Thesis_Master_RBRUNET_PG.pdf

8/21/2019 Thesis_Master_RBRUNET_PG.pdf

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Numerical simulation of fluid flow inabsorbent diapers, using FeFlow

Robert Brunet Sol

FINAL THESIS 309131Master in Chemical Engineering and Processes

Universitat Rovira i Virgili

Procter & Gamble

Schwalbach Technical CenterR&D Baby Care

Supervisor P&G: Mr. Rodrigo RosatiSupervisor URV: Prof. Laureano Jimenez

May-2009


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This thesis and all documents forming part thereof may contain

Procter&Gambleproprietary information and are to be treated as confidential.


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P&G Confidential- Restricted use 3

Firstof all, I would like to give my thanks and gratitude to my supervisor Rodrigo Rosati,for his advice, his support during the project, training me in physics and modeling concepts,

for providing me an opportunity to grow as a student and engineer in this incredible research

environment.

Also I am thankful to my section head Ana Montilla and my buddy Fernando Sierra for theirhelp and involvement in my project and for clarify specific problems. I would like to extend

this thanks to the people that I have meet here, the people of the department, the rest of R&D

scientist and the rest of the P&G employees that I had the pleasure to know. In general the

P&G company for providing me an opportunity to grow as a student and engineer in this

marvelous research group.

Moreover I would like to give my thanks for my family, mainly my father for his continuous

support in our decisions; he was always there to listen and to give advice. He taught me how

to ask questions and express my ideas. He showed me different ways to approach a problem

and the need to be persistent to accomplish any goal. He is an example to follow as an

engineer and as a father. I also I would like to extent to the rest of my life; my mother and my

two brothers, since they are the people whose I love more in this world.

Besides, I would like to thank my university for the education I have been given during these

last four years of studies. It has been essential to achieve the technical skills that are

necessary to become a good engineer.

Very special thanks go out to Dr. Laureano Jimnez, one of the best professors that I had in

my life, whose expertise, understanding, and patience, added considerably to my graduate

experience.

ACKNOWLEDGEMENTS


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TABLE OF CONTENTS

1 INTRODUCTION

1.1 Project description.

8

1.2 Literature overview... 9

2 BACKGROUND

2.1 The Procter & Gamble Company.... 11

2.2 Baby care (Pampers)........ 12

2.3 The disposable diaper....

12

2.3.1 Diaper history....... 12

2.3.2 Diaper composition.......... 14

2.3.2.1 Diaper Core...... 15

2.3.2.2 Diaper Chassis...... 16

2.4 Absorbent gelling material (AGM).............. 18

2.4.1 Structural characteristics...... 19

2.4.2 Swelling behavior.... 19

2.4.3 Gel blocking.... 20

2.5 Disposable diaper manufacturing process.. 21

2.5.1 Disposable diaper materials ........ 21

2.5.2 Nonwoven fabric manufacturing .....

21

2.5.3 The manufacturing process ..... 22

2.6 Disposable diaper sustainability...... 24

2.6.1 Introduction.. 24

2.6.2 Goal and scope. 24

2.6.2.1 Number of changes... 25

2.6.2.2 Disposable diapers 25

2.6.2.3 Reusable diapers... 26

2.6.3 Life cycle inventory. 26

2.6.3.1 Inventory data for disposable diapers... 26


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2.6.3.2 Inventory data for reusable diapers.. 27

2.6.4 Life cycle impact assessment 28

2.6.4.1 Disposable diapers 282.6.4.2 Reusable diapers... 28

2.6.5 Interpretation.... 29

2.7 How can start a new diaper factory?... 30

2.7.1 How much capital is required?.....................................................

30

2.7.2 How many people would needed to be hire?............................... 302.7.3 What should be the size of the building?..................................... 31

2.7.4 Where can be purchased diaper raw materials?........................... 32

3 FUNDAMENTALS OF FLUID FLOW IN POROUSMATERIALS

3.1 Introduction.

34

3.2 Capillary effects describing fluid flow in porous materials 34

3.2.1 Interfacial tension. 34

3.2.2 Interfacial tension in liquid- vapor systems............. 36

3.2.3 Interfacial tension in solid- liquid- vapor systems... 363.2.3.1 Capillary pressure in a tube ..... 37

3.2.3.2 Contact angle ... 40

3.2.3.3 Non-wetting (Hydrophobic) / Wetting (Hydrophilic) :.... 41

3.3 Hysteresis effects.... 42

3.4 Osmotic forces describing fluid flow in AGM.

43

3.5 Properties describing fluid flow in porous materials..

45

3.5.1 Porosity.

45

3.5.1.1 Defnition of porosity........ 45

3.5.1.2 Experimental test method......... 47

3.5.2 Capillary pressure.

48

3.2.2.1 Defnition of capillary pressure..... 48


3.5.3 Permeability. 50

3.5.3.1 Definition of permeability........ 50


3.5.4 Swelling kinetics (only for swelling materials)... 52

3.5.4.1 Definition of swelling kinetic parameters.... 52



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4 MATHEMATICAL MODELING OF FLUID FLOW INPOROUS MEDIA

4.1 Introduction

54

4.2 Mathematical modeling of fluid flow in non-swelling porousmaterials..

55


4.2.2 Balance equations.

56

4.2.2.1 Mass conservation equation..... 56

4.2.2.2 Momentum conservation equation....... 57

4.2.3 Derivation of the Richards equation.

57

4.2.4 Constitutive relationships. 584.2.4.1 Relative permeability-saturation relationship.. 58

4.2.4.2 Capillary pressure-saturation equation........ 58

4.3 Numerical solution of fluid flow in non-swelling porous

materials..

59


4.3.2 Richards equation re-formulations... 59

4.3.3 Discretization of the model... 60

4.3.4 Linearization of the non-linear equation systems... 60

4.4 Mathematical modeling of fluid flow in swelling porousmaterials..

61


4.4.2 Assumptions. 61

4.4.3 Set of balance equations...... 62

4.5 Numerical solution of fluid flow in swelling porousmaterials

64

4.5.1 Discretization... 64

5 LAB TEST METHODS

5.1 Introduction

66

5.2 Speed of acquisition test........ 66

5.3 Results..... 67

5.3.1 Speed of acquisition..... 67

5.3.2 Length distribution.. 69

5.3.3 Liquid load in the different layers... 71


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6 SIMULATION FLUID FLOW IN ABSORBENTDIAPERS

6.1 Introduction

72

6.2 Input parameters....... 73

6.2.1 Material parameters......

73

6.2.1.1 Non-swelling materials..... 73

6.2.1.2 Swelling materials..... 76

6.2.2 Geometry parameters... 806.2.2.1 Geometry inputs........ 80

6.2.2.2 Layer profiles............ 81

6.2.3 Mesh discretization...... 816.2.4 Test protocol.... 82

6.3 Simulation of fluid flow in diaper cores....... 82

6.3.1 Simulation results describing fluid flow in diaper cores. 83

6.3.2 Simulation results. 85

6.4 Validation of virtual acquisition test against lab data........ 86

6.4.1 Correlation plot between predicted and lab acquisition times 87

6.4.2 Sensitivity analysis, maximum difference 10%,,,,,. 89

7 CONCLUSIONS & NEXT STEPS7.1 Conclusions.

92

7.2 Next steps........ 93

8 BIBLIOGRAPHY.. 95

APPENDIX

A LIST OF FIGURES. 98

B LIST OF TABLES 100

C NOMENCLATURE..... 101


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Chapter 1. INTRODUCTION

1.1. Project description

An existing model, based on FEFLOWDHI-Wasy software, is used in this project to simulate

the fluid flow in the diapers core, composed of the acquisition, distribution and storage layer.

Simulation results with this model have an important dependency on three intrinsic propertiesin non-swelling porous materials: porosity, capillary pressure and permeability. In swelling

porous materials are determined by four, the previous three and the swelling kinetics.

Furthermore, the equations that determine these intrinsic properties are more complex in

porous materials.

Therefore, in the diaper core simulation, two mathematical models are used; one described

by the Richards equation for the non-swelling materials and the other is a non-linear set

balance of equations describing flow, absorption and deformation process in the AGM. These

equations are derivedfrom the capillary and osmotic flow and the total volume equation.

