Fitting Fick’s model to analyze water diffusion into chickpeas during soaking with ultrasound treatment

Journal of Food Engineering 104 (2011) 134–142

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Journal of Food Engineering

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Fitting Fick’s model to analyze water diffusion into chickpeas during soakingwith ultrasound treatment

Ali Yildirim a, Mehmet Durdu Öner b,⇑, Mustafa Bayram b

a Department of Food Technology, Vocational School of Higher Education in Nizip, Gaziantep University, 27700 Nizip, Gaziantep, Turkeyb Department of Food Engineering, Faculty of Engineering, Gaziantep University, 27310 Gaziantep, Turkey

a r t i c l e i n f o

Article history:Received 15 September 2010Received in revised form 27 November 2010Accepted 4 December 2010Available online 15 December 2010

Keywords:ChickpeaFittingFick’s modelUltrasoundWater diffusion

0260-8774/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.jfoodeng.2010.12.005

Abbreviations: AOAC, official methods of analysisacoustic energy density in W cm�3; Deff, water diffusimoisture content in dry basis (%); inci, a special tyÇukurova Agricultural Research Institute (Adana, Turk⇑ Corresponding author. Tel.: +90 342 3172305; fax

E-mail address: [email protected] (M.D. Öner).

a b s t r a c t

Fick’s model together with Arrhenius relationship were successfully used to evaluate water absorption ofchickpea during soaking at a temperature range of 20–97 �C with 25 kHz 100 W, 40 kHz 100 W and25 kHz 300 W ultrasound treatments. Use of ultrasound, increase in ultrasound power and soaking tem-perature significantly (P < 0.05) increased the water diffusion coefficient (Deff) of chickpea during soaking.Average gelatinization temperature of chickpea was found as 61.47 �C. Activation energy (Ea) values ofchickpea for below and above gelatinization temperature were found to be 28.69 and 9.34 kJ mol�1,respectively. Ultrasound treatments significantly decreased the soaking time of chickpea.

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1. Introduction

Chickpea (Cicer arietinum L.) is one of the oldest and mostwidely consumed legumes in the world, particularly in tropicaland subtropical areas. Major chickpea producer and exportercountries are India, Turkey, Pakistan, Iran Islamic Republic, andAustralia. Chickpea is an important source of proteins, carbohy-drates, B-group vitamins and certain minerals (Chavan et al.,1986; Christodoulou et al., 2006). Food legumes decreased inci-dence of several diseases, such as cancer, cardiovascular diseases,obesity and diabetes (Bhathena and Velasquez, 2002). Legumesare usually cooked before being used in the human diet to improvethe protein quality by destruction or inactivation of the heat labileanti-nutritional factors (Wang et al., 1997). Recently, there hasbeen increasing demand for research to improve cooking of chick-peas in developed countries where chickpeas are mainly consumedto improve overall nutritional status by replacing animal foodswith legumes (Guillon and Champ, 1996). The most commonprocess of pre-soaking usually is not sufficient to decrease overallcooking time of chickpea. Understanding water absorption in

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of AOAC International; EAD,on coefficient in m2 s�1; d.b.,pe of chickpea produced byey).: +90 342 3172362.

legumes during soaking is of practical importance since it affectssubsequent processing operations and the quality of the finalproduct.

Ultrasound is a form of energy generated by sound waves of fre-quencies that are too high to be detected by human ear, i.e. above16 kHz (Jayasooriya et al., 2004). Ultrasound cavitations could re-sult in the occurrence of micro streaming which is able to enhanceheat and mass transfer. Ultrasonic is a rapidly growing field ofresearch, which is finding increasing use in the food industry(Jayasooriya et al., 2004; Zheng and Sun, 2006). Ultrasound hasbeen used to enhance mass transfer in solid/liquid food systems(Fuente et al., 2004; Riera et al., 2004). Ultrasound applicationswere reported to promote the leaching of oligosaccharides inlegumes (Han and Baik, 2006) and to reduce cooking time of rice(Wambura et al., 2008).

In the food industry, chickpea is pre-processed in the factories toproduce humus (as Arabic food), canned products, blended powderproducts. To produce these products, chickpea is soaked and cooked.Therefore, this study supplies important information and ultrasonictechnique to process it easily. In addition, it is known that chickpeais a hard legume to cook. Therefore, ultrasonic technique supplies anew solution to decrease soaking and cooking time.

