M. A. Karim (2015) A 3.

micro-level investigation of the solid displacement method for porosity

determination of dried food. Journal of Food Engineering,166, 156–164

[I.F. 2.77]

M. U. H Joardder, R. J. Brown, C. Kumar, and M. A. Karim (2015) 4.

Effect of cell wall properties on porosity and shrinkage of dried apple.

International Journal of Food Properties, 18(10), 2327-2337. [I.F. 0.92]

C. Kumar, M. A. Karim and M.U.H. Joardder (2014) Intermittent Drying 5.

of Food Products: A Critical Review. Journal of Food Engineering, 121,

48–57 [Impact Factor 2.77]

M. U. H Joardder, R. J. Brown, C. Kumar, and M. A. Karim, Prediction 6.

of porosity of food materials during drying: current challenges and future

directions. Trends in Food Science & Technology (Under review) [IF 4.65]

Joardder et al., Prediction of porosity considering material properties and 7.

process conditions during drying. Food Biophysics (To be submitted)

[IF 1.63]

vi Pore Formation and Evolution, Food Quality and Intermittent Microwave Convective Drying

Joardder et al., Multiphase porous media model for Intermittent 8.

microwave-convective drying (IMCD) of food: Considering shrinkage and

pore evolution. International Journal of Heat and Mass Transfer (To be

submitted) [I.F. 2.38]

Joardder et al., Effect of pore formation and evolution during Intermittent 9.

microwave-convective drying (IMCD) on the quality of dried food,

Innovative Food Science and Emerging Technologies (To be submitted)

[IF 3.03]

C. Kumar, M. U. H. Joardder, T.W. Farrell, G. J. Millar, M. A. Karim 10.

(2015) A Modelling of Intermittent Microwave-Convective Drying

(IMCD) of Food materials. Drying Technology, (Online available).

C. Kumar, M. U. H. Joardder, T.W. Farrell, and M. A. Karim, (2015) 11.

Multiphase porous media model for Intermittent microwave-convective

drying (IMCD) of food: Model formulation and validation. Journal of

Thermal Science. (Under review) [IF 0.4]

C. Kumar, M. U. H. Joardder, T.W. Farrell and M. A. Karim (2015) A 12.

3D coupled electromagnetic and multiphase porous media model for

IMCD of food material. AIChE Journal, (Under Review ) [2.75]

M. I.H. Khan, C. Kumar, M.U.H. Joardder, and M. A. Karim, 13.

Determination of appropriate, effective diffusivity for different food

materials, Journal of Food Engineering, (Under Review) [IF 2.77]

Conference paper (11)

M. U. H. Joardder, M. A. Karim, C. Kumar, and R. J. Brown (2014) 14.

Prediction of shrinkage and porosity during drying: Considering both

material properties and process conditions. 12th International Congress on

Engineering and Food, At Québec City Convention Centre, Québec City,

Kuala Lumpur, Malaysia, June14-18, 2015.

Pore Formation and Evolution, Food Quality and Intermittent Microwave Convective Drying vii

M. U. H. Joardder, M. A. Karim, and C. Kumar (2013) Effect of 15.

moisture and temperature distribution on dried food Microstructure and

Porosity. From Model Foods to Food Models, the DREAM Project

International Conference, 24– 26 June 2013, Nantes, France. [Achieved

outstanding paper and plane fare to attend the conference]


Effect of cell wall properties on porosity and shrinkage during drying of

Apple. 1st International Conference on Food Properties (iCFP2014),

Kuala Lumpur, Malaysia, January 24–26, 2014. [Achieved best paper

award].

C. Kumar, M. U. H Joardder, M. A. Karim, G. J. Millar, and Z. M. Amin 17.

(2014) Temperature redistribution modelling during intermittent microwave

convective heating. Procedia Engineering, 90(2014), 544–549.

M. U. H Joardder, M.A. Karim, R.J. Brown, and C. Kumar (2014) 18.

Determination of effective moisture diffusivity of banana using

thermogravimetric analysis. Procedia Engineering, 90, 538–543.

M. U. H. Joardder, M.A. Karim, and C. Kumar (2013) Effect of 19.

temperature distribution on predicting the quality of microwave-

dehydrated food. Journal of Mechanical Engineering and Sciences, 5,

562–568.


Fractal dimension of dried foods: A correlation between microstructure

and porosity. Food Structures, Digestion and Health International

Conference 22–24 October 2013 - Melbourne, Australia.

M. U. Joardder, M. A. Karim, and C. Kumar (2013) Better 21.

Understanding of Food Material on the Basis of Water Holding Capacity.

International Conference on Mechanical, Industrial and Material

Engineering, 1–3 November 2013, Rajshahi, Bangladesh.

viii Pore Formation and Evolution, Food Quality and Intermittent Microwave Convective Drying

C. Kumar, M. U. H. Joardder, T. W. Farrell, G. J. Millar, and M.A. 22.

Karim (2014) Multiphase porous media model for heat and mass transfer

during drying of agricultural products. In 19th Australasian Fluid

Mechanics Conference, 8–11 December 2014, RMIT University,

Melbourne, VIC.

C. Kumar, M. A. Karim, M. U. H. Joardder, G. J. Miller, M. A. Karim, 23.

and Z. M. Amin (2014) Intermittent microwave convective heating:

modelling and experiments. 10th International Conference on Mechanical

Engineering, 20–21 June 2014, BUET, Dhaka, Bangladesh.

C. Kumar, M. A. Karim, S. C. Saha, M. U. H. Joardder, R. J. Brown, and 24.

D. Biswas (2013) Multiphysics modelling of convective drying of food

materials. Global Engineering, Science and Technology Conference, 28–

29 December 2013, Dhaka, Bangladesh.

C. Kumar, M. A. Karim, M. U. H. Joardder, and G. J. Miller (2012) 25.

Modelling Heat and Mass Transfer Process during Convection Drying of

Fruit. 4th International Conference on Computational Methods, 25–27

November 2012, Gold Coast, Australia.

Pore Formation and Evolution, Food Quality and Intermittent Microwave Convective Drying ix

List of Abbreviations

IMCD Intermittent Microwave-Convective Drying

MCD Continuous Microwave-Convective Drying

MW Microwave

CD Convective drying

COR Coefficient of Rehydration

GTT Glass Transition Temperature

DSC Differential Scanning Calorimeter

SEM Scanning Electron Microscope

PL Power Level (microwave power level)

PR Pulse Ratio (microwave intermittency)

RH Relative humidity (%)

db Dry basis

wb Wet basis

SSMF Solid structure mobility factor

ASD Air space deformation

x Pore Formation and Evolution, Food Quality and Intermittent Microwave Convective Drying

Table of Contents

Keywords .................................................................................................................................. i

Abstract ................................................................................................................................... iii

List of Publications ................................................................................................................... v

List of Abbreviations ............................................................................................................... ix

Table of Contents ..................................................................................................................... x

List of Figures ....................................................................................................................... xiv

List of Tables ....................................................................................................................... xviii

Statement of Original Authorship ......................................................................................... xix

Acknowledgements ................................................................................................................ xx

Chapter 1: Introduction ...................................................................................... 1

1.1 Background and motivation ........................................................................................... 1

1.2 Research problems ......................................................................................................... 2

1.3 Aims and objectives ....................................................................................................... 3

1.4 Significance and scope ................................................................................................... 4

1.5 Thesis outline ................................................................................................................. 5

Chapter 2: Literature Review ............................................................................. 8

2.1 Food drying .................................................................................................................... 8

2.2 Intermittent drying ....................................................................................................... 11

2.3 Intermittent microwave convective drying (imcd) ....................................................... 11 2.3.1 Combined microwave and another drying ......................................................... 12 2.3.2 Intermittent application of MW in CD............................................................... 13

2.4 Drying Models ............................................................................................................. 14 2.4.1 Empirical models ............................................................................................... 14 2.4.2 Diffusion-based (single phase) models .............................................................. 15 2.4.3 Multiphase models ............................................................................................. 17 2.4.4 MCD and IMCD model ..................................................................................... 18

2.5 Food structure .............................................................................................................. 19 2.5.1 Structural Homogeneity ..................................................................................... 20 2.5.2 Anisotropy ......................................................................................................... 22 2.5.3 Pore characteristics ............................................................................................ 23

2.6 Pore formation mecHanism.......................................................................................... 26 2.6.1 Moisture content ................................................................................................ 27 2.6.2 Water distribution .............................................................................................. 29 2.6.3 Structural mobility ............................................................................................. 32 2.6.4 Phase transition (Multiphase) ............................................................................ 33

2.7 Prediction of porosity ................................................................................................... 34 2.7.1 Empirical models ............................................................................................... 34 2.7.2 Theoretical models of porosity .......................................................................... 36

Pore Formation and Evolution, Food Quality and Intermittent Microwave Convective Drying xi

2.8 Effect of process parameters on quality ........................................................................41

2.9 Summary of literature and research gaps ......................................................................43

Chapter 3: Research Design .............................................................................. 45

3.1 Methodology and Research Design ..............................................................................45 3.1.1 Prediction of pore evolution ...............................................................................45 3.1.2 IMCD model .......................................................................................................46

3.2 Solution procedure ........................................................................................................47

3.3 Experimental investigation ...........................................................................................51 3.3.1 Sample preparation .............................................................................................52 3.3.2 Drying experiments ............................................................................................52 3.3.3 Ripeness..............................................................................................................55 3.3.4 Glass transition temperature ...............................................................................55 3.3.5 Power absorption ratio ........................................................................................56 3.3.6 Thermal imaging ................................................................................................56 3.3.7 Particle density determination ............................................................................56 3.3.8 Porosity Determination .......................................................................................61 3.3.9 Microstructure analysis ......................................................................................61 3.3.10 Mechanical properties determination .................................................................62 3.3.11 Image analysis ....................................................................................................63 3.3.12 Rehydration ........................................................................................................64

3.4 Statistical analysis .........................................................................................................65

Chapter 4: Single Phase Convective Drying and Pore Formation ................ 67

4.1 Model development ......................................................................................................67 4.1.1 Prediction of pore evolution ...............................................................................67 4.1.2 Single phase convective drying model ...............................................................75

4.2 Governing equations .....................................................................................................76

4.3 Initial and boundary conditions ....................................................................................76 4.3.1 Heat transfer boundary conditions ......................................................................77 4.3.2 Mass transfer boundary condition ......................................................................77 4.3.3 Change in dimension ..........................................................................................77 4.3.4 Input parameters .................................................................................................77

4.4 Result and discussion ....................................................................................................84 4.4.1 Effective diffusivity ............................................................................................84 4.4.2 Glass transition temperature ...............................................................................85 4.4.3 Average moisture content ...................................................................................85 4.4.4 Temperature evolution........................................................................................87 4.4.5 Porosity evolution ...............................................................................................88 4.4.6 Case Anisotropy shrinkage and case hardening .................................................92

4.5 Sensivity analysis .........................................................................................................94 4.5.1 Effect of air temperature .....................................................................................94 4.5.2 Effect of air velocity ...........................................................................................96

4.6 Conclusions ..................................................................................................................96

Chapter 5: Single Phase IMCD and Pore Formation ..................................... 99

5.1 Model development ....................................................................................................100 5.1.1 Governing equations .........................................................................................103 5.1.2 Initial and boundary conditions ........................................................................104 5.1.3 Microwave power absorption using Lamberts Law .........................................105

xii Pore Formation and Evolution, Food Quality and Intermittent Microwave Convective Drying

5.1.4 Input parameters .............................................................................................. 106

5.2 Results and discussion ............................................................................................... 107 5.2.1 IMCD optimisation .......................................................................................... 107 5.2.2 Average moisture curve ................................................................................... 110 5.2.3 Temperature evolution ..................................................................................... 110 5.2.4 Equilibrium vapour pressure ............................................................................ 112 5.2.5 Porosity evolution ............................................................................................ 113 5.2.6 Shrinkage and case hardening .......................................................................... 114

5.3 Conclusion ................................................................................................................. 115

Chapter 6: Multiphase IMCD Model: Considering Shrinkage and Pore

Formation 117

6.1 IMCD multiphase modelling...................................................................................... 119 6.1.1 Governing equations ........................................................................................ 121 6.1.2 Initial conditions .............................................................................................. 129 6.1.3 Boundary conditions ........................................................................................ 129 6.1.4 Input parameters .............................................................................................. 130

6.2 Results and discussion ............................................................................................... 135 6.2.1 Average moisture content ................................................................................ 135 6.2.2 Distribution and evolution of water and vapour .............................................. 135 6.2.3 Temperature evolution and distribution ........................................................... 137 6.2.4 Vapour pressure, equilibrium vapour pressure, and saturated pressure ........... 139 6.2.5 Gas pressure ..................................................................................................... 140 6.2.6 Evaporation rate ............................................................................................... 141 6.2.7 Liquid water and vapour fluxes ....................................................................... 142 6.2.8 Gas porosity ..................................................................................................... 146 6.2.9 Thermal conductivity ....................................................................................... 146 6.2.10 Effective specific heat capacity ....................................................................... 147 6.2.11 Effective density .............................................................................................. 148 6.2.12 Comparison between single phase and multiphase .......................................... 148

6.3 Conclusions ................................................................................................................ 149

Chapter 7: Effect of Porosity on Food Quality .............................................. 151

7.1 Rehydration capacity .................................................................................................. 153 7.1.1 Weight gain ...................................................................................................... 153 7.1.2 Coefficient of rehydration (COR) .................................................................... 154 7.1.3 Relative height and diameter ........................................................................... 155 7.1.4 Relationship between relative mass increase and relative volume increase .... 156

7.2 Microstructural changes during drying ...................................................................... 157 7.2.1 Microstructure of exposed surface ................................................................... 158 7.2.2 Case hardening ................................................................................................. 161 7.2.3 Cell wall Nano-pores ....................................................................................... 162 7.2.4 Effect of microwave power on microstructure ................................................ 163 7.2.5 Internal pores ................................................................................................... 164

7.3 Mechanical properties of dried foods ......................................................................... 165 7.3.1 Cell Stiffness and Drying Rate ........................................................................ 167 7.3.2 Cell Dimension and Porosity ........................................................................... 169 7.3.3 Stiffness variation with load variation ............................................................. 169 7.3.4 Comparison of mechanical properties of IMCD treated and dried

connective sample ............................................................................................ 170

Pore Formation and Evolution, Food Quality and Intermittent Microwave Convective Drying xiii

7.4 Appearance of dried food ...........................................................................................172 7.4.1 Change of shape ...............................................................................................172 7.4.2 Change of colour ..............................................................................................173

7.5 Associations among drying conditions, pore characteristics and food quality ...........174 7.5.1 Process parameters and quality correlations .....................................................175 7.5.2 Hypothesised relationships among process parameters, pore

characteristics, and food quality .......................................................................176

7.6 Conclusion ..................................................................................................................178

Chapter 8: Conclusions ................................................................................... 181

8.1 Overall summary ........................................................................................................181

8.2 Conclusions ................................................................................................................182

8.3 Contribution to knowledge and significance ..............................................................183

8.4 Limitations ..................................................................................................................184

8.5 Future direction ...........................................................................................................185

Bibliography ........................................................................................................... 187

Appendices .............................................................................................................. 207

xiv Pore Formation and Evolution, Food Quality and Intermittent Microwave Convective Drying

List of Figures

Figure 1-1: Organization of the dissertation (P1 – P14 refers to book and

journal publications) .............................................................................. 6

Figure 2-1: General classification of drying models in literature .............................. 14

Figure 2-2: Demonstration of the hierarchical structure of different food

materials............................................................................................... 20

Figure 2-3: Different types of pores in food sample .................................................. 25

Figure 2-4: Factors that affect pore formation and evolution ................................... 26

Figure 2-5: Change of porosity as a function of water content ................................ 27

Figure 2-6: Water distribution within plant based cellular tissue ............................ 31

Figure 2-7: Multiphase mass flows in food materials during drying ........................ 33

Figure 3-1: Framework of this research .................................................................... 45

Figure 3-2: Typical plant based cellular tissue .......................................................... 46

Figure 3-3: Steps toward IMCD multiphase model ................................................... 47

Figure 3-4: Simulation strategy in COMSOL Multiphysics ..................................... 48

Figure 3-5: Intermittency function of microwave power ......................................... 48

Figure 3-6: Mesh for the simulation of CD and IMCD drying ................................. 49

Figure 3-7: Mesh independence check of the simulation .......................................... 50

Figure 3-8: Determination of Glass transition temperature using DSC ..................... 55

Figure 3-9: Particle density determination of sample using He pycnometer ............ 57

Figure 3-10: Envelope (bulk) volume determination of dried fruit using

displacement method ........................................................................... 58

Figure 3-11: Glass bead entrance into open and connected pores of the sample ...... 59

Figure 3-12: Microstructure of apple slice, a.) without coating and b.) with

coating ................................................................................................. 60

Figure 3-13: Porosity of dried apple slice with and without coating ....................... 61

Figure 3-14: Mechanical properties observation using universal testing

machine ................................................................................................ 62

Figure 3-15: Pore distribution determination using image J software ...................... 64

Figure 4-1: Conceptual maps of different pathways of water migration from

plant tissue ........................................................................................... 68

Figure 4-2: Hypothetical pore evolution theory over the course of drying ............... 70

Figure 4-3: Water migration and pore formation during drying ................................ 70

Figure 4-4: Variation of glass transition temperature with moisture content .......... 72

Pore Formation and Evolution, Food Quality and Intermittent Microwave Convective Drying xv

Figure 4-5: (a) The actual geometry of the sample slice and (b) simplified 2D

axisymmetric model domain. .............................................................. 75

Figure 4-6: Finding the activation energy of apple sample ...................................... 81

Figure 4-7: Change of Effective diffusivity with time .............................................. 84

Figure 4-8: Effect of water content (wet basis) on glass transition temperature

of apple tissue ...................................................................................... 85

Figure 4-9: Moisture evolution obtained for experimental and simulation with

shrinkage and without shrinkage ......................................................... 85

Figure 4-10 Water distribution within apple sample during drying ........................... 86

Figure 4-11: Validation of predicted surface temperature profile with

experimental data ................................................................................ 87

Figure 4-12: Effect of shrinkage on temperature profile of apple slice ..................... 87

Figure 4-13: Temperature distribution within the apple sample ................................ 88

Figure 4-14: Change in porosity with moisture content of apple slice during

drying ................................................................................................... 89

Figure 4-15: Variation of mobility factor with moisture content ............................... 89

Figure 4-16: ASD factor of dried apple as a function of moisture ............................. 90

Figure 4-17: Relationship between volume reduction and migrated water

volume of selected food samples ......................................................... 91

Figure 4-18: Case hardening during drying at 600

C in sample with average

moisture content (0.5 db) ..................................................................... 93

Figure 4-19: Effect of mobility factor on shrinkage of the sample ............................ 94

Figure 4-20: Porosity at different moisture content with different drying

temperature .......................................................................................... 95

Figure 4-21: Effect of drying air velocity on porosity evolution ............................... 96

Figure 5-1: 2D an axisymmetric domain showing symmetry boundary and

transfer boundary ............................................................................... 101

Figure 5-2: Effect of different drying parameters on different variables on the

desirability of the ............................................................................... 109

Figure 5-3: Moisture content with time during IMCD and convective drying ....... 110

Figure 5-4: Temperature curve obtained from the model (average top surface)

and experimental validation .............................................................. 111

Figure 5-5: Thermal images and model temperature distribution of top surface

at selected times ................................................................................. 112

Figure 5-6: Evolutions of equilibrium vapour pressure at the surface of the

sample ................................................................................................ 113

Figure 5-7: Computed and measured porosity as a function of moisture content .. 113

Figure 5-8 : Volume ratio at different moisture content during IMCD drying ........ 114

xvi Pore Formation and Evolution, Food Quality and Intermittent Microwave Convective Drying

Figure 5-9: Case hardening during drying at 600

C in sample with average

moisture content (0.5 db) ................................................................... 115

Figure 6-1: Classification of different drying models ............................................ 117

Figure 6-2: Schematic showing 3D sample, 2D axisymmetric domain and

Representative Elementary Volume (REV) with the transport

mechanism of different phases .......................................................... 119

Figure 6-3: Flow chart showing coupling between multiphase transport and

solid mechanics.................................................................................. 120

Figure 6-4: Boundary condition of multiphase IMCD model .............................. 129

Figure 6-5: Comparison between predicted and experimental values of average

moisture content during IMCD with and without shrinkage ............. 135

Figure 6-6: Spatial distribution of water saturation with times for IMCD1 and

IMCD2 ............................................................................................... 136

Figure 6-7: Spatial distribution of vapour with different time for IMCD1 and

IMCD2 ............................................................................................... 136

Figure 6-8: Average vapour mass fraction in apple sample during IMCD

drying ................................................................................................. 137

Figure 6-9: Top surface average temperature obtained for IMCD1 and IMCD2 ... 138

Figure 6-10: Temperature distribution within apple sample during IMCD1

and IMCD2 ........................................................................................ 139

Figure 6-11: Average vapour pressure, equilibrium vapour pressure and

saturation pressure at surface ............................................................. 139

Figure 6-12 Gas pressure gradient across the half thickness the sample in

different times during IMCD1 and IMCD2 ....................................... 140

Figure 6-13: Spatial distribution of evaporation rate at different drying times

during IMCD1 and IMCD2 ............................................................... 141

Figure 6-14: Spatial distribution water flux due to capillary diffusion at

different drying times during IMCD1 and IMCD2 ........................... 143

Figure 6-15 Spatial distribution water flux due to gas pressure gradient at


Figure 6-16: Spatial distribution vapour flux due to binary diffusion at


Figure 6-17: Spatial distribution of vapour flux due to gas pressure at different

drying times during IMCD1 and IMCD2 .......................................... 145

Figure 6-18: Change of porosity with moisture removal ........................................ 146

Figure 6-19: Effective thermal conductivity with moisture content during

IMCD ................................................................................................. 147

Figure 6-20: Effective specific heat capacity with moisture content during

IMCD ................................................................................................. 147

Pore Formation and Evolution, Food Quality and Intermittent Microwave Convective Drying xvii

Figure 6-21: Effective specific heat capacity with moisture content during

IMCD ................................................................................................. 148

Figure 7-1: Classification of food quality attributes ............................................ 152

Figure 7-2: Weight gain of samples during rehydration ...................................... 154

Figure 7-3: COR of IMCD and CD treated apple samples. ................................ 154

Figure 7-4: Relative diameter of apple sample during rehydration ........................ 155

Figure 7-5: Relative height of apple sample during rehydration ............................ 156

Figure 7-6: Relationship between relative volume change and relative mass

change ................................................................................................ 156

Figure 7-7: Exposed surface porosity in different type of drying ........................ 158

Figure 7-8 : Microstructural change of apple slice during convective drying

(left) microwave (right) (40X magnification in SEM image) ........... 159

Figure 7-9: Microstructural change of apple slice during IMCD drying (40X

magnification in SEM image) ........................................................... 160

Figure 7-10: Open porosity of dried product achieved from different drying

conditions .......................................................................................... 161

Figure 7-11: Case hardening and internal pores in convective dried apple slice

(40X magnification in SEM image) .................................................. 161

Figure 7-12: Development of nano-pores during CMD, convective drying and

IMCD ................................................................................................. 162

Figure 7-13: Effect of microwave power on microstructure and porosity ............. 163

Figure 7-14: Internal pores in dried apple slice ...................................................... 164

Figure 7-15: Compressive extension characteristics of apples .............................. 168

Figure 7-16: Weight loss of apple slice in convective drying at 700 C .................. 168

Figure 7-17: Microstructure of fresh and dried apple samples (500x).................... 169

Figure 7-18: Effect of speed of load on stiffness of the apple tissue ..................... 170

Figure 7-19: Strain-stress curves of apple tissue at moisture content 2.6 (db) in

IMCD and CD ................................................................................... 170

Figure 7-20: Variation of Young Modulus with moisture content for IMCD

and CD-treated apple slice................................................................. 171

Figure 7-21: Change of roundness during CD and IMCD ..................................... 172

Figure 7-22: Colour change over the time of drying.............................................. 173

Figure 7-23: Different factors that influence porosity during drying of food

materials ............................................................................................ 176

Figure 7-24: Hypothesised relationships between the drying parameters, pore

formation and evolution, and dried food qualities ............................ 177

xviii Pore Formation and Evolution, Food Quality and Intermittent Microwave Convective Drying

List of Tables

Table 2-1: Internal moisture transfers mechanisms during drying of solid foods ...... 9

Table 2-2 Differences in physical properties between crystalline and

amorphous states of materials. ............................................................. 21

Table 2-3: Changes of porosity with a decrease in moisture content during

drying of various fruits and vegetables. ............................................... 28

Table 2-4: Summary of empirical models predicting porosity during drying .......... 35

Table 3-1: List of instruments with their measured quantity .................................... 51

Table 3-2: Some selected key factors of rehydration of dehydrated sample ........... 64

Table 4-1: Input parameters for the model ................................................................ 78

Table 4-2: Physical properties of some selected food materials ............................... 91

Table 5-1: Variables of IMCD optimisation .......................................................... 103

Table 6-1: Input properties for the model ............................................................... 130

Table 7-1: Crust thickness of the IMCD and CD treated samples .......................... 162

Pore Formation and Evolution, Food Quality and Intermittent Microwave Convective Drying xix

Statement of Original Authorship

The work contained in this thesis has not been previously submitted to meet

requirements for an award at this or any other higher education institution. To the

best of my knowledge and belief, the thesis contains no material previously

published or written by another person except where due reference is made.

Signature:

Date: 10 February 2016

QUT Verified Signature

xx Pore Formation and Evolution, Food Quality and Intermittent Microwave Convective Drying

Acknowledgements

The greatest thanks go to the Creator of the Universe. I would like to thank

Him for giving me the opportunity, strengths and blessing in completing this thesis.

Then, I would like to thank my principle supervisor, Dr Azharul Karim, for his

supervision and effort. Thank you very much for your invaluable advice, inspiration

and perseverance throughout this research. I also appreciate the exceptional support,

supportive comments, guidance and recommendation given by my co-supervisor,

Associate Professor Richard Brown. I sincerely thank both of my supervisors for

their many hours of assistance, supervision and direction.

I would also like to express my love and gratitude to my beloved family

members, for their understanding and endless love.

Furthermore, I also wish to express my gratitude for the numerous scientific

discussions and assistance given by my colleagues and the members of the Energy

and Drying Group at Queensland University of Technology, in particular, Dr.

Chandan Kumar for his continued support during my candidature especially with

experiments and idea development, Dr. Majedul Islam, Dr. Zakaria Amin, Md. Imran

Hossain Khan, Kazi Badrul Islam, Duc Nghia Pham. I also Thank all undergraduate

students who were involved in different parts of the project.

The technical aspects of the experimental works demonstrated in this thesis

would not have been possible without the support of the research facilities at the

Queensland University of Technology.

A ‘thank you’ to my thesis proof-reader, Dr Michael Clancy for his

contribution to the polishing of this work

I gratefully acknowledge financial support from the QUT Postgraduate Award

(QUTPRA) scholarship and QUT HDR Tuition Award. Last, but by no means the

least, I would like to thank the government of the People’s Republic of Bangladesh

for providing me with a high-quality education for almost free.

Pore Formation and Evolution, Food Quality and Intermittent Microwave Convective Drying

Chapter 1: Introduction

This chapter outlines the background and motivation (Section 1.1), research

objectives (Section 1.2), and aims of this study (Section 1.3). The significance and

scope of this research have been described in Section 1.4. Finally, Section 1.5

provides an overview remaining of the chapters of the dissertation.

1.1 BACKGROUND AND MOTIVATION

Currently, one-third of produced food is wasted annually due to a lack of

proper processing and preservation (Gustavsson et al., 2011; UN, 2007). This loss is

even greater in developing countries, amounting to 30–40% of seasonal fruit and

vegetables (Karim & Hawlader, 2005b). On the other hand, according to the UN

food agency, every day 18,000 children die of hunger and malnutrition and 850

million people go to bed every night with empty stomachs (UN, 2007). The World

Food Programme (WFP) identifies hunger as the number one health risk, and it kills

more people every year than AIDS, malaria and tuberculosis combined (World Food

Programme, 2012). Therefore, proper food processing must be emphasised to reduce

this massive loss, promote food security and combat hunger.

Drying is one of the easiest and oldest methods of food processing and

preservation, which prevents food from microbial spoilage. It increases shelf life,

reduces weight and volume thus minimising packing, storage, and transportation

costs and enables storage of food under an ambient environment. However, it is

probably the most energy intensive technique of the major industrial processes

(Kudra, 2004) and accounts for up to 15% of all industrial energy usage (Chua et al.,

2001a). Moreover, drying causes changes in the food qualities including

discolouration, aroma loss, textural changes, nutritional degradation, and changes in

physical appearance and shape (Quirijns, 2006). Researchers have been striving to

improve energy efficiency and product quality in food drying for many years.

Intermittent Microwave-Convective Drying (IMCD) is an approach that increases

both energy efficiency and product quality (Kumar et al., 2014a).

2 Pore Formation and Evolution, Food Quality and Intermittent Microwave Convective Drying

Although there are some experimental investigations of IMCD, modelling

studies of this process remain under-developed. The modelling of IMCD is essential

to understand the physical mechanism of heat and mass transfer and finally to

optimise the process of food preservation. Pore formation and evolution, and

inevitable structural deformation prevail over the course of drying. This porous

structure of plant-based materials is a dominant factor that significantly affects the

heat and mass transfer phenomenon, as well as quality characteristics during

drying.Therefore; this research aims to develop a comprehensive multiphase model

for IMCD taking pore formation and evolution into account.

1.2 RESEARCH PROBLEMS

Although there have been some studies highlighting the advantages of

intermittent microwave-convective drying (IMCD) of food materials, most of these

are experimental. There has been no mathematical model that correctly describes the

physical understanding of the heat and mass transfer phenomenon occurring within

food material during IMCD. A proper understanding of the internal heat and mass

transfer mechanism involved is essential for optimisation of the drying process.

Mathematical modelling of moisture transport inside food can be developed by

two approaches: (i) a single-phase model, which considers transport only water, is

present in the food material, and (ii) a multiphase porous media model that considers

transport of liquid water, vapour, and air inside the food materials. The multiphase

models are more comprehensive and provide better insight into the transport

mechanisms. These models are divided into two groups: equilibrium and non-

equilibrium. Most of the multiphase models of food drying consider equilibrium.

However, equilibrium conditions may not be valid at the surface of food where the

moisture content is lower. Therefore, the non-equilibrium approach is a more

realistic representation of the physical situation while drying (Zhang & Datta, 2004).

There is no IMCD model developed considering the non-equilibrium approach. In

this study, non-equilibrium multiphase porous media models were developed for

food drying.

Apart from transport mechanisms, pore formation and evolution is a crucial

factor that needs to be considered in IMCD model. Without a proper understanding

of the pore formation mechanism, while drying, other mechanical properties of

Chapter 1 | Introduction

Pore Formation and Evolution, Food Quality and Intermittent Microwave Convective Drying 3

shrinkage, texture and the microstructure cannot be appropriately predicted. Several

studies have developed theoretical models of pore formation of foodstuff during hot

air and freeze-drying, but there is still insufficient information about pore formation

during IMCD drying leading to erroneous predictions of drying kinetics and

structural deformation during the drying process. The available literature

demonstrated that the drying temperature and the microwave power affect the

porosity of dried fruits.

Consideration of some fundamental parameters like glass transition

temperature and moisture distribution and case hardening can generalise the pore

formation predictions to some extent.

Therefore, extensive research on the development of an appropriate pore

formation model is necessary for a better understanding of the effects pores in IMCD

drying. The modelling and simulation of pore formation will help in understanding

its effect on shrinkage, texture and microstructure other quality attributes. The aim of

this research project, therefore, is to investigate pore formation and evolution to

develop a fundamental pore formation model. An appropriate IMCD model taking

shrinkage and porosity into consideration will then be developed. This research also

explores the effects of IMCD on quality attributes of food including texture,

microstructure and rehydration.

1.3 AIMS AND OBJECTIVES

Primary objectives of this study are to (i) develop a theoretical model to

describe pore formation and evolution during drying and (ii) develop an appropriate

IMCD model taking shrinkage and pore evolution into consideration. Correlation of

process parameters with quality attributes during IMCD will also be established.

Since convection-drying modelling is a prerequisite for developing an IMCD model,

a convection drying model is initially developed taking shrinkage into consideration.

The final model is a multiphase porous media IMCD model that takes account of

variable porosity and shrinkage. More specific objectives of this work were to:

Develop fundamental porosity model considering process parameters and

sample properties, and then validate these with experimental data;

Develop mathematical models for convection drying with and without

considering shrinkage;


Develop a multiphase porous media model for IMCD considering

shrinkage and variable porosity;

Conduct comprehensive experimental investigation and validate the

models developed;

Study the effect of pore formation and evolution during IMCD on

rehydration capacity, mechanical properties, microstructure and change of

appearance of dried sample.

1.4 SIGNIFICANCE AND SCOPE

A theoretical model has been developed for the prediction of pore formation

considering process parameters such as drying temperature and moisture flux and

sample properties including initial porosity and glass transition temperature to

accommodate a wide range of food materials. Eventually, a more accurate

mathematical model of IMCD has been developed for food, taking the evolution of

pore characteristics that enables an understanding of heat and mass transport, and

structural deformation during IMCD.

The temperature distribution and redistribution have also been investigated

using the model. Since the temperature distribution and redistribution during IMCD

are the keys to overcoming the overheating of the product, the model in this work

makes a significant contribution to improving food product quality. The multiphase

model, which is an advanced approach to modelling the drying process, enables

investigation of temporal and spatial profiles of temperature, liquid water, water

vapour, and air inside the food material. Two IMCD models (i) IMCD1 (neglecting

shrinkage) and (ii) IMCD2 that considers shrinkage and pore evolution have been

developed in this study. Finally, the effect of pore formation and evolution over the

course of IMCD on physical attributes of dried food investigated in this study will

help in developing appropriate drying processes for better product quality.