The objective of this work is to validate the acquisition test model for diaper cores against the

lab data, (e.g. comparing acquisition times, liquid content per layer, distribution lengths,

liquid distribution, void saturation distribution,...).

However the real work of an engineer and a R&D scientist is to understand the importance of

the inputs in the model, how the model works, which equations and relations are used, and

finally what can be extracted for the results to optimize and/or improve the product. For this,

it is very important to have the theoretical and experimental knowledge to obtain results for

this project. Therefore, the first part of the thesis explains these theoretical concepts, (such

as: disposable diaper background, fundaments and properties that describe the fluid flow in

non-swelling and swelling porous media and the mathematical models used to predict the


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liquid dynamics in the diaper core) a methodological concepts (such as: lab methods used to

obtain the parameters and Feflow DHI-Wasy software modeling). Feflow is a software basedin Finite-elements, which was developed for the calculation of the fluid flow inside the

porous materials of the core.

The section of the model simulation and validation represents a part of the project work done

at P&G, while the rest of the work will not be presented due to confidential reasons. The

model is validated using experimental data obtained from the lab tests known as Speed of

Acquisition test. The simulation results must be satisfactorily physically accurate and

analyzed with the Lab data obtained to determine some possible gaps in the input parameters

or model assumptions that explains the results obtained. Once improved or corrected the

input parameters for the model is done a new iteration until reach the validation of the model.

This model is very important, and will be used for future product design, where validation

criteria is relatively strict.

Finally, the last part of the thesis will involve the sections that are not included and/or related

with the internship that I am doing in Procter & Gamble, but are mandatory in the guide

How to elaborate a final thesis by the PFC coordinators, such as: disposable diaper process

production, diaper sustainability and economical studied. I have done this part using non-

confidential data.

1.2. Literature overview

This thesis is Procter & Gamble confidential, therefore some of the literature and knowledge

used is obtained from Procter & Gamble confidential documents.

The company background and brand introductions are available at www.pg.com. However,

the information used for disposable diaper and the superabsorbent material descriptions are

obtained from training manuals by P&G R&D scientists.

There is some information about the physics fundamentals describing fluid flow in absorbent

diapers on the internet, but this section was written using, Capillary Liquid Transport


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Training R.Rosati and the non-confidential book, Chattorjee, P.K. Gupta.B.S. Textile

science and Technology, Amsterdam, The Netherlands: Elsevier 2002.

General information on numerical modeling of fluid flow and transport in porous media is

obtained from a P&G internship student Project Thesis that describes the numerical modeling

in non-swelling material, and from internal document Modeling unsaturated flow in

absorbent swelling porous media.

In the last chapters, Lab test methods and Simulation of fluid flow in absorbent diapers,

using FeFlow, presents the relevant work on this thesis. In this case, the literature used todevelop the hypothesis and the results definition are the information described in the

previous chapters, mainly the fundamentals that describes the fluid flow in porous materials.

Furthermore, the recommendations and explanations of my supervisor, Rodrigo Rosati, and

the rest of the people related with the project were the key resources used in this Thesis.


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Chapter 2. BACKGROUND

2.1. The Procter & Gamble Company

In 1837, The Procter & Gamble Company was founded in Cincinnati, Ohio, the United States

by William Procter, a candlemaker, and James Gamble, a soap-maker, who met when they

married sisters [1]. Since then the company, has spread worldwide and is one of the most

important American, multinational corporations. In 2008, P&G was the 8th largest

corporation in the world by market capitalization and 14th largest US company by profit[2].

P&G has business operations in more than 130 countries and company-sites in US, Canada,

Central and South America, Europe, and others. Although it has expanded impressively

throughout its history, its headquarters still remains in Cincinnati. The company presided by

A.G.Lafley, employs 138,000 people worldwide.

P&G product operations are categorized into three Global Business Units (GBUs): Beauty

care (Beauty segment and grooming segment), household care (Baby Care, Family Care,

Fabric Care and Home Care) and health & well-being (Health Care, snacks, coffee and pet

care)[1].

These GBUs include around 300 brands. Among them, 23 brands net more than 1 billion

dollars in annual sales[3]. These include: Ariel, Always (Ausonia), Braun, Duracell, Gillette,

Head & Shoulders, Ivory Soap, Mr. Proper, Pampers (Dodot), Pantene, Pringles, Tampax,

Vicks , Wella, and others [1].


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Background


2.2. Baby care (Pampers)

Pampers is a brand of disposable diapers marketed by Procter & Gamble. Pampers were

produced and commercialized in 1961. This product was created by Victor Mills, one of the

most important scientists in the history of P&G[4].

The first disposable diapers were composed of fluff pulp as absorbent, cellulose fibers in

topsheet and polyethylene backsheet. During the following years there were some

improvements to obtain better performance in the disposable diaper. These improvements

reduced the weight and the thickness, increased comfort and reduced leakage and dryness.

One of the most important improvements was the introduction of the absorbent gelling

material in place of fluff pulp in 1986. In the 90's, we saw the introduction of gender specific

Pampers and also the return to unisex diapers at the end of the decade.

Actually Pampers is an $8 billion brand, on of the most important brands in The Procter &

Gamble Company.

2.3. The disposable diaper

A diaper is a sponge-like garment used for the people who cannot control their urine and

bowel movements. They are used mainly by babies, but can be used by adults in special

cases. The most important factors in consumer opinion are the diapers ability to absorb and

lock away liquid, and its storage capacity. These factors help to avoid leakages and prevent

skin irritation[5].

2.3.1 Diaper history

The need for a baby diaper dates as far back as the history itself, i.e. The Egyptians, Aztecs,

the Romans, and others. All used different natural resources including milkweed leaf wraps

and animal skins to dress their babies. In later years, the diapers of many European societies


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Background


consisted of swaddling bands made of linen and wool. In the 1800s with progressing

industrialization the progenitor of the disposable diaper was developed. In 1889 it was firstcreated by Maria Allen, an American woman, and consisted of a piece of linen folded into a

rectangular shape and held in place with safety pins[6].

The diaper evolved in 20th century through the innovations of many different people. In

1942, Paulistrm, a Swedish company, developed the first absorbent diaper in which the pad

was made by cellulose tissues. A few years later in 1946, an American housewife, Marion

Donovan, replaced the dangerous pins for plastic snaps. In 1947 the nonwoven fabric was

introduced. In this period the disposable diaper was a luxury product, used only in special

occasions.

In 1961 Pampers diapers by Procter & Gamble was lunched into the US market. These

diapers were conceptualized at the end of 50s by Victor Mills, and employee of the

company, when he was looking for better products to use on his grandson. Since the first

Pampers appeared in the market, the company has always focused to develop this product by

searching for better materials, creating different sizes and reducing leakage.

In the 70s, disposable diapers become available in all developed countries and even in some

other, less developed areas of the world. At the same time, the competition between Procter

& Gamble and Kimberly Clark resulted in rapid diaper design improvements and lower

prices for the consumer. During the following years, some advances were made such as: an

increase in absorbent capacity, diaper machine running speed (250 diapers per minute), better

materials for baby skin and diaper fit using elastomers.

In 1982 super-absorbent particles (SAP) were introduced into the diaper by Unicharm in

Japan. With their introduction, diapers became thinner and reduced the leakage below 2%.

Diaper rush, as well as diapers weight were reduced by about 50% from the previous.


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Background


In the 90s, the main developments resides in the mechanical tapes, which were introduced in

the form of Velcro, as well improved SAP, which used a new surface cross linker, to reducedgel blocking. Gel blocking is the phenomena which prevents liquid movement when the

absorbent is saturated. In addition, diapers machines began to run above 300 diapers per

minute[6].

In this decade, diapers are becoming thinner, have more absorbance capacity (30 g/g of

urine), leak less and can better protect babys skin. On top of that, diaper machines can now

achieve a production of 1000 diapers per minute. The recent diaper sales volumes for the

year 2006 are around 50 billion units around the world. Of all the diapers sold around the

world, 18.6 billion units where sold in the United States and 20.4 billion in Europe[7].

2.3.2 Diaper composition

A diaper is composed of the chassis and the core. The core, which is the focus of our

investigations, is composed of different layers, each designed and distributed, to absorb high

amounts of liquid (urine) in a short time and to retain it in the absorbent gelling material

(AGM), against external pressures. The chassis functions to keep the core in place, avoiding

possible leakages maintaining dry clothes. The chassis also allows for different diapers sizes

which can fit a large range of babies[8].