These studies show that thermosonication can be used to in-crease the water absorption during soaking operation. The objec-tive of this study was to determine the applicability of Fick’ssecond law of diffusion in modeling the water diffusion character-

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A. Yildirim et al. / Journal of Food Engineering 104 (2011) 134–142 135

istics of ultrasound treated chickpea in an attempt to determinesuitable processing conditions for rehydration.

2. Materials and methods

2.1. Raw materials

Certified chickpeas (inci-2003) with initial moisture content of11.58% (d.b.) and an average diameter of 8.00 (±0.27) mm (mea-sured with Mutitoyo No. 505-633, Japan, digital micrometer) ob-tained from Çukurova Agricultural Research Institute (Adana,Turkey), were used throughout this study. After removing foreignmaterials and damaged seeds, they were sieved to standardizethe sizes, 7.5 –9 mm.

2.2. Water absorption determination during soaking operation

The soaking of chickpea was performed at 20, 30, 40, 50, 60, 70,87, 92, and 97 �C without, and with 25 kHz 100 W (acoustic energydensity (EAD) of 0.025 W cm�3), 40 kHz 100 W (EAD of0.025 W cm�3) and 25 kHz 300 W (EAD of 0.017 W cm�3) ultra-sound treatments. One hundred grams of chickpea seeds were im-mersed in 2000 ml deionized water (1:20); conventional andultrasonic soaking were both performed in ultrasonic (US) tanks(Intersonik Co., Turkey) until seeds were fully hydrated. Fourgrams of chickpea and 80 ml soaking water (1:20) were quickly re-moved from the tanks for the moisture content determinationwithin 30 min intervals. Chickpea seeds were gently wiped withclean paper towel to remove excess water and ground for the mois-ture content determination. The moisture contents of randomly se-lected grains (5 g) were determined in dry basis at 105 �C for 48 husing oven drying method (AOAC, 2002) and used for Fick’s mod-eling of water diffusion. The experiments were replicated twiceand measurements were duplicated.

2.3. Determination of soluble solids loss during soaking of chickpeas

Four grams of chickpea and 80 mL of soaking water (1:20 ratio)were removed from the soaking chamber after 3.5 h of soakingoperation at 97 �C. Soluble solids content (Brix, g/g%) of the soakingwater was measured at 25 �C by using Abbe-refractometer (Opton-F.G. Bode and Co., Germany) and was reported as maximum solu-ble solids loss.

istu

re c

onte

nt (

% g

/g, d

.b.)

40

60

80

100

120

140

160

20 oC

30 oC

40 oC

50 oC

60 oC

70 oC

87 oC

92 oC

2.4. Determination of gelatinization temperature of chickpeas

Birefringence images of the chickpea samples at soaking tem-peratures of 40, 50, 60, and 70 �C were captured in a PC using apolarized light microscope (OLYPOS TX51, Euromex Microscopen,Ed Arnhem, Netherlands) equipped with a video camera (VC3031, Euromex Microscopen, Ed Arnhem, Netherlands) connectedto the PC (Fig. 6). A solution of 1% (cooked chickpea flour/water)samples were prepared. After 30 min of mixing, 20 lL of samplesolution was spread on lamella, and the birefringence images werecaptured through the microscope. The gelatinization temperatureof the grains is defined as the temperature at which the birefrin-gence of starch starts to diminish (Hoseney, 1994).

Time (min)0 100 200 300 400 500 600 700 800

Mo

0

2097 oC Fick's Model

Fig. 1. Means of experimental and predicted moisture contents (% g/g, d.b.) ofchickpeas during soaking at different temperatures.

2.5. Statistical analysis

SIGMA PLOT 10 (Jandel Scientific, San Francisco, USA) were usedto fit the models and to plot the data. ANOVA and DUNCAN Multi-ple Range Tests, using SPSS version 16, at P < 0.05 were performedto determine effect of processing parameters.

3. Results and discussion

3.1. Water diffusion characteristics of chickpea during soaking

Food legumes are usually soaked before cooking to provide suf-ficient amount of moisture for gelatinization of starch and/or gela-tion of protein. The most important property for soaking ofchickpea is the moisture content to achieve the proper cookingoperation. It could be achieved either through conditioning belowthe gelatinization temperature and then cooking above the gelati-nization temperature, or through direct cooking above the gelatini-zation temperature. Mass transfer plays a key role in foodprocessing, like humidification and dehumidification, dehydration,distillation, absorption, etc. The driving force for mass diffusion isthe concentration difference. In solids, there can obviously be noconvection and all movements are by molecular diffusion due torandom molecular movements.