The insights of physical phenomena acquired from the models in this thesis

will make a great contribution to the field of drying. The mathematical models used

in this research are fundamental; therefore, they can be easily modified and adapted

to any food material without considerable effort. Furthermore, the models developed

in this research will also be useful in developing realistic models for other food

processing applications including frying, baking, cooking and eventually optimising



those processes. Successful implementation of these theoretical models in the food

industry can lead to a significant improvement in food quality, energy efficiency, and

optimisation.

1.5 THESIS OUTLINE

This thesis consists of a total of eight chapters, including this introductory

chapter. Chapter 2 presents a literature review and Chapter 3 describes the

methodology used in this study. Chapter 4 begins by laying out the theoretical

approach of porosity prediction and finishes by looking at how porosity varies over

the course of convection drying. Chapter 5 and Chapter 6 present the gradual

development of IMCD models along with a prediction of pore formation. The thesis

progresses from simple diffusion-based models (Chapter 4 and 5) to multiphase

porous, deformable media model for IMCD (Chapter 6). The effects of IMCD drying

on food quality are presented in Chapter 7. Finally, the conclusion chapter (Chapter

8) gives a brief summary and critique of the findings and includes a discussion of the

implication of the findings for future research into this area.

An overview of the dissertation is also illustrated in Figure 1.1 and a chapter-

wise brief description is given below.

In Chapter 1, (the current chapter), background and motivation, research

problems, objectives, significance and outline of the thesis are presented.

In Chapter 2, a review of contemporary literature relevant to this thesis scope

is presented. This chapter begins with the general background of drying of food

materials; it then provides an extensive review of IMCD and its modelling.

Following this, details of the structural characteristics of food material are presented.

Then, pore formation mechanism and its prediction models during drying are

discussed in detail. Finally, the key research problems and gaps are identified and

presented.

In Chapter 3, experimental procedures for determining different model

parameters and sample properties are discussed.

In Chapter 4, a single-phase convection model is developed considering

shrinkage phenomenon. An effective moisture diffusivity that varies with moisture

content and temperature of drying air is considered in this model. A theoretical


approach to pore formation is discussed. Finally, drying kinetics and pore formation

during convection drying are determined in this chapter.

Figure 1-1: Organization of the dissertation (P1 – P14 refers to book and journal publications)

In Chapter 5, a single-phase IMCD model is developed by adding the

convection drying model and intermittent microwave heating. This model considers

Lambert’s Law for microwave heat generation. Optimisation of IMCD is presented

in this chapter.

In Chapter 6, multiphase porous media model is implemented for IMCD

considering shrinkage phenomenon and porosity evolution during drying. This

chapter presents fundamental formulations of heat, mass, and momentum transfer



along with input parameters and variables for the model. Transport of different

phases due to pressure-driven, capillary diffusion, and binary diffusion are

investigated. Pore formation and evolution over the drying time is discussed. The

variation of different parameters that are achieved by both deformation and non-

deformed domain are compared.

In Chapter 7, effects of pore formation during IMCD on different quality of

dried food are investigated. In particular, rehydration capacity, microstructure,

mechanical characteristics and change of appearance of IMCD treated sample are

compared with the convection dried sample. Finally, a hypothetical relationship

among process parameters, pore characteristics and dried food quality has been

proposed.

In Chapter 8, the major conclusions, contribution to knowledge, limitations,

and recommendations of this research are presented.


Chapter 2: Literature Review

This Chapter will inform our approach towards the main research topic starting

with a detailed background of the subject, and a comprehensive review of the most

relevant literature presented to identify research gaps.

We begin with the basics of food drying (Section 2.1) and the rest of the

chapter deals with reviewing literature on the following topics: intermittent

microwave-convective drying (IMCD) (Section 2.2); food structure (Section 2.3);

pore formation mechanism (Section 2.4); models of porosity (Section 2.5); modelling

of drying (Section 2.6) and effect of process parameters on quality (Section 2.7).

Section 2.8 highlights the summary of literature review and identifies research gaps.

2.1 FOOD DRYING

The main purpose of drying in food processing is to guarantee safe storage of

the material to prevent microbial growth. The process of drying commonly means

moisture evaporation due to simultaneous heat and mass transfer (Karim &

Hawlader, 2005a).

The surface contains free moisture and therefore during the first stage of

drying, a constant drying rate is observed. In this stage vapourisation of this free

moisture takes place. The drying rate at this stage is surface-based and governed by

external factors such as the area exposed to the dry air, the temperature difference

between wet surface and dry air, as well as the external heat and mass transfer

coefficients (Srikiatden & Roberts, 2007). After this period, to facilitate drying, the

moisture has to be diffused from the inside of the material to the surface. Therefore,

beyond the point called critical moisture content (Mc), the drying rate moves from

the constant rate stage to first falling stage. In this phase, the drying rate is mainly

dependent on thickness, shape and the collapse of internal tissues. Heat damage may

occur at the surface at this stage due to lack of moisture at the surface. In the first

falling-rate period, the drying rate reduces as the moisture content decreases because

of the additional internal resistance for moisture transfer and to the reduction of heat

flux.

Chapter 2 | Literature Review


In the second falling rate, moisture moves from the centre to the surface due to

diffusion result from concentration gradient between the core region and the surface.

The diffusion rate decreases in the falling rate drying period due to shrinkage and

lowers moisture gradient that results in a longer drying time. The drying rate of this

later falling rate period is much too slow; literature shows to remove the last 10% of

water from food materials it takes almost equal time to that required for removing the

first 90 % of water content. Drying behaviour of some biological and most food

materials experience this second falling rate period. Supplying more energy by

increasing the drying air temperature in this stage accelerates drying. But higher

temperature may damage the surface of the product resulting in hard crust formation

while the moisture content at the centre is still high (Zeki, 2009). Because food

materials are poor heat conductors, it limits the supply of heat from the surface to the

inner part. Thus, the surface gets overheated and damaged. This damaged surface

ultimately deters the heat and mass transfer rate hindering subsequent drying (Botha

et al., 2012).

However, depending upon the drying process condition and sample properties

different types of internal moisture transfer mechanisms can take place during drying

as presented in Table 2.1 (below).

Table 2-1: Internal moisture transfers mechanisms during drying of solid foods

Moisture removal mechanism during drying Reference

Diffusion Lewis (1921),

Sherwood

(1929a) ,

Sherwood

(1929b)

Capillary Ceaglske and

Hougen (1937)

Evaporation-condensation Henry (1948)

Transfer of liquid

water

Capillary

Liquid diffusion

Surface diffusion

Transfer of water vapour

Differences in partial pressure

(diffusion)

Differences in total pressure

(hydraulic flow)

Görling (1958)

Capillary

Diffusion

Surface diffusion in liquid layers absorbed at solid interfaces

Water vapour diffusion in air-filled pores

Gravity

Vaporization-condensation sequence.

Van Arsdel

(1963)


Moisture removal mechanism during drying Reference

Hydraulic flow

Capillary flow

Evaporation-condensation

Vapour diffusion

Keey (1970)

Molecular diffusion

Capillary flow

Knudsen flow

Hydrodynamic flow

Surface diffusion

Bruin and Luyben

(1990)

Transfer of liquid water

Capillary (saturated )

Molecular diffusion

(within solid )

Surface diffusion

(absorbed water)

Liquid diffusion (in

pores)

Hydraulic flow (in pores)


Diffusion (in pores): - Knudsen,

- Ordinary,

-Stephan

diffusion.

Hydraulic flow (in pores)


Hallstöm (1990)

Transfer of liquid water

Capillary

diffusion

Surface diffusion

Hydraulic flow


Mutual diffusion

Knudsen flow

Diffusion

Slip flow

Hydrodynamic (bulk) flow

Stephan diffusion

Poiseuille flow


Waananen et

al.(1993)

It can be seen from Table 2.1 (above) that more than one mass transfer

mechanism can be involved in the drying process. Therefore, difficulty arises where

several mechanisms can account for moisture transfer as drying proceeds though

only one of the mechanisms dominates moisture transfer at any given time (Karel &

Lund, 2003).

Crust formation, longer drying time and poor quality of food are the main

disadvantages of the Hot air drying. To solve these problems, an advanced drying

technique such as intermittent microwave-convective drying (IMCD) can be

implemented.



2.2 INTERMITTENT DRYING

Intermittent drying can be attained by maintaining the supply of drying energy

which generally can be practiced by varying the drying temperature, air , humidity,

or operating pressure (Kumar et al., 2014a). It can also achieved by changing the

mode of energy input (e.g., microwave, convection, radiation, conduction). Supply of

same amount of energy during entire drying process causes quality degradation

(Zeki, 2009) and wastage of energy. One possibile reason for this is that at the later

stage of drying process, the drying rate decreases as there is insufficient moisture in

the sample to be removed. Case hardening or other heat damage is occurred on the

surface of the sample if constant external energy source is applied. The concept of

the intermittency is developed to provide intermittent application of secondary

energy source which is appropriate for energy removal from the core of the sample.

Consequently, surface damage and overall quality degradation can be minimized by

implementing intermittent drying.

Extensive research have been done on intermittent drying where the intermittency

were achieved by changing drying air conditions (Chin & Law, 2010; Chua et al.,

2002a; Chua et al., 2000a; Ho et al., 2002). In recent times, intermittency of energy

input in combined drying method e.g., microwave/radiofrequency (Ahrné et al.,

2007; Botha et al., 2012; Esturk, 2012a; Esturk et al., 2011; Soysal, 2009),

ultrasound (Schössler et al., 2012).

Types of intermittency influence the energy efficiency and product quality and.

Therefore, the intermittency of secondary energy source should not be chosen

arbitrarily, rather it has to be chosen based on the physics involved in the drying

method. Otherwise, better product quality and the optimum energy efficiency will

not be attained.

2.3 INTERMITTENT MICROWAVE CONVECTIVE DRYING (IMCD)

Microwaves are electromagnetic radiation in the frequency range of 300MHz–

300GHz with a wavelength 1mm–1m. This is the propagation of electromagnetic

energy through space using time-varying electric and magnetic fields (Feng et al.,

2012). Microwaves penetrate the material until moisture is located and heats up the

material volumetrically thus facilitating a higher diffusion rate and pressure gradient

to drive off the moisture from inside of the material (Turner & Jolly, 1991). There


are two main mechanisms of microwave heating; bipolar re-orientation and ionic

conduction. Water molecules are bipolar in nature and try to follow the electric field

that alternates at very high frequency. For a commonly used microwave frequency of

2.45 GHz, the electric field changes direction 2.45 billion times a second, making the

dipoles move with it (Datta & Rakesh, 2009). Such rotation of molecules produces

friction and generates heat inside the food material (Zhang et al., 2010). Ionic

conduction is a second major mechanism of microwave heating which is caused by

ions, such as those present in salty food, which migrate under the influence of the

electric field.

Due to its volumetric heating capability, application of microwaves with other

drying methods can significantly increase the drying rate. The main advantages of

microwave assisted drying are:

Volumetric heating: Microwave energy interacts with water molecules

within the food leading to volumetric heating and increased moisture

diffusion rates (Turner et al., 1998). This can thereby significantly reduce

drying times (Mujumdar, 2004; Zhang et al., 2006). It is clear from the

literature that microwave convection (MWC) drying shows remarkably

lower drying time than hot air (CD) drying (Orsat et al., 2007; Wojdyło et

al., 2014; Zhang et al., 2010).

Controlled heating: The fidelity of heating can be controlled using

microwave energy as it can be applied intermittently by varying the pulse

ratio and the power level of the microwave. (Gunasekaran, 1999).

Selective heating: Preferential heating of wetter areas is possible with

microwave heating and also bound water molecules can be excited by

microwaves (Gunasekaran, 1999; Turner et al., 1998).

2.3.1 Combined microwave and another drying

Microwaves are combined with hot air-drying, freeze-drying, vacuum drying

and osmotic drying (Huang et al., 2012; Jiang et al., 2013; Jiang et al., 2014b; Liu et

al., 2012b; Wang et al., 2012). Due to less cost being involved, convection drying is

most widely combined with a microwave to make convective microwave drying

(MCD) (Andrés et al., 2004).



To mitigate longer drying times and formation of a crust over the course CD,

incorporation of microwaves (MW) can increase the diffusion rate and supplying

moisture to the surface. This is the reason that MCD can significantly shorten drying

time and improve energy efficiency and product quality (Zhang et al., 2006). From

the experimental studies, a substantial reduction in the drying time (25–90%) has

been found in MCD drying when compared with convection drying (Cinquanta et al.,

2013; Izli & Isik, 2014; Prabhanjan et al., 1995). A number of studies found MCD

treated products possess superior quality when compared to hot air drying

(Argyropoulos et al., 2011; Cinquanta et al., 2013; Jindarat et al., 2011).

2.3.2 Intermittent application of MW in CD

Due to uneven power distribution of MW, continuous MW energy supply to

food material causes uneven heating and overheating. To overcome this problem, the

introduction of MW energy intermittently can be an option. This intermittent

application of MW maintains the expected temperature of the food materials during

drying and the uniform distribution of moisture within food materials, which

improves product energy efficiency and quality (Soysal et al., 2009a). Many

researchers incorporated intermittent microwave energy with different drying

techniques such as vacuum drying (Jiang et al., 2014a; Mothibe 2014) and freeze

drying (Wang et al., 2013), and they found superior quality attributes of dried

samples in comparison with vacuum and freeze dried product.

In addition to these, the advantages of IMCD in terms of quality and energy

efficiency have also been reported in the literature. Soysal et al. (2009) compared

IMCD and convective drying for oregano and found that the IMCD was 4.7–11.2

times more energy efficient compared to convective drying. For instance, Soysal et

al. (2009a) found that IMCD treated red pepper showed better sensory attributes,

colour, texture, than CD and MCD.

Advantages of IMCD in terms of improving energy efficiency and product

quality, and significantly reducing drying time have been found in many products

such as sage leaves (Esturk, 2012b; Esturk et al., 2011), bananas (Ahrné et al., 2007),

oregano (Soysal, 2009), pineapple (Botha et al., 2012), red pepper (Soysal et al.,

2009a), and carrots and mushrooms (Orsat et al., 2007).


2.4 DRYING MODELS

Mathematical modelling is a good tool to discover the possible solution of a

given problem in drying. It is necessary for evaluating the effect of process

parameters on energy efficiency and drying time, and optimising the drying process

(Kumar et al., 2014a).

Developing a physics based drying model for agricultural products is a

challenging task. This is because of the complex structural nature of agricultural

products and changes in the thermo-physical properties during drying. Moreover,

heat and mass transfer are highly coupled during drying. Therefore, some

assumptions are indispensable if mathematical models are to be developed, but these

should be carefully made to represent the physical phenomena during the process. In

this section, the modelling approaches of drying are discussed together with their

limitations. The models can be classified into three categories: empirical models,

diffusion based (single phase) models and multiphase models as shown in Figure 2.1

and discussed in detail in the subsections of this paragraph.

Figure 2-1: General classification of drying models in literature

2.4.1 Empirical models

The empirical or observation based models can be rapidly developed based on

experimental data. These models are derived from Newton’s law of cooling and

Fick’s law of diffusions (Erbay & Icier, 2010). These are simpler to apply and often

used to describe the drying curve. Despite these advantages, they do not provide



physical insight into the process. Also, these models are only valid for specific

process condition and material. In contrast to empirical models, the physics-based

models can capture the inherent drying mechanism better (Chou et al., 2000; Chua et

al., 2003; Ho et al., 2002).

2.4.2 Diffusion-based (single phase) models

The diffusion-based models are very popular because of their simplicity and

good predictive capability (Arballo, 2010; Perussello et al., 2014). These models

assume conductive heat transfer for energy and diffusive transport for moisture.

These models need an effective diffusivity (phenomenological coefficient) value,

which has to be experimentally determined. The effective diffusivity calculation is

crucial for drying models because it is the main parameter that controls the process

with a higher diffusion coefficient implying increased drying rate. This effective

diffusion coefficient changes during drying due to the effects of sample temperature

and moisture content (Batista et al., 2007). Some authors considered effective

diffusivity as a function of shrinkage or moisture content (Karim & Hawlader,

2005b), whereas, others postulated it as temperature dependent (Chandra Mohan &

Talukdar, 2010).

Several fundamental mathematical models have been developed for food

drying. For example, Barati and Esfahani (2011) developed a food drying model

wherein they considered the material properties to be constant. However, in reality

during the drying process physical properties such as diffusion coefficients and

dimensional changes occur to the extent of drying progress. Consequently, if these

latter issues are not considered, the model predictions may be erroneous regarding

estimating temperature and moisture content (Wang & Brennan, 1995b). In

particular, the diffusion coefficient can have a significant effect on the drying

kinetics.

Calculation of the effective diffusivity is crucial for drying models because it is

the main parameter that controls the process with a higher diffusion coefficient

implying increased drying rate. The diffusion coefficient changes during drying due

to the effects of sample temperature and moisture content (Batista et al., 2007).

Alternatively, some authors considered effective diffusivity as a function of

shrinkage or moisture content (Karim & Hawlader, 2005b); whereas, others

postulated it as temperature dependent (Chandra Mohan & Talukdar, 2010).


In the case of a temperature dependent effective diffusivity value, the

diffusivity increases as drying progresses. On the other hand, effective diffusivity

decreases with time in the case of shrinkage or moisture dependency. This latter

behaviour is ascribed to the diffusion rate decreasing as moisture gradient drops.

However, Baini and Langrish (2007) mentioned that shrinkage also tends to reduce

the path length for diffusion that results in increased diffusivity. Consequently, there

are two opposite effects of shrinkage on effective diffusivity that theoretically may

cancel each other.

Silva et al.(2011) analysed the effect of considering constant and variable

effective diffusivities in banana drying. They found that the effective variable

diffusivity (moisture dependent) was more accurate than the constant effective

diffusivity in predicting the drying curve. However, there are limited studies

comparing the influence of temperature dependent and moisture dependent effective

diffusivity. Recently, Silva et al. (2014) considered effective diffusivity as a function

of both temperature and moisture together (i.e. D=f(T, M)), not temperature or

moisture dependent diffusivities separately. Therefore, it was not possible to

compare the impact of considering temperature and moisture dependent effective

diffusivities. Moreover, they did not report the impact of variable diffusivities on

material temperature. A comparison of drying kinetics for both temperature and

moisture dependent effective diffusivities can play a vital role in choosing the correct

effective diffusivity for modelling purposes. Though there are several modelling

studies of food drying, there are limited studies that compare the impacts of

temperature dependent and moisture dependent effective diffusivities.

Understanding the exact temperature and moisture distribution in food samples

is important in food drying. (Joardder et al., 2013c)showed that temperature

distribution plays a critical role in determining the quality of dried food. Similarly,

moisture distribution plays a critical role in food safety and quality. Vadivambal and

Jayas (2010) showed that despite the fact that the average moisture content was

lower than what was considered a safe value, spoilage started from the higher

moisture content area. Therefore, it is crucial to know the moisture distribution in the

sample. Unfortunately, it is difficult to measure temperature and moisture

distribution inside the sample experimentally, which means that appropriate



modelling approaches are required to determine the moisture distribution. Mujumdar

and Zhonghua (2007) argued that technical innovation can be intensified by

mathematical modelling that can provide a better understanding of the drying

process. Karim and Hawlader (2005b) developed a mathematical model to determine

temperature and moisture changes with time, but it did not provide temperature and

moisture distribution within the sample. The moisture distribution is a key parameter

for evaporation because evaporation depends on surface moisture content.

Although this model can provide a good match with experimental results, it

cannot provide an understanding of other transport mechanisms such as pressure

driven flow and evaporation. The drawbacks of these kinds of models are discussed

in detail in the work of Zhang and Datta (2004). Lumping all the water transport as

diffusion cannot be justified in all situations. Therefore, multiphase models

considering transport of liquid water, vapour, and the air inside the food materials are

more realistic.

2.4.3 Multiphase models

The multiphase models incorporate the transition from the individual phase at

the ‘microscopic’ level to the representative average volume at the ‘macroscopic’

level, which provides a fundamental and convincing basis of heat and mass transport

(Datta, 2007b; Whitaker, 1977). Multiphase models can be categorised into two

groups: equilibrium and non-equilibrium approach of vapour pressure. In equilibrium

formulations, the vapour pressure, vp , is assumed to be equal to the equilibrium

vapour pressure, eqvp ,

, and vice versa. There are some multiphase models

considering equilibrium approach applied in vacuum drying of wood (Turner &

Perré, 2004) and convection drying of wood and clay (Stanish et al., 1986),

(Chemkhi et al., 2009), microwave spouted bed drying of apple (Feng et al., 2001)

and large bagasse stockpiles (Farrell et al., 2012). Some multiphase porous media

models combine the liquid water and vapour equations together to eliminate the

evaporation rate term (Farrell et al., 2012; Ratanadecho et al., 2001; Suwannapum &

Rattanadecho, 2011). By doing this, the concentrations of liquid water and vapour

cannot be determined.

However, equilibrium condition may be valid at the surface with lower

moisture content because equilibrium condition may not be achieved due to lower


moisture content at the surface during drying. Therefore, the non-equilibrium

approach is a more realistic representation of the physical situation while drying

(Zhang & Datta, 2004). Moreover, the non-equilibrium formulation for evaporation

can be used to express explicit formulation of evaporation, thus allowing calculation

of each phase separately. Furthermore, non-equilibrium multiphase models are

computationally effective and applied to wide range of food processing such as

frying (Bansal et al., 2014; Ni & Datta, 1999), microwave heating (Chen et al., 2014;

Rakesh et al., 2010), puffing (Rakesh & Datta, 2013) baking (Zhang et al., 2005),

meat cooking (Dhall & Datta, 2011) etc. However, application of these non-

equilibrium models in the drying of food materials is very limited. To the authors’

best knowledge, there is no IMCD model considering non-equilibrium and shrinkage

in multiphase porous media.

2.4.4 MCD and IMCD model

To model MCD and IMCD, a heat source due to microwave heating is added to

the energy equation. This heat source can be mostly modelled using two formulations

(Lambert’s Law and Maxwell’s equations). As mentioned before, Lambert’s Law is a

simple approximation of microwave heat generation, whereas Maxwell’s equations

are a more comprehensive and accurate means of predicting microwave heating

(Chandrasekaran, 2012; Rakesh et al., 2009).

A physical understanding of heat and mass transfer, and interaction of

microwaves with food products is important for optimisation of the drying process

(Feng et al., 2012). Coupled heat and mass transfer models have to be developed to

predict the temperature and moisture distribution inside the material, which will help

to improve the understanding of the underlying physics and develop better strategies

for the control of IMCD. There are some single phase diffusion based models

available for microwave heating only (Chen et al., 2014; Pitchai et al., 2012), MCD

(Malafronte et al., 2012; McMinn et al., 2003), however, intermittency of microwave

has not been dealt with in these outlined models. In light of the literature, it is clear

that despite there being some single phase models that considered intermittency,

these are only for heating without consideration of mass transfer (Gunasekaran &

Yang, 2007b; Yang & Gunasekaran, 2001), and thus they cannot be applied to

drying.



Thus, there is a lack of understating of the physical phenomena involving heat

and mass transfer in IMCD. Successful modelling of heat and mass transfer during

IMCD, as well as in-depth knowledge concerning food structure, and the nature of

deformation during drying and multiphase distribution is essential.

In addition to process condition, drying kinetics and dried food quality depend

on the material properties and its change during drying. In particular, pore formation

and evolution over the course of drying needs to consider while developing heat and

mass transfer model for any drying.

2.5 FOOD STRUCTURE

Most of the food materials subjected to drying process can be treated as

hygroscopic porous and amorphous media with the multiphase transport of heat and

mass. Natural as well as processed foods encompass hierarchical structure and span

scales from nano to millimetres as shown in Figure 2. 2. From cellular to tissue level,

different food materials show significantly different structure. This variation of the

structure causes completely dissimilar reaction during different food processing. It is

assumed that higher level structures are progressively assembled from the molecular

to the macro scale until the desired properties and functions are achieved (Baer,

Cassidy, & Hiltner, 1991). Cellular materials, for example, organised from glucose to

tissue level with the size of nano to the macro scale. A similar pattern can be found,

as shown in Figure 2.2, in other types of food structures including crystalline, fibrous

and gel.


Figure 2-2: Demonstration of the hierarchical structure of different food materials

Moreover, the cellular tissue of plant materials encompasses different

component broadly intercellular air (initial porosity), intercellular water (free water),

intracellular water (bound water) and solid matrix (cell wall).

Chemical composition and physical structure of food materials influence both

heat and mass transfer mechanisms (Rosselló, 1992). If food is treated as the

material, it can be classified as porous or nonporous according to its void containing

features. On the other hand, most of the food materials behave as amorphous nature

rather than crystal.

Overall, foods are complex material regarding physical characteristics than

solid crystal materials. In the following sections, different material-related

characteristics of plant-based food stuff have been discussed in detail.

2.5.1 Structural Homogeneity

Where the arrangement of the material of atoms or molecules is concerned, it

can be classified as crystalline, polycrystalline or amorphous. The proportion of these

two states dominates the functional and physical properties as shown in Table 2.2.

[Adapted from (Bhandari, 2012)].Some food processing cause crystallisation of food

materials, such as freezing of foods by crystallisation of water, sugar and salt.

Consequently, the shelf life of food materials prolonged significantly. On the other



hand, to retain the flavour, taste and colour of food materials, amorphous state of

food microstructure are essential (Roos, 1995).

Crystal and Polycrystalline

Crystal materials are those which periodically repeated lattice of atoms or

molecules. In this type of material, molecules are packed tightly (Bhandari, 2012).

Thermodynamically, crystals are found in the stable equilibrium state (Hartel R. W.,

2001). Introducing heat up to a certain level melts the material. In addition to this,

crystalline materials follow the heat capacity concept that means temperature

increased proportionally in response to heating. As soon as crystal materials reach

melting temperature then these take the latent heat of melting without increasing the

temperature until reaching a melting stage. In general, melted liquid has more heat

capacity as this liquid phase demonstrates lower temperature as a result of heating.

Table 2-2 Differences in physical properties between crystalline and amorphous states of materials.

Properties Crystalline state Amorphous state

Density High Low

Mechanical strength Strong (Ductile) Brittle

Compressibility Poor Good

Internal porosity Low High

Hygroscopicity Low High

Softening

temperature High ( Melting)

Low (glass

transition)

Chemical reactivity Low High

Interaction with

solvent Slow Rapid

Heat of solution Endothermic Exothermic

Amorphous materials

Amorphous materials have a disordered molecular structure, in this type of

material atoms or molecules are arranged in a lattice that duplicates periodically in

space. The examples included all amorphous solids, water glasses, organic polymers,

or even metals. Due to the more open and porous nature of the arrangement of

molecules in an amorphous state, individual molecules easily interact with external

materials. An example of this is water that can be straightforwardly absorbed by

amorphous food materials. Amorphous solids have higher entropy than crystalline

materials since the microstructure of amorphous materials may consist of a short

range array and regions of high and low densities (Lian, 2001).


The glass transition temperature (Tg) is the critical temperature at which a

material changes its criteria from being 'glassy' to being ‘rubbery’ (Roos, 1998,

2003). 'Glassy' in this instance means hard and brittle that allows breakage easily

while a 'rubbery' state is elastic and flexible. Contrary to melting, when an

amorphous material undergoes the glass transition heat capacity change, it does not

have latent heat associated with the change of state.

Slade and Levine (Slade & Levine, 1991) first introduced the concept of glass

transition to explain or identify the physicochemical modifications in food materials

during food processing and storage. In addition, this theory has been proposed in

order to give details on the process of shrinkage, collapse, fissuring, and cracking

during drying (Cnossen & Siebenmorgen, 2000; Karathanos et al., 1993; Karathanos

et al., 1996a). Contrary to these findings, Rahman (2001) identified that the glass

transition theory does not always hold true interpretation for many products or

processes.

2.5.2 Anisotropy

An anisotropic structure is one which displays different properties or structure

of tissue when observed from a different direction. In general, fruit flesh or cortex

consists of parenchyma-type cells. There is a variation of cell size across the apple

fruit with cells under the skin being smaller (70 µM), increasing in size (approx. 250

µM) towards the centre of the flesh (Bain & Robertson, 1950; Reeve, 1953).

Towards the inner cortex, the apple cells become more elongated, spreading out in a

radial pattern, lying alongside air gaps (Khan & Vincent, 1990). Growth within the

plant based tissue varies according to the position, with more rapid growth occurring

at the calyx than at the stalk. There is a strong possibility of the water distribution,

and water holding capacity varying with this cell size variation.

The variation in cell size significantly affects the amount of collapse occurring

during the drying, and this leads to non-uniform porosity (Fito & Chiralt, 2003).

Larger cells with relatively thin cell wall weakened the tissue of the plant-based food

materials (Zdunek & Umeda, 2005). Due to this, non-uniform porosity is observed in

the dried product with less porosity where bigger cells exist in the sample. Therefore,

the anisotropic geometrical nature of the cells of the plant tissue should be taken into



consideration as it is an important parameter that determines the structural properties

in the course of drying.

2.5.3 Pore characteristics

Most of the parenchyma tissue contain intercellular spaces filled with water

and air. This initial volume of air is known as “initial porosity”. From the study of

Reeve (1953), it emerged that the width of the intercellular space varies from 210 to

350 µm whereas the length ranged between 438–2000 µm. The initial porosity in

fruits and vegetables varies between 0.02–0.34 (Boukouvalas et al., 2006; Ting et al.,

2013). However, the distribution of these intercellular spaces is anisotropic in nature.

They play a significant role in overall shrinkage during drying. The same material

with different initial porosity ends up with different amounts of volumetric

shrinkage. This is because of the influence of the amount of initial porosity on the

rigidity of the tissue.

It is found that material with higher initial porosity shows higher shrinkage

than the material with a lower initial porosity of same raw materials. In addition to

these, the initial intercellular spaces control the transport of mass and heat at the time

of drying. Therefore, most of the macroscopic properties are affected directly or

indirectly by corresponding microstructural properties (Aguilera, 2005; Mebatsion et

al., 2008).

A lot of literature has been published on the many food materials that behave

like porous media as these contain porous structures. Many food materials are highly

porous for example, white bread and butter cookies, with porosities of 0.90 and 0.55,

respectively. Powdered-based materials, such as milk powder, flour, chocolate

pudding have porosities of 0.454–0.610, 0.69 and 0.5, respectively. The minimum

and maximum value of porosity of a wide range of food categories have been

compiled in the review works of Boukouvalas et al. (Boukouvalas et al., 2006).

Difficulties arise when an attempt is made to classify a material as porous or

non-porous. About this, Goedeken and Tong (1993) investigated measurements of

permeability on pregelatinized flour dough where they took porosity as a function of

the range of 0.10–0.60. A significant correlation was found between permeability

and porosity. The results revealed that the porosity range 0.1 to 0.6 showed

permeability values ranging from 1.97 × 10−14

m2 to 2.27 × 10−

11 m

2. For porosity, a


value less than 0.4 showed more resistance to air flow through to samples due to the

permeability being low (7.9 × 10−13

m2).From this finding, the authors came to the

conclusion that a material can be defined as porous when it possesses a porosity of

0.4 or more. However, Waananen and Okos (1996) proposed that a material having

porosity over 0.25 can be classified as a porous material.

In light of the findings in literature, materials having porosity lower than 0.25

can be classified as non-porous, intermediate porous material are those having

porosity between 0.25 to 0.4 , and a highly porous structure would have a porosity

above 0.4 (Karathanos et al., 1996b; Krokida & Maroulis, 1997; Rahman et al., 1996;

Waananen & Okos, 1996). Most of the pores in the fresh and dried porous sample are

non-uniform in size and irregular in geometry (Yao & Lenhoff, 2004). Therefore, to

interpret the complex nature of pore geometry, pore types and pore size is important.

Pore size

In general, most of the food materials are the combination of solid, liquid and

gases; porosity is the volume of void or gas to the total volume. Porosity refers to the

ratio of the free space that exists in the material to the total volume of the material. It

can be obtained from the following relationship.

Total

Void

V

VPorosity

V

VV

VVV

Vws

gws

g

1

(2.1)

Where, Va ,Vw, Vs and V are the gas, water, solid and total volume

respectively.

Porosity can be alternatively expressed according to the following equation as

it is usually estimated from the apparent density and the true density of the material.

p

b

1

(2.2)

Depending on the nature of pores, three types of pores can be developed during

drying namely blind pore, closed pore, and interconnected pore. These are as shown

in Figure 2.3.



Figure 2-3: Different types of pores in food sample

It can be seen from this figure that blind pores are those that have one end

closed while interconnected pores are those which allow flowing of any fluids, and

closed pores refer to the pores that are closed on all sides.

Taking into account all types of pores, an apparent porosity of food material

can be determined by the following relationship.

blindopencloseapp (2.3)

Pore size

Pore size is important in both water transport and mechanical properties of the

plant tissue during drying. The size of pore determines the pattern of internal water

transport mechanism over the time of drying.

On the basis of pore size, pores in porous materials can be classified as macro,

micro and mesopores. Micropores have a width of greater than 2 nm while pores

with a width greater than 50nm are called macropores, and pores between these two

sizes are termed mesopores.

In terms of porosity, materials can be divided into two groups (i) porous and

(ii) capillary porous materials. This classification is defined by the pore size. Porous

materials are defined as those having a pore diameter greater than or equal to 10-7

m

while materials with a pore diameter of less than 10-7

are called capillary-porous

materials (Datta, 2007a). However, most of the food materials are treated as

capillary- porous materials.


However, the pore characteristics of the food materials do not remain constant;

rather they change significantly due to simultaneous heat and mass transfer.

Therefore, insight into the pore formation mechanism will assist us to understand the

physics behind the structural change of food materials over the course of drying.

2.6 PORE FORMATION MECHANISM

Properties and structures of the dried product are influenced by the type of

drying, the its associated variables and the raw structure and components of the food

materials (Aguilera & Chiralt, 2003). Similarly, the properties of food material,

drying methods, and their conditions have pronounced effects on the porosity of the

final product. Even the same type of raw materials demonstrate different pore

characteristics are depending upon the drying method and conditions (Sablani et al.,

2007). On the whole, porosity is directly dependent on initial water content,

temperature, pressure, relative humidity, air velocity, electromagnetic radiation, food

material size, composition and initial microstructure and viscoelastic properties of

the biomaterial, as shown in the Figure 2.4 (Guiné, 2006; Krokida et al., 1997;

Saravacos, 1967).