Figure 2.1.Typical disposable diaper design[4]


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Background


2.3.2.1 Diaper Core

The requirements of the core are fast acquisition times with good liquid distribution, keeping

the skin dry and healthy, and leakage prevention. At the same time, that the core geometry

should be optimized in order to use much thinner and smaller cores.

The core is studied depending on the size, with gushes with an average of 50-75 mL of urine

with a flow rate up to 22 mL/s. The urine gushes are expected every 60 to 70 minutes. The

fulfillment of diaper requirements has to be reliable under different external pressures

conditions. Babies perform a variety of activities, such as: standing, walking, sitting,crawling or laying[9]. The top core layer in contact with the baby skin has to be dried in short

times, e.g. within few minutes, and the urine storage has to be enabled up to 300-500 mL

depending on the size of the diaper core.

The diaper core is composed by 5 layers glued to each other, topsheet (TS), acquisition layer

(AL), distribution layer (DL), storage layer (SL) and the backsheet (BS). Remarkably, that in

the storage layer is composed of 2 nonwoven layers enclosing the super-absorbent material

and fluff between them.

Each layer in the diaper core has its own functions, characteristics and requirements.

Topsheet has the function of separating the core materials from the baby skin, keeping it dry

and healthy. This surface layer contains lotion stripes to protect the baby skin against

possible irritations.

TopsheetAcquisition layer

Distribution layer

Storage layer

Backsheet

Figure 2.2.Layers composed the diaper core


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Background


The acquisition patch, consists of an acquisition layer and a distribution layer. The

acquisition layer is an open structure with a high permeability, so that the liquid can getquickly below the topsheet. This material has a very low storage capacity. The distribution

layer is a cross-linked cellulose, which can temporarily store the liquid until the super-

absorbent takes it up. The advantage of this layer is that the liquid can be distributed rapidly

along the patch so that in the storage layer all the liquid is not focused at the same point.

The function of the storage layer is to take up as much urine as possible and lock it away.

This property, called storage capacity, transports the urine within the swollen gel bed and

works reasonably fast. Storage layer contains AGM and fluff, wrapped by two nonwovens.

Generally the nonwoven on the top is hydrophilic and the nonwoven on the bottom is

hydrophobic.

The backsheet is a polyethylene film, which prevents the liquid from leaking through the

bottom of the diaper.

2.3.2.2 Diaper Chassis

The chassis geometry impacts the fit and the size of the diaper in addition keeping the core in

place. The main parts that compose the chassis are[10]:

Topsheet (TS)

The topsheet is also considered in some cases a part of the core. Topsheet material is

made from a hydrophilic polymer or coated with hydrophilic surfactant in order to allow

the acquisition through it. Taking into account that it has to keep the skin dry, it can also

be hydrophobic with apertures or holes. Backsheet (BS)

The diaper backsheet consists of a poly film hydrophobic laminate. This film functions to

prevent possible leakage from the storage core, through the visible exterior of the diaper.

Barrier Leg Cuffs (BLCs)

These are the primary chassis leakage protection. They consist of a nonwoven material

with a couple of elastic strings folded into them in order to keep them in contact with the


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Background


babys skin. These cuffs are made from hydrophobic material to prevent the liquid

flowing through them.

Fastening system

The Landing zone and mechanical fasteners belong to the fastening system. The

adjustment of tapes allows the possibility of refastening to engage a better fit. A

permanent fastening during use is guaranteed.

Elastics/ Stretch

Elastics are used to improve the waist sizing as well as the leg sizing to have a closed

circumference. They expand the size range and allow tolerance of a wide variety of baby

shapes and sizes. They play an important role in leakage protection, as are crucial in

providing a good fit and gasketing.

Front ears (FE) & Back ears (BE)

Front ears help to close the diaper at the front during the application of the diaper onto

the baby.

Figure 2.3. Diaper chassis schema (1- Front ears; 2- Back ears; 3-Barrier Leg cuffs)

1

2

3


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Background


The diaper chassis study is divided into three specific areas:

Engineering fit:study the mechanics of the interactions between diaper and child. This

mainly includes pressures that the diaper puts onto the baby and product gasketing on the

body to prevent leakage.

Technical fit:is focused in sizing. The physical range of sizes that a products geometry

can accommodate and the consumer size perception must be considered.

Aesthetic fit: this area involves the colour, style, and texture of the product.

2.4. Synthetic superabsorbents

The superabsorbent used is a hydrophilic polymer with the ability to absorb and retain

aqueous solution, e.g. urine. There are several names used to describe it, the most used are:

absorbent gelling material (AGM) and superabsorbent polymer (SAP)[11]. In the following,

the term AGM will be used.

One gram of this absorbent gelling material can absorb and keep around 1000-1200 mL

deinoized water, or in the case of the urine around 30-50 mL. This is a ten times higher

capacity than that of the fibers and foams used as absorbents in original diapers[11].

AGM is the key material in diapers. Its function is to absorb urine and lock it away. The

amount of urine that can be absorbed, is referred to as gel volume capacity. Another

important parameter is permeability, since it has to allow the transport of urine within itself.

It is also important that the superabsorbent works reasonably fast to absorb the material.

Therefore, the key properties of the AGM are storage capacity, permeability and absorbance

velocity. These properties are determined mainly by four intrinsic characteristics of the

material: porosity, capillary pressure, permeability and swelling kinetics. These properties

are analyzed and explained in the section 3.5.


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Background


The principle behind AGM absorption is that it is soluble in water and at the same times has

the tendency to also be dissolved in water. At this point, the crosslinks between the polymerchains do not allow the polymer get dissolved, because they act as retractive springs.

Consequently, the water is absorbed via diffusion into the network and the molecules expand

until equilibrium is reached between the driving and retractive forces.

2.4.1. Structural characteristics

Most common and commercially AGM is polyacrylates crosslinked with organic

crosslinkers. Their chains are neutralized with sodium hydroxide

[7]

.

2.4.2. Swelling behavior

In the dry state, AGM is flowing powder. After absorbing liquid, e.g. water or urine, it turns

into a softer and more flexible gel. The softness and hardness of this gel bed is a function of

the number of crosslinks and the amount of liquid absorbed.

CO2H CO2HCOO-

Na+C=O

O

RC - Et

O

C=O

COO-

Na+

CO2HCO2H

Na+COO-

Na+COO-

Na+COO-

Adding liquid

Figure 2.4.AGM molecule [7]

Figure 2.5.AGM swelling behavior


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Background


Liquid flows into the AGM particles and the particle swells until the system reaches the

equilibrium between the driving and retractive forces. Equilibrium forces are described bythe equation 1.1.

extelastosmmix PPPP

The driving forces are Pmix which describes the interactions between the phases and the

osmotic pressure (Posm) involves electrostatic interactions in the particle. In the other side the

network elasticity (Pelast) and the external pressure (Pext) are the retractive forces.

2.4.3. Gel blocking

Gel blocking occurs when the swelling effect blocks the void spaces between AGM particles.

This causes permeability to decrease, increasing diaper leakage drastically. In this case, the

liquid can flows through the material only by diffusion.

Gel blocking is reduced by using higher gel strength or by lowering external pressure.

Pext

Pelas

PmixPosm

Figure 2.7.Gel blocking in an AGM bulk [7]

Uncontrolled Swelling/ Gel blocking Controlled Swelling/ High permeability

Figure 2.6.Balance of forces in an AGM particle

(1.1)


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Background


2.5. Disposable diaper manufacturing process

The data and information showed in this section is not related with P&G, as well is not

related with P&G manufacturing process for disposable diapers. This section is mandatory

for the University Rovira i Virgili (Tarragona). The information shared is obtained from

internet. The link used is www.madehow.com/Volume-3/Disposable-Diaper

2.5.1. Disposable diaper materials

Actually disposable diapers are made with synthetic fibers which far exceed the capacity of

natural fibers, e.g. cotton material. Disposable diaper will absorb 15 times its weight in

water, due to the absorbent pad design found in the core of the diaper. The pad is composed

of two essential elements, a hydrophilic polymer and fibrous materials.