The water absorption characteristics of chickpea were analyzedusing moisture content (%, d.b.) values in this study. The meanmoisture contents and the statistical analysis of soaked chickpeasat 20–97 �C without ultrasound, and with 25 kHz 100 W, 40 kHz100 W and 25 kHz 300 W ultrasounds treatment were illustratedin Figs. 1–4 and tabulated in Tables 1–4. The moisture contents(%, d.b.) of chickpea during soaking were significantly (P < 0.05) in-creased as the temperature, time and power of ultrasounds in-creased (Figs. 1–4 and Tables 1–4). Chickpea water absorptioncurves are characterized by an initial phase of rapid water pickupfollowed by an equilibrium phase, during which the chickpea ap-proaches its full soaking capacity. The rate of water absorption in-creased with increasing temperature as suggested by the slopes ofthe absorption curves getting steeper with increased temperature(Figs. 1–4).

3.2. Primary modeling of chickpea water diffusion as a function of time

Many theoretical, empirical, and semi-empirical models havebeen employed for modeling, to relate experimental results withphysical laws, the water absorption behavior of agricultural prod-ucts during soaking. The theoretical mechanisms for the kinetics ofthe diffusion process have been proposed for the Fickian diffusionmodel by some researchers before (Bello et al., 2004; Kashaninejadet al., 2007; Sabapathy et al., 2005; Seyhan-Gürtas� et al., 2001;Gowen et al., 2007).

Moisture diffusivity is an important transport property neces-sary for the design and optimization of all the processes that in-volve internal moisture movement. Diffusion coefficient is the

Time (min)

0 100 200 300 400 500 600

Moi

stur

e co

nten

t (%

g/g,

d.b

.)

0

20

40

60

80

100

120

140

20 oC (control)

20 oC + 25 kHz 100 W US

20 oC + 40 kHz 100 W US

20 oC + 25 kHz 300 W US

Fick 's model

Time (min)0 100 200 300 400 500

Moi

stur

e co

nten

t (%

g/g,

d.b

.)

0

20

40

60

80

100

120

140

30 oC (control)

30 oC + 25 kHz 100 W US

30 oC + 40 kHz 100 W US

30 oC + 25 kHz 300 W US

Fick's model

Time (min)

0 100 200 300 400 500

Moi

stur

e co

nten

t (%

g/g,

d.b

.)

0

20

40

60

80

100

120

140

40 oC (control)

40 oC + 25 kHz 100 W US

40 oC + 40 kHz 100 W US

40 oC + 25 kHz 300 W US

Fick 's model

A

B

C

Fig. 2. Means of experimental and predicted moisture contents (% g/g, d.b.) ofchickpeas during soaking at 20 (A), 30 (B) and 40 (C) �C temperatures without andwith ultrasound treatments.

Time (min)0 100 200 300 400

Moi

stur

e co

nten

t (%

g/g,

d.b

.)

0

20

40

60

80

100

120

140

160

180

50 oC (control)

50 oC + 25 kHz 100 W US

50 oC + 40 kHz 100 W US

50 oC + 25 kHz 300 W US

Fick 's model

Time (min)0 100 200 300

Moi

stur

e co

nten

t (%

g/g,

d.b

.)

0

20

40

60

80

100

120

140

60 oC (control)

60 oC + 25 kHz 100 W US

60 oC + 40 kHz 100 W US

60 oC + 25 kHz 300 W US

Fick's model

Time (min)

0 100 200 300 400

Moi

stur

e co

nten

t (%

g/g,

d.b

.)

0

20

40

60

80

100

120

140

160

70 oC (control)

70 oC + 25 kHz 100 W US

70 oC + 40 kHz 100 W US

70 oC + 25 kHz 300 W USFick's model

A

B

C


136 A. Yildirim et al. / Journal of Food Engineering 104 (2011) 134–142

factor of proportionality representing the quantity of substancediffusing across a unit area through a unit concentration gradientin unit time. Total amounts of diffusing substance entered a spher-ical grain of radius r can be obtained from the following Fick’s ser-ies type equation (Crank, 1975):

M �Me

Mo �Me¼X1n¼1

6n2p2 exp

�Deffp2

r2 n2t� �

ð1Þ

where M, Me, Mo are moisture contents (%, d.b.) at any time,equilibrium and initial, respectively. Deff and r are effective diffu-sion constant (m2 s�1) and average radius of chickpea (m), respec-tively. A fit of the experimental data for soaking times leads to thedetermination of an average diffusion coefficient, Deff, via Eq. (1)which is Fick’s law of diffusion of water in solids of spherical shape.