Figure 2-4: Factors that affect pore formation and evolution



Moreover, different food materials demonstrate different values of porosity due

to their diverse structures. For example, an apple develops the highest porosity,

whereas banana and carrot show less porosity at the same drying conditions. This

could be due to their initial structures and compositions. Therefore, in order to

control or predict food porosity, both the process conditions and product properties

are to be taken into consideration.

After an extensive review of the literature, it is clear that changes in porosity in

food materials over the period of drying mainly depends on volume change and void

formation due to water migration. Both of these the phenomena occur simultaneously

depending on the material properties and drying conditions. However, the followings

are the significant factors that must be considered to predict porosity in dried

products.

2.6.1 Moisture content

Moisture content is the distinctive factor that causes porosity to vary

significantly. Porosity, in general, increases with the removal of water. However,

shrinkage of the food sample also increases with the removed water volume, owing

to the higher contraction stresses developed within the material. These two opposite

physical changes determine different patterns of pore formation and evolution.

Figure 2-5: Change of porosity as a function of water content

(A and B: with inversion; C and D: no inversion point).


Under such circumstances, it becomes difficult to predict the nature of pore

formation. To relate the relationship between water content and porosity, two

experiment-based generic trends are available in the literature, as shown in Figure

2.6 (Rahman, 2001). One of these generic trends has an inversion point (A and B),

and the other does not (C and D).

In most of the cases, inversion begins at a critical moisture point. The two

generic trends cover all manner of possible changes in porosity.

A study by Lozano et al. (1983) is relevant here, as it has investigated all four

types of porosity trends for selected agricultural products. In that study, the porosity

of pear and carrot were found to change as a function of water with an inversion. It

appeared that pear showed an upward inversion, while a downward inversion trend

was reported in the case of carrot.

Table 2-3: Changes of porosity with a decrease in moisture content during drying of various fruits

and vegetables.

Porosity relationship with

moisture content

Food Stuff References

Upward

inversion

Pear (Lozano et al., 1983)

Downward

Inversion

Carrot,

pineapple,

ginseng

(Lozano et al., 1983; Martí et al.,

2009; Martynenko, 2011; Yan et

al., 2008a)

Increasing

without

inversion

Sliced and

whole pear,

carrot, whole

garlic, cube-

shaped garlic,

potato, mango,

avocado,

strawberry,

banana, apple,

prune

(Boukouvalas et al., 2006;

Djendoubi Mrad, 2012; Guiné,

2006; Karathanos et al., 1996b;

Katekawa, 2004; Krokida et al.,

1997; Liu et al., 2012a; Lozano et

al., 1983; Martí et al., 2009; Sablani

et al., 2007; Tsami & Katsioti,

2000; Vincent 2008; Wang &

Brennan, 1995a; Yan et al., 2008a)

Decreasing

without

inversion

Sliced garlic (Lozano et al., 1983; Sablani et al.,

2007)



On the other hand, some other food materials show porosity without inversion.

For example, sliced garlic was found to have decreased porosity with a decrease in

moisture content, whereas an increase in porosity and a decrease in moisture content

were found for potato. Based on an extensive literature review, changing patterns of

porosity with moisture content for various food materials are presented in Table 2.3

below.

In light of the above-mentioned discussion, knowledge of only moisture

content is not sufficient information to predict the porosity closely. Therefore, other

related factors concerning pore evolution need to be taken into consideration.

2.6.2 Water distribution

Water in fresh fruits and vegetables primarily remains contained in the cells

(intracellular) and stays intact before any processing. A small amount of water exists

within the intercellular spaces. Haldar et al. (2011b) found that more than 85–95% of

the water within selected fresh fruit and vegetable tissues is intracellular, and the rest

of the water is present in the intercellular spaces.

The internal moisture transport takes place using three transport mechanisms:

(i) Transport of free water,

(ii) Transport of bound water, and

(iii) Transport of water vapour.

The liquid may flow due to the capillary and gravitational forces, transport of

water vapour by diffusion, and transport of bound water by desorption and diffusion.

Crapiste et al. (Crapiste et al., 1988) divided water flux inside plant tissue into

three types of transport during drying:

(i) Intercellular refers to the water vapour movement through

intercellular spaces,

(ii) Wall-to-wall represents the capillary water flow through the cell wall

tubes, and

(iii) Cell-to-cell refers to water flux through the vacuoles, the cytoplasm

and the cell membranes.


In general, at high moisture contents, liquids flow due to dominating capillary

forces. With decreasing moisture content, the amount of liquid in the pores also

decreases, and a gas phase is built up, causing a decrease in the liquid permeability.

Gradually, the mass transfer is taken over by vapour diffusion in a porous structure,

with increasing vapour diffusion (Datta & Rakesh, 2009).

Porosity evolution during drying is mainly caused by the void space left by the

migrated water. However, shrinkage of the solid matrix towards the centre of the

sample compensates for the void volume. Therefore, insight into heat and transfer

mechanisms and the structural deformation phenomenon are essential to

understanding the evolution of porosity in the course of the drying process. On the

other hand, these transfer mechanisms and structural changes are significantly

influenced by both the material properties and the process parameters.

Pore formation is prevented by shrinkage, collapse or expansion of food

material during drying. The degree of these structural changes depends on the

distribution of water within the food tissue. In a broad classification, water in food

materials can be grouped as free and bound water. Also, on the basis of the spatial

position of water it can be termed as intercellular and intracellular water and cell wall

water as presented in Figure 2.6.The term intercellular refers to any water found

inside a cell of any material while the intercellular water is that which is present in

capillaries. Intracellular water varies between 78-97 % (wet basis) in different fruits

and vegetables (Halder et al., 2011a), and the rest of the water exists as intercellular

water.



Figure 2-6: Water distribution within plant based cellular tissue

However, intracellular water encompasses water in cells and the cell walls.

Though, it is hard to determine the proportion of water within cells and cell walls,

however, some literature attempted to determine this (Joardder et al., 2015a; Joardder

et al., 2013a).

In general, plant tissues undergoing drying are subjected to stresses leading to

shape modification and deformation (Mayor & Sereno, 2004). These stresses are

developed due to simultaneous thermal and moisture gradients. The stresses

generated by moisture gradients take place during the entire period of the drying

process while the thermal stress is most significant at the earlier stage of the drying

(Jayaraman et al., 1990; Lewicki & Pawlak 2003). Therefore, the stress generated by

the moisture gradient is the dominant cause of the shrinkage of plant tissue during

drying.

It is essential to know the mechanisms and pathways of water migration from

the plant tissue during drying to understand the nature of collapse that is a

consequence of moisture transfer.


Literature dealing with the classification of water migration from samples

during drying is common. For example, Le Maguer and Yao (1995) proposed three

possible ways for the movement namely, (i) apoplastic transport (cell wall to free

space), (ii) symplastic transport (movement of water between two neighbouring

cells) and (iii) transmembrane transport (across the cell membrane).

In addition to this, Crapiste et al. (1988) presented different ways of water flux

inside plant tissues during drying; intercellular (vapour movement through

intercellular spaces), wall-to-wall (capillary flux across the cell walls) and cell-to-

cell (water flux through vacuoles, the cytoplasm and the cell membranes).

2.6.3 Structural mobility

To explain the physicochemical changes, Slade and Levine (Slade & Levine,

1991) first introduced the glass transition concept in food materials during storage

and drying. The glass transition temperature (Tg), is defined as the temperature at and

above which the amorphous material changes from a glassy state to a rubbery state

(Champion et al., 2000). In the glassy state, the material matrix has very high

viscosity with the range of 1012

to 1013

Pas. Effectively, the matrix behaves like a

solid as it can retain the rigidity of the structure by supporting its body weight against

the flow of solid matrix due to gravity (Angell, 1988; Lewicki, 1998b).Therefore,

)( gTTT can be treated as the driving force of structural collapse (Del Valle et

al., 1998), where T is the temperature of a sample undergoing drying. In this paper,

mobility temperature will be used to refer to T .

The glass transition theory is proposed in order to gain insight into the process

of shrinkage, collapse, and cracking during drying (Cnossen & Siebenmorgen, 2000;

Karathanos et al., 1993; Karathanos et al., 1996a; Krokida et al., 1998a; Rahman,

2001). Once over the glass transition temperature, the cell membrane collapses

significantly. At higher temperatures, cell walls cannot retain their intact structures,

and rupturing begins. Subsequently, water from the cells migrates into extracellular

spaces. Later, the water predominantly migrates from this extracellular space to the

outside of the material.

Although the glass transition concept can be applied to explain or identify the

physicochemical changes during food processing, many experimental studies were



unable to establish the relevant relationship in order to support this concept (Del

Valle et al., 1998; Wang & Brennan, 1995a).

2.6.4 Phase transition (Multiphase)

Plant-based porous food materials, in general during drying, encompass three

phases namely solid, liquid and gas (Chen & Pie, 1989). In addition to this, the void

spaces are filled with multiphase materials including water, vapour and air. The

pores change with the transport of those phases.

Figure 2-7: Multiphase mass flows in food materials during drying

The phase change from liquid to vapour is an important phenomenon because

the vapour phase diffusion is a significant mass transfer mechanism in a porous food

sample. Therefore, multiphase mass transfer phenomena, as presented in Figure 2.7,

occur during drying time. In many cases, vapour diffusion accounts for 10-34% of

moisture flux in convective drying at 55 to 71oC (Waananen & Okos, 1996). In

addition to this, vapour diffusion is faster than liquid water diffusion in porous media

during drying. The crust formation effect can be observed if drying conditions allow

a phase transition (liquid water to vapour) in the outer zone material, even at high

drying rates (Mayor & Sereno, 2004). Another remarkable phenomenon, crust

formation occurred due to the precipitation of non-volatile compounds on the surface

(Ramos et al., 2003).


Evaporation rate has a substantial effect on the pore formation during drying.

In particular, while drying under microwave energy, higher microwave power leads

to increased evaporation rate; consequently, the more porous structure developed in

comparison with the convection dried product. Therefore, quick evaporation of water

retains the porous structure and causes less collapse of the solid matrix.

In brief, the microstructures and solid matrix architecture of plant tissue vary

so much that there are many exceptions to these explanations of the pore formation.

Therefore, various concepts such as water-holding capacity, ratio of extracellular and

intracellular water content, glass transition temperature, exchange surface area of the

sample, phase change of liquid water, gas pressure and internal moisture transport

mechanisms need to be taken into consideration in order to explain pore formation

clearly for a particular material in a selected drying condition.

2.7 PREDICTION OF POROSITY

The models are classified into empirical and fundamental groups. Empirical

models are obtained using regression and analysis of experimental data for different

variables relating to porosity. Theoretical models are based on a physical

interpretation of the structure of food materials. Predictions of porosity are made

considering mass removal and volume variation of the different phases within the

food system along the drying process. Before discussion of the models, the

definitions of porosity-related terms are presented in the following sections.

2.7.1 Empirical models

Empirical models are developed using experimental data to fit parameters for a

particular system. Methods, materials and the processing environment confine these

models, and the fitting parameters usually have no physical significance. Even with

these limitations, the empirical models still provide a good explanation of the

experimental data. Table 2.4 provides empirical models for porosity measured in the

last three decades for different types of food materials in different drying conditions.

Coefficients a, b and c in different models holds different values to fit the

experimental value in the proposed model.



Table 2-4: Summary of empirical models predicting porosity during drying

Empirical Equation Drying

condition

Food

item R

2 References

)exp()exp(

)exp(

jXfeXd

cXbaY

Air Drying

(600 C)

Apple 0.97 Lozano et al.(1980)

xc

baX

aXY

)(

Air drying,

550C

Apple,

pears,

Potato

N/A Mattea et al.(1986)

Air Drying,

(700C)

Squid 0.97 Rahman et al.(1990)

Air drying

(700C)

Garlic N/A Modamba et

al.(1994)

bXa

Air Drying (

47 0C)

Pumpkin

Seed

0.988 Joshi et al.(1993)

Air Drying

(700C)

Onion 0.974 Rapusas et al.(1995)

Air Drying

(700C)

Calamari

Mantle

Meat

N/A Rahman et al.(1996)

c

Xba exp

Air Drying 30,

45, 600C

Air velocity:

3m/s

Potato 0.998 Magee et al. (2004)

bX

a

1

Air and Solar

Drying

Pear N/A Guiné (2006)

2cXbXa Air Drying

(50,80,1050C)

Apple 0.93-

0.97

Rahman et al.(2005)

5.02

0

ln

X

Xba

Air Drying

(40,500C)

Banana N/A Katekawa et

al.(2004)

Thermal

conduction

Meat N/A Perez et al.(1984)

In Table 2.4, all the empirical models were developed by correlating the

moisture content of the sample with porosity. It was also found that the empirical

relationships highly agree with the experimental data. Alongside linear relationships

between moisture content and porosity, other trends like exponential and power

relationships were also found. For example, Modamba et al. (1994), Lozano et

al.(1980) and Rapusas et al. (1995) expressed porosity using quadratic, exponential

and power law equations respectively.

0W

Wba

2cWbWa

3bWbWa

2

00

W

Wc

W

Wba

bWWa 0


Empirical models show a high accuracy in the prediction of porosity, but these

models have the following limitations:

They are not generic as they depend on the type of product, the drying

conditions (e.g. temperature, pressure, humidity and processing time, etc.)

The entire empirical model is specially developed to fit the experimental

data into a model while having to consider the particular drying conditions

and material properties. Therefore, these models cannot be replicated to

predict the expected parameters for slightly diverse systems and materials.

The empirical model is based on experimental data with no consideration

of the fundamental knowledge of the interrelation between process

variables and sample properties. For this reason, a fundamental

understanding of the physics that governs the process, and structural

change (formation of the pore) cannot be understood in the empirical

models.

It is essential to develop theoretical models as they have a wider insight of

physical parameter changes that can be used for a wide range of processes and

products.

2.7.2 Theoretical models of porosity

Most of the theoretical predictions are based on the conversion of mass and

volume principles. The first theoretical porosity model was developed by Kilpatric et

al. (1955). It was simple and considered the volumetric shrinkage of fruits and

vegetables during drying. This model is shown in Equation 2.4 and only considers

bulk and solid density (Miles et al., 1983).

(2.4)

Although this model has physical significance, it needs an instantaneous

experimental value of a bulk density of the sample. This basic model can be used as

the definition of porosity when the experimental value of both densities is available.

Later, Lozano et al. (1983)developed the following generalised equation to

predict the porosity of foodstuffs. In their next modified model, apparent shrinkage

s

b

1



coefficients and apparent and solid densities were taken into consideration. It

assumes that during drying, the shrinkage phenomenon is a linear function of

moisture content:

ε =(X + 1)

(X0 + 1)

ρb0

ρb

(2.5)

Their experimental results provided a good approximation for garlic, sweet

potato and potato, but the predicted porosity of other materials was not accurate. This

model also completely failed to predict the porosity of carrots with varied moisture

contents. This inconsistency may be due to the assumption of the shrinkage

phenomenon as a linear function of moisture content. In general, many of the food

materials do not show the linear relationship between volume shrinkage and volume

of migrated water at any time during drying (Lozano et al., 1980; Madamba et al.,

1994; Rapusas & Driscoll, 1995).

To resolve this shrinkage and moisture content relationship, Zogzas et al.

(Zogzas et al., 1994), proposed a model considering the volume shrinkage coefficient

( ). Three other fitting parameters were also considered and included the density of

dry solids ( ), enclosed water density ( ) and the bulk density of the dry solids (

) and are shown in Equation 16.

𝜀 = 1 −ρb0[ρw + Xρs]

ρwρs[1 + βX]

(2.6)

Despite the frequent use of this model, the prediction abilities of different

materials and methods were not accurate. One possible explanation would be that all

of the parameters associated with this model significantly affected by the drying

method and material properties (Krokida & Maroulis, 1997). The effect of process

parameters and product variants on the four fitting parameters is described below:

Dry solid density ( ) is an innate material property that is significantly

affected by the type of material being studied, as it is highly dependent on

material composition and structure. However, for some materials

undergoing drying, the value of solid density does not vary due to change

in drying conditions if the drying conditions (such as high temperature) do

not cause migration of other components.

s w

b

s


Enclosed water density ( ) has no discernible effect on either drying

method or material (Krokida & Maroulis, 1997).

The bulk density of dry solids ( ) is the principle issue that is robustly

affected by both material properties and process parameters factors. In

addition to this, online (instantaneous) measurements of this parameter are

vital but require a separate device for measurement.

To incorporate more practical physical phenomena, Rahman (Rahman, 2003)

proposed a hypothesis where the author identified that capillary force was the main

force seen in the collapse of tissue and observed that the counterbalancing of this

force handled the formation of pores and lowering the shrinkage. The

counterbalancing force was reported as any of the following: (i) strengthening of the

solid matrix (ice formation, case hardening and matrix reinforcement), (ii) generation

of internal pressure, (iii) mechanism of moisture transport or (iv) environmental

pressure. Therefore, the parameters (especially the shrinkage-expansion coefficient)

have been introduced to represent this force-balancing hypothesis. The author

developed two models for the pattern of shrinkage considering ideal and non-ideal

conditions.

In ideal conditions, it was assumed that the volume of developed pores did not

contribute to shrinkage and was equal to the volume of water removed during drying.

For apparent porosity of porous food materials the following equation was

developed:

(2.7)

Where, the volume of formed pores due to loss of water is

and volume of water along with solids at any water level was

By adding the shrinkage expansion coefficient to the ideal model, the non-ideal

model for real food materials can be obtained. Considering initial porosity and actual

measured porosity using the values of α and β, the shrinkage-expansion coefficient

can be calculated by the following equation:

w

b

'0 )1(

o

w

M

1

m

M

'



(2.8)

(2.9)

From Equation 2.8, it is noted that the shrinkage expansion coefficient requires

experimental values of initial and instantaneous porosity. Initial porosity is the

material property; however, instantaneous porosity requires experimental

measurement. Clearly then, the main difficulty seen in using this model is the

measurement of the shrinkage-expansion coefficient , as it is significantly

influenced by process parameters and characteristics of food materials.

Determination of this coefficient also requires experimental data and consequently

the porosity model becomes dependent on the empirical value of these variables. In

addition to this, the accuracy of these models is also not substantially proven using

experimental results.

It is assumed that initial porosity ε0 remains constant throughout the drying

process, although, the initial air volume is severely affected when the product is

under extreme heating. Therefore, collapse, as well as shrinkage, takes place in the

food material during drying. It needs to be mentioned that shrinkage refers to an

overall volume reduction phenomenon, whereas collapse represents irreversible

changes of volume (Prothon et al., 2003).

To introduce the collapse phenomenon, Khallofi et al.(2009) took into account

the possible change of volume over time during the drying processes. In their

prediction model of porosity, both collapse function and shrinkage function

were taken into consideration. The authors defined the collapse function as:

(2.10)

Where, is the evolution of air within the solid matrix.

Finally, the following expression was obtained for the theoretical model of

porosity considering the collapse function and the shrinkage function:

)1(

)( 0

'

'

'

X X

0

/

a

aa

V

XVX

)(/ XV aa


(2.11)

Where,

Despite the incorporation of some physics in the above model, some critical

questions were raised:

This model suggested using shrinkage and collapse function; however

there is no clear guideline for the use of these. In other words, for a

particular method or product, it is hard to determine whether to consider

one or both functions.

Measurement of these functions is not quite clear from the description of

the respective functions. For this reason, the model becomes the dependent

of two functions; both are affected by different variables including the

types of food materials and methods of drying.

The drying process that uses internal heating like microwaves is not

considered in this model. Therefore, it is not clear as to whether other

drying methods, as opposed to freezing and air-drying, are suitable for

using this model. Due to this, it becomes less generic for different types of

drying.

Although extensive analysis of the empirical and theoretical models on

porosity found that accurate and reliable prediction of porosity during the drying

process still needs the further attention of the researchers. A central issue is that there

is no generic model that can be applied to different products and drying processes.

Analysed literature confirmed that both product type and drying technology

discernibly affect pore formation and the pore evolution during drying of food

materials. To adapt the material properties, the previous studies mainly considered

the amount of the water migrates from the sample. Previous models involved other

structural parameters, like the volumetric shrinkage coefficient, shrinkage-expansion

DXC

BXAX

)(

)()1)(()( 0000 XXXXA

)1)(( 0 XB

)()1)(()(1 00000 XXXXC

)(1)1( 0 XD



coefficient and shrinkage-collapse coefficient. Most of the material properties varied

due to change in the drying conditions.

The measurement of the structural parameters meant there was a necessity for

experimental data. So by avoiding these structural parameters, which vary in drying

conditions, the formulation of a generic model of porosity was facilitated. In contrast,

a model containing different parameters that are not influenced by the drying

conditions can be treated as generic, regardless of the drying method. Therefore, a

model considering process parameters and material properties can address this

necessity.

2.8 EFFECT OF PROCESS PARAMETERS ON QUALITY

The methods of drying vary with the process. There are more than 200 types of

dryers (Mujumdar, 1997). For every dryer, the process conditions, such as the drying

chamber temperature, pressure, air velocity (if the carrier gas is air), relative

humidity, and the product retention time, have to be determined according to feed,

product, purpose, and method.

The various drying processes have different process conditions which are

important in influencing the product structure and causing different final outcomes

with differences in quality, and in particular, porosity (Krokida & Maroulis, 2001a;

Krokida & Maroulis, 2001b). For the example purpose, we only discuss the effect of

different drying process on porosity.

The porosity of freeze-dried materials (80–95%) is always higher in

comparison to all other dehydration processes. Microwave-dried potato has a higher

porosity (75%) while microwave-dried Apple does not develop high porosity (25%).

Vacuum-dried Apple develops high porosity (70%); while vacuum-dried potato’s

porosity values are lower (25%). Table 2.5 (below) provides the varying porosity of

some fruits and vegetables under various drying methods.

Taken together, porosity is affected by a combination of sample properties and

process parameters, the latter of which we have a significant amount of control over.

Therefore, proper choice of process conditions can provide an expected structure of

the finished product.


Table 2.5 Comparison of porosity of different foodstuffs under various drying methods

Food

Material

Porosity in different drying processes

Reference Convective

Drying

MW

Drying

Osmotic

Drying

Vacuum

Drying

Freeze

drying

Apple 0.6 0.75 0.55 0.50-

0.73

0.75-

0.92

(Giraldo, 2003;

Karathanos et al.,

1996b; Krokida et

al., 1998b; Krokida

et al., 1997)

Banana 0.20 0.25 0.20 0.20-

0.70

0.80-

0.90

(Krokida, 1997)

Potato 0.20 0.70 - 0.15-

0.25

0.78-

0.87

(Karathanos et al.,

1996b; Krokida et

al., 1997)

Carrot 0.10 0.70 - 0.10-

0.50

0.88-

0.94

(Karathanos et al.,

1996b)

Blueberry 0.15 0.21 - 0.45 0.70 (Yang & Atallah,

1985)

Quince 0.17 - 0.08 - 0.72 (Koç et al., 2008;

Tsami & Katsioti,

2000)

Tuna

strips

0.24 - - 0.46 0.76 (Rahman et al.,

2002)

Though most of the previous studies showed improvement in different quality

attributes, they fail to explain the relationship between moisture and temperature

distribution. There are limited studies on the effect of process variables on textural

attributes of IMWC drying. In some cases, however, it is reported that fruits and

vegetables (e.g., potatoes, apples, bananas and carrots) undergoing drying and other

thermal processing exhibit an initial tissue-softening stage; followed by a tissue

hardening stage (Devahastin & Niamnuy, 2010b; Krokida et al., 2000). This

transition could be moisture dependent, and desired quality can be obtained by

investigating the problem. Bourne (1992) showed that textural properties of apples

largely depend on water activity.Krokida et al. (2000) investigated the effect of

moisture content on elastic parameters. So it is interesting and essential to explore

the textural properties during IMWC drying and its dependency on moisture and

temperature distribution in the same process.

Similar to porosity, other qualities of dried products are affected by both

sample properties and process conditions. However, there is a lack of literature

concerning dried food quality yield from IMCD.



2.9 SUMMARY OF LITERATURE AND RESEARCH GAPS

Based on the above literature review, we can make the following conclusion:

Optimisation of energy and quality is the prime focus in food drying

research;

MCD treated products achieve superior quality when compared to CD;

IMCD technique reduces energy requirement and drying time and

produces better quality finished food compared to CD and MCD;

Although some studies attempted to investigate sensory quality attributes

of dried food; in-depth study on textural, rehydration and thermos-physical

attributes of IMCD treated food has not been done.;

IMCD allows redistribution of temperature and moisture resulting uniform

distribution of moisture and temperature that eventually mitigate the

problems of overheating;

Although drying is a multiphase transfer process involving internal

moisture, vapour and air transfer over the course of drying, one of these

dominates over the other depending on the process parameters and

material properties;

Single-phase models are simple and effective to some extent. However,

these models require experimental determination of effective diffusion

coefficients. Effective diffusivity coefficients cannot provide detailed

information about different moisture transport phenomena such as pressure

driven flow and evaporation as single phase model lumps all moisture flux

together;

Shrinkage and pore evolution during drying are obvious phenomena;

however, there is no IMCD model that considers these factors;

Shrinkage and porosity depend on process parameters and sample

physicochemical properties;

Proper prediction of pore formation and evolution is necessary to develop

more realistic multiphase IMCD model and accurate interpretation of the

quality of dried food;


Various concepts such as water-holding capacity, the ratio of extracellular

and intracellular water content, glass transition temperature, exchange

surface area of the sample, phase change of liquid water, gas pressure and

internal moisture transport mechanisms need to be taken into consideration

in order to explain pore formation accurately.

A porosity model considering process parameters and material properties

can provide a more realistic prediction than existing models.

From these conclusions, it is clear that a comprehensive multiphase porous

media IMCD model considering shrinkage and pore evolution is necessary to

describe actual drying process, and this is not available in the literature. To address

this necessity, an investigation on pore formation and evolution is carried out to

develop an IMCD multiphase porous model taking shrinkage and pore evolution into

consideration.

Chapter 3 | Research Design


Chapter 3: Research Design

In this chapter, a method of model development and solution, and experimental

investigation are discussed. The framework of this research is presented in Figure

3.1.

Figure 3-1: Framework of this research

A brief description of the models is provided here; however, detail descriptions

of the models are presented in Chapters 4, 5 and 6.

3.1 METHODOLOGY AND RESEARCH DESIGN

As the primary objectives of this study are to (i) develop a prediction model to

describe pore formation and evolution during drying and (ii) develop a multiphase

IMCD model taking shrinkage and pore evolution into consideration. The research

has been designed in the following two stages:

3.1.1 Prediction of pore evolution

Both product type and drying conditions discernibly affect pore formation and

evolution during drying of food materials. Therefore, a porosity prediction model

that takes both material properties and drying conditions into consideration can be


treated as more theoretical than the current models of porosity prediction. To adapt

the material properties; water content, initial porosity, particle density and glass

transition temperature have been included in the porosity prediction model.

Figure 3-2: Typical plant based cellular tissue

As plant-based cellular tissue encompasses air, water and solid matrix (shown

in Figure 3.2), structural deformation depends on all of these components. Therefore,

in our porosity prediction model the followings consideration has been taken into

account.

I. Pore formation is proportional to the amount of migrated moisture. The

proportionality depends on nature of water (free or bound) and solid

matrix mobility. Intracellular and intercellular water will be considered

separately. In addition, the nature of solid mobility will be determined

from information of drying air temperature and glass transition

temperature of the sample.

II. Pore evolution due to deformation of air spaces is predicted by the

structural strength of the sample. A density ratio obtained from particle

density and water density will be incorporated to predict the initial air

space deformation.

3.1.2 IMCD model

A 2D axisymmetric IMCD multiphase model considering shrinkage and pore

evolution has been developed in three steps, as shown in Figure 3.3.



Step 1: Development of single phase convection drying model: a single-

phase convection model is developed considering shrinkage phenomenon. An

effective moisture diffusivity that varies with moisture content and temperature of

drying air is considered in this model.

Figure 3-3: Steps toward IMCD multiphase model

Step 2: Development of single phase IMCD model: By adding an

intermittent microwave heating source in the energy conservation equation, a single-

phase IMCD model is developed. This model considers Lambert’s Law for

microwave heat generation.

Step 3: Development of multiphase IMCD porous media model:

Considering transport of different phase (liquid water, vapour and air) due to two

different internal mass transfer mechanisms such as convection flow and diffusion

flow, a multiphase IMCD porous media model has been developed. In this model,

shrinkage and pore evolution during drying are also taken into account.

Details of step1-3 have been provided in Chapter 4, Chapter 5 and Chapter 6

respectively.

3.2 SOLUTION PROCEDURE

The simulation was performed by using COMSOL Multiphysics 4.4, a finite

element based engineering simulation software programme. COMSOL Multiphysics

has a wide range of predefined physics interfaces for application ranging from fluid

flow and heat transfer to structural mechanics and electromagnetic analysis. It also

has the flexibility of adding own partial differential equations (PDEs) and link them

to other equations. Material properties, source terms and boundary conditions, can all

be arbitrary functions of the dependent variables which are important in drying


application as transport properties for both heat and mass changes with temperature

and moisture content in drying operation.

Figure 3-4: Simulation strategy in COMSOL Multiphysics

The software facilitated all steps in the modelling process, including defining

geometry, meshing, specifying physics, solving, and then visualising the results.

COMSOL Multiphysics can handle the variable properties, which are a function of

the independent variables. Therefore, this software was very useful in drying

simulation where material properties changed with temperature and moisture content.

The simulation methodology and implementation strategy followed in IMCD

multiphase is shown in Figure 3.4.

Figure 3-5: Intermittency function of microwave power



A combination of a rectangular function and an analytic function in COMSOL

Multiphysics was used to develop a microwave intermittency function as shown in

Figure 3.5. Then it was multiplied by the heat generation term in the energy

equations to implement intermittency of the microwave heat source. Rectangular

function in COMSOL Multiphysics has been defined in order to define the

intermittency of MW power.

Since heat and mass transport phenomena are happening at the transport

boundaries, a finer mesh (maximum element size 0.01mm) was chosen at those

boundaries to capture this phenomenon more accurately.

Figure 3-6: Mesh for the simulation of CD and IMCD drying

Moreover, triangular mesh with a homogenous element size was used to the

better performance of resolving the physics within the rectangular domain. Figure 3.6

shows the mesh chosen for the model. To accomplish the grid independent

simulation, the following two conditions were checked.

- Remaining RMS Error qualities have lessened to an acceptable value as for

our study 10-3

– 10-4

.

- Monitor points for selected values have come to an unfaltering solution

Once the simulation solution satisfies these conditions, the solution is

independent of mesh.

In order to observe the mesh independency, variation of average temperature

with a number of cells is plotted, as shown in Figure 3.4.

From Figure 3.7, it is clear that up to 30000 cells there is a significant

variation found in the selected parameter (average volumetric temperature). It can


also be seen from the figure that acceptable difference exists for cell number more

than 60000. This manifest that we have achieved a solution value that is not

dependent of the mesh resolution. Therefore, for the further study we can use 60000

cells.

Figure 3-7: Mesh independence check of the simulation

The maximum time step was set 1s to prevent the solver from taking too large

time steps that can result in convergence problems. In addition to this, linear element

order for all dependent variables was used to get the robust performance of solving

linear elements.

Moving mesh module of COMSOL Multiphysics, Arbitrary–Lagrangian–

Eulerian (ALE) approach has been used to account structural deformation happening

in food sample. This approach can provide structural shrinkage along with domain

mesh movement. As ALE is implemented in this thesis, a brief discussion is

presented below.The partial differential equations of physics are usually formulated

either in a spatial coordinate system (Eulerian formulation), with coordinate axes

fixed in space, or in a material coordinate system (Lagrangian formulation), fixed to

the material in its reference configuration and following the material as it deforms.

A prime shortcoming with the pure Eulerian formulation is that it cannot deal

moving domain boundaries as physical quantities are referred to fixed points in

space, whereas the set of spatial points instantaneously inside the domain boundaries

changes with time. Therefore, to allow moving boundaries, the Eulerian equations

must be rewritten. The finite element mesh offers one such system: the mesh

59

59.5

60

60.5

61

61.5

62

0 20000 40000 60000 80000 100000 120000

Aver

age

volu

met

ric

tem

pura

ture

( 0

C)

Number of cells



coordinates.Rewriting physics equations on a freely moving mesh, turns in an

arbitrary Lagrangian-Eulerian (ALE) method. The ALE method is therefore an

intermediate between the Lagrangian and Eulerian methods, and it combines the best

features of both—it allows moving boundaries without the need for the mesh

movement to follow the material.

To solve the circular dependency of the variables, the variables were treated as

dependent variables. To ensure that the results are grid-independent, several grid

sensitivity tests were conducted. The simulation was repeated using updated sample

size and materials properties after each cycle. The total number of degrees of

freedom to be solved for was 805526. The simulations were run on a 12 core, 2.0

GHz Windows workstation with 16 GB memory for a total run time of 10 hours. The

simulations were performed using a Windows 7 computer with Intel Core i7 CPU,

3.4GHz processor and 16 GB of RAM.

3.3 EXPERIMENTAL INVESTIGATION

Prediction of porosity and modelling of IMCD require numerous properties of

the sample. Many of these parameters are obtained from literature; however, a great

number of parameters are unavailable in literature. To find out the value or

correlations of those parameters, experiments have been conducted. In this study

models developed have been validated by experimental results. Table 3.1 presents

the lists of the instruments was used in this study.

Table 3-1: List of instruments with their measured quantity

Instrument Measured quantity Unit

Differential scanning calorimeter (DSC) Glass transition temperature K

Refractometer Ripeness o

Brix

Thermal imaging camera Temperature K

Gas (helium) pycnometer Solid density kg/m

3

Tapped density analyser Bulk density kg/m

3

Scanning electron microscope (SEM) Micrograph

Profilometer Surface roughness

Nuclear magnetic resonance (NMR) Water distribution

2kN Instron universal testing machine Mechanical properties

Electronic Moisture Analyser Moisture content


In addition to these, quality investigation, in particular, microstructure,

rehydration and mechanical properties, changes in appearance require an

experimental process. Details of these experimental procedures are provided in the

following sections.