Diaper core is composed by 5 layers glued to each other, topsheet is an hydrophilic

nonwoven fabric, polypropylene with lotion stripes applied applied in the top to maintain

baby skins healthy. Acquisition layer is a nonwoven with an open structure, commonly

polystyrene, distribution layer is a cross-linked cellulose treated with citric acid. Storage

layer (SL) is composed for the AGM, cross-linked polymer network, e.g. poly acrylate salts

and two nonwoven between two nonwoven fibers, the nonwoven in the top is hydrophilic

and the nonwoven in the back is hydrophobic. Finally the bottom layer is the backsheet (BS),

hydrophobic polymer. Manufacturers have optimized the combinations of polymers and

fibrous material to yield the most efficient absorbency possible.

2.5.2. Nonwoven fabric manufacturing

Nonwovens are typically made from plastic resins, such as nylon, polyester, polyethylene, o r

polypropylene, and are assembled by mechanically, chemically, or thermally interlocking the

plastic fibers. The principal method of assembling nonwovens, called the dry laid process,

consist in a plastic resin is melted and extruded, through tiny holes by air pressure. As the

Not related with P&G- Mandatory URV- www.madehow.com


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Background


air-blown stream of fibers cools, the fibers condense onto a sheet. Heated rollers are then

used to flatten the fibers and bond them together. With this process is produced the topsheetlayer, polypropylene and the backsheet layer polyethylene.

2.5.3. The manufacturing process

The first part of the process to produce an absorbent pad is composed by a movable conveyer

belt. Which is composed for various pressurized nozzles spray either polymer particles or

fibrous material along the conveyer. In the bottom is perforated, and as the pad material is

sprayed onto the belt, a vacuum is applied from below so that the fibers are pulled down to

form a flat pad.

It is applying polymer and fiber involves application of the absorbent material onto the top

surface of the pad after it has been formed. However, it is produced a pad which has

absorbent material concentrated on its top side and does not have much absorbency

throughout the pad. Another disadvantage is that a pad made in this way may lose some of

the polymer applied to its surface. This approach tends to cause gel blocking.

These problems are solved by controlling the mixture polymer and fibrous material. Multiple

spray dispensers are used to apply several layers of polymer and fiber. As the fiber is drawn

into the chamber and the bottom of the pad is formed, a portion of the polymer is added to

the mix to form a layer of combined polymer and fiber. One of the principal advantages of

this process is that the polymer just where it is needed.

Figure 2.8.Disposable diaper manufacturing process



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Background


The second part of the process consist to proceeds down the conveyor path to a leveling

roller near the outlet of the forming chamber. This roller removes a portion of the fiber at thetop of the pad to make it a uniform thickness. The pad then moves by the conveyor through

the outlet for next operations.

Sheets of nonwoven fabric are formed from plastic resin using the meltblown process as

described in the section 2.5.2. These sheets are produced as a wide roll known as a "web,"

which is then cut to the appropriate width for use in diapers. There is a web for the top sheet

and another for the bottom sheet. This step is in sequence after pad formation in the case that

the nonwoven fabrics are made in the same location. The production of these large bolts of

fabric are connected to special roller equipment that feeds fabric to the assembly line.

Stretched elastic bands are attached to the backing sheet with adhesive. After the diaper is

assembled, these elastic bands contract and gather the diaper together to ensure a snug fit and

limit leakage.

Generally in the process there are still three separate components, the absorbent pad, the top

sheet, and the backing sheet. These three components are in long strips and must be joined

together and cut into diaper-sized units. This is accomplished by feeding the absorbent pad

onto a conveyor with the polyethylene bottom sheet. The polypropylene top sheet is then fed

into place, and the compiled sheets are joined by gluing, heating, or ultrasonic welding. The

assembled diaper may have other attachments, such as strips of tape or Velcro, which act

as closures. Finally the long roll is then cut into individual diapers, folded, and packaged for

shipping.



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Background


2.6. Disposable diaper sustainability


related with P&G life cycle assessment and sustainability studies for disposable diapers. This

section is mandatory for the University Rovira i Virgili (Tarragona). The information shared

is obtained from internet. The link used is a science report titled An update lifecycle

assessment study for disposable and reusable nappies by UK Environmental Agency life

cycle assessment model

2.6.1. Introduction

The target of this section is to realize a Life cycle assessment between the disposable diapers

and reusable diapers. The goal of LCA is to compare the full range of environmental and

social damages assignable to products and services, to be able to choose the least oppressive

one. A Life Cycle Assessment is executed in four steps.

Goal and scope:Formulates and specifies the goal and scope of study in relation to

the intended application. the goal and scope phase includes a description of the

method applied for assessing potential environmental impacts and which impact

categories that are included.

Life cycle inventory: involves data collection and modeling of the product system, as

well as description and verification of data.

Life cycle impact assessment: is evaluating the contribution to impact categories such

as global warming, acidification, etc.

Interpretation: Involves an analysis of major contributions, sensitivity analysis and

uncertainty analysis

2.6.2. Goal and scope

The study realized is aimed to explain the significance, of the environmental impact of the

diapers. These included considerations of how actions can be, and have been. The functional

Not related with P&G- Mandatory URV


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Background


unit used is defined as the use of diapers during the first two and a half years of a childs

life. These results are the same for disposable and reusable diapers.

2.6.2.1. Number of changes

In the case of disposable diapers, the number of changes per day decreased from an average

of seven at birth to an average of five at two and a half years. While in the case of reusable

diapers, the average number of changes per day for children decreased from eight at birth to

an average of six at two and a half years.

2.6.2.2. Disposable diapers

Disposable diapers typically consist of a palstic outer layer with integral fastening and a core

of absorbent materials with protective top layer. The diaper core is composed of fluff pulp

(cellulose fibre) and water-absrobent polymer (AGM), sodium polyacrylate. In the following

table is shown the disposable nappy composition and weight.

Totalweight

Fluffpulp

AGM PP LDPE Adhesives PET Other

40 g 35% 33% 15% 5% 5% 2% 5%

Age of child Children wearingdiapers (%)

Up to 6 month 100.0 %6 to 12 months 95%12 to 18 months 89%18 to 24 months 45%24 to 30 months 20%30 to 36 months 5%36 to 42 months 2%32 to 48 months 0.5%48 to 66 months 0.1%

Table 2.1.Children wearing diapers by child age

Table 2.2.Average disposable diapers composition and weight



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Background


Using an average of 4.16 diapers used per day, and an average diaper weight of 40g, an

average of child will use 146.5 kg of nappies over the two and a half year period consideredhere.

The manufacturers have reduced the environmental impact of disposable diaper through

product design and development. Since 2001/02, the industry has reduced diaper weight by

13.5%.

2.6.2.3. Reusable diapers

There are several types of reusable cotton diapers. The different diapers systems can be

divided into the following categories:

All in ones shaped, fitted diapers with velcro or popper fastening, which include a

waterproof cover.

Shaped nappies, similar to all in ones, but wraps or pants have to be purchased

separately to provide waterproof cover.

Prefolds, require folding and a separate waterproff wrap/pant, with fasteners used in

some cases.

The major retail routes for reusable diapers appear to be through high street shops, mail order

and via the internet. Reusable diapers are sold in birth to potty packs.

2.6.3. Life cycle inventory

The basis of any life cycle inventory is the creation of a model, that contains the amounts of

all inputs and outputs of processes that occur during the life cycle of a product.

2.6.3.1. Inventory data for disposable diapers

The number of diapers used over the average of two and a half period that a child is in

diapers taken from the previous table 2.3.

Waste management: It was assumed that 365kg of excreta was disposed with diapers as

municipal solid waste over two and a half years. The composition of excreta was assumed to



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Background


be, 18% faeces and 82% urine. The model the 100 per cert anaerobic digestion sensitivity

scenario, the MBT- Hydro-Mechanical Spearation and Aerobic Digestion (with energyrecovery) technology.

2.6.3.2 Inventory data for reusable diapers

An average weight of 140 g per reusable diaper is assumed. The reusable diapers are 100%

cotton. A minimum of 30 nappies are required over two and a half year period.

WrapsIs calculated a wrap weight of 50 g, and a minimum of 12 wraps required for two and a half

period. The composition of these wraps was 20% cotton, 40% polyester and 40%

polyurethane.

Washing data

Calculated domestic washing and drying performance, stock average for: water use and

electricity use. The table 2.4. shows the electricity and water used for washing a reusable

diaper. Table 3.2. shows the electricity and water consumption used in pre-wash cycle. And

table 3.3. shows the electricity and water use figures for driers.