The chickpea seeds may be approximated as spheres with a meandiameter of 0.0040 m (±0.0001). Fick’s laws of diffusion (Eq. (1))and its derived equations account for most of the models used infood science, as can be observed from publications (Garcia-Pascualet al., 2006; Gowen et al., 2007; Sabapathy et al., 2005). Some ofthe common assumptions and simplifications often made for solv-ing Fick’s second law (Eq. (1)) include the following: (1) the mois-ture transfer is one dimensional, unsteady state in the radialdirection, (2) chickpea is considered to be an almost spherical ob-ject, (3) the initial temperature and moisture distributions are uni-form, (4) there is a moisture gradient in the chickpea with respectto time, (5) the thermal properties are constant, (6) chickpea isconsidered as a homogeneous isotropic solid, (7) moisture transferto and from the seed is due to concentration gradient, (8) the quan-tity of solid loss in the grains during cooking was neglected, (9) for

Time (min)0 50 100 150 200 250

Moi

stur

e co

nten

t (%

g/g,

d.b

.)

0

20

40

60

80

100

120

140

160

87 oC (control)

87 oC + 25 kHz 100 W US

87 oC + 40 kHz 100 W US


Time (min)0 50 100 150 200 250

Moi

stur

e co

nten

t (%

g/g,

d.b

.)

0

20

40

60

80

100

120

140

160

92 oC (control)

92 oC + 25 kHz 100 W US

92 oC + 40 kHz 100 W US


Time (min)

0 50 100 150 200 250

Moi

stur

e co

nten

t (%

g/g,

d.b

.)

0

20

40

60

80

100

120

140

160

97 oC (control)

97 oC + 25 kHz 100 W US

97 oC + 40 kHz 100 W US

97 oC + 25 kHz 300 W US Fick's model

A

B

C


Table 1Summary of multiple range analysis (Duncan test) on moisture contents (%, d.b.) of soake

Time (min) Moisture content (%, d.b.)

20 �C 30 �C 40 �C 50 �C

0 11.58a,1 11.58a,1 11.58a,1 11.58a,1

30 33.55b,1 37.40b,2 46.10b,3 62.36b,4

60 43.88c,1 57.54c,2 62.58c,3 84.70c,4

90 56.27d,1 66.99d,2 80.53d,3 95.43d,4

120 65.50e,1 78.98e,2 88.24e,3 108.69e,4

150 72.52f,1 82.27f,2 97.30f,3 115.84f,4

180 76.91g,1 84.53g,2 101.90g,3 120.82g,4

210 81.93h,1 93.76h,2 110.18h,3 122.71h,4

a–h Indicate statistical differences between each row at a = 0.05.1–9 Indicate statistical differences between each column at constant temperatures, a = 0


long soaking times, only the first term of series equation wassignificant.

In this study, the effect of loss of soluble solids from chickpeaseeds was not taken into account in calculating the moisture con-tent because maximum loss of soluble solids from chickpea at tem-peratures of 97 �C for 3.5 h soaking was about 2.06% of the originalmass which in comparison with the water gain was assumed to benegligible. Other researchers have also reported similar assump-tion for other seeds (Sayar et al., 2001; Sabapathy et al., 2005).When these assumptions were applied on Fick’s second law, thefollowing equation was obtained.

M ¼ Me þ ðMo �MeÞ6p2 exp �Deffp2t

r2

� �ð2Þ

The Fick’s law of diffusion function is related to diffusion ofwater and diffusion coefficient (Deff). For mathematical modelingof the variation of moisture content of chickpea during soakingat each temperature without, and with ultrasounds treatment,Fick’s law model was tested. The parameters in this model suchas Deff (main parameter), Me, were estimated by using the non-linear regression analysis of Eq. (2) and presented in Table 5. Theperformance parameters of the model, the coefficient of determi-nation (R2) and percentage of root mean square error (% RMSE)are given on Table 5. The course of the hydration, adequately fittedby a non-linear equation (Eq. (2)), and reveals the fact that the seedmoisture content increases with soaking time, use of ultrasoundtreatments and increase in used ultrasound power at all tempera-tures (Figs. 1–4 and Tables 1–5). Water absorption ceases when theseed attained the equilibrium water content (Sayar et al., 2001).The diffusion process, which obeys the Fick’s law model, was foundto be a thermally activated process and sensitive to temperature,time, ultrasound treatment and its power.