3.3.1 Sample preparation

Fresh Granny Smith apples used for the intermittent microwave drying

experiments were obtained from local supermarkets. The samples were stored at

5±10C to keep them as fresh as possible before they were used in the experiments.

The apples taken from the storage unit were washed and put aside for one hour to

allow their temperature to elevate to room temperature prior to each drying

experiment. The samples were cut to a thickness of 10mm and a diameter of

approximately 40mm.

Electronic Moisture Analyser (KERN MLS_A Version 3.1) was used to

measure the moisture content of the samples. Ten samples were used for the moisture

content measurement. The initial moisture content of the fresh apple was found to be

85±0.75% wb.

3.3.2 Drying experiments

Drying tests were performed based on the American Society of Agricultural

and Biological Engineers (ASABE S448.1) Standard. The procedures for ASABE

standard are as follows:

Tests should be conducted after the drying equipment has reached steady-

state conditions. Steady state is achieved when the approaching air stream

temperature variation from the set point is less than or equal to 10C.

The sample should be clean and representative in particle size. It should be

free from broken, cracked, weathered, and immature particles and other

materials that are not inherently part of the product. The sample should be

a fresh one having its natural moisture content.

The particles in the thin layer should be exposed fully to the airstream.

Air velocity approaching the product should be 0.3 m/s or more.



Nearly continuous recording of the sample mass loss during drying is

required. The corresponding recording of material temperature (surface or

internal) is optional but preferred.

The experiment should continue until the moisture ratio, MR, equals 0.05.

Me should be determined experimentally or numerically from established

equations.

The IMCD drying was achieved by heating the sample in the microwave for

60s and then drying for 120s in the convection dryer. In other word, in order to get

the intermittency of the microwave power application, the sample is placed in MW

after the tempering period for 120s.The experiments were conducted with a

Panasonic Microwave Oven having inverter technology with cavity dimension of

355mm (W) x251mm (H) x365mm (D). The inverter technology enables accurate

and continuous power supply at lower power settings. Whereas, with conventional

oven, the lower power is achieved by turning the microwave on and off at maximum

power (Kumar et al., 2015b) . The microwave oven can supply 10 accurate power

levels with a maximum of 1100W at 2.45GHz frequency. The apple slices were

placed in the centre of the microwave cavity, for an even absorption of microwave

energy. The moisture loss was recorded at regular intervals at the end of power-off

times by placing the apple slices on a digital balance (specification: 0.001g

accuracy).

The convection drying was conducted to compare the results with IMCD. For

convection drying, the same samples were placed in a convection dryer and the

temperature was set to 600C. The moisture loss was recorded at regular intervals of

10 mins with the digital balance (specification: 0.001g accuracy). All experiments

were done in triplicate, and the standard deviation was calculated.

Uncertainty analysis

Uncertainty analysis of the experiments was done according to Kumar et al.(2014b).

If the result R of an experiment is calculated from a set of independent variables so

that, N321 .,..........,, XXXXRR , Then the overall uncertainty can be calculated

using the following expression


2/1

1

2

i

i

.

N

i

XX

RR

(3.1)

and the relative uncertainty can be expressed as follows:

2/1

1

2

i

i

..1

N

i

XX

R

RR

Re

(3.2)

Uncertainty analysis of temperature

The temperature was directly obtained from the calibrated thermal image and the

accuracy was within the ASHRAE recommended range, which is ±0.50C. Therefore,

the uncertainty of the temperature would be

5.0measured TT (3.3)

Uncertainty analysis of moisture content

The dry basis moisture content, ratio of the weight of moisture, mW to that of bone

dry weight, dW , of the sample was calculated from the following equation.

d

d

d

m

W

WW

W

WM

(3.4)

Therefore, 2

d

d

d

d

d

...

W

WW

W

WW

W

MW

W

MM

and

dd

d

d .

.

WWW

WW

WW

W

M

M

Now the relative uncertainty associated with the measurement of moisture content of

sample can be expressed:

2/12

dd

d

2

d

m.

.

WWW

WW

WW

We

(3.5)

Now the present work considers following valued of the apple sample to be dried in

the drying chamber. gW 10 and gW 1d .As these two values are obtained using

the same load cell, and as per manufacturer’s specification, the percentage error of

load cell is %1.0 , therefore, 0001.0d WW . Substituting all the valued in Eq.

24, the relative uncertainty for moisture content, me , is obtained, the value is found to

be %1.1 .



3.3.3 Ripeness

Physico-chemical properties of plant-based sample vary significantly the

variation of ripeness. Therefore, samples with consistent ripeness were chosen in this

study. The stage of ripeness regarding Brix was measured using refractometer (RFM

342 Refractometer). Brix is reported as "degrees Brix" and is equivalent to a

percentage. According to this, 1o

Brix represents 1% sucrose solution in water. To

carry out the Brix measurement, a test measurement was carried out using water at

the start of each series of ripeness measurements. After this, a small amount of

extracted juice from fresh apple is deposited on the prism with a pipette. The average

ripeness (Brix) of the apples was found to be 13.04 ± 0.30.

3.3.4 Glass transition temperature

In order to measure heat flows and temperature associated phase transitions in

any materials, a thermal analysis technique named DSC is used. The measured

parameters are expressed as a function of temperature and time. Firstly, about 10 mg

of Granny Smith samples of different moisture content were placed into aluminium

pans (20 µl) of differential scanning calorimeter (DSC). Samples were weighted after

hermetically sealed with lids. The mass of each sample was checked prior to sample

preparation and found ± 0.1mg weight differences from the empty reference pan.

Figure 3-8: Determination of Glass transition temperature using DSC

In this study, DSC Q100 (TA Instruments, USA), as shown in Figure 3.8 was

used. N2, 50 ml/min was deployed as purge gas. After cooling the sample at -650C,

thermos-analytical curves obtained by heating the sample to 1000C. The thermos-

analytical curves were investigated using TA software for measuring glass transition

temperature.


3.3.5 Power absorption ratio

The Panasonic Inverter microwave oven was used in the experiments to

determine the power absorption. The tests were conducted at three power levels

100W, 200W and 300W, with a water sample. The volume of water sample was

taken as the same volume of apple to obtain accurate power absorption. Water was

heated for 60s, and thermal images were taken by the thermal imaging camera (FLIR

i7) before and after heating. The water was properly agitated to measure the average

rise of temperature. The absorbed power, 0P , can be calculated by Equation 3.1 for

various load volume and applied microwave power.

t

TCmP pww

0

, (3.1)

The incident power absorbed by the sample for three different power levels and

various loads was calculated by Equation 3.1, Power absorption ratio defined as the

ratio of absorbed power by sample and microwave set power, was then calculated.

3.3.6 Thermal imaging

A thermal image camera allows monitoring temperature distribution in the

heated material. An FLIR i5 thermal camera that provided 10000-pixel images was

used for this. It allowed temperature accuracy calibrated within ± 2°C or 2% of

reading to meet the standard. It is capable of tracing the optimised temperature range

from -20° to 250°C. An FLIR i7 thermal imaging camera was used to measure the

temperature distribution on the surface. Accurate measurement of temperature by

thermal imaging cameras depends on the emissivity values. The emissivity value of

apple was found in the range between 0.94 and 0.97 (Hellebrand et al., 2001) and set

in the camera before taking images.

3.3.7 Particle density determination

Particle density was determined with the gas (helium) pycnometer

(Quantachrome pentatype 5200e, USA), as presented in Figure 3.9. Helium is used to

measure the skeleton (particle/solid/true) density due to its small molecular size,

which makes it possible to access the smallest pores of up to 3.5X10-10

m. Therefore,

all of the pores, even the closed intercellular pores, can be accessed, as the cell walls



contain numerous pores that are larger than 3.5 X10-10

m. Ten measuring cycles were

carried out using this instrument to calculate the mean value for particle density of

each sample. Therefore, particle volume, Vp can be determined from the known mass

and particle density of the sample.

Figure 3-9: Particle density determination of sample using He pycnometer

Bulk density determination

The bulk density, ρb, was calculated from the bulk volume and the weight of

the sample. Bulk volume was measured by the glass bead displacement method. The

density of the same sample was measured both before and after coating. The sample

was first covered with conventional correcting fluid to fill up the open pores as there

are many open pores that are large enough to allow the glass beads access (Lab

Glass, 57 µm) into the pores. The density of glass beads (glass bead packing density)

was determined from the weight of glass beads required to fill the known volume

vial as shown in Figure 3.10. The tapped density is expressed as:

Tapped density = mass of glass beads / tapped volume (empty vial volume)

The process of determining the glass bead packing density has been repeated

three times.This process of tapping was carried out by using a tapped density

analyser (Quantacrome Autotap, follow ASTM B527 standard). The tapping

frequency was 60 taps/min and 260 tap/min for manual tapping and autostop

respectively. Tap height 3 mm is fixed in the tapped density analyser. The effect of

the number of taps of the vial on the packing density has been carefully observed,

and taken into consideration in determining the glass beads’ density. Therefore, to


eliminate variance, the considerable endeavour was made to maintain constant glass

bead density. Next, the sample was placed in the vial. The rest of space within the

vial was filled with glass beads and tapped up to the same number at which the glass

bead density was measured. The top of the vial was levelled with a plastic ruler. The

bulk volume Vb can be determined by the following equation:

c

c

gb

gb

vcgbvb

mmVVVVV

(3.2)

Where, vV and are the vial and glass bead volume respectively.

In addition to this, some of the real-time volume measurement was done by

image analysis technique when necessary arises.

The dense random packing of monosized spherical glass beads has been

studied experimentally by tapping a filled vial (container) for 0-150 times. The true

density of the glass bead was found to be 2.44±0.002 g /cm3. After a certain number

of taps (90 in the case of manual tapping and 120 for the auto top), the almost

constant packing density of glass beads with the value 0.99-1.0 g /cm3 was obtained.

Although a large number of taps increases the measuring time, it provides more

reproducible packing density of the glass beads. It was found that glass bead density

Figure 3-10: Envelope (bulk) volume determination of dried fruit using displacement method



becomes almost constant after a certain number of taps. It can be concluded that a

minimum number of taps are necessary (after which density does not change much)

to reach a constant glass bead packing density.

In addition, this, sizes of the investigated pores were in the range of 50 µm-260

µm (Levi & Karel, 1995; Marousis & Saravacos, 1990; Yan et al., 2008b).

Therefore, it can be confirmed that many glass beads may enter into the open,

connected pores of dried foods. This phenomenon has also been observed by using

SEM after measuring bulk density using glass beads, as shown in Figure 3.11.

Figure 3-11: Glass bead entrance into open and connected pores of the sample

It is very clear that a large numbers of glass beads penetrated into the pores due

to the larger size of the pores. It can also be seen that some surface pores are large

enough to accommodate multiple beads. Pursuing this further, there are multilayers

of glass beads packed into the pores. In light of these findings, it can be assumed that

many pores are not only open but also connected with other internal pores. Under

these circumstances, it is obvious that bulk volume determined in this method would

provide lower bulk volume than the actual volume. Therefore, the coating of the

sample is a solution to overcoming this error in bulk volume measurement.


As previously discussed, in many cellular plant tissues, the cell dimension is

more than 100 µm and in the case of apple, it was found to be 100–250 µm.

Similarly, the open pores on the surface of the dried apple were found to be 50 nm to

200 µm (Joardder et al., 2015a). Therefore, an uncoated sample during glass

displacement allows smaller glass beads access into these larger open pores.

The coated sample (in Figure 3.12b) shows that there were no micro-pores

exposed on the outer surface of the sample. This layer eventually resists glass beads

entering the pores underneath it. Following this method, the bulk volume

determination would be more accurate than the measurement without coating.

To assess the porosity of the sliced apple at different moisture contents,

repeated experimental measurements were conducted. A comparison between

porosity of dried apple samples measured at different moisture content with and

without a coating of the surface is made and presented in Figure 3.13.

Figure 3-12: Microstructure of apple slice, a.) without coating and b.) with coating



Figure 3-13: Porosity of dried apple slice with and without coating

As Figure 3.13 shows, there is a significant difference between the porosity of

the coated and uncoated samples. As uncoated surface allows a lot of glass bead

penetration into the dried sample, it can be concluded that in order to achieve more

accurate porosity, the surface of the sample must be coated with the appropriate

coating material. It is also appeared from the figure more difference and standard

deviation has been observed in the case of the sample with very less moisture

content. This is also manifest the effect of open pores on pore calculation.

3.3.8 Porosity Determination

Porosity of dried food is determined by the ratio of particle volume and bulk

volume as expressed by the following equation:

b

p

V

V1

(3.3)

Where, Vp and Vb are the particle volume and bulk volume of the dried food

material.

3.3.9 Microstructure analysis

A Scanning Electron Microscope (Quanta 200 SEM, Oregon, USA) was used

to analyse the microstructure of both coated and uncoated apple slices. Image J 1.47v

software was used to analyse the microstructure to achieve the pore distribution on

the surface. A profilometer (Nanovea Profiler, Irvine, CA) was used for 3D mapping

of the dried foodstuff. This software allows the determination of the size of the area

or line to be measured, as well as measurement of the fractal dimension.


3.3.10 Mechanical properties determination

The compression speed was 2, 5, 10 and 20mm/min, as proposed in ASAE

standard 368.1 (Ekrami-Rad et al., 2011). Experiments were carried out using the

2kN Instron universal testing machine as shown in Figure 3.14. After slicing apple

sample to 10 mm thickness, cylindrical samples of diameter 10 were prepared using

a bore. After checking the dimension of the cylinder, the samples were placed on

sample holder (lower compression plate). After setting up required speed of the load,

the instrument was run for operation. Force and deformation data from the

compression test were recorded on a connected computer.

Young’s modulus (apparent elastic modulus, ASAE standard 368.1) was

obtained from the slope of the force-deformation curve at the point of its highest

gradient (Khan, 1993).

Figure 3-14: Mechanical properties observation using universal testing machine

The Poisson’s ratio was calculated by measuring the diminution before and

after deformation under compression test. Young’s modulus, Poisson’s ratio and

stiffness were calculated using the following formulas (Bentini et al., 2009; Emadi et

al., 2009; Grotte, 2002):

Young’s modulus,

L

l

D

F

Strain

StressE

2)2/( (3.4)



Poisson’s ratio,

l

lD

d

(3.5)

Where, d is transverse deformation (mm), D is sample width (mm), l is axial

deformation (mm) and L is sample length (mm).

From Young’s modulus, Hooke’s law can be derived, which describes the

stiffness of the material.

Stiffness, k=l

F

L

AE where A is the cross-sectional area of the sample.

3.3.11 Image analysis

Digital image and SEM images were analysed using Image J, cross-platform

image analysis tool developed by the US NIH,software. To determine colour change,

cell dimension, cell wall thickness, open pores calculation the software was used.

Colour analysis

Colour analysis in the RGB colour model was done using colour picker

software. RGB-triplets for every pixel in the image where the red (R), green (G) and

blue (B) is intensities of mentioned colours in the range from 0 to 255. Colour

analysis was done in terms of hue angle and colour change. The hue angle value

corresponds to whether the object is red, orange, yellow-green, blue, or violet

(Mohammadi et al., 2008). Hue angle is defined as:

BGR

BGh

2

)(3tan 1

0 (3.6)

Eventually,

BGR

BG

2

)(3tanh0

(3.7)

Colour changes in the RGB colour model were defined as:

])()()[( 222 BGRERGB (3.8)

Where, ∆𝐸 is the colour changes value of raw apple slice and dehydrated apple.


Open porosity

In addition to this the surface porosity is determined by the steps as shown in

Figure 3.15 using Image J software. First of all, SEM image is opened in the image J

environment and after selecting scale, a threshold value is set. Following this, the

threshold image is converted to binary image. After that, particles (pores) are

analysed and data is imported in Microsoft Excel. Finally, the output data is analysed

with MS excel for achieving pore size and distribution.

3.3.12 Rehydration

Rehydration was performed by shaking the dried samples at room temperature

with defined weight in distilled water (100 cm3) at 25

0C. The samples were removed,

dried off with tissue paper and weighed at regular intervals. The measurements were

repeated three times. Some of the key factors in connection with rehydration are

calculated using the equation as presented in Table 3.2.

Table 3-2: Some selected key factors of rehydration of dehydrated sample

Factor Equation Significance

Coefficient of

rehydration

dhd

inr

MW

MWCOR

100

100

The degree of structural

disruption. How much drying

causes reduction of water

retention

Weight gain

d

dt

wW

WWRC

)(%

Gaining of weight over the time

of rehydration.

Volume gain

d

dt

vV

VVRC

)(%

Gaining of volume over the time

of rehydration.

Figure 3-15: Pore distribution determination using image J software



3.4 STATISTICAL ANALYSIS

Each of the experiments and measurements was carried out three times. The

results presented were the mean value with standard deviation (S.D.). To determine

the variability of data in different observations, standard deviation (SD) is calculated.

Also, the standard error of mean was used to determine the precision of the average

values. Standard deviation (SD) and standard error of mean can be calculated by

using the following equations:

Standard deviation,

1

1

n

xxn

i

i

(3.9)

Standard Error of the Mean (SEM):

NM

(3.10)

Where,

Σ M = standard error of the mean

σ = the standard deviation

xi=Each of the values of the data

n= number of values

N = number of observation

Moreover, the value of standard deviation can also be referred as the index of

reproducibility of the experiments.

Coefficient of Determination calculation:

The Coefficient of Determination is one of the most important tools in statistics

which is widely used in data analysis. The formula that was used for calculating the

coefficient of determination is given below:

])([])([

][2222

22

YYnXXn

YXXYnR

(3.11)

Where, R2 is the coefficient of determination, X is the simulated or theoretical

data, and Y is the observed or experimented data.

Chapter 4 | Single phase convective drying and pore formation model


Chapter 4: Single Phase Convective Drying

and Pore Formation

Due to simultaneous thermal and moisture gradients, plant tissue undergoes

stress, shrinkage and deformation during drying. The stresses generated by the

moisture gradient take place during almost the entire drying period while the thermal

stress is more prominent in the earlier stages (Jayaraman et al., 1990; Lewicki &

Pawlak 2003). Therefore, the stress generated by the moisture gradient is the

dominant contributor to plant tissue shrinkage during drying. Taken together, a

model considering thermal and moisture gradient, glass transition temperature, and

drying time can be the right approach to predicting structural changes over the period

of drying. Therefore, we choose a shrinkage velocity as a function of moisture and

temperature dependent effective diffusivity, glass transition temperature for porosity

prediction. Implementing this concept, simulation of shrinkage velocity-based

porosity of plant-based food materials is carried out. Single phase convective drying

model with considering shrinkage is developed in this chapter.

The aims of this chapter are threefold; to (i) Simulation of single-phase

convective drying model based on effective diffusivities considering shrinkage

phenomenon develop (ii) validate porosity models based on sample parameters and

process parameters (iii) conduct a parametric study with validated models.

4.1 MODEL DEVELOPMENT

4.1.1 Prediction of pore evolution

Even though porosity development is mainly due to the void spaces created by

migrated water, the shrinkage of a solid matrix towards the centre of the sample

compensates the void volume. Therefore, insight into the heat and mass transfer

mechanisms, as well as the structural deformation is essential to an understanding of

the evolution of porosity in the course of the drying. These transfer mechanisms and

structural changes are significantly influenced by both material properties and

process parameters; with moisture content, solid density, initial density, particle

density and glass transition temperature being the important material properties that

need to be taken into consideration.


The air temperature is the prime process factor that significantly influences the

structural modification of the food material. An improved interpretation of pore

formation and evolution considering these material properties and process conditions

is discussed below. At this point, a theoretical interpretation of pore formation can be

hypothesised based on water distribution including free and bound water as shown in

Figure 4.1. The plant tissue undergoes stresses during shrinkage and deformation

because of simultaneous thermal and moisture gradients.

Concept of Moisture Distribution

Water from the three different spaces namely cell, cell wall and intercellular

zones take various pathways to migrate to the atmosphere during the period of

drying. However, there are different paths of water flux depending upon the food

structure, composition, and drying conditions (Joardder et al., 2015b). By

considering these, a conceptual map of different pathways of water migration from

plant tissue can be described as shown in Figure 4.1.

Figure 4-1: Conceptual maps of different pathways of water migration from plant tissue

Figure 4.1 show that water from different spaces of a plant tissue can migrate

through different routes. For example, water from cells migrate trough cell walls

including cell membranes into intercellular space before finally ending up in the

atmosphere. This phenomenon continues while the cell wall remains intact due to

lower drying temperature.

At higher temperatures, on the other hand, the cell membrane and walls are

ruptured; resulting in some of the water travelling directly to its the surroundings



when the rest of the water migrates through intercellular spaces to the atmosphere.

Cell wall water migration requires relatively higher energy as it passes through inter-

micro-fibrillary spaces that are approximately 10 nm in cross section and many times

longer in length (Lewicki & Lenart, 1995).The inter-micro-fibrillary spaces are build

up due to the gap between micro-fibrils which are unbranched and fine threads,

measuring roughly 10-25 nm diameter (Gibson, 2012; Lewicki, 1998a).

The stresses generated by the moisture gradient take place during almost the

entire drying period, while the thermal stress is more marked in the earlier stages

(Jayaraman et al., 1990; P.P. Lewicki & Pawlak 2003). Therefore, the stress

generated by the moisture gradient is the dominant contributor of plant tissue

shrinkage during drying. As discussed, the structural modification is mainly caused

by the water migration from the tissue. However, the bulk moisture content at a

different time cannot describe the structural changes at that very time. Water contents

in terms of the free (intercellular) and bound (intracellular) water can represent

structural changes during drying.

Based on microstructure studies and water migration analysis, a step in step

pore formation mechanism has been presented in Figure 4.2.

At the very initial stage of the drying process, only intercellular (free)

water migrates from the tissues, but this causes ideal shrinkage of the

sample. In the initial stages, food materials do not encounter shrinkage.

However, these empty spaces then behave like the initial air space.

After migration of the intercellular water (known as a falling rate stage of

drying), the intracellular water starts migrating from the cells and causes

cell shrinkage.

The volumetric shrinkage is proportional to the amount of removed water

without collapse.


However, cell breakage is observed as the drying time increases. This does

not, however, collapse the cell severely. This usually occurs during cell

wall water migration. Parenchyma cells in plant tissue are typically thin-

walled and abundant. Vacuoles that serve as cell water storage containers

are located inside these cells. Vascular solutes are usually osmotically

active, which push against the cell membrane lining the cell wall. The

turgor pressure develops and keeps the cells in a state of elastic stress, thus

maintaining the shape and tension in the tissue (Ilker & Szczesniak, 1990).

If the turgor pressure is lost, the structure of the fruit collapses and once

this occurs, it cannot be reversed (Reeve, 1970).

Figure 4-3: Water migration and pore formation during drying

Figure 4-2: Hypothetical pore evolution theory over the course of drying



Cell shrinkage then occurs due to a lower turgor pressure. This is caused

due to the migration of large amounts of cell water. It is vital to predict the

proportion of shrinkage of the sample with the migration of water at this

stage (Figure 4.3 presents this concept).The proportionality can be

redirected to solid structure mobility factor.

Pore expansion occurs in the later stage of drying when the food matrix

becomes sufficiently dry and increases in viscosity (Del Valle et al., 1998),

thus hindering both shrinkage and collapse (Karathanos et al., 1996a).

Further drying may also cause enlargement of the intercellular space. The

cell wall and solid matrices of the plant based cellular tissues are flexible

enough to allow migration of water from the vacuole, allowing shrinkage

of the entire tissue but not increasing the volume of the intercellular spaces

(Hills & Remigereau, 1997).

Solid structure mobility factor (SSMF)

Glass transition temperature and drying air temperature affect the nature of

pore evolution. The key points on the solid structure mobility factor are discussed

below (Figure 4.4)

The rate of shrinkage is closely related to its physical state (Levi & Karel,

1995). When the material is in a rubbery state, it has high mobility within

the matrix and conversely, low mobility in the glassy state. Volume

shrinkage eliminates almost the entirety of the void volume developed due

to water migration .

Shrinkage characteristics depend greatly on the value of mobility

temperature. High rates of shrinkage are caused due to a high mobility

temperature, which can be observed in the early stage of drying. As drying

progress, the mobility temperature decreases and the shrinkage rate sharply

declines due to the increase of collapse resistance in the dried material

(Karathanos et al., 1993; Katekawaa & Silvaa, 2007). This is due to the

moisture content decreasing the glass transition temperature of the sample

rises above the drying temperature.


Figure 4-4: Variation of glass transition temperature with moisture content

The sample shrinks until the mobility temperature factor reaches zero or

close to zero. So drying at higher temperature causes shrinkage even with

very low moisture content (Kurozawa et al., 2012). Therefore, an SSMF

can be written as:

00 g

g

TT

TT

On the basis of the above-mentioned assumptions, the following

relationship has been proposed to calculate shrinkage velocity. In this

thesis, the shrinkage velocity will refer to the rate of shrinkage.

For ideal shrinkage, equilibrium is reached between moisture removal and

structural changes, the shrinkage velocity can be found from boundary flux

(mol.m-2

.s-1

) and the average concentration of moisture (mol.m-3

). After

simplification, a mathematical equation of shrinkage velocity (Aprajeeta et

al., 2015; Datta, 2007a; Golestani et al., 2013; Jomaa & Puiggali, 1991;

Karim & Hawlader, 2005b) can be written as follows :

L

Dv

eff2 (4.1)

Where, Deff is the effective moisture diffusivity and L is the half thickness of the

sample. Moreover, this expression can also be derived from the integration of Fick’s



second law of diffusion as the material does not follow an ideal shrinkage pattern

throughout the drying time due to phase change from rubbery to glassy phase. On the

basis of the hypothesis described in previous sections, a modified equation

considering glass transition temperature concept in order to accommodate effect of

process condition has been proposed and shown in Equation 4.2. Considering this

factor in effect, we can multiply the SSMF (00 g

g

TT

TT

) with equation 4.2 and we

can get the following expression

00

2

g

geff

sTT

TT

L

Dv (4.2)

The term gTT in Equation 4.2 represents level of collapse during drying that

can be found in different literature (Del Valle et al., 1998; Kurozawa et al., 2012;

Levi & Karel, 1995). This expression can represent, the effect of temperature, drying

time, the material properties (effective diffusivity), and characteristic length of the

sample. After getting the instantaneous bulk volume from the above shrinkage

velocity approach, we can predict porosity of the material during drying by the

following equation:

tvLtvr

VV

ss

sw

0

2

0

1

(4.3)

Where, Vw is the instantaneous volume of water and Vs is the volume of solid

material of the sample that is considered constant throughout the drying process.

Also, t is the time of drying, r is the instantaneous radius of the sample and L is the

instantaneous thickness of the sample.

Air space deformation factor (ASD)

Shrinkage due to water migration can be predicted considering the water

distribution concept and the solid structure mobility factor. However, deformation of

air space (initial porosity) still is not clear from the above-mentioned discussion.

Moreover, the initial porosity changes over the course of drying. The shrinkage of

initial porosity depends on stength of the adjacent cell wall strcture (Joardder et al.,

2014a). Primarily, this change of the air space can be correlated with the change of


particle density and water density and it is defined as air space deformation (ASD)

factor ( ) as demonstrated in Equation 4.4.

wp

wp

00 (4.4)

It is hypothesised that, if the density ratio is close to unity, as most of fresh

material demonstrate during early part of drying, there will be a complete a

shrinkage. Therefore, the porosity model considering variable initial porosity can be

written as following:

)()1()()1(

)()(1

00

0 000

0 00

0

0

ff

w

nt

t bbt

nt

t ff

w

bbt

XXm

XXV

XXm

XX

t

t

(4.5)

Where, Xb and Xf are the bound (intracellular) and free (intercellular) water content

respectively. An assumption is made that the free water migrates before bound water.

The percentage of intracellular and intracellular water for the plant-based material is

available in literature (Halder et al., 2011a). For apple, Halder et al. (2011a) found

that approximately 90% water is intracellular water. It is also assumed that the air

space developed due to the migration of free water behaves like the initial porosity

over the course of drying.

Therefore, Equation 4.3 represents porosity prediction model considering shrinkage

velocity whereas equation 4.5 represents porosity prediction model with the

information of free water, bound water, SSMF, initial porosity and density factor. In

brief, both of the models take process parameters and sample quality into

consideration to predict porosity.



4.1.2 Single phase convective drying model

An effective diffusivity based single-phase convective drying model is

developed in Chapter 4. The energy balance is characterised by Fourier flux, and the

moisture flux is considered due to Fickian diffusion.

The model developed in single-phase convection drying considers the

cylindrical geometry of the food product as shown in Figure 4.5.

Figure 4-5: (a) The actual geometry of the sample slice and (b) simplified

2D axisymmetric model domain.

The following assumptions are applied when developing the mathematical

model:

The sample is a homogeneous matter;

Uniform initial temperature and moisture distribution exist within the

sample;

The thermo-physical properties vary with moisture content of the food

material;

Heat and mass transfer co-efficient (hm, hT) values are assumed constant

over the entire surface of the sample and an average value based on a flat

plate empirical correlation are used. In order to avoid complexity, it is

assumed h does not vary with radial distance the sample.

Moisture from the inside of the sample is migrated by the diffusion

mechanism towards the surface.

Drying air is supplied continuously with constant velocity;

The heat transfer inside the sample takes place by conduction mode only.


Shrinkage is considered throughout the drying process.

4.2 GOVERNING EQUATIONS

Heat transfer

The energy balance is characterised by a Fourier flux equation with a null heat

generation as there is no heat generation inside the sample:

Qz

TT

rr

Tr

rrk

t

Tcp

2

2

2

2

2

11

(4.6)

Here, T is the temperature (0K), is the density of sample (kg/m

3),

pc is the

specific heat (J/kg/K), and k is the thermal conductivity (W/m/K). This heat

generation, Q (W/m3) is null as there is no heat generation inside the food material.

Mass transfer

We assume that the mass flux of moisture is due to Fickian diffusion; therefore,

01

dr

CrD

rrt

ceff

(4.7)

Where, c is the moisture concentration (mol/m3),

effD is the effective diffusion

coefficient (m2/s).

Change in dimension

The relationship obtained from the effective diffusivity and glass transition

temperature for dimension change (the shrinkage velocity), as presented in Equation

4.8 was used for simulation studies.

00

2.

g

geff

nTT

TT

L

Dvn

dt

dr (4.8)

4.3 INITIAL AND BOUNDARY CONDITIONS

The initial conditions for heat and mass transfer are given by,

CT t

0

)0( 30 and 0)0( cc tw



Here, 0c is the initial moisture concentration of the apple (mol/m3).

4.3.1 Heat transfer boundary conditions

Both convection and evaporation were considered at the transport boundaries

as shown Figure 4.5 Heat and mass transfer in the transport, and sample domain

deformation boundaries can be expressed by Equation 4.9.

fg

airveqv

mairT hRT

-pphTThTk

,)().( n ,

(4.9)

where, ℎ𝑇 is heat transfer coefficient (W/m2/K), ℎ𝑚 is mass transfer coefficient

(m/s), 𝑇𝑎𝑖𝑟 is drying air temperature (0C), Me is equilibrium moisture content (kg/kg)

dry basis and ℎ𝑓𝑔 is latent heat of evaporation (J/kg).

The heat transfer boundary condition at the symmetry boundary is given by,

𝒏. (𝑘𝛻𝑇) = 0. (4.10)

4.3.2 Mass transfer boundary condition

The mass transfer boundary condition at the transport boundaries are given by,

𝒏. (𝐷𝛻𝑐) = ℎm(𝑐b − 𝑐), (4.11)

where, 𝑐𝑏 is bulk moisture concentration (mol/m3).

The mass transfer boundary condition at the symmetry boundary is given by

𝒏. (𝐷𝛻𝑐) = 0. (4.12)

4.3.3 Change in dimension



4.8 was used for simulation studies.

nvn

dt

dr. (4.13)

Where, Vn is the shrinkage velocity of the sample.

4.3.4 Input parameters

The input parameters of the model are listed in Table 4.1 below, and some of

the parameters are discussed later in this section.


Table 4-1: Input parameters for the model

Parameter Value Reference

Sample diameter,

Dias

40 mm This work

Sample thickness, Ths 10 mm This work

Initial temperature, T0 303K

Vapour mass fraction,

0.026 Calculated

Constants

Drying air

temperature, Tair

333K This work

Universal gas

constant, Rg

8.314 (Çengel & Boles,

2006)

Molecular weight of

water, Mw

18.016 g mol-1

(Çengel & Boles,

2006)

Latent heat of

evaporation, hfg

2.26e6 J kg-1

(Çengel & Boles,

2006)

Ambient vapour

pressure, Calculated

Heat transfer

coefficient,

16.746 W/(m2K) Calculated

Mass transfer

coefficient,

1.79X10-2

m/s Calculated

Thermo-physical properties

Specific heat

Apple, 𝑪𝒑𝒂𝒑𝒑𝒍𝒆 )22.34.1(1000 dapplep MC J kg-1

K-1

Białobrzewski (2006)

Air, 𝑪𝒑𝒂 1005.68 J kg-1

K-1

(Carr et al., 2013)

Thermal conductivity

Apple dM

apple eK206.0

443.049.0

(Mattea et al., 1986)

Air, kair 0.026 W m-1

K-1

(Rakesh et al., 2012)

Water, 0.644 W m-1

K-1


Density

Apple solid, 𝝆𝒔 1419 kg m-3

This study

Initial bulk density,

ρapple0

842, kg m-3

Measured

Air, Ideal gas law, kg m-3

vw

airvp ,

Pa2992

Th

mh

sthk ,

wthk ,

v




Water, 1000, kg m-3

Particle density

(Krokida et al., 1997;

Zogzas et al., 1994)

Initial porosity

(Krokida et al., 1997;

Rahman, 2003;

Rahman et al., 1996;

Santos & Silva, 2008;

Zogzas et al., 1994)

Equilibrium vapour pressure

The vapour pressure of the food is assumed to be always in equilibrium with

the vapour pressure given by an appropriate sorption isotherm. For apple, the

correlation of equilibrium vapour pressure with moisture and temperature is given by

(Kumar et al., 2014b)

)](ln[232.0182.0exp)(0411.0949.43696.0

,, TPMeMTPP satdb

M

dbsatveqv

(4.14)

TTx

TxTTP satv

ln656.61001445.0

104176.00486.03915.1/2206.5800exp

37

24

, (4.15)

Here, dbM is the moisture content dry basis and Psat are the saturated vapour

pressure as given by equation 4.10 (Vega-Mercado et al., 2001).