Washingtemperature

Electricity use:stock average

Water use: stockaverage

40C 0.8 kWh per load 70 litres per load60C 1.0 kWh per load 70 litres per load

90C 1.8 kWh per load 70 litres per load

Washingtemperature



20C 0.25 kWh per load 35 litres per load

Scenario Urine Faeces Plastics Pulp Miscellaneous

Disposable diaper 300 kg 70 kg 80 kg 50 kg 15 kg

Table 2.3.Disposable diaper composition after it used

Table 2.4.Summary washing performance

Table 2.5.Summary pre-washing performance



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Background




3 kWh per load 20 litres per load

2.6.4. Life cycle impact assessment

2.6.4.1 Disposable diapers

Table 4.2. summarizes a selection of the life cycle inventory flows for the manufacture and

use of disposable diapers. Table 4.. show the whole life impact profile for the disposablediaper. The main driver for the impacts is the production of materials used to construct the

disposable diapers.

The greatest influence this scenario has is on the water pollution impact categories. The

anaerobic digestion sensivity analysis shows that diversion of disposable diapers away from

current residual waste management routes can benefit greenhouse gas profiles through

digestion and energy recovery from the biogas produced. If we consider that the potential

global warming impact scenario is 600kg carbon dioxide equivalents per child over two and a

half year period, this equates to an estimated global warming potential of approximately

0.4Mt carbon dioxide equivalents per year. This assumes that all children wear disposables

(based on 1.7 million children in diapers at any one time).

Coal Oil gas

natural

Carbon

dioxide

Methane SOx NOx N2O Total

water

50 kg 100 kg 450 kg 1 kg 2 kg 2 kg 0.05 kg 150 m3

Abioticdepletion

Acidification Eutrophication Global warmingpotential

Humantoxicity

5 kg Sb eq 3.5 kg SO2 eq 0.5 kg PO43-eq

600 kg CO2 eq 50 kg 1,4-DB eq

Table 2.6.Summary drying performance

Table 2.7.Inventory analysis sensitivity scenario (Manufacture and use excluding disposal)

Table 2.8.Impact for disposable diapers and sensitivity scenarios (Whole Life- Includes disposal)



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Background


2.6.4.2 Reusable diapers

Table 4.5 summaries a selection of life cycle inventory environmental consumptions and

flows for the manufacture and use of shaped diapers for these two scenarios.

Electricity consumption Water consumption

Washing Drying Washing Drying

High temperature 700 kWh 150 kWh 5000 L 1500 L

Reuse, high load efficiency 250 kWh 0 3500 L 0

2.6.5. Interpretation

The average of disposable diapers would result in a global warming impact of approximately

550 kg of carbon dioxide equivalents used over the two and a half year a child is typically in

diapers.

For reusable diapers, based on average washer and drier use produced a global warmingimpact of approximately 570 kg of carbon dioxide equivalents. However the impacts for

reusable nappies are highly dependent on the way they are laundered.

The environmental impacts of using shaped reusable diapers can be higher or lower than

using disposables, depending on how they laundered. The report shows that, in contrast to the

use of disposable diapers, it is consumers behaviors after purchase that determines most of

the impacts from reusable diapers.

Table 2.9.Electricity and water consumption



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Background


2.7. How can start a new diaper factory?


related with P&G. This section is mandatory for the University Rovira i Virgili (Tarragona).

The information shared is obtained from internet. The link used is www.disposablediaper.net

In this section is it explained some of the requirements and issues to take into account to start

a new business in disposable diapers

2.7.1. How much capital is required?

A modest used diaper line (10 to 20 years old) costs a few hundred thousand dollars

($300,000 to $700,000). A brand new baby diaper machine, complete with peripheral

equipment and most basic features, can cost anywhere between $750,000 and 3.5 million

dollars, depending on the design of the diapers proposed to be produced and the speed of the

machine.

In addition to the capital required to buy the diaper machines, another very important issue isthe working capital. The raw material suppliers, especially at the very start of your

operations. Capital required to have just 15 days inventory of raw materials and 15 days

inventory of finished products could be around one half of the capital invested in the whole

diaper machine. Another important point is to rent or buy a building.

A diaper factory is much more than just buying a diaper machine, a building, and a few raw

materials. It is necessary to have to set up diaper specifications and an internal laboratory,

give the right training to your technical staff. As well to be aware of the building and layout

requirements, the peripheral equipments, the required logistics, etc.

Not related with P&G- Mandatory URV- www.disposablediaper.net


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Background


2.7.2. How many people would I need to hire?

Considering a larger machine, for example, 300 to 600 or more diapers per minute, it will be

needed an important group of operators to make sure the equipment runs 24 hours a day.

One of the most important factors affecting the number of operators required to run a diaper

line has to do with the number of packages and whether or not you plan to use automatic or

manual packaging equipment.

A diaper machine producing 300 to 600 or more diapers per minute, will require at least one

operator and one assistant to help him feed the raw materials. In addition, at least onepacker is required for every 10 to 12 bags produced per minute. For example, if the

company wants a 20 count bag and you run your machine at 400 diapers per minute with

manual packaging, it will be needed two people just for stacking the diapers into the bags and

sealing them. As well is needed a person to stack the sealed bags into the box, or an

automatic case sealer. Depending on the number of bags inside the box, will be needed two

people to do this job. Have to be considered some extra staff to be able to operate

continuously without a stop during the lunch break. A typical machine with manual

packaging will need about eight people per shift; if you use automatic packaging, you will

probably need only about four or five per shift. You need to multiply these numbers by the

number of shifts that you want to run.

In fact, to run the plant for all the 30 days in a month, you need at least four teams to be able

to keep the machine running during weekends and holidays. Remarkably that all these people

are just for the direct labor in-line.

It is needed more employees to run the laboratory, the diaper inspections, the spare parts

room, the instrumentation, the finished products warehouse, the raw material warehouse, in

addition to all of the engineering infrastructure required to run an efficient factory. A typical

diaper factory running only one diaper machine at 300 to 600 diapers per minute and three

shifts per week (full capacity) with manual packaging and using a typical count of 20 diapers

per bag, will require about 50 people.



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Background


2.7.3. What should be the Size of the Building?

Lets assume that we are looking for a large size diaper machine, something between 200 to

600 diapers per minute. For this typical diaper machine, the length of the diaper line can be

expected to be in the range of 20 to 50 meters, including the packaging equipment. There are

several issues that affect the total length of a baby diaper machine, like the required features

in your diaper design and whether or not you want to have all the equipment installed in a

straight line. If the machine is to be installed in a straight line, you will probably need an

area of 30 to 60 meters in length and 8 meters in width.

This was the space requirement for the diaper machine itself; there are other areas that

require plenty of space. Raw materials and finished products warehouses will be required,

in tune with the expected inventory levels. For example, if its planed to have only one mid

size diaper machine (200 to 400 diapers per minute), will be enough with 1,000 square

meters of space. However your inventory will then have to be limited to less than a weeks

raw materials and finished goods. In some locations, it is possible to operate just in time,

specially if the suppliers have their own inventories close by. In that case, it may be possible

to operate with less than a weeks inventory of raw materials. Other locations may require

as much as a months inventory due to complicated logistics or customs regulations, which

involve bringing raw materials from far away places. Another important factor to take into

account is the required changes in diaper size on the machine itself; the higher the inventory

of finished products you hold, the lower will be the need for machine stoppages for size

change (example: from large to newborn); on the other hand, working capital requirements

go up. All diaper companies must consider working capital requirements. Some part of

working capital is indeed met by credits from raw material suppliers but a new company

starting from scratch, without commercial references, is unlikely to get any credit from the

suppliers, at least in the beginning. You need to look at costs and benefits to decide the

optimal size for your warehouse, based on your financial situation and ability to buy

materials on credit. Finally, you will also have to take into account space for office, spare

parts storage, quality control laboratory, training room and the required space for the trucks



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Background


to manoeuvre, besides space for peripheral equipment (dryers, compressor, dust collector,

scrap collector, machine shop room, etc.).

2.7.4. Where can be purchased diaper raw materials?

Another important issue to take into account is to research the market to find the suppliers to

purchase the raw materials for the disposable diapers production, in the following points are

showed some suppliers for the disposable diapers raw materials.