When the temperature was raised from 20 to 97 �C, Deff valueswere increased from 1.40 � 10�10 to 7.72 � 10�10 m2 s�1, also sig-nificant (P < 0.05) increase was observed in the equilibrium mois-ture content (Me) (from 119.82 to 150.05 (%, d.b.)) (Table 5). R2

and % RMSE values were in the range of 0.9894–0.9960 and2.51–8.03, respectively. The magnitude of diffusion coefficient re-ported by Sayar et al. (2001) for temperatures ranging from 20 to100 �C were 2.43 � 10�10 to 39.16 � 10�10 m2 s�1 for spring chick-pea and 1.99 � 10�10 to 36.94 � 10�10 m2 s�1 for winter chickpea.The water diffusion coefficient of chickpea ranged from9.71 � 10�11 to 5.98 � 10�10 m2 s�1 in the study of Seyhan-Gürtas�et al. (2001). The diffusion coefficients of chickpeas for tempera-ture range of 45–98.7 �C were found as 0.14 � 10�10–5.51 � 10�10 m2 s�1 in another study (Sabapathy et al., 2005). Dif-fusivity values reported in this study were similar to the literatureresults. Moisture absorption at elevated temperatures may induce

d chickpeas as a function of processing time and temperature.

60 �C 70 �C 87 �C 92 �C 97 �C

11.58a,1 11.58a,1 11.58a,1 11.58a,1 11.58a,1

70.61b,5 76.09b,6 86.85b,7 91.54b,8 97.05b,9

97.89c,5 99.01c,6 108.58c,7 111.16c,8 121.06c,9

108.05d,5 110.19d,6 122.38d,7 125.43d,8 136.49d,9

115.63e,5 119.45e,6 129.30e,7 131.36e,8 144.71e,9

124.02f,5 126.35f,6 135.41f,7 137.76f,8 148.59f,9

126.57g,5 129.78g,6 138.37g,7 142.44g,8 150.72g,9

128.99h,5 130.68h,6 140.17h,7 142.67h,8 151.97h,9

.05.

Table 2Summary of multiple range analysis (Duncan test) on moisture contents (%, d.b.) of soaked chickpeas at 20, 30, and 40 �C with and without ultrasound treatments.


20 �C 20 �C + 40 kHz 100 W 20 �C + 25 kHz 100 W 20 �C + 25 kHz 300 W

0 11.58a 11.58a 11.58a 11.58a

30 33.55a 34.82b 40.61c 43.18d

60 43.88a 44.97b 54.06c 55.93d

90 56.27b 56.24a 65.76c 69.60d

120 65.50b 64.60a 70.64c 74.85d

150 72.52b 70.24a 78.20c 86.92d

180 76.91b 76.55a 85.14c 91.89d

210 81.93b 80.54a 89.48c 95.66d

240 88.39b 86.14a 95.14c 102.30d

270 90.63a 92.05b 99.12c 106.56d

300 98.06b 97.69a 103.11c 111.56d

30 �C 30 �C + 40 kHz 100 W 30 �C + 25 kHz 100 W 30 �C + 25 kHz 300 W0 11.58a 11.58a 11.58a 11.58a

30 37.40a 39.79b 41.04c 49.85d

60 57.54a 57.79b 60.40c 60.88d

90 66.99b 66.24a 73.77c 72.19d

120 78.98b 78.37a 79.63c 90.31d

150 82.27b 81.72a 86.40c 100.06d

180 84.53a 84.87b 92.52c 107.72d

210 93.76b 93.20a 98.00c 111.05d

240 104.78b 104.40a 106.25c 113.29d

270 107.75b 107.39a 108.23c 115.60d

300 109.96b 109.75a 112.03c 118.85d


30 46.10b 45.55a 54.71c 59.86d

60 62.58a 63.92b 72.20c 77.41d

90 80.53b 78.70a 84.23c 97.25d

120 88.24a 89.43b 93.59c 107.08d

150 97.30a 100.21b 109.76c 115.29d

180 101.90b 100.62a 115.10c 121.19d

210 110.18b 109.70a 118.23c 128.12d

240 111.00a 112.58b 122.29c 127.27d

270 117.95b 116.90a 125.34c 128.00d

300 121.84b 120.49a 125.47c 128.12d

a-d Indicate statistical differences between each column at constant temperatures, a = 0.05.

Table 3Summary of multiple range analysis (Duncan test) on moisture contents (%, d.b.) of soaked chickpeas at 50, 60 and 70 �C with and without ultrasound treatments.