Effective diffusivity

Understanding the drying behaviour of food material is essential in order to get

a better prediction of quality and obtain optimum drying condition. The complex

nature of food materials causes more than one internal mass transfer mechanism

during the time of drying. Different modes of mass transfer may exist at the same

time in a system. However, one of them dominates at a certain time in the system.

Drying of apple dominantly follows the falling rate period. Furthermore, diffusivity

is commonly used to describe drying kinetics of plant tissues (fruits and vegetables)

in their falling rate stage, and the driving force of diffusion is concentration gradient.

This falling rate period of drying can be modelled using Fick’s law. Fick’s second

law can be expressed as:

𝜕𝑀𝑅

𝜕𝑡= ∇[𝐷𝑒𝑓𝑓(∇𝑀𝑅)] (4.16)

Where, moisture ratio MR, is calculated using the following equation

w

ws

ws

wsp X

X

VV

mm

1

1

00

00 11

V

VV ws

p

b


𝑀𝑅 =𝑀−𝑀𝑒

𝑀0−𝑀𝑒 (4.17)

It is assumed that the initial moisture content is uniform in banana slabs. It is

also assumed that external mass transfer resistance is negligible, and moisture

migration from the food material occurs in one dimension. For one-directional drying

in an infinite slab, Crank [13] gave an analytical solution, as given below:

𝑀𝑅 =8

𝜋2∑

1

(2𝑛+1)2∝𝑛=0 𝑒𝑥𝑝 (−

(2𝑛+1)2𝜋2𝐷𝑒𝑓𝑓𝑡

4𝐿2 ) (4.18)

Where, n is a positive integer, t is drying time (sec), and L is sample thickness

(m). Considering uniform initial moisture distribution and negligible shrinkage,

Equation (4.18) is suitable for determining effective moisture diffusivity. A

simplified approach is shown in Equation 4.19 can be obtained taking only the first

term of series solutions in Equation (4.19). This equation could be further simplified

into Equation 4.20 by taking the first term of a series solution as follows(A. Vega-

Gálvez, 2010).

ln (𝑀−𝑀𝑒

𝑀𝑜−𝑀𝑒) = ln (

8

𝜋2) − (𝜋2𝐷𝑒𝑓𝑓

4𝐿2 𝑡) (4.19)

Effective moisture diffusion could be determined from the slope (k) obtained

from the plot of ln(𝑀−𝑀𝑒

𝑀𝑜−𝑀𝑒) versus time. The slope of the straight line can be

expressed as follows;

slope =𝜋2𝐷

4𝐿2 = 𝐾 (4.20)

Where L = the thickness of the slab, if drying occurred only on one large face.

In this study, drying occurred on two faces, as slabs were placed on a mesh tray. In

this case L = half thickness.

In this work, two different simulations were performed with two different

effective diffusivities namely, temperature dependent effective diffusivity, and

moisture dependent effective diffusivity for each food material.



Temperature dependent effective diffusivity calculation

Temperature dependent effective diffusivity is calculated from the Arrhenius-

type relationship, as shown below:

TR

EDTD

g

oeff exp)( (4.21)

Where, 𝐷𝑜 is the Arrhenius factor (m2/s), E is Activation energy (kJ/mol), 𝑅𝑔 is

molar gas constant (kJ/mol/K).

The effect of temperature on effective diffusivity is presented in Figure 4.6.

Figure 4-6: Finding the activation energy of apple sample

The activation energy was calculated from the slope of a refDln versus (1/T)

graph (Figure 4.7) resulting in the values D0=061047.2 X and aE = 36.5 KJ/mol.

Moisture-dependent effective diffusivity

Karim and Hawlader (2005a) proposed the following equation for moisture

dependent effective diffusivity.

-21.2

-21

-20.8

-20.6

-20.4

-20.2

0.00288 0.00292 0.00296 0.003 0.00304 0.00308 0.00312

ln (

Def

f)

T-1 (K-1)


2

b

b

D

Do

eff

ref (4.22)

Where b

bo is called thickness ratio and 𝐷𝑟𝑒𝑓 is called the reference effective

diffusivity which is calculated by determining slope from experimental value, 𝑏0 and

b are the half thickness of the material at time 0 and t respectively.

Average effective moisture diffusivity

Diffusivity is affected by both sample properties and process parameters.

Process parameters can easily be controlled compared to sample properties. Several

authors reported that the diffusion coefficient is a function of sample temperature and

moisture content (Batista et al., 2007; Chandra Mohan & Talukdar, 2010; Hassini et

al., 2007; Karim & Hawlader, 2005b). Baini and Langrish (Baini & Langrish, 2007)

claimed that shrinkage tends to reduce the path length for diffusion that results in

increased diffusivity. However, the effective diffusivity varies throughout the process

due to moisture and temperature gradient. Therefore, a necessity arises to take the

average of the moisture dependent diffusivity and temperature dependent diffusivity

for aligning closer prediction of effective diffusivity during drying.

For this study we took average diffusivity using the following expression:

2

)()(),(

TDMDTMDeff

(4.23)

After putting all of the value, we get the following moisture and temperature

dependent effective diffusivity.

2

22115exp1047.21081.3

),(

06

2

10

TRX

b

bX

TMDg

o

eff.

(4.24)

Glass transition temperature determination

To describe the plasticizing effect of water on Granny Smith apples, the Glass

Transition Temperature (GTT) of the sample at different moisture content was

obtained using the Gordon-Taylor model (Gordon & Taylor, 1952)

(4.25)

11

)1(

kX

TkXTXT

w

gwwgsw

g



The GTT of water (gwT ) is -135

0C (Johari et al., 1987), Tg and Tgs are TGT of

the binary mixture and dry matter (solid) respectively. Whereas, Xw indicates water

mass fraction.

Heat and mass transfer coefficient calculation

The heat transfer coefficients are calculated from well-established correlations

of Nusselt number for laminar and turbulent flow over flat plates as shown in

equations 4.26 to 4.27 (Golestani et al., 2013; Montanuci et al., 2014; Perussello et

al., 2014).

33.05.0T PrRe664.0h

k

LNu (Turbulent) (4.26)

33.05.0T PrRe0296.0h

k

LNu (laminar) (4.27)

where L is characteristics length (m), Re is the Reynolds number, and Pr is the

Prandtl number.

Mass transfer coefficient by the Sherwood number (Sh) and the Schmidt

number (Sc), respectively, as in the following relationships:

33.05.0m Re332.0h

ScD

LSh

va

(Turbulent) (4.28)

33.08.0m Re0296.0h

ScD

LSh

va

. (laminar) (4.29)

Here vaD is the binary diffusivity of vapour and air (m2/s).

The values of Re, Sc and Pr, were calculated by

𝑅𝑒 =𝜌𝑎𝑣𝐿

𝜇𝑎, (4.30)

𝑆𝑐 =𝜇𝑎

𝜌𝑎𝐷𝑣𝑎, (4.31)

and 𝑃𝑟 =𝐶𝑝𝜇𝑎

𝑘𝑎, (4.32)

Here, 𝜌𝑎 is density of air (𝑘𝑔

𝑚3), 𝜇𝑎 is dynamic viscosity of air(𝑃𝑎. 𝑠), 𝑣 is drying air

velocity (m/s), 𝑘𝑎 is thermal conductivity of air (𝑊

𝑚𝐾).


After gathering the required input parameters and initial conditions for the

governing equations and boundary conditions, the model was simulated in COMSOL

Multiphysics. The simulated results were validated by experimental data as discussed

in the following section.

4.4 RESULT AND DISCUSSION

4.4.1 Effective diffusivity

Different effective diffusivities obtained from the simulation is compared with

experimental effective diffusivity are presented in Figure 4.7.

Figure 4-7: Change of Effective diffusivity with time

From the data presented in Figure 4.8, it is apparent that temperature dependent

moisture diffusivity increases with time whereas a decreasing trend is observed for

moisture dependent diffusivity. However, an average of these two effective

diffusivities shows a clear agreeable trend with the effective experimental

diffusivity.It is worthy to mention that, when the temperature rises to reach

equilibrium with the drying air, the effective moisture diffusivity start decreasing.

Consequently, a second falling drying rate is observed after this stage. Therefore,

effective moisture diffusivity while considering the effect of moisture and

temperature is more realistic.

0

2E-10

4E-10

6E-10

8E-10

1E-09

1.2E-09

0 5000 10000 15000 20000 25000

Eff

ecti

ve

dif

fusi

on (

m2s-1

)

Time (s)

D(M)

D(T)

D(M,T)

Experimental



4.4.2 Glass transition temperature

The variation of GTT of apple tissue with water content is presented in Figure

4.8. As can be seen from the above figure, apple tissue stays at the rubbery phase at

room temperature even with very low moisture content. The value of the glass

transition temperature of apple solid matrix was found 600C, while there is no

moisture fraction. This demonstrate that the sample stays rubbery throughout the

drying time if the drying temperature is equal or above 600 C.

Figure 4-8: Effect of water content (wet basis) on glass transition temperature of apple tissue

4.4.3 Average moisture content

The comparison of moisture content obtained from experiments and simulation

is shown in Figure 4.9.

Figure 4-9: Moisture evolution obtained for experimental and simulation with shrinkage and without

shrinkage


The model considering shrinkage provided a quite satisfactory match with the

experimental result. However, a significant difference between the model data (not

considering shrinkage) and experimental data is observed. This rather contradictory

result may be due to consider constant bulk density in the calculation of moisture

content during the modelling. It can be also seen from Figure 4.9 that the moisture

content (dry basis) of apple slice dropped from its initial of 6.14 kg/kg to 0.6 kg/kg

after 500 minutes. Diffusion rate decreases in the falling rate drying period due to

shrinkage and low moisture gradient result in longer drying times.

To check the agreement between predicted values with shrinkage and

experimental results, the coefficient of correlation (R2) was found to be 0.99 (with

shrinkage) and 0.96 (without shrinkage). This manifests very good agreement with

the model that consider shrinkage and experimental data. Therefore, a clear benefit

of considering shrinkage in drying kinetics prediction is found in this analysis.

Figure 4-10 Water distribution within apple sample during drying

In addition to this, Figure 4.10 reveals that moisture easily dries out from the

outer surface of the sample. The results, as shown in Figure 4.10, indicate that

relatively high concentration of moisture exists near the centre of the sample

throughout the drying time. To remove this extremely core water, a very slow falling

rate period is to prevail in the drying phenomenon. Literature shows that in order to



remove the last 10% of water from food material it takes almost equal time to that

required removing first 90 % of water content (Halder et al., 2011b; Joardder et al.,

2013a; Joardder et al., 2013d) .

4.4.4 Temperature evolution

The temperature profile of the sample over the time of drying process is shown

in Figure 4.11. At the initial stage, the rapid increment of temperature was observed

followed by almost steady but slower increase of temperature. On the other hand,

edge temperature rises at a higher pace. In the figure, surface temperatures from

model and experiments are compared.

Figure 4-11: Validation of predicted surface temperature profile with experimental data

Simulated results of temperature were compared with the experimental data

and found 0.964 R2 value. Moreover, the effect of shrinkage on temperature is

shown in Figure 4.12.

Figure 4-12: Effect of shrinkage on temperature profile of apple slice


It is clear from Figure 4.12 that temperature distribution within the sample is

insignificantly influenced by the shrinkage. As the major heat penetration happens

during the first stage of drying, it makes the temperature distribution less dependent

on shrinkage. However, a minimal discrepancy of average surface temperature of

these two models is observed over the middle part of drying. On the other hand, there

is no significant difference existing at the initial and final stages of drying.

The spatial temperature distribution is presented in Figure 4.13. Similar to

moisture distribution, an ununiformed temperature exists within the sample

throughout the drying process.

The temperature distribution is very important as it is crucial to understand the

glass transition temperature and case hardening of food sample during drying.

4.4.5 Porosity evolution

Figure 4.14 shows the porosity of the sample against moisture content (dry

basis). The trend of the computer model that consider shrinkage velocity shows a

slower increment of porosity at the early stage of drying; however, it increases

Figure 4-13: Temperature distribution within the apple sample



rapidly during the final stages of the drying. Both of the models considers shrinkage

is caused due to moisture migration with considering solid structure mobility factor

as presented in figure 4.15.

On the other hand, Computed model considering air space deformation (ASD)

shows a decrease of porosity during the early stage of the drying.

Figure 4-14: Change in porosity with moisture content of apple slice during drying

However, there are a slightly decreasing trends of porosity is observed at the

early stage of drying. It may be due to shrinkage of intercellular air spaces and

completed shrinkage of migrated water volume.

Figure 4-15: Variation of mobility factor with moisture content


On the other hand, the computed model considering ASD shows decrease of

porosity during the early stage of the drying. The relationship between the ASD

factor and moisture ratio is given in Figure 4.16. It is clearly apparent from the figure

that the air spaces shrink significantly throughout the drying.

As it is an assumed nature of air space deformation, it led some discrepancy

between experimental and the predicted model (ASD based) of porosity at the later

part of drying. More research on the initial air space shrinkage pattern can provide a

realistic prediction formula of porosity. However, a preliminary observation of the

shrinkage or collapse has been done in this study. To manifest the nature of initial air

space shrinkage, the volume ratio together with moisture ratio of some selected

materials with different degrees of initial porosity has been investigated.

Initially, food material encounters shrinkage without collapse. After the

removal of most of the water, breakdown occurs during the latter part of drying. In

short, ideal shrinkage occurs when the volume reduction of the solid matrix is equal

to the volume of the removed mass from the food materials. It may happen when

there are no mechanical restrictions to shrinkage of the solid matrix. This type of

shrinkage is also called as “free” or “ideal” shrinkage in the literature (Katekawa &

Silva, 2006). Figure 4.17 below shows the nature of shrinkage of some selected food

materials.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Air

spac

e def

orm

atio

n f

acto

r

Moisture ratio

Figure 4-16: ASD factor of dried apple as a function of moisture



Figure 4-17: Relationship between volume reduction and migrated water volume of selected food

samples

Moreover, the nature of collapse and shrinkage depend on the strength of the

cell wall, intercellular adhesion and porosity of the tissue. Tissue with high porosity

shrinks in response to moisture migration; whereas, tissue with low porosity and

strong intercellular adhesion would fail by the collapse (Ormerod et al., 2004). Apart

from shrinkage, cell collapse is one of the important phenomena that significantly

alter porosity.

Table 4-2: Physical properties of some selected food materials

Food Initial Moisture

content

Bulk density (Fresh)

(g/cc)

Solid density

(g/cc)

Apple 84 ±1.5 0.87 1.28 ±0.01

Pear 84 ±1 1.00 1.38 ±0.004

Potato 78 ±1.4 1.08 1.36 ±0.003

Eggplant 90 ±1.9 0.56 1.43 ±0.004

Parsnip 79.5 ± 0.8 0.73 1.29 ±0.004

From Table 4.2, we see that food material having a lower bulk density leads to

high initial porosity causing more volume reduction than the volume of migrated

water. In other word, materials with a bulk density lower than water show more

volumetric shrinkage than the volume of migrated water. However, all of the plant

tissue behaves like ideal material for the initial part of drying regardless of their


initial properties. Further investigation is required to determine exactly how initial

porosity changes during drying.

The initial average experimental porosity was found to be 0.19, and the final

porosity reached nearly 0.60. The ASD based model shows close prediction at the

early stage of drying than shrinkage velocity model; whereas, the shrinkage velocity

based model prediction at the later part of drying is more accurate.

Simulated results of porosity were compared with the experimental data and an

R2 value of 0.98 was achieved. This type of trend has been reported for various plant-

based foods such as potato, carrot, and apple, pear (Guiné, 2006; Karathanos et al.,

1996a; Rahman, 2003; Sereno et al., 2007).

4.4.6 Case Anisotropy shrinkage and case hardening

Shrinkage is an obvious occurrence during drying of food materials. The

structural changes in cellular levels occur over the period of drying due to loss of

water. Consequently, damage and collapse of cell walls may happen (Devahastin &

Niamnuy, 2010a; Ramos et al., 2003). Porous foods tend to shrink less than non-

porous foods during drying because porous foods normally have less initial moisture

content than non-porous foods (Srikiatden & Roberts, 2007).

The ideal shrinkage happens when the volume reduction is equal to the volume

of the migrated water volume. However, this is not found for most of the food

materials. In other words, shrinkage does not compensate for the entire space left by

the migrated water during drying. The shrinkage velocity was found from

experiments is with range of 71065.1 to

71065.3 whereas the average

shrinkage velocity from model was found with the range of 7108.1 to

7105.3 .

Case hardening or crust formation is a common phenomenon during drying of

food samples. However, the thickness of this crust depends significantly on the

material properties and drying conditions. Hardening represents the transition to a

glassy state of the material from the rubbery state. In this study, the value of this is

treated as the degree of case hardening.

Case hardening is very common phenomenon during food drying (Costa et al.,

2001; Gulati & Datta, 2015; Moyano et al., 2007; Moyano, 2007) and it is common

with the type of foods that contain dissolved sugars and other solutes. This



phenomenon can be explained from the different pathways of water migration from

sample as described in section 4.1.In brief, some amount of the water leave dissolved

substance behind as it is evaporated within the sample and migrates as water vapour

to the surface. On the other hand, a portion of water, mainly water in pores and

capillaries, migrates as liquid water with dissolved substance. This type of water is

evaporated on the surface and the dissolved sugar and other substances are deposited

on the surface; consequently, case hardening happens.

Figure 4-18: Case hardening during drying at 600 C in sample with average

moisture content (0.5 db)

Figure 4.18 shows the degree of case hardening for the apple sample during

drying at 600 C. It is clear from the figure that the core shows a rubbery state even at

low average moisture content, whereas the surfaces reach a glassy state due to faster

moisture migration from the surface.


Figure 4-19: Effect of mobility factor on shrinkage of the sample

In addition to this, anisotropy shrinkage can clearly observe from Figure 4.19.

As the model consider solid mobility factor in shrinkage velocity, anisotropy

shrinkage can be predicted successfully. The edge of the sample shows very low

shrinkage as it reaches the glassy state at the early stage of drying. Whereas, the

portion of the sample towards the centre manifest more shrinkage. On the other hand,

the simulation that has not considered solid mobility factor shows uniform shrinkage

throughout the sample. Therefore, incorporating glass transition temperatures in

shrinkage prediction model successfully demonstrate anisotropy nature of plant-

based tissue deformation over the course of drying.

4.5 SENSIVITY ANALYSIS

One of the main advantages of modelling is the capability to predict the

influence of different process conditions and sample properties on the quality

parameters of different drying product without having to conduct expensive and

complicated experimentations. In this section, the effect of drying air temperature, air

velocity and sample thickness on the porosity of the sample will be analysed.

4.5.1 Effect of air temperature

A range of air temperatures (50-650

C) was taken into consideration, as these

temperatures are typical in convective air-drying. The drying temperature, in general,

influences the structure of the outer and inner portion of the food sample, and



determines whether the external and internal structure will be porous or not. Figure

4.20 below shows the effect of different drying temperature on the porosity of the

apple sample. From the figure, it is evident that the porosity increases with the

increase in drying air temperature.

Figure 4-20: Porosity at different moisture content with different drying temperature

At a high drying rate, a transition of rubber-glassy states prevailed on the outer

surface due to low moisture content, which gave rise to rigid porous crust on the

surface (Rahman et al., 2005; Wang & Brennan, 1995a). Subsequently, the surface

moisture decreases very quickly, and internal stresses are developed in tissue.

Consequently, it negatively affects the shrinkage and results in the highly porous

interior (Aguilera & Stanley, 1999; Mercier et al., 2011). This phenomenon is widely

known as case hardening (Souraki et al., 2009). Experimental results from various

studies show that the porosity increases with the temperature at different moisture

contents. In the case of drying banana at 30, 40, 500C, a higher porosity was found at

a temperature of 500C (Katekawa, 2004). For potato (Wang & Brennan, 1995a) and

eggplant (Russo et al., 2012) significantly higher porosity was found during air

drying in 700C when compared with 40 and60

0C.

Drying time is a vital factor that influences the collapse of cells significantly in

the course of drying. Therefore, a lower drying temperature (i.e. longer drying time)

could cause structural damage to the food product as most of the food materials show

a rubbery state during the period of drying. Due to this, longer drying time causes the

collapse of plant tissues even when they are dried at low temperature as plant tissues

have a very low glass transition temperature (Karathanos et al., 1993).


4.5.2 Effect of air velocity

A range of air velocities (0.5-1 m/s) was taken into consideration, as these air

velocities are typical in convective air-drying. The response of air velocity to

porosity is presented in Figure 4.21.

Figure 4-21: Effect of drying air velocity on porosity evolution

In light of Figure 4.21, it is clearly apparent that the porosity increases with the

rise of drying air velocity. Ratti et al. (1994) found an increase of air velocity causes

higher porosity for potato, apple and carrot. This may be caused due to higher drying

rate occurred at higher air velocity. Consequently, the surface moisture decreases

quickly in the case of higher air velocity, internal stresses are developed in the tissue

resulting in a higher porous interior.

4.6 CONCLUSIONS

The drying kinetics of convection drying, considering shrinkage phenomenon

has been investigated. In addition to this, the characteristics of structural

modification and porosity changes due to simultaneous heat and mass transfer were

also investigated in this work. The model is validated with extensive experimental

results. The simulated data concerning moisture content and temperature evolution

over the time of trying were found quite agreeable with experimental data. Pore

evolution and shrinkage were predicted with high accuracy and a remarkable

correlation with process parameters and sample properties were observed.The single

most striking observations to emerge from this study was the prediction of anisotropy

shrinkage and case hardening during convection drying.



To get a proper insight of heat and mass transfer during the dehydration

process, precise predictions of shrinkage and pore evolution are required. The

comprehensive understanding of the prediction of the pore formation mechanism

needs to be researched further. A wider variation of process conditions and various

food properties can be considered in the future research to develop a more realistic

and generic model for pore formation.

Chapter 5 | A Single Phase IMCD and Pore Evolution Model


Chapter 5: Single Phase IMCD and Pore

Formation

Intermittent microwave convective drying (IMCD) is an advanced technology,

which improves both energy efficiency and food quality in drying. Modelling of

IMCD is essential to optimise the microwave power level and intermittency during

the process. However, there is still a lack of modelling studies dedicated to IMCD.

Mathematical modelling can help us to understand the heat and mass transfer

involved in IMCD and thereby be used to determine the optimum pulse ratio and

power levels for drying. Previously mentioned work related to IMCD has only been

limited to experimental analysis. To date, relatively few studies have presented

theoretical models of the IMCD of food.

Recently, Bhattacharya et al. (2013) and Esturk (2012b) have developed a

purely empirical model for MCD (not IMCD) of oyster mushroom (Pleurotus status)

and stage respectively. However, these empirical models do not provide physical

insight into the process and are only applicable to a specific experimental range

(Perussello et al., 2014). Some diffusion-based single phase models exist for MCD

(Arballo et al., 2012; Hemis et al., 2012), but, none of them considered intermittency

of the microwave energy applied. However, there are some simulation models

considering intermittency of microwave power (Gunasekaran, 1999; Gunasekaran

& Yang, 2007a, 2007b; Yang & Gunasekaran, 2004); mass transfer was neglected

in those models.

In addition to this, deformation of the sample and pore evolution have not been

considered in any previous IMCD model. Extensive analysis of the empirical and

theoretical models on porosity found that accurate and reliable prediction of porosity

during the drying process still needs the further attention of researchers. A central

issue is that there is no generic model that can be applied to different products and

drying processes. Literature analyses confirmed that both product type and drying

technology discernibly affect pore formation and the pore evolution during drying of

food materials. To adapt the material properties, the previous studies mainly

considered the amount of the water migrates from the sample. Previous models


involved other structural parameters, such as the volumetric shrinkage coefficient,

shrinkage-expansion coefficient and shrinkage-collapse coefficient. Most of the

material properties varied due to change in the drying conditions.

The measurement of the structural parameters meant there was a necessity for

experimental data. So by avoiding these structural parameters, which vary in drying

conditions, the formulation of a generic model of porosity was facilitated. In contrast,

a model containing different parameters that are not influenced by the drying

conditions can be treated as generic, regardless of the drying method. In addition to

this, there is no theoretical model of pore formation available for IMCD drying.

Taken together, there is very limited study dealing with modelling the IMCD

considering shrinkage of food, which considers the whole drying period, as well as

porosity prediction. Furthermore, the temperature redistribution due to the

intermittency of the microwave, which is crucial in IMCD for quality improvement,

is not properly investigated.

In the current study, we present a model of IMCD of food that accounts for the

intermittency of the microwave power, variable thermos-physical and dielectric

properties of the material, and large deformation. Pore evolution during IMCD

drying was also predicted using a theoretical model and validated by experimental

data.

5.1 MODEL DEVELOPMENT

In an attempt to develop an IMCD model, a volumetric microwave energy

source is incorporated in energy balance equation. The model uses Lambert Law for

microwave power absorption and transport model from the convection model. Prior

to commencing the modelling appropriate pulse ratio (will be discussed later) and

microwave power optimised using response surface method (RMS).

To develop a single phase IMCD model, a 2D axisymmetric geometry of a

cylindrical slice apple was considered as presented in Figure 5.1.



Figure 5-1: 2D an axisymmetric domain showing symmetry boundary and transfer boundary

As we already discussed single-phase convection model in Chapter 4, the

repeated initial conditions and model parameters are not presented here.

Microwave intermittency

Depending on the heat and mass transfer characteristics the different

samples/loads may require different intermittency or pulse for better product quality

and energy efficiency. Intermittency or pulse ratio is defined as

PR =ton+toff

ton (5.1)

Where, 𝑡𝑜𝑛 is the microwave on time, and 𝑡𝑜𝑓𝑓 is the microwave off time.

PR should be considered carefully because it is possible to obtain a given PR

with a different combination of power on and off time. Therefore, cycle power on

time should be considered along with PR (Gunasekaran, 1999). Cycle power on time

and PR should be carefully selected to maximise the advantages of pulse microwave

drying. Gunasekaran (1999) reported, increasing the PR and lowering the power of

time is better for energy utilisation and lower energy cost. However, this increases

the drying time. Therefore, the PR ratio should be selected based on the transfer

characteristics of the material.

To get the closer surface temperature of CD of the IMCD dried sample, the

effect of microwave power level pulse ratio and MW on time were investigated.


IMCD optimisation

To investigate the relative contributions of the selected variables pulse ratio

(PR), microwave power (P) and microwave ON time (MT) to sample surface

temperature at the time of drying, response surface methodology (RSM) was used.

However, this optimisation does not intend to optimise the quality of the IMCD

product which needs further research. In this optimisation analysis, the objective is to

find out the appropriate value of the process variables that can lead the surface

temperature closer to connective air temperature. RSM is a statistical method that is

used for the optimising problem-associated multivariable. This methodology can

successfully correlate measured response/s and manifold input variables. In addition

to this, RSM requires less experimental data to deliver statistically satisfactory

results (Kaur et al., 2009).

A second-order polynomial equation, as presented in Equation 5.2, was used

for analysis of input variables data and to correlate response function to coded

variables (Balusu et al., 2005; Maddox & Richert, 1977).

exixjxiiixik

ji kij

k

i

k

i kik

11

2

10 (5.2)

Where, ‘ ’ is the regression coefficient, k the number of input variables, ‘xis’

are coded process variables, ‘β’ is the response, and ‘e’ is random error.

A desirable function D, an approach of optimisation of multiresponse, was

determined for optimisation of the multiple responses to the statistical analysis using

the following equation (Giri & Prasad, 2007).

nnddddD

1

321 )..............( (5.3)

Where, n is the total number of responses in the study. The overall composition

function represents the desirability ranges of different response (di).

ANOVA (analysis of variance) was conducted for finding the statically

significance of the model variables and for fitting the model. A statistical software

package, Design Expert (Version: 9.0.5.1, Minneapolis, MN) was used to analyse

IMCD data, 3D graphs of response, numerical optimisation of input variables and

perform RSM. In addition to this, the software can analysis the result to find the

maximum value of desirability function (Yadav et al., 2010). Optimisation criteria



for various factors and responses are given in Table 3.1. Equal-weight was taken into

consideration for all of the responses.

Table 5-1: Variables of IMCD optimisation

Variable

symbol

Responses Unit Goal Lower

limit

Upper

limit

P Microwave Power W In range 100 300

R Pulse ratio 1 In range 0.25 1

MT Microwave on time s In range 30 120

Tmax Maximum surface

temperature

0C minimize 60 170

t Drying time s minimize 1500 4500

5.1.1 Governing equations

Heat transfer

The energy balance is characterised by a Fourier flux equation with heat

generation source Q:

QTkt

Tcp

).(

(5.4)

Here, T is the temperature (0K), is the density of sample (kg/m

3),

pc is the

specific heat (J/kg/K), and k is the thermal conductivity (W/m/K) and Q (W/m3) is

the heat generation.

Mass transfer

We assume that the mass flux of moisture is due to Fickian diffusion; therefore,

0

c-D.

t

ceff

(5.5)

Where, c is the moisture concentration (mol/m3),

effD is the effective diffusion

coefficient (m2/s).

Change in dimension

The shrinkage velocity obtained from the effective diffusivity and glass

transition temperature for dimension change, as presented in Equation 5.6

was used for simulation studies. The concept of shrinkage velocity can


also be found in other literature (Aprajeeta et al., 2015; Datta, 2007a;

Golestani et al., 2013; Karim & Hawlader, 2005b)

nvn

dt

dr. (5.6)

5.1.2 Initial and boundary conditions

The initial conditions for heat and mass transfer are given by,

CT t

0

)0( 30 and 0)0( cc tw

Here, 0c is the initial moisture concentration of the apple (mol/m3).

Heat transfer boundary conditions

Heat and mass transfer in the transport, and sample domain deformation

boundaries (as shown in Figure 5.1) can be expressed by the equation:

fg

airveqv

mairT hRT

-pphTThTk

,)().( n , (5.7)

where, ℎ𝑇 is heat transfer coefficient (W/m2/K), ℎ𝑚 is mass transfer coefficient

(m/s), 𝑇𝑎𝑖𝑟 is the drying air temperature (0C), Me is equilibrium moisture content

(kg/kg) dry basis and ℎ𝑓𝑔 is latent heat of evaporation (J/kg).

The heat transfer boundary condition at the symmetry boundary is given by,

𝒏. (𝑘𝛻𝑇) = 0. (5.8)

Mass transfer boundary condition

The mass transfer boundary condition at the transport boundaries are given by,

𝒏. (𝐷𝛻𝑐) = ℎm(𝑐b − 𝑐), (5.9)

where, 𝑐𝑏 is bulk moisture concentration (mol/m3).

The mass transfer boundary condition at the symmetry boundary is given by

𝒏. (𝐷𝛻𝑐) = 0. (5.10)

Change in dimension



5.11 was used for simulation studies. The concept of shrinkage velocity has been in



other literature (Aprajeeta et al., 2015; Datta, 2007a; Golestani et al., 2013; Karim &

Hawlader, 2005b)

For boundaries 3 and 4 in Figure 5.1 the deformation condition is presented by

this equation.

ndt

dr.

00

2

g

geff

sTT

TT

L

Dv (5.11)

5.1.3 Microwave power absorption using Lamberts Law

In literature, it is mentioned that for relatively thicker samples both Maxwell’s

and Lambert equation for predicting microwave power absorption can be applied

(Budd & Hill, 2011). Therefore, many researchers deploy Lamberts Law for

microwave energy distribution in food products during drying (Abbasi Souraki &

Mowla, 2008; Arballo et al., 2012; Hemis et al., 2012; Khraisheh et al., 1997;

Mihoubi & Bellagi, 2009; Salagnac et al., 2004; Zhou et al., 1995). In this study,

microwave energy absorption within the sample was calculated using Lamberts Law

that considered exponential attenuation of microwave absorption within the product,

namely,

h-zα-

mic=PP 2

0 exp . (5.12)

Here, 𝑃0 the incident power at the surface (W), α is he attenuation constant

(1/m), and h is the thickness of the sample (m) and (h-z) represents the distance from

surface (m). The measurement of 0P via experiments is presented in section 5.10.The

attenuation constant, α is given by

2

1'

''1

'2

2

(5.13)

Where is the wavelength of the microwave in free space ( cm24.12 at

2450MHz and air temperature 200C) and ε' and ε" are the dielectric constant and

dielectric loss, respectively.


The volumetric heat generation, micQ (W/m3) in equation is then calculated by:

V

PQ mic

mic , (5.14)

Where, V is the volume of apple sample (m3).

Microwave incident power absorption calculation procedure is described in

details in Section 3.3.2.

From experimentollowing correlation between absorption power (P0),

microwave power (Pmic) and sample volume ( V) is found.

)06.11897.0(0 VPP mic (5.15)


The input parameters of the model are listed in below. It is worthy to mention

that, the repeated input parameters used in convection model are not presented here.

Some of the parameters are briefly described in the below.

Table 5.1: Input properties of the model


Microwave power 100 W This work

Pulse ratio 3 This work

Microwave on time 40 s This work

Dielectric properties of apple

' 1.0289.30638.36'2

wbwb MM Martín-Esparza

et al. (2006) 1.0.8150.26543.13

2 wbwb MM

Equilibrium vapour pressure

For apple, the correlation of equilibrium vapour pressure with moisture and

temperature is given by (Kumar et al., 2014b)

)](ln[232.0182.0exp)(0411.0949.43696.0

,, TPMeMTPP satdb

M

dbsatveqv

(5.16)

TTxTxTTP satv ln656.61001445.0104176.00486.03915.1/2206.5800exp 3724

,

(5.17)

Here, dbM is the moisture content dry basis andsatvP ,

is the saturated vapour

pressure as given by equation 5.118 (Vega-Mercado et al., 2001).