Fluff Pulp (Cellulose and Air Laid): Asia Pulp and Paper, Bowater Incorporated,

Buckeye Technologies, Celanese Acetate, Cellutissue Holdings, Great Lakes Pulp, Ilim

Pulp, Klabin, Koch Cellulose, Mercer, Rayonier, Rexcell, Walkisoft, Weyerhaeuser,

SAP (Sodium prolyacrylate): Arkema, BASF, Degussa Superabsorber, Elf Atochem,

Formosa Plastics, Incopack, Kolon Chemical, Lysay, Mc Airlaids, Nanning Qiaohong,

Sanyo Chemical, Sumitomo Seiki,

Nonwovens: Advanced Fabrics SAAF, BBA Fiberweb, Bonlam, Buckeye Technologies,

Consolidated Fibers, DuPont, Fibertex, Libeltex, Mada Nonwovens, Mediane, Nikoo

Group, Providencia, RKW AG Rheinische Kunststoffwerke, Tenotex,

Elastomerics: Arimatex, Caligen, ExxonMobil, Fillatice, Koester GmbH, Nordenia,

Woodbridge Group,

Bags: A-Roo, Flexico Moreau, Imbalplast SRL, Pelsan, Pliant Corporation, Relapasa,


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Chapter 3. FUNDAMENTALS OF FLUID

FLOW IN POROUS MATERIALS

3.1. Introduction

The basic principle of the diaper design is to absorb and store liquid in the different layers of

the core and prevent leakage. To design the core well, it is essential to study the effects that

describe the fluid flow in the different porous materials that composes the core. There are

two different groups the non-swelling porous materials (e.g. acquisition layer, distribution

layer and topsheet) and the swelling porous materials (e.g. AGM in the storage core).

The liquid movement in porous media is described mainly by the capillary effects, as well

the hydrostatic pressure, gravity, external pressure and hysteresis effects, associated with

capillary pressure[12]. In swelling porous media the fluid flow is additionally described by

fluid absorption into AGM particles, which is essentially driven by osmotic pressure.

3.2. Capillary effects describing fluid flow in porous media

One of the key driving forces that describe the liquid movement in porous media is the

wetting phenomenon. This physical phenomenon is determined by the capillary effects and

describes the fluid flow in the microscopic pore channels. Furthermore it explains the liquid

absorption into the porous material.[12]

3.2.1. Interfacial tension

Some fluids tend to keep contact with the solid surface of the porous materials. This effect is

called wetting. When liquid is in contact with another immiscible liquid, gas or solid,

intermolecular interactions are generated producing an interfacial energy between these two

phases. The force of these interactions depends on both substances, whereas Hydrogen-


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bridges dominate in the interaction between water and miscible liquid, Van-der-Waals forces

dominate in the interaction with gas.

The interfacial tension is the work done to separate a liquid and another substance (Wseparate)

per unit of area (Surface Area). The surface tension () will increase with a stronger

interaction of the molecules[12] [13].

AreaSurface

Wseparate

In the following system water and gas are present. The interactions among water molecules

are stronger than the interactions with the gas molecules. Since the system tends to minimize

the energy, water molecules and gas molecules tend to be separated in two phases.

Dispersion and polar forces are the two types of forces which produce the molecular

interaction of different phases in contact and are the cause of the existing phase interface.

Dispersion forces of attraction affects any neighboring par of molecules without influence of

their chemical composition. These forces of attraction depend exclusively of the distance

between both molecules (F=1/r6). The polar force of attraction is a function of the molecules

charge, i.e. ion-dipole, dipole-dipole, induced dipole interactions or to any combinations of

these[12] [13].

Vapor-Vaporinteraction

Vapor Liquidinteraction

Liquid-Liquidinteraction

(3.1)

Figure 3.1.Molecular interactions between two fluid phases


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3.2.2. Interfacial tension in liquid-vapor systems

Across the interface (gas-liquid interaction zone) showed in the figure 3.1 exists a

discontinuity of pressure. This difference of pressure from the non-wetting (Pnon-wet) and the

wetting side (Pwet), is called capillary pressure (Pc).

wetnonwetc PPP

Capillary pressure is a function of the interfacial tension. This relation between the pressure

difference with the curvature in the interface and the resulting tension is described in the

equation 3.3, also known as Laplace equation on the interfacial tension.

21

21

11

rrPPPc

In system equilibrium, P1-P2 is constant on the surface. For spherical interface r1=r2, and

consequently the equation 3.3 is reduced to the equation 3.4. [12] [13]

rPPPc 221

Where; Pcis the capillary pressure, P1 the pressure from the wetting side, P2 the pressure from

the non-wetting side, r is the radius of the capillary and is the interfacial tension.

3.2.3. Interfacial tension in solid-liquid-vapor systems

In a three-phases (SLV) system the total free energy is calculated from the free energies of

the interface produced by liquid-vapor (LV), solid-vapor (SV) and liquid-solid (LS). The free

energies of each phase are multiplied by their respective interfacial contact areas.

SVSVSLSLLVLV AreaAreaAreaF

Where; F is the interfacial energy, LV is the interfacial tension in the liquid-vapor interface,

SL the interfacial tension between the solid and the liquid phases and SVbetween the solid

and vapor phases. AreaLV, AreaSL,AreaSV are their respective contact areas.

(3.2)

(3.3)

(3.4)

(3.5)


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The interfacial energy (F) tends to be minimized to reach to the equilibrium system. The

relationship among the surface tension values is described by the Youngs equation,

equation 3.6 relating the three interfacial tensions with a contact angle obtained in the

system in thermodynamic equilibrium. The variables of the contact areas will be optimized

because they are the free variables of the system. [12] [13]. The importance of the contact angle

in the capillary pressure is showed more detailed in the figure 3.4.

LV

SLSVLVSLSV

coscos

3.2.3.1. Capillary pressure in a tube

A simpler way to explain the Laplace equation could be using a tube with zero contact angle

( 0 ) as a reference system. When the system reaches its equilibrium, the capillary

pressure obtained is a balance between the hydrostatic and capillary forces [14].

rhgPPPP ch

221

Where; Phis the hydrostatic force, is the density of the liquid and g is the gravity constant.

Laplace equation defines the surface tension.

2

hgr

The flow velocity is expressed by the equation 3.9, as a function of the permeability and

viscosity. Nevertheless, neither parameters have an effect in the equilibrium system.

h

hhKg

dt

dh c

(3.6)

(3.7)

(3.8)

(3.9)


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Where; dh/dt describes the liquid height at any time, K is the permeability, is the viscosity

of the material, and hc is the height of the liquid column that would produce the equivalent of

the capillary pressure.

As it can be observed in the figure 3.2, and according to equation 3.4, a high capillary

pressure will be obtained in small pores. Assuming that the material is the same and the

radius B is two times the radius A, the difference of height is one half, equation 3.10.

2

1

b

a

a

b

r

r

h

h

In porous materials, the pores are normally interconnected forming a multipore network. In

these systems the hydrostatic forces tend to move the liquid from those pores containing

more liquid or hydrostatic pressure to those containing less. Capillary pressure effects tend to

transport the liquid from the large to the small pores. In the beginning (1) there is more liquidin the bigger pores, hydrostatic and capillary pressure transports the liquid to the smaller

pores. When the liquid reaches the same level for both pores (2) no hydrostatic force is left.

Nevertheless capillary pressure has still an effect and moves the liquid from the bigger to the

smaller pores until the system reaches the equilibrium (3). In this point the capillary pressure

and the hydrostatic pressure have the same magnitude in opposite directions. [14].

ha

hb

ra rb

(3.10)

Figure 3.2.Liquid transport between pores of different diameters


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In the case that the contact angle is non-zero, the radius curvature is calculated by the

equation 3.8. Capillary pressure is also a function of the contact angle, as shown in equation

3.10.

cos

cl

rr

c

crr

P cos22

The value of the contact angle is a function of some surface properties explained in the

following section 3.2.3. One of these parameters is the solid material. In the following case

the height of the cylinders with same radius is determined for two different materials with

0 and 60 (see figure 3.4).

c

chr

hgPP

cos2

grh

c

cos2

(2)

(1)

(1)

(2)

(3)(3)

Pc

Pc

Ph

Ph

(3.11)

(3.12)

(3.13)

(3.14)

Figure 3.3.Liquid transport in interconnected multipore systems


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3.2.3.2. Contact angle

The contact angle is defined as the angle between two of the interfaces at the three phase line

in contact. It is obtained when the system arrives at the thermodynamic equilibrium. The

value of the contact angle does not depend on the geometry of the system. Moreover, it is

totally governed by the interfacial tensions between the three phases [15]. Therefore, the

contact angle only makes sense for a given solid-liquid-vapor system.

Material A

(3.15)

01cos

Material B

605.0cos

Figure 3.4.Liquid transport between different materials

2

1

cos

cos

a

b

a

b

h

h


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3.2.3.3.Non-wetting(hydrophobic) / wetting (hydrophilic)

Assuming that the gas phases and the external conditions are the same in the studied system,

the contact angle will be a function of the type of material of the solid surface and the type of

liquid. Solid surfaces with a contact angle higher than 90 ( 90 ) are called non-wetting

(see figure 3.6) and hydrophobic in the case that the liquid phase is water.

In case that the contact angle is lower than 90 ( 90 ) the liquid wets in the solid surface

phenomena known as wetting in the case that the liquid phase is water the material of the

solid surface is hydrophilic. A zero contact angle ( 0 ) represents a complete wetting[16]

.

SV

LV

SL

Figure 3.5.Contact angle of a liquid to a solid

Figure 3.6.Non-wetting contact angle, e.g. mercury on glass surface 120


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3.3. Hysteresis effects

The hysteresis effect is one of the phenomena that explain why there are a certain differencesbetween the drying and wetting curve in a porous matrix. The most common hysteresis

effects are the contact angle hysteresis and the ink bottle effect.

Contact angle hysteresis is the difference between the maximum (advanced/advancing) and

minimum (receded/receding) contact angle values. The hysteresis effect is significantly

present in systems where the solid surface is heterogeneous and has roughness and mobility,

and also if the interface is in contact with a pre-wet surface, e.g. wet versus dry fibers. The

ink bottle effect can be produced if some of the pores are larger than their openings [17].

Figure 3.7.Wetting contact angle, e.g. water on glass surface 14

Absorption curveDrying curve

Wetting curve

Sat.

Figure 3.8. Wetting and drying curve of capillary pressure

Capillary pressure


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3.4. Osmotic pressure describing fluid flow in porous

media

Osmotic pressure is one of the key parameters that describe the fluid absorption into AGM. It

is one of the driving forces in the swelling behavior of the polymer network. At the same

time the external pressure Pext, the network elasticity Pelastand the polymer interactions also

have an affect in the balance of driving and retractive forces. However the balance of forces

depends mainly of the osmotic pressure [12].

extelastosmmix PPPP

Osmotic pressure is the hydrostatic pressure produced by a difference in concentration

between solutions on the two sides of a surface. Osmotic pressure is calculated by the

equation for the ideal gases:

TRnVP mols

Where;Pis the pressure, V is the volume of the substance, nmolsthe number of mols, R is the

constant of the ideal gases (8.31 J/mol/K) and T is the temperature.

In the case of the osmotic pressure between the urine and the AGM in the storage core, in the

following example is calculated:

Pext (0-0.1 atm)

Pelas (0-0.1 atm)

Pmix (00.1 atm)

Posm (0500 atm)

(3.16)

(3.17)

Figure 3.9. Balance of driving force in an AGM particle


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Osmotic pressure in the urine

Osmotic pressure in the liquid inside the AGM

Osmotic pressure produces the main driving force behind the superabsorbent swelling

materials. The presence of ions in the absorbed liquid reduces the amount of the liquid that

can be absorbed because the difference of the osmotic pressure is lower[12].

psiatmP

PaKKmol

LPa

L

molP

LmolClandNabothcountWe

LmolNaClurineIn

1105.7

455,75529531.8308.0

/308.0:

/154.09.0

psiatmP

PaKKmol

LPa

L

molP

lmolmlNamol

gtoswollenGM

1363.9

100,92929531.8379.0

/379.030/01136.0

/30,1


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3.5. Properties describing fluid flow in porous materials

There are three intrinsic properties that describe the fluid flow in porous media: porosity,

capillary pressure and permeability. If the porous media has the capacity to swell, an

additional property called swelling kinetics must be considered, as well as that all properties

can change with the swelling extent of the material.

3.5.1. Porosity

3.5.1.1. Definition of porosity

Porosity in porous material describes the ratio of the void space over the total volume of the

material. The value of the fraction is between 0 and 1.

total

void

V

Vn

The value of porosity can be calculated in function of these material components: the caliper

(d), the basis weight (BWi) and the material density (i)[12]

.

total

solid

total

solidtotal

V

V

V

VVn

1

ABdVABBW

V totalS

solid

;

(3.18)

(3.19)

(3.20)

Figure 3.10.Porous media structure


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sd

BWn

1

Porosity has an important effect in the maximum absorption capacity (C m). Cm is reached

when the void pores are fully saturated [8]. Saturation is the ratio between the volume of fluid

and the total void volume of the material. When the total void volume of the material is full

of liquid the saturation values is 1. Then, the maximum absorption capacity is reached.

void

liquid

V

VS

The porosity of the material has a direct influence in the maximum absorption capacity as the

following graphic shows.[12]

Figure 3.12.[9]Influence of porosity in the maximum absorption capacityNotes: Graphic obtained by density liquid used 1000 kg/m3density solid 500 kg/m3

0 %S = 0

50%S = 0.5

100%S = 1

n

nC

s

liquid

m

1

(3.21)

Figure 3.11.Saturation in porous media

(3.23)

(3.22)


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The porosity in swelling porous materials is also defined as the void volume divided by the

core total volume. However, in this case the volume of the porous material is not constant.For diaper materials under confining pressure, porosity tends to decrease as the porous media

absorbs liquid and swells. Therefore, the relation of swollen porous materials involves the

effects of swelling, core design variables and the expansion of the composite system.

Material Porosity

Aquistion Layer 0.70-0.95

Distribution Layer 0.75-0.99

Storage Layer @full load 0.05-0.50

3.5.1.2. Experimental test method

Non-swelling porous materials

In non-swelling materials the porosity is calculated by the equation 3.24, where the basis

weight, the caliper and the density are calculated experimentally.

sd

BWn

1

Where; n is the porosity, d is the caliper, BW is the basis weight and the material density.

Swelling porous materials

In swelling materials the porosity is not constant. Therefore it has to be calculated at different

x-loads.

The swelling material sample is placed in contact with the liquid with weight on the top toapply a pressure in the sample. Liquid is then filled in the glass frit. The liquid is absorbed by

the swelling material until reaches the maximum absorption capacity of this material at the

applied pressure. When the equilibrium is reached, the caliper of the sample and the wet

weight is obtained. The method is repeated for different saline concentrations. The porosity is

obtained by the ratio between void volume and the total volume [18].

Table 3.1.Porosity values of the materials used

(3.24)


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3.5.2. Capillary pressure

3.5.2.1. Definition of capillary pressure

In porous materials, the pores normally have an irregular geometry of different sizes and

shapes. This is very important to determine the effective radius of the pores in order to

determine the real free volume of the material. Remarkably that can be considered three type

of pores, through pores, blind pores and closed pores[12].

The capillary pressure is defined as two times the surface tension times the cosine of the

contact angle divided by the radius of the curved interface, equation 3.25 by calculating the

capillary pressure experimentally, the effective radius r of any pore could be defined using

the same equation, equation 3.26.

rPc

cos2

Pcr

cos2

Where; r is the effective radius of the pore, Pcis a pressure difference across the liquid air

meniscus, is the surface tension of the liquid, is the contact angle of the liquid.

(3.25)

Closed Pores

Through Pore

Blind Pore

(3.26)

Figure 3.13.Pore volume distribution in a swelling material


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The pore volume distribution of porous materials is measured by the Capillary Sorption

Isotherm (Cap-sorption) test. The Cap-sorption test measures the capillary sorption

(absorption and desorption) isotherms of absorbent materials as well as the maximum

capacity of the material. These properties describe how liquid moves in the material

structure. The same test is done for non-swelling and swelling materials.