Effective Diffusivity Calculation

The procedure of finding moisture and temperature dependent diffusivity is

already discussed in chapter 4. Finally, average effective diffusivity, ),( TMDeff,

which is average of the temperature and moisture dependent effective diffusivities

given by

2

22115exp1047.21081.3

),(

06

2

10

TRX

b

bX

TMDg

o

eff

(5.18)

Glass transition temperature

To manifest the plasticizing effect of water on apple, the GTT data were fitted

in Gardon and Taylor equation as mention below.

11

)1(

kX

TkXTXT

w

gwwgsw

g (5.19)

The GTT of water (gwT ) is -135

0C (Johari et al., 1987), Tg and Tgs are GTT of

the binary mixture and dry matter (solid) respectively, where Xw indicates water

mass fraction. The value of Tgs and k were found 600C and 3.4 respectively.

Heat and mass transfer coefficient

The heat and mass transfer coefficients were discussed in Section 4.. and found

to be Th =16.746 W/(m2·K) and mh =0.067904 m/s, respectively.

After gathering the required input parameters and initial conditions for the

governing equations and boundary conditions, the model was simulated in COMSOL

Multiphysics. The simulated results were validated by experimental data as discussed

in the following section.

5.2 RESULTS AND DISCUSSION

5.2.1 IMCD optimisation

From the ANOVA analysis, as presented in Table 5.2, Microwave power, pulse

ratio and microwave on time were significant 05.0p .


Table 5.2: Output of ANOVA analysis

Source df F

Value p-value, Prob > F Significance

Model 10 3553.84 < 0.0001

significant

P 1 3000.00 < 0.0001

R 1 5415.00 < 0.0001

MT 1 1815.00 < 0.0001

P*R 1 60.00 0.0045

P*MT 1 60.00 0.0045

R*MT 1 2535.00 < 0.0001

P2

1 364.50 0.0003

R2

1 1682.00 < 0.0001

P2R 1 187.50 0.0008

P2*MT 1 3967.50 < 0.0001

The following regression equation (R2 =0.99) was obtained for Maximum

surface temperature (Ts) relating to the levels of input variables.

MTPRPRP

MTRMTPRPMTRPTs

2523223 103.6*1066.11031042.4

*96.0*02.0*73.035.333.7381.119.133

To maintain surface tempurature, optimum values of the drying process

variables obtained the maximum desirability function (0.965) from the investigation

result obtained from Design Expert 9 were: 100 W, 3 and 40 s of microwave power,

pulse ratio and microwave on time respectively. The relationships between

desirability and variables are presented in Figure 5.2.



Figure 5-2: Effect of different drying parameters on different variables on the desirability of the

(a) Pulse ratio and microwave on time

(b) Pulse ratio and microwave power at 40 s microwave on time

(c) Microwave power and microwave on time at 2.5 pulse ratio


5.2.2 Average moisture curve

The comparison of moisture content obtained from experiments and simulation

is shown in 5.3. This figure also demonstrates the comparison of the kinetics of

IMCD and convective drying. It was found that, in 75 minutes of drying, convection

drying reduced the moisture content to 3 kg/kg db, whereas by using IMCD reduced

the moisture content to 0.4 kg/kg db.

Thus, IMCD significantly reduces the drying time. To reduce the moisture

content to 0.4 kg/kg db by convection drying took around 300min, which is 4 times

longer than the IMCD with intermittency 60s on and 120s off. It is found that a high

correlation is obtained between the model and experimental values with R2=0.98.

Figure 5-3: Moisture content with time during IMCD and convective drying

5.2.3 Temperature evolution

Figure 5.4 (below) shows the temperature at the centre of the top surface

predicted from our model while Figure 5.6 shows the temperature distribution of the

surface obtained experimentally from thermal imaging. The thermal images were

taken immediately after microwave heating for 40 s and after tempering for 80s in

the convection dryer.

0

1

2

3

4

5

6

7

0 1000 2000 3000 4000 5000

Moic

ture

con

ten

t (g

wate

r/g s

oli

d)

Time (s)

Experiemntal (IMCD)

Predicted (IMCD)

Convective drying



Thus, this measurement allows the investigation of temperature to rise during

microwave heating and drops during tempering in the process of IMCD. An

assessment of the experimental results for the range of sample surface temperature

shows a wide range of fluctuation due to uneven microwave power distribution and

non-uniform moisture distribution.

The temperature curve from the model shows that the temperature rises during

each heating cycle. The temperature then falls during the 80s convection-drying

phase (when the microwave is turned off).

It is obvious from Figure 5.4 that the temperature gradually increases up to the

end of drying. A similar rise in temperature with cycled microwave heating was

found by Rakesh et al. (2010) and Yang et al. (2001).Counter to this, the temperature

trend of this model is not consistent with that of Sunjka et al.(Sunjka et al., 2004)

who found a stable temperature at the later part of drying. This issue is discussed in

details in Section 6.2.3.

Figure 5-4: Temperature curve obtained from the model (average top surface) and experimental

validation

To illustrate the temperature distribution, an experimental and model

temperature distribution of two selected times (heating and tempering) are presented

in Figure 5.5.


Figure 5-5: Thermal images and model temperature distribution of top surface at selected times

From the figure, it is clear that the temperature is higher towards the centre of

the surface during drying. However, the spatial gradient is temperature is less during

the tempering period resulting in a more uniform temperature distribution.

5.2.4 Equilibrium vapour pressure

Equilibrium vapour pressure,eqvP ,

, is an important parameter for surface

evaporation and thus moisture loss. The equilibrium vapour pressure at the surface is

presented in Figure 5.6 and it is observed that eqvP ,

initially increases rapidly because

of increase in temperature and the higher moisture content. However, when the

material becomes drier, near the end of the drying, the equilibrium vapour pressure

decreases. This indicates that initially the moisture loss is higher and that the drying

rate starts to decrease when the equilibrium vapour pressure starts reducing at about

15 mins. However, due to diffusion the vapour pressure is still higher than the

ambient vapour pressure, airvP ,

, and evaporation occurs.



Figure 5-6: Evolutions of equilibrium vapour pressure at the surface of the sample

5.2.5 Porosity evolution

Figure 5.7 shows the porosity evolution of the sample against moisture ratio. In the

figure, there is a clear trend of increasing porosity with a decrease of moisture

content.

Figure 5-7: Computed and measured porosity as a function of moisture content

The porosity of the sample was found slowly increasing at the early part of the

drying up to moisture ratio 0.7. After that, porosity sharply increased with moisture

content up to the end of drying. This may be due to less mobility of solid matrix of

0

2000

4000

6000

8000

10000

12000

14000

16000

0 500 1000 1500 2000 2500 3000 3500

Equ

ilib

riu

m v

apo

ur

pre

ssu

re (

Pa)

Time (s)

Sample surface

Ambient

0

0.1

0.2

0.3

0.4

0.5

0.6

0.1 0.3 0.5 0.7 0.9

Poro

sity

Moisture Ratio

Experiemnt

Predicted


the sample while is approaching glass transition due to less temperature difference

and between sample and surrounding. It is found that a high correlation is obtained

between the model and experimental values of porosity with R2=0.985.

5.2.6 Shrinkage and case hardening

Shrinkage is an obvious occurrence during drying of food materials. The

structural changes in cellular level occur over the period of drying due to loss of

water. Consequently, damage and collapse of cell walls may happen (Devahastin &

Niamnuy, 2010a; Ramos et al., 2003). Porous foods tend to shrink less than non-

porous foods during drying because porous foods normally have less initial moisture

content than non-porous foods (Srikiatden & Roberts, 2007).

The ideal shrinkage happens when the volume reduction is equal to the

volume of the migrated water volume. However, this is not found for most of the

food materials. In other words, shrinkage does not compensate the entire space left

by the migrated water during drying.

Figure 5-8 : Volume ratio at different moisture content during IMCD drying

Volume reduction of apple slice with respect to time is shown in Figure 5.8.

From the figure, it is apparent that volume reduction continues up to very low

moisture content. The model results were compared with experimental images and

found good agreement with R2 values 0.99.



Figure 5-9: Case hardening during drying at 600 C in sample with average moisture content (0.5 db)

In addition to this, case hardening or crust formation is a common phenomenon

during drying of food samples. However, the thickness of this crust significantly

depends on the materials properties and drying conditions. As case hardening

represents the transition to a glassy state of the materials from the rubbery state. As

the moisture and temperature are more uniformly distributed during IMCD resulting,

less case hardening as shown in Figure 5.9.It is clear from the figure that the IMCD

treated sample has very thin case hardening. This issue is discussed in details in

Section 7.2.2.

5.3 CONCLUSION

In this study, a novel model of IMCD, considering shrinkage, has been

developed and compared with experimental data collected from a sample of apple.

Optimisation of IMCD has been determined to achieve reasonable temperature

development during IMCD by a response surface method. Optimum values of the

drying process variables obtained the maximum desirability function (0.965) from

the investigation result obtained from Design Expert 9 were: 100 W, 3 and 40 s of

microwave power, pulse ratio and microwave on time respectively. The predicted

moisture content, temperature distribution, porosity and shrinkage showed good

agreement with experimental data. The IMCD found quite faster compared to

convection drying. In addition to this, the intermittency during IMCD allows more

uniform temperature and moisture distribution resulting less altered structural

modification. The single phase models lump all water fluxes with an effective


diffusion coefficient, but this assumption cannot be justified by the situation of

IMCD, where pressure driven flow and evaporation is involved. Therefore, to

investigate IMCD accurately multiphase models need to be developed and

considered.


Chapter 6: Multiphase IMCD Model:

Considering Shrinkage and Pore

Formation

Food materials are complex in nature as they have heterogeneous, amorphous,

hygroscopic and porous properties. In addition to this, during processing, the

microstructure of food materials change and this significantly affects other properties

of food (Joardder et al., 2015b).

Therefore, an appropriate understanding of the microstructure of the food raw

material and its evolution during processing is critical to understand and accurately

describe dehydration processes and quality anticipation. There are many modelling

scenarios available in literature for different food processing such as (i) drying ,

frying (Ni & Datta, 1999), (ii) microwave heating (Ni et al., 1999; Rakesh et al.,

2010), (iii) thawing (Chamchong & Datta, 1999a), baking (Zhang et al., 2005), and

(iv) puffing (Rakesh & Datta, 2013). These model can be classified into two main

categories; empirical models and theoretical models as shown in Figure 6.1.

Figure 6-1: Classification of different drying models


Empirical models are built by fitting the model’s parameters to the

experimental data. Although empirical models provide high accuracy, they are not

generic and do not offer physical insight.

In contrast, theoretical models are built, based upon the understanding of the

fundamental phenomena and mechanisms that may be involved in heat and mass

transfer. Diffusion-based theoretical models are very popular due to their simple

nature of implementation that assumes diffusive transport for moisture and

conductive heat transfer for energy (Chandra Mohan & Talukdar, 2010; Perussello et

al., 2014; Perussello et al., 2012). However, this type of model requires

experimentally determined moisture diffusivity and cannot provide insight of other

internal moisture transfer mechanisms (a compilation of different internal moisture

transfer mechanisms is discussed in Section 2.1).

Considering sharp moving boundaries between dry and wet regions, improves

the diffusive model to some extent (Farkas et al., 1996; Mascarenhas et al., 1997).

Whereas, multiphase porous media models consider distributed evaporation that

deals with the transition from the individual phase at the ‘microscopic’ level to the

representative average volume at the ‘macroscopic’ level (Datta, 2007b). Due to

computational effectiveness this model has been implemented in different food

processing applications such as frying (Bansal et al., 2014; Ni & Datta, 1999),

microwave heating (Chen et al., 2014; Rakesh et al., 2010), puffing (Rakesh & Datta,

2013), baking (Zhang et al., 2005), meat cooking (Dhall & Datta, 2011), and drying

(Kumar et al., 2015a).

However, there is no multiphase model for IMCD drying along with

considering shrinkage. As shrinkage is indispensable during drying, a realistic model

demands consideration of shrinkage. Moreover, shrinkage phenomenon completely

depends on pore formation and evolution during drying. Therefore, proper prediction

of porosity is essential in order to develop comprehensive porous media model.

In this study, two multiphase porous media IMCD models have been

developed. One of these does not consider sample shrinkage and the other one

considers a proper prediction of structural deformation. In this section, the model

without considering shrinkage is presented as IMCD1 and the model that takes into

consideration pore evolution and shrinkage is named as IMCD2. In addition to this,

Chapter 6 | Multiphase IMCD model


non-equilibrium evaporation rates consider all transport mechanisms such as

capillary diffusion, and pressure driven flow evaporation of water, vapour, and air.

6.1 IMCD MULTIPHASE MODELLING

In this section, the equations for multiphase porous media are developed

describing heat, mass and momentum transfer for IMCD of an apple slice.

Mathematical problem formulation, description of heat and mass transfer,

implementation of solid mechanics are discussed in this section

The model developed in this research considered transport of liquid water,

vapour, and air inside food materials. The mass and energy conservation equations

included convection, diffusion, and evaporation. The non-equilibrium formulation

for evaporation has been used to describe the evaporation, which allows

implementation of the model in commercial software. Momentum conservation was

developed from Darcy’s equations. Evaporation was considered as being distributed

throughout the domain, and a non-equilibrium evaporation formulation was used for

evaporation condensation-condensation phenomena.

Heat and the mass transfer considered to take place at all boundaries except the

symmetry boundary. The apple slice was considered as a porous medium, and the

pores were filled with three transportable phases, namely liquid water, air and water

vapour as shown in Figure 6.2.

Figure 6-2: Schematic showing 3D sample, 2D axisymmetric domain and Representative Elementary

Volume (REV) with the transport mechanism of different phases


It is assumed that all phases (solid, liquid, and gases) are continuous and local

thermal equilibrium is valid, which means that the temperatures in all three phases

are equal. Liquid water transport occurred due to convective flow resulting from gas

pressure gradient, capillary flow and evaporation. Vapour and air transport arose

from gas pressure gradients and binary diffusion.

The driving force of deformation is associated with a change in moisture

content and the gradients in gas pressure (negligible for convection drying).

Deformation changes to structure and porosity of the materials affecting multiphase

transport, while, heat and mass transfer change mechanical properties of the sample

that influence pore formation and evolution. Eventually, the drying problem

experiences two-way coupled with material deformation, and heat and mass transport

as illustrated in Figure 6.3.

To develop the porous multiphase model for IMCD of an apple sample, the

following assumptions are taken into consideration:

The model developed in this research considered transport of liquid water,

vapour, and air inside multiphase food materials.

The mass and energy conservation equations included convection,

diffusion, and evaporation.

Figure 6-3: Flow chart showing coupling between multiphase transport and solid mechanics



The non-equilibrium formulation for evaporation has been used to describe

the evaporation.

Momentum conservation was developed from Darcy’s equations.

Evaporation was considered as being distributed throughout the domain.

All phases maintain local thermal equilibrium.

Moisture-dependent physical, thermal, mechanical has been considered.

The governing equations for multiphase transport in porous media,

electromagnetics, ALE for moving mesh and solid mechanics for large

deformations were solved using Finite Element software COMSOL

Multiphysics 4.4 (COMSOL, Burlington, MA).Mass, energy and

momentum conservations for different species and phases were solved

using general form of PDEs, Transport of Dilute Species, Heat Transfer in

Fluid modules, Darcy’s Law, respectively, using the MUltifrontal

Massively Parallel Sparse direct Solver. ALE framework and Non-linear

Solid Mechanics module were used for moving mesh and solid momentum

balance respectively.

6.1.1 Governing equations

The mathematical model consisted of conservation equations for all

transportable phases, transport mechanisms and structural deformation for IMCD

considering shrinkage and without shrinkage.

Mass balance equations

The instantaneous representative elementary volume (REV), the smallest

volume over which an estimation can be made that will represent a quality

illustrative of the whole sample, as presented in Figure 6.2 V (m3) summation of

the volume of three phases, namely, gas, water, and solid, namely,

swg VVVV . (6.1)

Where, wV is the volume of water (m3),

gV is the volume of gas (m3), and sV was

the volume of solid (m3).

The apparent porosity, , is defined as the volume fraction occupied by water

and gas. Thus,


V

VV wg

. (6.2)

Water saturation ( wS ) and gas saturation (gS ), are defined as the fraction of

pore volume occupied by the individual phase,

V

V

VV

VS w

gw

ww

, (6.3)

and w

g

gw

g

g SV

V

VV

VS

1

, (6.4)

The mass concentrations of water( wc ), vapour ( vc ), and air ( ac ) in kg/m3 are

calculated by,

www Sc , (6.5)

gv

v SRT

pc , (6.6)

and g

aa S

RT

pc , (6.7)

Where, R is the universal gas constant (J/mol/K), w is the density of water (kg/m3),

vp is the partial pressure of vapour (Pa), T is the temperature of product (K) and

ap is the partial pressure of air (Pa).

Mass conservation of liquid water

The mass conservation equation for the liquid water is expressed by,

*

InSt

www

,

(6.8)

Where, wn

is water flux (kg/m2s), and

evapRI *

is the evaporation rate of liquid water

to water vapour (kg/m3s).

The total flux of the liquid water is due to the gradient of liquid pressure,

cw pPp , as given Darcy’s Law (Bear, 1972), namely,



c

w

wrw

w

w

wrw

ww

w

wrw

ww pkk

Pkk

pkk

n

,,,

. (6.9)

Here, P is the total gas pressure (Pa), cp is the capillary pressure (Pa), wk is

the intrinsic permeability of water (m2),

wrk , is the relative permeability of water, and

w is the viscosity of water (Pa.s).

The capillary pressure depends upon concentration ( wc ) and temperature (T)

for a particular material (Datta, 2007a). Therefore, further breakdown of equation

(6 can be presented as,

TT

pkkc

c

pkkP

kkn c

w

wrw

ww

w

c

w

wrw

w

w

wrw

ww

,,,. (6.8)

The capillary diffusivity due to the temperature gradient is known as a Soret

effect, is insignificant than the capillary diffusivity due to concentration gradients

(Datta, 2007a). Therefore, this will be neglected in this work.

Substituting the above into Equation (6 can be written as,

evapc

w

wrw

w

w

wrw

www RT

pkkP

kkS

t

,, (6.11)

Mass conservation of water vapour

The conservation of water vapour can be written as follows:

evapvvgg RnSt

, (6.12)

Where, v is the mass fraction of vapour, g is the density of the gas (kg/m

3) and

vn

is the vapour mass flux (kg/m2s).

As the gas is binary mixture and vn

can be written as (Bird et al., 2007),

vgeffgg

v

grg

vvv DSPkk

n

,

,, (6.13)

where, grk ,is the relative permeability of gas (m

2),

gk is the intrinsic permeability of

gas (m2),

geffD ,is the binary diffusivity of vapour and air (m

2/s) , and

g is the

viscosity of gas (Pa.s) .


Mass fraction of air

After calculating the mass fraction of vapour, v from water vapour mass

conservation equation, the mass fraction of air, a , can be calculated from

va 1 . (6.14)

Continuity equation to solve for pressure

The gas pressure, P, can be determined via a total mass balance for the gas

phase,

evapgg RnS

t

g

, (6.15)

Where, the gas flux,gn

, is given by,

Pkk

ni

grg

gg

,

. (6.16)

Here, g is the density of gas phase, given by,

RT

PM gg , (6.17)

Where, gM is the molecular weight of gas (kg/mol).

Energy equation

After assuming thermal equilibrium of the phases, the energy balance equation

that considers conduction and convection, radiation heat transfer, and energy

sources/sinks due to evaporation/condensation can be presented as,

)().( tfQRhTkhnhnt

Tc mevapfgeffwwggeffpeff

(6.18)

Here, eff is the effective density (kg/m

3), T is the temperature (K) of each

phase, gh is the enthalpy of gas (J),

effk is the effective thermal conductivity (W/m/K),

wh is the enthalpy of water (J), fgh is the latent heat of evaporation (J/kg),

effpc is the

effective specific heat (J/kg/K), and f(t) is an intermittency function of microwave



source (Qmic). Equation 6.18 considers energy transport due to conduction and

convection and energy sources/sinks due to evaporation/condensation.

Thermos-physical properties

The thermo-physical properties of the REV are obtained by the volume-

weighted average of the different phases and can be calculated by the following

equations,

swwggeff SS 1 , (6.19)

pspwwpggeffp ccScSc 1 , (6.20)

and sthwthwgthgeff kkSkSk ,,, 1 . (6.21)

Here s is the solid density (kg/m3).

gthk ,,

wthk ,, and

sthk ,are the thermal

conductivity of gas, water, and solid, (W/m/K) respectively.pgc ,

pwc , and psc are the

specific heat capacity of gas, water, and solid (J/kg/K), respectively.

Evaporation rate

A non-equilibrium formulation as described in Ni et al. (1999) is considered to

calculate the evaporation rate, namely,

veqvv

evapevap ppRT

MKR ,

. (6.22)

Here, eqvp ,

is the equilibrium vapour pressure (Pa), vM is the molecular weight

of vapour (kg/mol), vp is the vapour pressure (Pa), and Kevap is material and process

dependent the evaporation constant (s-1

).

It is worthy to mention that K denotes evaporation rate constant and defined as

transition of a molecule from liquid water to water vapour. For different plant based

food materials, K value is used with the range of 1000-100000 s-1

(Halder et al.,

2011b). However, use of K=100000 s-1

value creates some convergence issues during

numerical scheme and significantly increased the computation time. In addition, it is

found that there is very negligable change of solution for the value of K=1000 s-1

and

above. Taken all these into consideration, K=1000 s-1

has been used in this study.

The equilibrium vapour pressure of apple, as presented in Equation 6.23, can

be obtained from the sorption isotherm (1989).


)](ln[232.0182.0exp)(0411.0949.43696.0

,, TPMeMTPp satdb

M

dbsatveqv

(6.23)

Here, dbM is the moisture content (dry basis), satvP ,

is the saturated vapour

pressure of water (Pa) and, which can be related to wS via,

s

wwdb

SM

1. (6.24)

The saturated vapour pressure of water, satvP ,

, is a function of temperature and

is taken the regression equation found by Vega-Mercado et al. (2001) as,

.

ln656.61001445.0

104176.00486.03915.1/2206.5800exp

37

24

,

TTx

TxTTP satv

(6.25)

The vapour pressure, vp , is obtained from partial pressure relations given by,

Pp vv , (6.26)

where, v is the mole fraction of vapour and P is the total pressure (Pa).

The mole fraction of vapour, v , can be calculated from the mass fractions and

molecular weight of vapour and air as,

vaav

avv

MM

M

, (6.27)

Where, vM is the molecular mass of vapour (kg/mol), aM is the molecular mass of air

(kg/mol).

Solid deformation

Plant-based food materials are deformable under the condition of drying due to

simultaneous heat and mass transfer. From the multiphase transport model, it is easy

to calculate the related forces that cases displacement during drying. However, the

material properties, the real dominants of the response of the forces, are vital.

Mechanical properties during drying conditions are not available in the

literature. Without the appropriate mechanical properties, the predicted elastic

volume ratio (elastic Jacobian, Jel ) will show significant error. If we consider a very



basic hyperelastic model, a Neo-Hookean constitutive model as presented in

Equation 6.19, can be used in order to characterise material deformation.

)ln(2

1ln)3(

2

11 elels JJIW (6.28)

In the equation, 1I is the first invariant of the right-Cauchy-Green tensor

(details of the term is not covered here due to the irrelevancy of the preceding

discussion). Whereas µ is the shear modulus of the material and λ is the Lame’s

constant and can be calculated using the following equations:

)21)(1(

E and

)1(2

E

Where, E is the Elastic modulus and m is the Poisson ratio.

Eventually, the constitutive model depends on E and . The value of these two

mechanical characteristics significantly changes throughout the drying process. This

variation is discussed in Chapter 7 Section 7.3.5 (page 169).

Therefore, there was no literature found that dealt with variable mechanical

characteristics during IMCD. However, Gulati et al (Gulati & Datta, 2015) applied a

moisture dependent Elastic Modulus for a potato sample in their constitution model

for multiphase modelling during convective drying (taken from Yang and Sakai (H.

Yang, & Sakai, N. (2001)..

After an investigation, Yang and Sakai (2001) revealed that the variable

Elastic modulus was calculated at room temperature for different moisture content

and found increasing E with decreasing moisture content. This variable E cannot be

taken into consideration as the variation of E happens in drying condition. In drying

conditions, the materials remain rubbery (with various degree of softness) due to a

higher temperature. Moreover, the E should show a decreasing trend with a decrease

of moisture content (Krokida & Philippopoulos, 2005) until the sample reaches the

Glass phase. This study has gone some way towards enhancing our understanding of

deformation of plant-based tissue during drying in particular IMCD.

In addition to this, Gulati and Datta (2015) considered that mechanical

properties are correlated only with moisture contents. However, the pathway of fluid

is important as this significantly influences the material properties. As the

mechanical properties of processed plant-based tissue depend upon cell wall strength,


inter-cellular adhesion, ease of fluid flow and cell wall porosity (Ormerod et al.,

2004). Furthermore, in addition to this, processing temperature has a significant

effect on mechanical properties. Most of the fruits and vegetables show decreasing

firmness of raw tissue with an increase of temperature (Bourne, 1982). Therefore, a

relationship of Elastic Moduli with moisture content cannot express the accurate

nature of the mechanical properties of the sample during drying. .

Due to this practical constraint, the strain-stress relationship determination

from the constitutive law is beyond the scope of this study.Therefore, the volumetric

deformation due to moisture migration will be calculated by using a semi-empirical

shrinkage velocity model as mentioned below.

00

2

g

gws

TT

TT

L

Dv (6.29)

Where, Dw can be obtained from the total flux of the liquid water at any

particular time of drying. The concept of shrinkage velocity has also been found in

other literature (Aprajeeta et al., 2015; Golestani et al., 2013; Karim & Hawlader,

2005b).

Porosity calculation

The instantaneous bulk volume from the above shrinkage velocity approach of

the material during drying can be calculated by the following equation:

tvLtvrV ss 0

2

0 (6.30)

Where, Vw is the instantaneous volume of water, while Vs is the volume of

solid material of the sample that is considered constant throughout the drying

process. Also, t is the time of drying, r is the instantaneous radius of the sample and

L is the instantaneous thickness of the sample.

Assuming the mass of solid phase remains constant, instantaneous total

porosity can be determined by the following equation:

)1()1( 00 VV ss

(6.31)



0

011

V

V

(6.32)

Therefore, gas porosity gS (6.33)

6.1.2 Initial conditions

The initial conditions for equations 6.8, 6.9, 6.15, and 6.18 are given by,

0)0( wwtw Sc , (6.34)

0262.0)0( tvw , (6.35)

ambt PP )0(, (6.36)

and KT t 303)0( , (6.37)

respectively.

6.1.3 Boundary conditions

The schematic of apple geometry presented in Figure 6.4, shows the boundary

conditions

Figure 6-4: Boundary condition of multiphase IMCD model

Vapour flux

Total vapour flux, totalvn ,

, from a surface ( hypothetical) with only gas phase

can be written as,

RT

-pphn airvv

mvtotalv ,

,

(6.38)


Where, totalvn ,

is the total vapour flux at the surface (kg/m

2s), mvh is the mass transfer

coefficient (m/s), and airvp ,

is the vapour pressure of ambient air (Pa).

In a multiphase problem, the total vapour flux on the surface encompasses

evaporation from liquid water and existing vapour on the surface. The boundary

conditions for water and vapour phase can be written as,

RT

-ppShn airvv

wmvw

, (6.39)

RT

-ppShn airvv

gmvv

, (6.40)

respectively.

In food drying, the pressure at the boundary (exposed to environment) is equal

to the ambient pressure, ambP . Hence, the boundary condition of pressure can be

expressed as,

ambPP . (6.41)

For the energy equation, energy can transfer by convective heat transfer and

heat can be lost due to evaporation at the surface, given by,

fg

airvv

wmvairTsurf hRT

-ppShTThq )( . (6.42)

Here, Th is the heat transfer coefficient (W/m2/K) and airT is the drying air

temperature (K).


The input parameters of the model are listed in.6.1 The rest of the parameters

that are not listed in this table are derived and discussed in the latter sub-sections.

Table 6-1: Input properties for the model


Sample diameter, Dias 40 mm This work

Sample thickness, Ths 10 mm This work

Equivalent porosity, initial, 0.922 (Ni, 1997; Rahman, 2008).

Water saturation, initial, 0.794 (Ni, 1997; Rahman, 2008).

Initial saturation of vapour, 0.15 (Ni, 1997; Rahman, 2008).

0

0wS

0vS




Gas saturation, initial, 0.19 (Ni, 1997; Rahman, 2008).

Initial temperature, T0 303K

Vapour mass fraction, 0.026 Calculated

Evaporation constant, Kevap 1000 This work

Drying air temperature, Tair 333K This work

Universal gas constant, Rg 8.314 J mol-1

K-1

(Çengel & Boles, 2006)

Molecular weight of water, 𝑀𝑤 18.016 g mol-1


Molecular weight of vapour, 𝑀𝑣 18.016 g mol-1


Molecular weight of gas (air),

𝑀𝑎

28.966 g mol-1


Latent heat of evaporation, ℎ𝑓𝑔 2.26e6 J kg-1


Ambient pressure, 𝑃𝑎𝑚𝑏 101325 Pa

Specific heats

Apple solid, 𝐶𝑝𝑠 3734 J kg-1

K-1

Measured

Water, 𝐶𝑝𝑤 4183 J kg-1

K-1

(Carr et al., 2013)

Vapour, 𝐶𝑝𝑣 1900 J kg-1

K-1

(Carr et al., 2013)

Air, 𝐶𝑝𝑎 1005.68 J kg-1

K-1

(Carr et al., 2013)

Thermal conductivity

Apple solid, 0.46 W m-1

K-1

(Choi & Okos, 1986)

Gas, 0.026 W m-1

K-1


Water, T4108.959.0 (Rakesh et al., 2012)

Density

Apple solid, 𝜌𝑠 1419 kg m-3

This study

Vapour, Ideal gas law, kg

m-3

Air, Ideal gas law, kg

m-3

Water, 1000, kg m-3

Permeability

Permeability is an important factor in relation to describing the water transport

due to the pressure gradient in unsaturated porous media. The value of the

permeability determines the extent of pressure generation inside the material. The

smaller the permeability, the lower the moisture transport and the higher the internal

pressure, and vice versa.

vw

sthk ,

gthk ,

wthk ,

v

v

w


Permeability is a property of porous materials that defines the resistance to

flow of a fluid through the material under the influence of a pressure gradient.

According to Darcy’s law for laminar flow, pressure drop and flow rate shows a

linear relationship through a porous material (Scheidegger, 1974). The slope of this

line is related to permeability as shown below.

PA

LQk

(6.43)

Where, k is the permeability, Q is the volumetric flow rate, 𝜇 is the fluid

viscosity, A is the sample cross sectional area, and ∆𝑃 is the pressure gradient.

Permeability, k, is further divided into two groups namely, intrinsic permeability, ki,

and relative permeability, kr, given by the following expression:

The permeability of a material to a fluid, k , is a product of intrinsic

permeability, ik , of the material and relative permeability, rik ,, of the fluid to that

material (Bear, 1972), namely,

riikkk , . (6.44)

The intrinsic permeability, ki, represents the permeability of a liquid or gas in

the fully saturated state. The relative permeability of a phase is a dimensionless

measure of the effective permeability of that phase. It is the ratio of the effective

permeability of that phase to the absolute permeability. Relative permeability of

gases is a function of saturation.

The intrinsic permeability depends on the pore structure of the material and

from literature it is found as following (Feng et al., 2004) as ,

77.039.0

110578.5

2

312

wk . (6.45)

The gas intrinsic permeability kg was 21212 102.1104.7 m and

21313 104.2105.6 m at a moisture level of 36.0% (db) of 60.0% (db)

respectively. In this study, we used an average of212100.4 m (Feng et al., 2004).

Relative permeabilities are generally expressed as functions of liquid

saturation. There are numerous studies which have developed such functions (Plumb,



1991). In this study, the relative permeabilities of water, wrk ,

, and gas, grk ,, for apple

were obtained from the measurement of Feng et al. (2004), namely,

3

, wwr Sk , (6.46)

and wS

gr ek86.10

, 01.1

, (6.47)

Viscosity of water and gas

Viscosities of water (Truscott, 2004) and gas (Gulati & Datta, 2013) as a

function of temperature are given by,

T

ww e

1540143.19

(6.48)

and

65.0

3

27310017.0

T

g .

(6.49)

Effective gas diffusivity

The effective gas diffusivity can be calculated as a function of gas saturation

and porosity according to the Bruggeman correction (Ni, 1997) given by,

3/4

, gvageff SDD . (6.50)

Here, binary diffusivity, vaD , can be written as,

81.1

0

05103.2

T

T

P

PDva ,

(6.51)

where 𝑇0 = 256𝐾 and 𝑃0 = 1 𝑎𝑡𝑚. For simplicity, In this study effective gas

diffusivity was considered as 2.6 × 10−6 𝑚2

𝑠 (Datta, 2007b).

Capillary diffusivity of liquid water

Liquid from food material can flow from material of higher concentration to

the lower concentration of water due to the difference in capillary action. This is

referred to as “unsaturated” flow and is extremely important in food processing, for

example, in the drying of food materials. During the modelling of multiphase flow

for different food processing systems, the property of capillary diffusivity is very

important.


Capillary force is one the main driving force of liquid water in drying (Ni,

1997). It is clear that in our formulation the capillary diffusivity, cD , is proportional

to w

c

S

p

, and is a function of capillary pressure.

It can be found from the literature that the capillary pressure increases

significantly at lower saturation levels and when it reaches irreducible saturation the

value becomes infinity. Therefore, that part is neglected to avoid numerical

instability. The underlying physics is that as wS approaches 1, more water becomes

free and the resistance of the solid matrix to the flow of free water is almost zero.

Therefore, cD is very large at high moisture content; as a result, the concentration

gradient is concomitantly small (Ni, 1997). As an outcome, the capillary diffusivity

can be very close to effective moisture diffusivity for very wet material when vapour

diffusion is insignificant. However, it can be quite different in the lower moisture

region.

Considering that the highest value corresponds to the highest saturation of

water, a similar relationship between capillary diffusivity and moisture as given by

Ni (1997) is used in this study, namely,

wbc MD 888.6exp10 8 . (6.52)

In this study, a similar function was developed for apple by analysing the value

of different effective diffusivity values presented in the literature (Esturk, 2012b;

Feng et al., 2001; Feng et al., 2000; Golestani et al., 2013)

Heat and mass transfer coefficient

The heat and mass transfer coefficients were calculated based on the empirical

relationship discussed in previous in Chapter 4 and found to be Th =16.746 W/(m2K)

and mh =0.017904 m/s, respectively.

After gathering all the required input parameters and initial conditions for the

governing equations and boundary conditions, the multiphase porous media IMCD

model was simulated in COMSOL Multiphysics. The simulated results were

validated by experimental data as discussed in the following section.



6.2 RESULTS AND DISCUSSION

In this section, profiles of moisture, temperature, pressure, fluxes and

evaporation rate are presented and discussed. Validation is also conducted by

comparing moisture content and temperature from experiments.

6.2.1 Average moisture content

The evolution of average moisture content obtained from IMCD1 and IMCD2

models and experiments are compared in Figure 6.5. It can be seen from the figure

that both of the models data show the agreeable trend as found in experiments.

However, IMCD2 shows better match at the end of drying; whereas IMCD1 shows

relatively low moisture content at 4500s.

Figure 6-5: Comparison between predicted and experimental values of average moisture content

during IMCD with and without shrinkage

It seems possible that this result is due to higher temperature developed in

IMCD1 model resulting higher moisture migration rate. It was found that moisture

content (dry basis) of apple slice dropped from its initial value of 6.14 kg/kg to 1.58

kg/kg after 4500 s of drying. In addition to this, due to extensive time requirement to

run the models until equilibrium condition, there is a room for future research.

6.2.2 Distribution and evolution of water and vapour

The predicted distribution of water saturation and vapour saturation along the

half thickness of the material at different times is shown in Figure 6.6 and 6.7,

respectively.


The result obtained from both the models show that over the course of drying

the water saturation near the surface was lower than in the centre region. Moreover,

due to an adequate supply of drying air, all of the water at the surface migrated

through convective flow instantly removed from the surface. This nature of moisture

distributions within the sample seem to be consistent with the findings of Chemkhi et

al. (2009), namely, that the core contained higher moisture content compared to the

surface. Along the drying time, it is clearly demonstrated from Figure 6.6 that

concentration of water is decreased for both of the models.

Figure 6-6: Spatial distribution of water saturation with times for IMCD1 and IMCD2

Figure 6-7: Spatial distribution of vapour with different time for IMCD1 and IMCD2



Unlike the moisture distribution, vapour saturation was found to increase with

drying time within the sample (as shown in Figure 6.7). However, the vapour

saturation at and near the surface was lower than the centre, because the vapour

coming from the surface was immediately removed by the drying air through

convection. In addition to this, it is clearly apparent from Figure 6.7 that

concentration of vapour of any point of the sample is decreased with time for both

the models.

A higher vapour fraction is found in these IMCD drying compared to

convective drying due to higher vapour generation in IMCD. It is also observed that

average vapour fraction fluctuates with the intermittency of microwave application.

However, vapour fraction is relatively higher (up to 0.45) in IMCD1 compare to

IMCD2, as shown in Figure 6.8. A possible explanation for this might be that

unchanged volume consideration causes more volumetric heating resulting higher

vapour generation during IMCD1.

6.2.3 Temperature evolution and distribution

Figure 6.9 shows the average surface temperature evolution of the material for

IMCD1 and IMCD2. Oscillations of temperature during both models are found as

expected because temperature increases during microwave on-time and drops during

the tempering periods. Due to sudden exposure of the sample to higher air

0

0.1

0.2

0.3

0.4

0.5

0.6

0 1000 2000 3000 4000 5000 6000

Aver

age

vap

our

frac

tio

n

Time (s)

Without shrinkage

With shrinkage

Figure 6-8: Average vapour mass fraction in apple sample during IMCD drying


temperature and volumetric heating, the surface temperature rose sharply at the

beginning of the drying process. Then, the temperature rose with the same rate for

IMCD1; however, a temperature fluctuation within a constant range 60-65 0C is

observed during IMCD2.

The inconsistency may be due to higher absorption of microwaves is taken into

consideration as the volume of the sample assumed constant for IMCD1 (as

absorption power maintain an association with sample volume as discussed in

Section 3.3.6). The trend of temperature obtained for IMCD2 is consistent with that

of Sunjka et al.(Sunjka et al., 2004) who found almost stable temperature for

Cranbarry during microwave convective drying after 15 min. of drying. It seems

possible that this result is due to low power absorption happened while the moisture

decreases. In addition to this, considering shrinkage and porosity evolution in

IMCD2 provides a realistic change of thermos-physical properties of the sample.

Figure 6-9: Top surface average temperature obtained for IMCD1 and IMCD2

To compare the temperature distribution within the apple sample during

IMCD1 and IMCD2, simulation results are shown in Figure 6.10. From the figure, it

is apparent that the surface temperature was always lower than the central

temperature over the course of drying. This higher interior temperature could be due

to evaporation cooling and higher absorption power towards the core due to higher

moisture content.



Figure 6-10: Temperature distribution within apple sample during IMCD1 and IMCD2

6.2.4 Vapour pressure, equilibrium vapour pressure, and saturated pressure

The comparison between vapour pressure, equilibrium vapour pressure and

saturation vapour pressure at the surface during IMCD1 and IMCD2 are presented in

Figure 6.11. A proper understanding the nature of these three pressures is essential to

an understanding of drying kinetics.

Figure 6-11: Average vapour pressure, equilibrium vapour pressure and saturation pressure at surface

0

10000

20000

30000

40000

50000

60000

70000

80000

0 500 1000 1500 2000 2500 3000 3500 4000

Pre

ssu

re (

Pa)

Time (s)

Vapour Pressure ( No shrinkage)

Equilibrium VP ( No shrinkage)

Saturation VP ( No shrinkage)

Vapour Pressure ( shrinkage)

Equilibrium VP (shrinkage)

Saturation VP (shrinkage)


The saturated vapour pressure varies with temperature, and data is available

from many sources. The saturated vapour pressure obtained from simulation is

compared with literature (Çengel & Boles, 2006) and this accords with available

data. The equilibrium vapour pressure data was calculated from the sorption isotherm

of apple and, was found to be lower than the saturation vapour pressure as expected

for IMCD. All of the pressures show fluctuation due to temperature oscillation

resulting from intermittency of microwave energy source.

At the initial stage of drying, vapour pressure found higher than equilibrium

vapour pressure that is resulting higher evaporation at this time. After this period

these pressures overlap for IMCD2; however, a constant discrepancy of this pressure

was found for IMCD1. For IMCD2, the overlapping is caused by the surface

becoming dried and the equilibrium vapour pressure then becomes lower.

6.2.5 Gas pressure

In Figure 6.12, spatial gradient of the gas pressure (ambg PPP ) within the

sample is presented.

Figure 6-12 Gas pressure gradient across the half thickness the sample in different times during

IMCD1 and IMCD2

Figure 6.12 indicates that the gas pressure is maximum at the core region and

progressively drops towards the surfaces. Due to lower gas porosity the migration of

gas from the interior is restricted while the sample contains higher moisture content,



and this causes a rise in total gas pressure. In microwave heating, this type of gas

pressure distribution is in agreement with the available literature (Feng et al., 2001;

Wei et al., 1985). The regions having zero gas pressure maintain atmospheric

pressure. Increasing with gas porosity, the amount of gas migration from the centre is

increased and the lower gas pressure gradient is observed.

6.2.6 Evaporation rate

As the IMCD models considered non-equilibrium approaches, calculation and

visualisation of evaporation within the sample are great advantages over other the

equilibrium approaches. Figure 6.13 illustrates the spatial distribution of the

evaporation rate over the course of IMCD.

From the figure, it is quite revealing that a higher evaporation rate occurs near

the surface and maintains a non- equilibrium condition.

Figure 6-13: Spatial distribution of evaporation rate at different drying times during IMCD1 and

IMCD2

It is clear from the figure is that the evaporation maintains a zone, which starts

not exactly from surface, rather beneath the surface and decreasing to zero

evaporation towards the core (as demonstrated in Figure 6.14). This result may be

explained by the fact that the liquid water saturation becomes lower near the surface

of the sample and contributes no difference between the vapour pressure and


equilibrium vapour pressure. Eventually, the evaporation front moves inside of the

material as drying progress.

Another interesting pattern emerged from the graph in Figure 6.13, the peak of

evaporation moves towards the centre. One possible reason for this is the gradual

increase of completely dried thickness from the surface. IMCD1 shows the random

nature of the evaporation zone throughout the drying time; whereas, IMCD2

provides a well-distributed evaporation zone. In other words, pore formation and

evolution consideration makes difference in IMCD1 and IMCD2 evaporation rate

profiles as porosity plays important role in determining the transport phenomena

during drying.

6.2.7 Liquid water and vapour fluxes

The major advantage of a multiphase porous media model is that the relative

contribution of liquid water and vapour fluxes due to diffusion (due to a

concentration gradient) and convection (due to gas pressure gradient) can be

illustrated.

Liquid water fluxes

Water fluxes due to capillary pressure (diffusive flow) and gas pressure

gradients (convection flow) are plotted in Figure 6.15 and Figure 6.16, respectively.

Water capillary flux

It can be seen from Figure 6.14 that the capillary flux is higher at about 0.4–0.8

mm beneath the surface and this peak is moving towards the core with drying time in

both models. It is worthy to note here that capillary flux ( wc cD ) is directly

proportional to moisture gradient ( wc ) of the sample. Moreover, the gradient is

higher initially near the surface and the peak of gradient moves towards the centre

with time. These factors may explain the nature of the spatial distribution of water

capillary flux within the sample.

In addition, with time the pick capillary flux reduces due to moisture migration

as shown in Figure 6.14. The capillary flux in IMCD1 does not represent the typical

trend concentration gradient.

Water convective flux



The water flux due to the gas pressure gradient (Figure 6.15) showed a similar

pattern of water diffusion flux distribution, although with lower magnitude than

capillary flux for IMCD2 as expected. Therefore, it is clear from this result that

diffusive water flux dominates over the convective flux throughout the food

processing time.

Figure 6-14: Spatial distribution water flux due to capillary diffusion at different drying times during

IMCD1 and IMCD2

Figure 6-15 Spatial distribution water flux due to gas pressure gradient at different drying times

during IMCD1 and IMCD2


The convective water flux increased from zero (at the centre) to a peak at

approximately 0.5 mm beneath the surface. This could be due to the higher-pressure

gradient near the surface resulting higher convective flow. However, in convection

drying, the gradient of pressure is needed a closer inspection, because there may not

be enough pressure development inside the sample.

However, IMCD1 showed higher convective flux than capillary flux with

increasing trend while drying progress, which cannot be justified. This rather

contradictory result may be due to higher temperature developed in the sample for

IMCD1.It is also apparent that the convective flux is higher than capillary flux in the

case of IMCD1, which also not acceptable as capillary flux water must be higher

than convective flux during low-temperature drying.

The patterns of liquid fluxes show that liquid water concentration prediction

differs in IMCD1 and IMCD2 mainly due to the differences in convective flux. As

convective flux is directly affected by available porosity of the sample, ignoring

shrinkage leads erroneous prediction of convective flux.

Vapour fluxes

Figure 6.16 and 6.17 show the spatial distribution of the diffusive and convective

fluxes of vapour, respectively.

Figure 6-16: Spatial distribution vapour flux due to binary diffusion at different drying times during

IMCD1 and IMCD2



Figure 6.16 shows that vapour flux due to binary diffusion occurring near the

surface with zero in the centre of the sample. It seems possible that this types of

spatial distribution of capillary flux of at the transport at the surface, which generated

large vapour concentration near the surface resulting in a higher diffusion flux. The

findings of this study in this regard is consistent with that found by Ousegui et al.

(2010) who found a similar pattern of capillary vapour flux.

The spatial distribution of convective flux during IMCD is presented in Figure

6.17 . Due to controlled application of microwave the temperature could not reach

such higher that causes huge evaporation.

Figure 6-17: Spatial distribution of vapour flux due to gas pressure at different drying times during

IMCD1 and IMCD2

Therefore, gas pressure developed within the sample is minimal ranging 1-10

Pa. From the above figure, it is clear that convective vapour flux is occurring near the

surface with zero centres depending on the gas pressure gradient at any time.

However, IMCD1 does not capture this trend due to unnatural temperature

development at the end of drying. Similar to water concentration, vapour

concentration prediction was not found correct in case of IMCD1 due to this

unnatural temperature development.

In brief, the vapour and water fluxes caused by all sources showed that the

fluxes were minimal at the centre and gradually increase until a peak is achieved.


From the pick, these start decreasing towards the surface and show zero fluxes

except vapour diffusive flux.

6.2.8 Gas porosity

Figure 6.18 shows the porosity evolution of the sample against moisture

content. In the figure, there is a clear trend of increasing porosity with a decrease of

moisture content. This increase of porosity is the direct consequence of the increase

in gas saturation during drying. Moreover, porosity prediction from IMCD2 agrees

closely with experimental value whereas IMCD2 failed to predict a reasonable value

of porosity over the course of drying.

The proper prediction of porosity is essential heat and mass transfer as porosity

affects thermo-physical properties of the sample. The effect of shrinkage and

porosity evolution on thermal conductivity, effective heat capacity and effective

density is discussed below:

6.2.9 Thermal conductivity

Thermal conductivity is defined as the ability of a material to conduct heat. The

structure of the foodstuff, its composition, heterogeneity of food and processing

conditions influence the thermal conductivity of foods (Hamdami et al., 2003;

Sablani & Rahman, 2003).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

2.5 3 3.5 4 4.5 5 5.5 6 6.5

Poro

sity

Moisture content (kg/kg of solid)

Without shrinkage

With shrinkage

Experimental

Figure 6-18: Change of porosity with moisture removal



It is clear from Figure 6.19 that the effective density decreases sharply for

IMCD1 without shrinkage resulting in higher gas porosity. Dry porous solids are

very poor heat conductors because air occupies the pores resulting in low thermal

conductivity. This is the case of IMCD1.

Figure 6-19: Effective thermal conductivity with moisture content during IMCD

6.2.10 Effective specific heat capacity

Like effective thermal conductivity, effective specific heat capacity

significantly depends on the pore characteristics and distribution of different phases,

such as air, water, ice, and solids.

Figure 6-20: Effective specific heat capacity with moisture content during IMCD

0.2

0.3

0.4

0.5

0.6

0.7

0.8

2.5 3 3.5 4 4.5 5 5.5 6 6.5

Eff

ecti

ve

ther

mal

conduct

ivit

y

(W/m

.K)

Moisture content (kg/kg solid)

Without shrinkage

With shrinkage

2000

2200

2400

2600

2800

3000

3200

3400

3600

3800

4000

2.5 3 3.5 4 4.5 5 5.5 6 6.5

Eff

ecti

ve

spec

ific

hea

t

capas

ity (

J/kg.K

)

Moisture content (kg/kg solid)

Without shrinkage

With shrinkage


It is clearly apparent from Figure 6.20 that effective specific diffusivity highly

depends on the porosity of the sample. Therefore, neglecting shrinkage during

multiphase model should not be justified.

6.2.11 Effective density

Effective density, generally, depends on shrinkage and pore evolution over the

course of drying.

Figure 6-21: Effective specific heat capacity with moisture content during IMCD

Figure 6.21 shows the effective density of the apple sample at different

moisture content. The graph clearly shows that effective density is significantly

affected by the distribution of multiphase in the sample. The effective density found

in IMCD2 is consistent with experimental results.

6.2.12 Comparison between single phase and multiphase

In order to demonstrate the advantages of multiphase model, a comparison

between the findings of single phase and multiphase are presented in this section.

Figure 6.22 shows the trend of temperature in the sample.

350

450

550

650

750

850

2.5 3.5 4.5 5.5 6.5

Eff

ecti

ve

den

sity

(kg/m

3)

Moisture content ( kg water/kg solid)

Without shrinkage

With shrinkage

Experimental



Figure 6.22: Volumetric average temperature evolution during drying

It is clearly apparent that temperature prediction using multiphase porous media

model is closer to experimental result than single phase model. In the single phase

model, an increasing trend in temperature is found throughout the drying time while

the multiphase provided more realistic temperature trend and agreed well with

experimental data. Our experimental result is consistent with Sunjka et al.(Sunjka et

al., 2004) who found a stable temperature at the later part of drying.

Similar to temperature profile, other results found in single phase and multiphase

model have differences. In most of the cases, proper prediction of temperature and

shrinkage in the multiphase makes these differences.

6.3 CONCLUSIONS

Two non-equilibrium multiphase porous media models for IMCD have been

developed. Incorporation of shrinkage and pore evolution proved a significant

advancement relative to existing approaches. A number of parameters of the model

were validated by experimental results and demonstrated that good agreement

existed. One of the more significant findings to emerge from this study is that

consideration of shrinkage and pore evolution during IMCD can explain more

accurately the physics of heat and mass transfer. In addition to this, the model can

manifest the characteristics of different parameters such as evaporation rate, capillary

diffusion, effective thermal conductivity, gas pressure successfully, which is not

possible by using simpler models. In addition to this, the results of above-mentioned


parameters can be utilised to answer particular inquiries in practical situations where

real time observation of these parameters is not possible. As this model is physics

based, which provides a deeper insight of heat and mass transfer over the course of

drying; eventually, it can be implemented for predicting energy requirement, quality

enhancement and process optimisation.


Chapter 7: Effect of Porosity on Food

Quality

Quality is the extent to which a product meets the needs of the consumer. It

includes sensory properties, psychological factors, and other characteristics such as

contributions to health and compatibility with lifestyle conditions (Bonazzi &

Vasseur., 1996; Bruhn, 1994). Several authorities have defined quality in various

ways, but the term appears to be associated with the degree of fitness for use or the

satisfaction derived from it by consumers (Rahman, 2005). Quality attributes can be

divided into two major categories: sensory and hidden.

The sensory characteristics of quality include colour, gloss, size, shape,

texture, consistency, flavour, and aroma, which consumers can evaluate

with their senses (Avila & Silva, 1999; Bruhn, 1994; Salunkhe et al., 1991)

. One of the most important sensory quality attributes is colour because it

measures the first impact of the product on consumer perceptions (Avila &

Silva, 1999; Bonazzi & Vasseur., 1996). Other important attributes to the

initial acceptance of food are appearance, flavour and texture.

Hidden quality attributes, which consumers cannot evaluate with their

senses are hidden characteristics, such as nutritive value and the presence

of harmful or toxic substances (Salunkhe et al., 1991) .

In addition to the preceding classification, Rahman (1999) proposed a

classification containing four major classes: (1) physical and physicochemical

properties, (2) kinetic properties, (3) sensory properties, and (4) health properties.

Quality attributes are presented in Figure 7.1.


Owing to the complex nature of food products and the wide range of

temperatures and moisture contents developed within the system, the quantitative

description of the relations between processing conditions and product quality has

proved difficult (Franzen et al., 1990). For example, the severity of processing also

results in higher nutritional loss and general poorer product quality. It is, therefore,

obvious that an optimum combination of processing time must be established to

obtain the desired food characteristics. In many cases, the right levels of various

processing parameters are needed to develop the appropriate flavour, texture, and

aroma.

However, the pore characteristics of biomaterials is a critical factor that affects

heat and mass transport in capillary-porous biomaterials (Krokida & Maroulis, 1999;

Luikov A.V., 1975), and quality attributes of food products. The influences of CD

and IMCD will be described in terms of pore characteristics of dried sample.

Rehydration capacity, microstructure, mechanical characteristics and optical

properties of finished product are described in the following sections.

Figure 7-1: Classification of food quality attributes

Chapter 7 | Food quality


7.1 REHYDRATION CAPACITY

It is indispensable for the porous dried biomaterials to rehydrate faster to obtain

the desired sensorial and textural properties. Therefore, rehydration is the process of

moistening a dry material. In most cases, dried foods are soaked in water before

cooking or consumption. Thus, rehydration is one of the most important qualities. In

practice, most of the changes that occur during drying are irreversible, and

rehydration cannot be considered simply as a process reversible to dehydration

(Lewicki et al., 1998). Different type of rehydration characteristics namely, weight

gain, the coefficient of rehydration, relative height and diameter, and the relationship

between volume gain and mass gain are compared for IMCD treated the product with

the convection dried product.

7.1.1 Weight gain

The characteristics of weight gain during rehydration of IMCD and CD treated

samples are presented in Figure 7.2. For both types of sample, absorption of water is

rapid in the beginning. A rapid moisture uptake is due to surface and capillary

suction. Porosity, capillaries and cavities near the surface, temperature, trapped air

bubbles, amorphous-crystalline state, soluble solids and pH of the soaking water are

the factor that affects the rehydration kinetics (Lewicki et al., 1998; Rahman M.S &

C.O., 1999; Weerts et al., 2003). However, porosity is found the dominating factor

affecting rehydration mechanisms (e.g.,. diffusion, capillary imbibition) of dried food

materials (Farkas & Singh, 1991; Karathanos et al., 1993; Marabi & Saguy, 2004).

In addition to this, the ability to reconstitute varies with drying conditions and

the same fresh materials might end up as an entirely different product. For example,

freeze-dried materials seem to have a higher and quicker rehydration ability, than air

and microwave dried products (Laurienzo et al., 2013; Oikonomopoulou & Krokida,

2013; Pei et al., 2014).


Figure 7-2: Weight gain of samples during rehydration

7.1.2 Coefficient of rehydration (COR)

The COR of IMCD and CD is presented in Figure 7.3 below. It is observed that

samples dried in IMCD condition had higher values of COR. COR of IMCD treated

was found 08.070.0 , whereas 18.063.0 was found for CD treated samples. The

higher value of COR for the IMCD treated implies that IMCD less irreversible

deformation than CD.

Furthermore, rehydration may be taken as a measure of the injury of the food

material caused by drying. Therefore, the rehydration capacity highly depends on the

nature of porosity, for example, low porosity leads to products with poor rehydration

0

0.5

1

1.5

2

2.5

3

3.5

0 100 200 300 400 500

Wei

gh

t g

ain

Time (min)

IMCD

Convection

Figure 7-3: COR of IMCD and CD treated apple samples.



capabilities (Mayor & Sereno, 2004; Mcminn & Magee, 1976). Marabi and Saguy

(2004) investigated the effect of porosity ranging between 0.13-0.90 on rehydration

of dried carrots and found faster rehydration kinetics for the samples with higher

porosity. This is due to the irreversible collapse phenomenon following the loss of

turgidity during drying.

7.1.3 Relative height and diameter

Relative diameter and height of the sample during rehydration with time are

presented in Figure 7.4 and Figure 7.5. At the initial stage of rehydration, water

enters through the open pores. During further rehydration, solid matrix (cell walls)

absorb water and the material swells (Witrowa-Rajchert & Lewicki, 2006). Due to

less resistance of penetration of water is observed for the IMCD treated apple

sample. This may be due to less or no case hardening is happening during IMCD

drying.

Unlikely the relative diameter, IMCD shows less relative height gain than the

CD treated sample. This may be due to the higher amount of water swallowed by the

thick crust on the exposed surface.

In addition of this, the height of the apple slice obtained from convection

drying increased quickly and afterwards a sudden collapse of the structure was

detected. The collapse occurred in the CD treated sample at different times and

appeared to be an explicit characteristic of the convection dried samples. Most

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

0 100 200 300 400 500

Rel

ati

ve

dia

met

er

Time (min.)

IMCD

Convection

Figure 7-4: Relative diameter of apple sample during rehydration


probably, it is the manifestation of uneven structural modification during convection

drying of the apple samples.

7.1.4 Relationship between relative mass increase and relative volume increase

Both IMCD and CD treated apple samples are porous and therefore, their mass

gains were greater than the volume increase. However, the speed of volume gaining

depends on pore characteristics of the dried samples. For example, initially, volume

gaining for the convective dried sample is much faster than that for the IMCD treated

sample, as shown in Figure 7.6.

Figure 7-6: Relationship between relative volume change and relative mass change

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

0 100 200 300 400 500

Rel

ati

ve

hei

gh

t

Time (min.)

IMCD

Convection

Figure 7-5: Relative height of apple sample during rehydration



As water penetrates first to the material through the thick crust in the case of

convective dried sample then that resulting swelling of solid matrix (Witrowa-

Rajchert & Lewicki, 2006).

On the other hand, slow volume gain is anticipated for the IMCD treated

sample at the initial stage. For IMCD treated sample, water penetrated first into open

pores that did not evoke an equivalent amount of volume gain.

In brief, the volume change over the period of rehydration predominantly

depends on the porosity and relaxation of the shrinkage stress of the dried plant

tissue (Witrowa-Rajchert & Lewicki, 2006). For this reason, dried food with higher

porosity gain less in its volume as the rehydrated water fills the pores significantly.

On the other hand, in the case of dried product with low porosity, rehydrated water

penetrating into the solid matrix and leads to swelling; consequently the volume of

the rehydrated sample increases profoundly.

7.2 MICROSTRUCTURAL CHANGES DURING DRYING

In most of the cases, food materials are complex in terms of physical

characteristics. Most of the food materials subjected to a drying process can be

treated as hygroscopic porous amorphous media with the multiphase transport of heat

and mass. Chemical composition and physical structure of food materials influence

both heat and mass transfer mechanisms (Rosselló, 1992). Since the correlations

between physical and microstructural changes could help identify optimum drying

conditions, several studies have been conducted to investigate such relationships in

various food products (Achanta & Martin, 1996; Askari et al., 2009; Gumeta-Chavez

et al., 2011; Riva et al., 2005; Yang et al., 2010).

Due to concurrent heat and mass transfer, complex microstructural changes

take place in the sample. Food properties, drying methods, and their conditions

influence the microstructural changes of the final dried product (Joardder et al.,

2015b). Even the same type of raw materials demonstrates different microstructural

changes and pore characteristics depending upon the drying method and conditions

(Joardder et al., 2013c; Sablani et al., 2007). Therefore, microstructural change is

directly dependent on initial water content, temperature, pressure, relative humidity,

air velocity, electromagnetic radiation, food sample size, composition and initial


microstructure and the viscoelastic properties of the biomaterial (Joardder et al.,

2013b; Krokida et al., 1997; Saravacos, 1967).

There are a number of studies that deal with the microstructural changes during

the conventional drying process. However, researchers have not studied

microstructural changes and pore formation during microwave and IMCD drying.

In this section, the effect of temperature distribution on microstructure and

porosity of the food material is investigated. Microstructural changes during

convective, microwave and IMCD drying are discussed in great detail. In addition to

this, case hardening, crust formation, hot spot and nano-pore formation are also

discussed.

7.2.1 Microstructure of exposed surface

In hot air drying of fruits and vegetables, in general, the tissue is featured by an

extensive shrinkage and microstructural changes, such as fruit ‘softening’ or loss of

‘firmness’ as shown in Figure 7.7 (Aguilera & Chiralt, 2003; Bolin & Huxsoll,

1987).

In addition to this, the evaporation rate is higher in microwave drying, and it

has a substantial effect on the pore formation during drying. In particular, over the

Figure 7-7: Exposed surface porosity in different type of drying



time of drying under microwave energy, higher microwave power leads to increased

evaporation rate; consequently, a more porous structure developed in comparison

with drying with lower microwave drying. Therefore, quick evaporation of water

retains the porous structure and causes less collapse of the solid matrix.

Due to thermal exposure of the cells of the surface of the sample, there is a

significant amount of collapse. Figure 7.8 shows a digital and microstructural image

of dried sample achieved from AD and MCD. It is clear from the figure that there is

little evidence of porosity present on the surface mainly due to case hardening.

On the other hand, avoidance of case-hardening can be achieved by balancing

the energy flow to the surface and volumetric heating. Application of microwave

develops a higher driving force for moisture flow by increasing vapour pressure

difference between the interior and surface of food materials. Sometimes, it may

cause puffing within the sample but eventually this increase of vapour pressure

enhances the porosity of the plant-based food materials (Therdthai & Visalrakkij,

2012).

CMD causes overheating those results in the burn of the solid materials as

shown in Figure 7.8. When the food materials get exposed to microwaves resulting

local overheating as the warmer areas are better able to absorb further energy than

Figure 7-8 : Microstructural change of apple slice during convective drying (left) microwave

(right) (40X magnification in SEM image)


the colder areas. It may be due to lower heat exchange rate between the hot spots and

the rest of the material. Similarly, due to the non-uniform higher temperature inside

the sample, rapid phase change happens.

Compared to convective drying, IMCD provides better product quality as

shown in Figure 7.9. Since the least efficient part of the conventional drying system

is near the end of drying. Therefore, incorporation of microwave energy would be

optimised if it is used to remove the last one-third of the moisture content (Joardder

et al., 2015b).

It can be claimed that the use of microwave energy in the early stage of drying

may result in cellular collapse and bulk shrinkage in the final products (Al-Duri,

1992) (Zhang et al., 2006).

From Figure 7.9, it is clear that the structural quality of IMCD finished product

is far better than convective, and continuous microwave dried product. Case

hardening is minimal, and the cells of the surface are not completely collapsed.

Therefore, a vast number of unbroken cells are present on the surface of the sample.

In the same way, the sample shape remains almost as round as it was initial. All of

these positive outcomes relate to uniform temperature distribution and the small

temperature gradient between the surroundings and the entire sample.

Figure 7-9: Microstructural change of apple slice during IMCD drying (40X

magnification in SEM image)



Figure 7-10: Open porosity of dried product achieved from different drying conditions

Furthermore, intermittency in microwave application combined with other

drying methods in many cases causes a uniform porosity throughout the sample, due

to uniform distribution-redistribution of moisture and temperature(Gunasekaran,

1999; Joardder et al., 2013b). Consequently, higher open pores are found for IMCD

treated dried food as presented in Figure 7.10.

7.2.2 Case hardening

SEM image of exposed and internal (sliced from top) surfaces have been

presented in Figure 7.11.

Figure 7-11: Case hardening and internal pores in convective dried apple slice (40X magnification

in SEM image)


In the entire exposed surface of convection dried sample, the presence of the

case hardening is evident. However, as shown in Figure 7.11, the internal cells do not

get damaged as much as happened to the cells of the surface.

From the figure, it is also clearly noticeable that some cells inside the food

remain unbroken and the inside is more porous than the surface. Moreover, the case

hardening occurred not only on the top surface but also on other exposed surface

(e.g. sides of the sample) for the convective dried sample. This case hardening

hinders the heat and mass transfer by acting as an insulator to these processes. This

may be one of the reasons why the convection drying takes longer time than IMCD

(Karathanos et al., 1996b). Image analysis provided the crust thickness of dried apple

tissue for CD and IMCD treated samples as presented in Table 7.1.

Table 7-1: Crust thickness of the IMCD and CD treated samples

Drying conditions Crust thickness (mm)

Convective drying 50-70 0C 0.86± 0.24

IMCD 600

C and 100W 0.46± 0.27

As can be seen from Table 7.1, the CD treated sample has significantly thicker

crust than the sample treated in IMCD.

7.2.3 Cell wall Nano-pores

In CMD, the higher driving kinetics causes water to migrate in such a way that

it develops numerous tiny pores, as shown in Figure 7.12, which is not observed in

air-dried samples.

Figure 7-12: Development of nano-pores during CMD, convective drying and IMCD



Moreover, microwave oven dried apple slice contains many tiny pores that are

completely absent in the hot air dried sample. In microwave drying, internal

volumetric heating drives moisture through the intracellular pathway. Consequently

many small pores are developed on the cell membranes that are absent in the case of

hot air convective drying. This type of small pores is significantly influenced by both

moisture and temperature distribution. Whereas, at low microwave power, the cell

structure is found intact due to weakly induced force (Khraisheh et al., 2004).Similar

to CMD, nano-pores prevail in the IMCD treated sample, however, it has less

diameter than CMD treated samples. For microwave, the nano-pore rage is 365-1239

nm and IMCD cell walls having nano-pores ranging between 201-580 nm.

7.2.4 Effect of microwave power on microstructure

SEM images of dried apple samples obtained for three different microwave

powers are presented in Figure 7.13.

From the figure, it is clear that both number and size of tiny pores increase with

the increase of power of microwave. This difference may be caused by higher mass

flow rate with higher temperature from the cells.

Figure 7-13: Effect of microwave power on microstructure and porosity

Apart from this, multiple tiny pores could be combined during the time of

microwave heating. Therefore, microwave power should be taken into considering

carefully achieving proper porosity in the samples.


7.2.5 Internal pores

Internal pores are arranged differently than external pores. In Figure 7.14, SEM

images of dried product from all of the selected three drying are presented. From the

figure, it is obvious that different drying conditions influence the internal structure of

the food as they do on the exposed surfaces. Sever uneven collapse and puffing is

observed in the MW dried food. This may be caused by significant uneven heat and

mass transfer during continuous microwave drying. On the other hand, there are both

collapsed and non-collapsed cells within the convective dried product. Whereas,

dried product achieved from IMCD possesses uniform pores throughout the sample.

Overall, the internal pore formation is closely dependent on the pattern of

temperature and moisture distribution (Joardder et al., 2013b).

In a nutshell, the spatial distribution of temperature and moisture is the most

substantial issue that influences the structural modification of the sample undergoing

simultaneous heat and mass transfer. In the light of these findings, the microstructure

produced during convective drying is severely collapsed; in particular, on the outer

surfaces, as it is exposed to the hot air for a longer period. On the other hand,

microwave heating reduces drying time with resulting uneven hot and cold zones

within the food sample. Consequently, the unexpected microstructure is produced

during CMD. Unlike convective and CMD, IMCD drying produces a relatively better

microstructure with higher porosity. Taken together, choosing proper intermittency

of microwave and temperature distribution, desired changes of microstructure and

Figure 7-14: Internal pores in dried apple slice



porosity can be obtained for dried food samples. The current study thus clearly

establishes the role of temperature distribution and redistribution on microstructure

and porosity over the time of drying.

7.3 MECHANICAL PROPERTIES OF DRIED FOODS

Mechanical properties of food materials, in particular, cellular food materials

are determined by the cell wall composition and solid matrix architecture. Among the

mechanical properties, stiffness, hardness and strength of food can be correlated with

the porosity, and other characteristics of pores (Bhatnagar & Hanna, 1997; Gogoi et

al., 2000; Ross et al., 2002). The variation in porosity, average pore size, pore size

distribution, and specific surface area also have significant effects on the mechanical,

textural, and other quality characteristics of dried foods. In general, porosity allows

the fluid to flow from the food under the compression during consumption, thus

influencing the mechanical properties of the dried food (Ralfs, 2002).