The material sample for analyzing is in a porous glass frit, which is connected hydraulically

to a fluid reservoir on a balance. This balance is connects to a computer. The porous materialabsorbs fluid, then the weight measured in the balance decreases and the glass frit goes down

from 80 cm to 70 cm. This sequence happens until a 0 cm. In this point all pores are filed

(saturation=1) and the x-load at this point corresponds to the maximum absorption capacity.

The desorption curve is obtained by moving the glass frit from 0 cm to the starting point[19].

Figure 3.14.Cap Sorption equipmnet

Computer0 cm

50 cm

80 cmPorous glass frit

Balance


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3.5.3. Permeability

3.5.2.1. Definition of permeability

Permeability describes the ability of the liquid to flow through a layer. Permeability is

defined by Darcys law[20].

L

AKPQ

Where; Q is the volumetric flow rate [m3

/s] of a fluid with viscosity [Pas], which throughinto a volume of porous material with length L [m] in the direction of the flow and section A

[m2]. P [Pa] is the pressure gradient, a property that, in general, includes capillary pressure,

gravity and external pressure, the driving forces present in the system. Permeability, K [m2],

is a function of the porosity, pore volume distribution, tortuosity and specific surface area.

Generally permeability depends on saturation. Therefore we introduce a relative permeability

function kr(S) and a full saturation permeability K0, according to the equation below.

)()( 0 SkkSK r

A typical model used to describe saturation dependency for permeability is a power model,

where the power parameter b is introduced according to the equation below.

Qw

d

L

P

(3.27)

Figure 3.15.Fluid through porous material

(3.28)


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bSkSK 0)(

While with laboratory methods it is possible to measure k0, for absorbent porous materials it

is very challenging to determine the power parameter b. This is normally in a range between

3-5.

Table 3.2 reports typical values of K0 for diaper materials.

Material Permeability [units]

AL @full load 20-100DL @full load 3-10

SL @full load 0.1-1

A typical dependency of Kr with S is shown in Figure below to adjust (take out non swell

and swell, only a plot for n=5)

What described above applies generally to porous materials. For swelling materials, when the

material absorbs liquid and starts to swell at the same time it is generally observed that the

permeability decreases, when increasing AGM load, i.e. the amount of liquid swollen into

AGM. For earlier AGM generations, without surface cross linking, this process was

eventually leading to gel blocking [20], i.e. permeability getting close to zero.

(3.29)

Figure 3.16.Relative permeability function of satruation

Table 3.2.Permeability values of the materials used


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As shown in Table 3.2 generally the permeability of the swelling material (SL Layer) is

much lower than the non-swelling materials (AL and DL). Taking into account that the value

of permeability has a dependency on porosity, it is normal to have less permeability in these

kinds of materials. There are other effects that explain the low value of permeability in

swelling materials. Gel deformation under pressure describes the effect that swelling AGM is

reducing the capillaries or void spaces therefore drastically increasing the flow resistance for

liquid.


The method to calculate the permeability is based on gravimetric determination, the quantity

of solution through a test piece of porous material under a constant pressure. The flow

conductivity is determined by Darcys Law and steady-states methods. This test determines

the permeability in x,y- direction or z direction[21].

3.5.4. Swelling kinetics

3.5.4.1. Definition of the swelling kinetics parameters

In the dry state the swelling particles are powders. When the swelling material absorbs liquid,

the powders turns to be softer and more flexible gel particles. Both characteristics are

determined by the structure and swelling ratio of the used super absorbent.

The swelling effect occurs until the superabsorbent particles arrive to equilibrium between

driving and retractive forces[12].

Pext

Pelas

PmixPosm

Figure 3.17. Balance of driving force in an AGM particle


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extelastosmmix

PPPP

The driving forces are Pmix and Posm. The first parameter describes the interactions between

the polymer and the solvent and the necessity to be dissolve. On the other side, osmotic

pressure, describes a hydrostatic force produced by the differences of pressure between the

liquid in the particle and the liquid in contact with the particle. In the other part of the

balance the balance are the retroactive forces. The network elasticity (Pelast) describes the

elastic chains formed by crosslink and the external pressure (Pext) is mainly the baby pressure

on a diaper. The osmotic pressure is calculated by the ideal gas law.

V

TRnP

Osmotic pressure depends on: V volume [m3], n the number of molecules [mole] in the

solution, the gas constant R (8.314 J/mol K) and the temperature T [K]. Thereby the particle

size, the temperature, and the NaCl concentrations have an important effect on the swellingkinetic parameters [20].

A small particle size offers a better absorption speed in the initial phase of swelling. In

contrast bigger particles achieve higher loads, because it has more volume. In addition high

temperature offers faster absorption speed. However in our case (diapers), it is a variable

impossible to control in the real life. The superabsorbent used has the capacity to absorb

around 800-1200 g/g of water, but if the liquid absorbed is urine, the maximum x-load is 25-

50 g/g. This is because the urine contains NaCl. As a result of the presence of (cations in the

absorbed liquid reduce), the liquid load for the swelling material is reduced.


The method measures continually the AGM load over a specific time period. In this case only

one saline concentration of 0.9% NaCl in water is used. [22]

(3.30)

(3.31)


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Chapter 4. MATHEMATICAL MODELING

OF FLUID FLOW IN POROUS MEDIA

4.1. Introduction

A mathematical model is created in order to deeply analyze a system which is desired to be

controlled and optimized. With a mathematical model built, it is possible to obtain some

hypotheses about how the system is working and estimate how some parameters could affect

the systems behavior. This avoids the necessity to invest a lot of money and time doing

these experiments in the laboratory.

A mathematical model usually describes a system by a set of variables and a set of equations

that establish relationships between these variables. The model is the set of functions that

describe these relationships. Mathematical models are classified as: linear vs. non-linear,

deterministic vs. probabilistic, static vs. dynamic and lumped vs. distributed parameters.

Models are carried out via a computer, calculating the values that describe an approximation

about how the system works as a function of the variables introduced and the model

hypotheses.

The model used in this project describes the fluid flow in porous media. It was designed to

study in more detail the liquid transport in hygiene products (e.g. diapers, wipes and pads)

and to optimize use data from the simulation to their materials and geometry[23].

In the case studied (the core of a diaper) the system simulated and analyzed is composed of

the acquisition layer, distribution layer and the storage layer. The first two layers are non-

swelling porous materials, whereas the third one is a swelling material. Therefore, there are

separate mathematical models for both non-swelling and swelling materials.


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Mathematical modeling of fluid flow in porous media


Fluid flow in non-swelling porous materials is described by the Richards equation, equation

4.8. It describes the flow of a two-phase system and is based on the mass and momentum

conservation equations.

The mathematical model that describes fluid flow in swelling porous materials is more

complex. It consists of balance equations of mobile and absorbed (immobile) liquid

combined with a series of constitutive relationships. The equation system obtained is strongly

non-linear and requires advanced numerical strategies for solving such as: spatial and

temporal discretization and mesh movement.

These models are based in FEFLOW DHI-Wasy software. This simulation program is used to

simulate the fluid flow in the diapers core. FEFLOW is a computer program for simulating

groundwater flow, mass transfer, and heat transfer in porous media. The program uses finite

element analysis to solve the groundwater flow equation of both saturated and unsaturated

conditions. It also solves for mass and heat transport, taking into account fluid density effects

and chemical kinetics for multi-component reaction systems [24].

4.2. Mathematical modeling of fluid flow in non-swellingporous materials

4.2.1. Introduction

In non-swelling, porous materials, the simulation program, FEFLOW, solves the Richards

equation. This non-linear partial differential equation represents the liquid flow in

unsaturated materials.

The Richards equation describes the flow of a two-phase system (liquid and gas phases). The

constitutive relations are dependent in the liquid phase and are solved with one primary

variable (saturation, S, or pressure head, ). However, in the gas phase flow is assumed to be

infinitely mobile [12].


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Mathematical modeling of fluid flow in porous media


The Richards equation is obtained from the mass conservation equation (continuity equation)

and the momentum conservation equation (Darcy law).

4.2.2. Balance equations

4.2.2.1. Mass conservation equation

In the system studied, mass can only be produced or reduced by external sources, namely:

liquid inflow or outflow.

The mass conservation equation (equation 4.1) used is only representative of the liquid

phase, since the gas phase will not be modeled by the Richards equation.

mqmt

m

)(

where; mis the mass, t the time, the velocity and qmthe density of external mass.

Density of external mass can also be expressed as:

Vqqm

Combini

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