Vincent (1989) pointed out that torsional stiffness (0.5-7 MPa ) changed with

the variation of porosity (0.84-0.54 ) in the case of fresh apple. It was also found that

stiffness maintained a linear relation when it was plotted as a dependent of 𝜀0

23⁄.

However, prediction of mechanical properties by considering porosity is complicated

and uncertain due to morphological anisotropy of food materials.

In addition to these, the hardness of the sample is strongly affected by pore

characteristics. Results from several sources have identified that increased pore size

decreases the hardness of the dried sample (Liu & Scanlon, 2003; Therdthai &

Visalrakkij, 2012). Furthermore, the softness of the dried tissue is attributable to the

portion where the larger pores exist. It seems possible that tissue with larger and

higher pores have a solid matrix of lower strength; consequently, it can be easily

broken.

Biological materials, especially plant tissue, encompass very complex natures

due to their anisotropy, porous, hygroscope attributes. Fresh apple has a large amount

of intercellular space which contains 22-38% air spaces of total tissue volume. In

other words, fresh apple flesh is intensely porous with initial porosity 0.22-0.38

(Lewicki & Pawlak 2003). Amongst different types of apples, Granny Smith is one

of the higher initial porous materials (0.33), due to larger cell dimension and thinner

cell wall thickness. Larger cells in plant tissue generally are found more loosely


packed than smaller cells. Despite having almost same moisture content 0.86 g/g

sample and 0.87 g/g of a sample for Granny Smith and Red Delicious respectively)

and density (789 kg/m3

and 766 kg/m3

for Granny Smith and Red Delicious

respectively), Granny Smith and Red Delicious apples show different drying rates.

Moreover, literature has confirmed the role of mechanical properties of plant-based

food with flavour, bio-availability of nutrients and textural perceptions (Ormerod et

al., 2004) .

Plant cell membrane and wall are semi-permeable and regarded as the

components that affect the transfer of water to and from parenchyma cells (Fanta et

al., 2012; Qi et al., 1999). Determination of moisture content in fruits and vegetables

is still a complex task as they contain both free and bound water. Determination of

the separate types of water is even more critical than the estimation of total water.

The drying rate of the later falling rate period is much too slow as the internal mass

transfer resistance increases due to water being transported through a thicker layer of

the dry solid matrix (Aversa et al., 2011).The literature shows in order to remove last

10% of water from food material it takes almost the same time that is required to

remove the first 90% of water content. In another word, bound water migration from

food materials during drying takes more time and energy to migrate from food

material. In plant tissue, water is distributed in intercellular, intracellular and cell

wall (Joardder et al., 2013a). Out of the total water, more than 90% water is

intracellular and cell wall water (Halder et al., 2011a).

Therefore, the macroscopic structural behaviour depends on turgor pressure,

cell wall properties and cell size (Aguilera & Lillford, 2007; Alamar et al., 2008;

Rojas et al., 2002). Generally, the cell wall of plants encompasses about 60% water,

2-8% pectin substances, 5-15% hemicellulose, 10-15 % cellulose, 1-2 % protein, 0.5-

3% lipids (Bach Knudsen, 2001). This proportion varies due to a variety of factors

such as environmental conditions, stage of maturity, processing after harvest, and

botanical origin of the plant(Eastwood, 1992) Determining the size and shape of the

cell is one of the most important functions of the cell walls in plant tissue.

Therefore, knowledge of the exact amount of bound water in the cell wall of

fruits and vegetable tissue is crucial for realistic modelling of heat and mass transfer



as well as more efficient drying system (Joardder et al., 2013e). However, there is an

insufficient study in order to determine cell wall bound water.

In addition to bound water, the stiffness of the cell wall is essential to correlate

the deformation (shrinkage/ expansion) during drying. The compression test provides

the mechanical response of the plant tissue (Sirisomboon & Pornchaloempong 2011).

As stiffness is one of the structural properties of the tissue and can be derived from

the material properties and shape of the sample. In addition to stiffness, Poisson’s

ratio and Young’s modulus are important apparent elastic properties of biomaterials

for the anticipation of load-deformation behaviour of those materials. These elastic

properties can be used in order to compare the relative strength of different plant

tissues (Kiani Deh Kiani et al., 2011).

Before comparing the mechanical properties of IMCD and CD treated apple

slice, a brief discussion of the overall mechanical response of apple slice is presented

in the following sections. Moreover, these sections would give more insight of the

mechanism of shrinkage and pore formation during drying.

7.3.1 Cell Stiffness and Drying Rate

The result, as shown in Figure 7.15, in order to achieve the same amount of

compressive deformation, Granny Smith requires less energy than Red Delicious

apple. As Red Delicious apple tissue is stiffer (23.03kN/m) than Granny Smith apple

(21.8kN/m). The average Young modulus is also higher for Red Delicious

(3.10MPa), while Granny Smith shows Young modulus 2.81MPa. It was found that

the value of Poisson’s ratio is 0.169-0.344 for Granny Smith (Grotte, 2002) and

0.155-0.25 for Red Delicious apples (Chappell & Hamann, 1968). Overall, the cell

wall stiffness presumed higher in Red Delicious as its tissue is stiffer than Granny

Smith. Consequently, this higher stiffness affects the rate of moisture migration from

the cell of apple flesh.


There is a significant similarity between compressive test and drying process. The

result, as shown in Figure 7.16, indicate that moisture migration rate is higher for

Granny Smith compared to Red Delicious. This result confirmed that in order to

remove the same amount of water Red Delicious apple took more heat energy than

Granny Smith.

Therefore, a positive relationship found between water migration by mechanical and

thermal energy as demonstrated by the similar trends. Interestingly, this correlation

can explain the nature of the cell wall stiffness that facilitate or hinders the water

migration in mechanical and thermal energy application.

Figure 7-15: Compressive extension characteristics of apples

Figure 7-16: Weight loss of apple slice in convective drying at 700 C



7.3.2 Cell Dimension and Porosity

Cell dimension influenced the rigidity of cell wall and tissue of plant materials.

Higher cell dimension caused loose packing of cells. Consequently, density, rigidity,

intercellular spaces were affected significantly. The microstructures of fresh and

dried Granny Smith and Red Delicious apples are presented in Figure 7.17.

Figure 7-17: Microstructure of fresh and dried apple samples (500x)

The results obtained from microstructure analysis of samples shows that

Granny Smith encompasses larger cells than Red Delicious, as shown in Figure 7.17.

This consistent with the previous literature which provides a high initial porosity of

Granny Smith is 0.33 (Vincent, 1989). It was also found from the pycnometer data

that dried Granny Smith apple comprises of higher porosity due to larger cell

dimension and loose packing of cells.

7.3.3 Stiffness variation with load variation

Due to porous and anisotropy nature, apple tissue shows variable stiffness in

response to the different speed of load. Figure 7.18 shows the variation of the

stiffness of apple slice with the speed of load.


It is clear from Figure 7.18 that the sample encountering a higher speed of load

showed higher stiffness. This trend of the stiffness of apple tissue can be expected for

different drying rate of the sample as will be discussed in Section 7.3.6.

7.3.4 Comparison of mechanical properties of IMCD treated and dried

connective sample

Stress and strain

Figure 7.19 shows strain- stress curves for the samples treated with IMCD and

CD with moisture content 2.6 (kg/kg d.b.). From the figure, it is obvious that the

sample dried in CD requires more stress to get the same amount of strain in IMCD

treated sample. This may be due to case hardening phenomenon that occurs during

convection drying.

Figure 7-19: Strain-stress curves of apple tissue at moisture content 2.6 (db) in IMCD and CD

Figure 7-18: Effect of speed of load on stiffness of the apple tissue



Modulus of elasticity

Figure 7.20 shows the Young’s modulus E with a moisture content of apple

slice. The following nonlinear equations were fitted for CD and IMCD treated

samples through regression analysis.

For convection dried samples, the relationship between Young modulus and

moisture content is presented in Equation 7.1.

]99.0[55027104876973582888337.2739 2234 RMMMME (7.1)

On the other hand, the relationship between Young modulus and moisture content for

IMCD treated sample is presented in Equation 7.2.

]99.0[55027104876973582888337.2739 2234 RMMMME (7.2)

For both cases, E decreased with a decrease in moisture content. However, is

start increasing once the sample reached to glassy phase with very low moisture

content. In Figure 7.20 there is a clear trend of increasing discrepancy between CD

and IMCD treated samples with decreasing moisture content. This increasing trend

is caused due to the formation of crust for CD treated samples.

Poisson's ratio

Parenchyma tissue of apple shows wide-ranging anisotropy nature meaning

cells have a non-equal diameter in all dimensions (Khan & Vincent, 1990). In

0

20000

40000

60000

80000

100000

120000

140000

160000

0 1 2 3 4 5 6

Yo

un

g M

od

ulu

s (P

a)

Moisture content (g water/ g solid)

IMCD

CD

Figure 7-20: Variation of Young Modulus with moisture content for IMCD and CD-

treated apple slice


addition to this, high initial porosity adds more complexity to achieving consistent

material properties of apple tissue and shows a wide range of Poisson’s ratio: 0.15-

0.34 (as discussed in Section 2.3.2, page 22).

An attempt was made to find out Poisson’s ratio at different moisture contents

after IMCD and convection drying of the samples. However, a wide range (0.2-0.4)

of porosity was found during IMCD and CD. These may be caused due to non-

uniform moisture migration causing both shrinkage and porosity within apple tissue

depending upon cell collapse and shrinkage.

Macroscopic structural behaviour depends on turgor pressure, cell wall

properties and cell size (Aguilera & Lillford, 2007; Alamar et al., 2008; Rojas et al.,

2002). Among these, cell wall components are the key structural components of

plants tissue as the mechanical properties of tissue depends on the cell wall

properties (Joardder et al., 2014b; Vincent 2008). Therefore, associations between

macroscopic structural behaviours, moisture content and porosity demands further

extensive research.

7.4 APPEARANCE OF DRIED FOOD

As much as closer the appearance of dried food to fresh food attracts consumer

attention (Oikonomopoulou & Krokida, 2013). Appearance is expressed by the

colour of food, shape and texture. In the following sections, change of shape and

colour are presented.

7.4.1 Change of shape

Shrinkage and change of shape, in most cases, cause a negative impression of

the customer (Mayor & Sereno, 2004).

Figure 7-21: Change of roundness during CD and IMCD



Figure 7.21 shows the changes of shape in terms of roundness of the sample. It

is apparent from the figure that convection drying causes more shape changes than

IMCD. As process parameters are the key dominators of the shape changes of food

material over the period of drying, shape changes differ during IMCD and

convection drying. In addition, uniform heat and mass transfer ensure uniform shape

change whereas case hardening restricts uniform deformation of the sample.

7.4.2 Change of colour

The colour of food material is changed over the time of drying. (Grabowski et al.,

2002; Hansmann & Joubert, 1998; Reyes et al., 2002). Figure 7.22 presents the hue

angle of fresh; IMCD treated and Convection dried sample. It is clearly seen from the

figure that convection drying causes more colour degradation than IMCD in the

sample with same moisture content. As both optical and browning characteristics

determine colour which depends on sample structure, and chemical reaction period

pattern. In the case of convective dried product, longer drying time and collapsed

surface causes more colour degradation.

Figure 7-22: Colour change over the time of drying

The prime cause of colour change during drying is the browning reaction due

to simultaneous heat and mass transfer (Fu et al., 2007). The kinetics of colour

change is notably affected by the structure of food tissue. Loss of cellular turgor

pressure leads to a change of porosity. Subsequently, it may increase the effective

0

20

40

60

Fresh IMCD CD

Hu

e an

gle

Drying condition


release of different chemical reacting agents; accelerating Maillard reaction resulting

higher browning rates (Acevedo et al., 2008).

In addition to this, the appearance of food materials directly depends on several

factors including the ability of food material to scatter, absorb, transmit and reflect of

visible light (Wyszecki & Stiles, 2000). Therefore, modifications of light reflectance

ability of food surface due to the evolution of porosity and changes of surface texture

must also be taken into consideration (Fornal, 1998; Lewicki & Duszczyk, 1998;

Lewicki & Pawlak 2003). Moreover, altered structure in the course of drying may

also influence the dispersion of photons on the surface resulting in changing the

degree of scattering (Romano et al., 2012).

However, a comprehensive investigation on the relationship of degree of

porosity and colour change during different drying methods would enhance the

understanding of colour change kinetics over the course of drying.

Considering overall customer satisfaction at first glance, colour and shape are

the most important factors that are needed to be taken into consideration.

Maintaining the proper degree of porosity can secure the appealing nature of dried

food materials.

7.5 ASSOCIATIONS AMONG DRYING CONDITIONS, PORE

CHARACTERISTICS AND FOOD QUALITY

Pore formation is one of the important structural changes that take place over

the course of drying. The degree of porosity depends both on the properties of the

food materials as well as drying process conditions. On the other hand, pore

characteristics affect heat and mass transfer mechanisms significantly. In addition,

the degree of porosity of food materials notably influences the nutritional, sensorial,

mechanical, and chemical quality of dried food products. An extensive review of the

literature in relation to porosity reveals that relationships among process parameters,

food qualities, and sample properties can be established. At the end of this section,

hypothesised relationships among process parameters, product quality attributes, and

porosity is discussed in detail.



7.5.1 Process parameters and quality correlations

Food preservation focuses on the stability of food materials in terms of its

physical, chemical, microbial, and nutritional aspects. Among preservation

techniques, drying provides a high level of stability. However, the consequence of

the simultaneous heat and mass transfer is damage to the food material tissue.

Sometimes these consequences result in consumer dissatisfaction. Porosity denotes

the level of physical modification with respect to the initial structure of food

materials. Knowledge of pore formation and evolution of food materials during

drying is fundamental for the design and development of efficient drying process

(Oikonomopoulou & Krokida, 2013). However, much uncertainty still exists about

the relation between drying process conditions and product quality. An

understanding of the interrelationship between the process conditions and dried

product quality will yield the following benefits with respect to the drying of food

materials:

Generic drying models: Most prediction models available in the literature

deal with a particular type of drying method. Even slight changes in

process parameters and material substantially alter the predicted result of a

model. Therefore, any theoretical model based on the interrelationship

between process parameters and product quality may lead to the

development of a generic model.

Maintaining optimal drying conditions: Various changes such as

shrinkage, porosity, and colour modification occur over the course of

drying; however, the rate of such changes is not uniform throughout the

drying process. On the other hand, moisture content and the kinetics of

heat and mass transfer directly influence the rate of quality change.

Therefore, success in establishing a relationship between the process

parameters and quality may pave the way toward optimising drying

conditions. The real-time analysis of food material qualities over the

course of drying and controlling the process parameters accordingly would

yield an effective drying system with an excellent quality of dried foods.

This would also improve energy efficiency and lead to a sustainable drying

system.


7.5.2 Hypothesised relationships among process parameters, pore

characteristics, and food quality

In light of this study, several factors involved in the drying process have been

shown to affect the pore formation and evolution throughout the drying process. The

intensity of these factors significantly affects the porosity and controlling these to

appropriate levels can result in the optimum degree of porosity.

Some factors cause an increase in porosity with an increase in their intensity, as

shown in Figure 7.23. These include sample shape, temperature, the mobility of the

solid, and the coating treatment. On the other hand, the porosity decreases with

increases in certain parameters, such as pressure in the drying system, and the drying

rate. However, in both cases, exceptions sometimes arise which are reported in the

literature. If these factors are regulated through the choice of the appropriate drying

process, then the porosity of the dried food can be controlled.

Just as different factors affect porosity, porosity exerts a considerable influence

on dried food quality. Based on findings of this study and as reported in the

literature, it can be hypothesised, as demonstrated in Figure 7.23, that pore

characteristics can be the bridging factor between drying parameters and dried food

quality.

Figure 7-23: Different factors that influence porosity during drying of food materials



In other words, by controlling the process parameters, an expected degree of

porosity can be achieved while confirming the level of porosity would determine the

anticipated quality of dried food. Accordingly, predicted quality attributes can be

managed by maintaining porosity within the dried food by controlling the process

parameters.

Since porosity influences water transport to a considerable degree, food quality

is significantly affected by the level of porosity. Therefore, successful establishment

of such interrelationships could confer the following benefits:

Real- time control of quality: The quality of dried food material strongly

depends on the various processing parameters. In addition to this, the

quality of food materials varies with the variations in the different

parameters of the drying process. Numerous interrelationships exist

between process parameters and quality attributes. Therefore, it becomes

almost impossible to monitor the process parameters as to control of all of

the quality attributes. Measurement of instantaneous porosity can be one

Figure 7-24: Hypothesised relationships between the drying parameters, pore formation and

evolution, and dried food qualities


route of controlling process parameters to manipulate the quality of dried

food materials.

Drying kinetics optimisation: Since porosity significantly affects

moisture transport, its real-time evaluation is essential for optimisation of

drying and quality control.

Energy optimisation: Quality optimisation demands moderate processing

conditions that lead to higher processing times. On the other hand,

increasing the efficiency of the process generally results in lower product

quality (Mahn et al., 2011). These conflicting and opposing influences of

the productivity of industrial operations and the final product quality can

be balanced to produce optimum energy application (Holdsworth, 1985).

Controlling the expected porosity can serve as the means for achieving the

optimum energy supply because porosity significantly influences the rate

of moisture transport and volume reduction.

Effective preservation system: Knowledge of the interrelationship

between structure and quality can be application to the design of better

storage and packaging systems.

In summary, if the correlations between the process parameters can be

developed in the function of pore characteristics, both an effective food processing

system and finished food with better quality would be achieved.

7.6 CONCLUSION

The intermittency of microwaves can provide a better option to control the

product temperature and finally improve the food quality than food processed by

MCD and CD. The IMCD treated samples showed higher moisture absorption than

the CD treated samples. The higher capacity for the IMCD treated sample implies

that IMCD causes less irreversible deformation than CD.

Uniform internal and external microstructure was observed in IMCD treated

samples due to the well-distributed moisture and temperature. A lesser amount of

case hardening was observed in the IMCD treated food sample due to faster and

better-distributed evaporation of water vapour.



Nanopores are developed on the cell wall due to the high rate of evaporation

which was caused by microwave heating. This is the first time an observation of

nanopores was conducted.

Drying conditions alter the mechanical properties of food materials during

drying. This change of mechanical properties should be taken into consideration

during modelling of deformation during drying to achieve real stress-strain

characteristics of the food sample.

Process parameters and structural changes significantly affect the variation of

colour and shape of the product. IMCD treated sample was more appealing that

convection dried sample.

Just as different factors affect porosity, porosity exerts a considerable influence

on dried food quality. Based on findings of this study and reported in the literature, it

can be hypothesised, that pore characteristics can be the bridging factor between

drying parameters and dried food quality. By controlling the process parameters, an

expected degree of porosity can be achieved while confirming the level of porosity

would determine the anticipated quality of dried food. Accordingly, predicted quality

attributes can be managed by maintaining porosity within the dried food by

controlling the process parameters.

Chapter 8 | Conclusions


Chapter 8: Conclusions

8.1 OVERALL SUMMARY

IMCD is an advanced drying technique that can provide a better quality food

using less energy than other conventional drying techniques. To properly understand

this drying technique, mathematical model development is essential. In particular,

physics-based insights of heat and mass transfer and structural modification are the

key factors for a better understanding of the drying process and optimisation.

The primary aim of this study is to establish a physics-based prediction of pore

formation and evolution and develop a comprehensive mathematical model of

transport of heat and mass transfer, and structural deformation of food materials

during IMCD drying. The outcome of this research and related innovations has led to

the publication of one book and 10 peer-reviewed (Q1) journal papers.

The study was initiated with a single-phase convection drying model to

identify the best way to predict porosity while drying (Chapter 4). The model was

validated by experimental data. Then the model was used to develop an IMCD

model, which calculates the microwave power generation using Lambert’s Law

(Chapter 4). The IMCD model was also validated with experimental data and then

was used to investigate the temperature redistribution during IMCD. However, these

models (discussed in Chapter 4 and 5) were single phase and considered an overall

moisture flux by a diffusivity effective term obtained from the experiments. In

Chapter 6, two multiphase porous media models namely, IMCD1 and IMCD2 were

developed to investigate how shrinkage and pore evolution affects the transport of

mass and energy within the porous media samples.

Chapter 4 presents a single-phase model and looks at how porosity varies over

the course of convection drying. Chapter 5 and Chapter 6 present the gradual

development of IMCD models along with pore formation prediction. The thesis

progresses from the simple diffusion-based models (Chapter 4 and 5) to multiphase

porous, deformable media model for IMCD (Chapter 6).The effects of IMCD drying

on food quality have been presented in Chapter 7. Finally, the conclusion (Chapter 8)


gives a brief summary and critique of the findings and includes a discussion of the

implication of the findings for future research into this area.

The overall outcome of the thesis was the better understanding of the heat and

mass transfer involved in IMCD including temperature redistribution, and moisture

and vapour fluxes due to different mechanisms. The final multiphase porous media

model for IMCD which consider shrinkage and pore formation during drying has

successfully fulfilled the main aim of this research. The modelling enhances the

understanding of IMCD and will help to optimise the process for better energy

efficiency and product quality.

The section below (Section 8.2) presents the main conclusions arising from this

study.

8.2 CONCLUSIONS

The primary objective of this study is to investigate pore formation and

evolution in order to understand the mechanisms involved in the heat and mass

transfer process during IMCD. We have done this by means of a comprehensive

mathematical model as well as by establishing its correlation with quality attributes

of dried food. The models developed were validated by experimental investigation.

The major conclusions are:

Prediction of porosity as a function of process parameters and sample

properties can represent a more realistic deformation while drying

(Chapter 4).

An interesting observation to emerge from the single-phase convective

drying model was the prediction of anisotropic shrinkage and case

hardening during convection drying. (Chapter 4)

Multiphase porous media models for IMCD showed that the higher fluxes

of vapour and water, due to gas pressure, make the IMCD faster (Chapter

6). This is a significant finding as these cannot be determined by the

single-phase model.



The lesser amount of case hardening was observed in IMCD treated food

sample due to faster and distributed evaporation of water vapour. (see

Chapter 7)

Nanopores are developed on the cell wall due to the high rate of

evaporation which was caused by microwave heating. This is the first time

an observation of nanopores was conducted (Chapter 7).

Drying conditions alter mechanical properties of food materials during

drying. This change of mechanical properties should be taken into

consideration during modelling of deformation while drying, so as to

achieve real stress-strain characteristics of the food sample (Chapter 7).

Just as different factors affect porosity, porosity exerts a considerable

influence on dried food quality. Based on findings of this study and

reported on literature, it can be hypothesised, that pore characteristics can

be the bridging factor between drying parameters and dried food quality

(Chapter 7).

The final multiphase IMCD model considering shrinkage and pore evolution

provides an in-depth understanding of the IMCD drying mechanism. After successful

simulation of the multiphase IMCD model, temperature distribution and

redistribution moisture distribution, evaporation, and fluxes due to different driving

forces, sample deformation has been demonstrated. These insights of transfer

mechanisms and sample deformation over the course of IMCD are essential to

understanding the effect of process conditions on drying kinetics, energy efficiency,

and product quality, and eventually to optimise the drying process.

8.3 CONTRIBUTION TO KNOWLEDGE AND SIGNIFICANCE

Fundamental physics-based mathematical models of IMCD and pore evolution

with relevant experimentations in this thesis offer some significant contributions to

knowledge. The significance and contribution of this research are listed below:

The considerations of the effective diffusion coefficient as a function of

moisture content and temperature has contributed some way towards

finding a more realistic process conditions and materials properties


dependent moisture diffusivity rather than assuming a constant effective

diffusivity. This makes the single phase model more realistic.

Consideration of process parameters and materials properties dependent

shrinkage, anisotropic nature of shrinkage has been demonstrated. This has

never been investigated before.

Prediction of porosity considering process parameters and sample

parameters has gone some way towards theoretical prediction of pore

formation and evolution.

Due to the flexible nature of the model parameters, the multiphase porous

media model considering shrinkage and porosity for heat and mass transfer

may be applied in different areas of the food process industry including

baking, frying, cooking and heating, and even in other field where

transport in porous media is involved including biological tissue, coal

drying, soil science, soil mechanics, etc.

The hypotheses related to correlations between drying conditions, pore

formation and dried food quality makes noteworthy contributions to the

understanding of the interrelationship between structure and quality and

can be applied to the design of better storage and packaging systems.

8.4 LIMITATIONS

Though this study developed advanced mathematical models for food drying

applications, the current study had several limitations.

Due to lack of time and appropriate experimental facilities, validations of

different fluxes during drying inside the product were not possible.

Due to the unavailability of the variation of capillary pressure during

drying of apple, the capillary flow was calculated using capillary pressure

rather than determining it as a function of moisture content.

In this study, all the water (intercellular and intracellular) is assumed to

have the same effective diffusivity which is not justified to some extent.



The shrinkage of the sample is determined from a shrinkage velocity

approach rather than obtaining it from solid mechanics due to inadequate

mechanical properties availability in the literature.

8.5 FUTURE DIRECTION

To overcome the above-mentioned limitations, the following suggestions and

recommendations are proposed:

Real time structural change and pore formation should be investigated in

order to achieve a realistic relationship of process parameters and

structural modifications.

Two types of water namely bound water and free water can be considered

separately in the model.

It would be interesting to compare a macro-scale model with a multi-scale

model which considers transfer mechanisms and structural deformation in

both macroscale and micro-scale.

A further study could assess instantaneous heat and mass transfer

coefficients by solving conjugate problems which simulate the airflow

inside the oven.

Future research should concentrate on the optimisation of the IMCD

process variable to achieve energy efficient drying system that provides

better-dried food.

Considerably more work will need to be done to determine initial air space

deformation characteristics in order to predict pore formation and

evolution more precisely.

A wider variation of process conditions and various food properties can be

considered in future research to develop a more realistic and generic model

for pore formation.

Therefore, researchers and scientists from different fields can incorporate their

knowledge and endeavour in order to establish a bridging relationship between

process conditions, food structure and product quality. To do so, a multiphase

multiscale porous material model needs to be developed where all of the

variables should be considered dynamic and theoretical.


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Appendices


Appendices

Appendix A

IMPLEMENTATION OF THE MODEL IN MATHEMATICAL INTERFACE

OF COMSOL

The mathematics interfaces were used to model heat and mass transfer for

solving as well as finding instantaneous value of some parameters that generally

show circular dependency. A coefficient form PDE, as given in the following

equation, was chosen to solve the equation and the coefficients were defined to

match with the formulated equations of the models.

fauuuuct

ud

t

ue aa

.)(

2

2

Where,

u is the independent variable,

ae is the mass coefficient,

ad is a damping coefficient or a mass coefficient,

c is the diffusion coefficient,

α is the conservative, flux convection coefficient,

β is the convection coefficient,

a is the absorption coefficient,

γ is the conservative flux source term and

f is the source term.

For example, the final equation for liquid water transport in the model is

evapwc

w

wrw

www RcDPkk

St

,. .


Therefore, to implement this equation in COMSOL the following settings were

used.

Description Value expression

Diffusion coefficient cD

Absorption coefficient wS

t

Source term evapR

Mass coefficient 0

Damping or mass coefficient wS

Conservative flux convection coefficient 0

Convection coefficient 0

Conservative flux source P

kk

w

wrw

w

,

Similar strategies were taken for vapour conservation and energy equations.

Appendices


Appendix B

THE CONVERSIONS OF MOISTURE CONTENT

The moisture content (dry basis), dbM , can be written as,

s

vwdb

ccM

1

Where, wc is the mass concentration of water (kg/m3), and vc is the mass

concentration of vapour (kg/m3).

The relationship between dry basis moisture content, dbM , and wet basis

moisture content, wbM , are shown by following equations,

db

dbwb

M

MM

1

wb

wbdb

M

MM

1


Appendix C

CELL WALL WATER ESTIMATION

An assumption is made that all of the cell wall water treated as physically

bound water due to their easy availability during drying and moisture removal

process. Measuring the cell wall thickness before and after drying can provide the

amount of water it holds. Some other assumptions of calculating cell wall water are

as follows:

1. Shape of cells is spherical, and consist hydraulic diameter. However, the ratio

of intracellular and cell wall water minimize the error of this assumption.

2. As most of the plant tissue shows heterogeneous nature of cell orientation and

content, average number of cell and intercellular space will be considered.

3. Density of cell wall water is same as the density of intracellular water.

4. Cell dimension varies within the plant tissue, average cell dimension has been

considered here.

Assuming that the difference of cell wall thickness represents the amount of

bound water. After calculating the volume difference of cell wall the following

equation can be used to achieve the bound water in the cell wall:

222

3

14 trtrtM cw (1)

Where, r and r1 are the radius of fresh and dried plant tissue cell (Figure 2), t is

the initial thickness and t 1 is the final thickness of cell wall. Shrinkage coefficient of

the cell wall thickness, t

t1

From the equation 1, it is clearly apparent that amount of cell water depends

directly on the cell wall thickness, cell dimension, and cell wall shrinkage

coefficient. Therefore, it is not enough to consider cell wall water only to represent

the amount water in food tissue rather ratio of intracellular and cell wall bound water

can provide more insight regarding the overall bound water present in plant tissue.

So, the ratio of intracellular and cell wall water can be obtained from the equation 2.

)33( 222

3

trtrt

tr

M

M

cw

iw

(2)

Appendices


Therefore, it is possible to obtain the quite accurate amount of bound water

from the microstructure of fresh and dried product.

Cell wall thickness analysis, presented in Table (below), shows that Red

Delicious has a thicker cell wall compared to the Granny Smith cell wall thickness

for 9.31±3.1 µm and 11.405±3.2 µm for Granny Smith and Red Delicious

respectively) in fresh state.

TableA-1: Cell wall thickness of fresh and dried apple

Granny Smith apple Red Delicious apple

Cell wall

thickness Cell wall

shrinkage

Coefficient

β

Ratio of

intracellular

and cell

wall water

Cell wall

shrinkage

Coefficient

β

Ratio of

intracellular

and cell wall

water Fresh

(µm)

Dried

(µm)

Fresh

(µm)

Dried

(µm)

Avg. 9.312 4.685 0.4969

4.2853

11.405 2.432 78.68

2.13 Min. 6.734 3.769 0.4403 7.678 1.65 78.51

Max. 11.785 6.281 0.4670 14.458 3.527 75.61

On the other hand, after drying the cell wall shrinks more (on average 78.68%

shrinkage) in Red Delicious compared to a Granny Smith (50% shrinkage). This

result indicates the presence of more bound water in Red Delicious within the cell

wall.

These findings of cell wall characteristics manifest the amount of bound water

in cell wall were higher in Red Delicious apple. This result might be the explanation

of why Red Delicious apples take more energy for compression and drying to certain

moisture content. It is relevant to compare this nature of the cell wall with the feature

of dietary fibre of apples. The ratio of insoluble and soluble dietary fibre in Red

Delicious is 4.37, whereas it is 3.21 for Granny Smith apple (Ferdous, 1997). This

implies that the cell wall of Red Delicious is highly dense with insoluble fibre. In

addition to this, it explains why more energy is required to remove the same amount

of water from Red Delicious apple.


Appendix D

ANISOTROPY NATURE OF APPLE TISSUE

The cells immediately underneath the surface are small and radially flattened.

Towards the interior, there is a gradual increase in cell size to a maximum diameter

of 20-300 µ.

As Figure A-1 shows, there is a significant difference of mechanical response

at a different section of the tissue. The tissue of the core of apple shows maximum

mechanical strength. However, the neighbouring tissue of the core has the minimum

strength, and an increasing trend of strength is found towards the peel of an apple.

As Figure 7.18 shows, there is a significant difference of mechanical response

at a different section of the tissue. The tissue of the core of apple shows maximum

mechanical strength. However, the neighbouring tissue of the core has the minimum

strength, and an increasing trend of strength is found towards the peel of an apple.

Figure A-1: Anisotropy nature of apple tissue

-1

0

1

2

3

4

5

6

7

0 0.2 0.4 0.6 0.8 1 1.2

Lo

ad

(N

)

Deformation (mm)

1

2

3

4

5

Appendices


Appendix E

SNAPSHOT OF SELECTED PUBLICATION

In this Appendix E, abstracts of the published the book, six selected journals

and two award winning conferences are presented. Please turn over to have a look

those snapshot of our selected publications.


Book: Porosity: Establishing the Relationship between Drying Parameters and

Dried Food Quality

Appendices


Journal 1:


M. U. H. Joardder; C. Kumar, R. J Brown, and M. A. Karim (2015) A micro-level

investigation of the solid displacement method for porosity determination of dried

food. Journal of Food Engineering, 166, 156–164 [I.F. 2.77]

Journal 2:

Appendices


M. U. H. Joardder, C. Kumar, and M. A. Karim (2015) Food Structure: Its

Formation and Relationships with Other Properties. Critical Reviews in Food Science

and Nutrition, (available online) [I.F. 5.55]

Journal 3:


M. U. H Joardder, R. J. Brown, C. Kumar, and M. A. Karim (2015) Effect of cell

wall properties on porosity and shrinkage of dried apple. International Journal of

Food Properties, 18(10), 2327-2337. [I.F. 0.92]

Journal 4:

Appendices


C. Kumar, M. A. Karim and M.U.H. Joardder (2014) Intermittent Drying of Food

Products: A Critical Review. Journal of Food Engineering, 121, 48–57 [Impact

Factor 2.77]

Outstanding paper award:


M. U. H. Joardder, M. A. Karim, and C. Kumar (2013) Effect of moisture and

temperature distribution on dried food Microstructure and Porosity. From Model

Foods to Food Models, the DREAM Project International Conference, 24– 26 June

2013, Nantes, France.

Appendices


Best paper award:


M. U. H. Joardder, M. A. Karim, C. Kumar, and R. J. Brown (2014) Effect of cell

wall properties on porosity and shrinkage during drying of Apple. 1st International

Conference on Food Properties (iCFP2014), Kuala Lumpur, Malaysia, January 24–

26, 2014.

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