0 11.58a 11.58a 11.58a 11.58a

30 62.36b 57.74a 64.74c 75.35d

60 84.70a 86.78b 91.31c 109.25d

90 95.43a 101.14b 106.73c 117.07d

120 108.69b 108.19a 115.86c 121.01d

150 115.84a 117.20b 123.87c 128.71d

180 120.82b 119.15a 126.11c 131.34d

210 122.71a 123.12b 127.22c 134.59d


30 70.61b 69.73a 72.96c 80.35d

60 97.89b 96.90a 99.89c 111.50d

90 108.05a 108.36b 113.06c 120.27d

120 115.63b 114.91a 119.91c 126.34d

150 124.02b 124.00a 127.76c 130.71d

180 126.57b 126.51a 128.99c 132.14d

210 128.99b 127.93a 130.74c 134.92d


30 76.09b 74.13a 82.82c 84.81d

60 99.01b 98.09a 105.95c 112.69d

90 110.19b 109.72a 114.24c 124.46d

120 119.45b 115.87a 122.16c 129.46d

150 126.35b 125.11a 129.20c 131.97d

180 129.78b 128.64a 131.50c 133.72d

210 130.68b 129.32a 132.30c 135.78d

a–d Indicate statistical differences between each column at constant temperatures, a = 0.05.


Table 4Summary of multiple range analysis (Duncan test) on moisture contents (%, d.b.) of soaked chickpeas at 87, 92 and 97 �C with and without ultrasound treatments.



0 11.58a 11.58a 11.58a 11.58a

30 86.85b 85.33a 92.25c 108.65d

60 108.58b 107.48a 115.49c 128.81d

90 122.38b 122.13a 128.16c 142.46d

120 129.30a 130.03b 132.48c 148.93d

150 135.41a 136.01b 138.23c 150.90d


30 91.54b 89.91a 102.61c 115.27d

60 111.16a 112.34b 122.37c 132.71d

90 125.43b 124.29a 139.77c 147.79d

120 131.36b 131.23a 146.11c 151.24d

150 137.76b 137.75a 150.54b 154.23c


30 97.05b 96.49a 106.98c 122.78d

60 121.06b 119.59a 139.07c 145.37d

90 136.49b 136.25a 148.67c 153.97d

120 144.71a 144.91b 151.23c 157.57d

150 148.59a 148.61b 158.93c 165.45d

a-d Indicate statistical differences between each column at constant temperatures, a = 0.05.

Table 5Predicted parameters of Fick’s model during soaking of chickpeas at different temperatures without and with ultrasound application.

Process Me (%, d.b.) Deff � 1010 (m2 s�1) R2 RMSE (%)

20 �C 119.82 1.40 0.9960 8.0320 �C + 25 kHz 100 W 119.48 1.70 0.9907 13.8820 �C + 40 kHz 100 W 123.10 1.28 0.9943 10.7620 �C + 25 kHz 300 W 120.94 2.01 0.9925 11.2930 �C 122.81 1.87 0.9894 9.7030 �C + 25 kHz 100 W 122.61 2.10 0.9910 10.9730 �C + 40 kHz 100 W 122.41 1.86 0.9885 12.0230 �C + 25 kHz 300 W 124.40 2.62 0.9904 8.7840 �C 128.44 2.39 0.9944 8.9340 �C + 25 kHz 100 W 129.86 2.98 0.9914 9.8840 �C + 40 kHz 100 W 127.56 2.46 0.9952 8.0140 �C + 25 kHz 300 W 130.79 3.79 0.9951 6.5950 �C 128.64 4.11 0.9942 2.7050 �C + 25 kHz 100 W 130.72 4.94 0.9988 2.7250 �C + 40 kHz 100 W 127.30 4.42 0.9981 2.5350 �C + 25 kHz 300 W 133.56 6.52 0.9944 2.9160 �C 129.76 5.58 0.9957 4.7460 �C + 25 kHz 100 W 131.68 5.92 0.9978 3.4360 �C + 40 kHz 100 W 129.17 5.57 0.9966 4.1060 �C + 25 kHz 300 W 133.67 7.29 0.9978 1.8770 �C 130.66 6.01 0.9944 5.8570 �C + 25 kHz 100 W 131.05 7.11 0.9924 5.4570 �C + 40 kHz 100 W 130.22 5.78 0.9935 6.1970 �C + 25 kHz 300 W 134.06 7.96 0.9993 1.2987 �C 137.47 7.12 0.9938 5.5587 �C + 25 kHz 100 W 139.06 8.19 0.9944 4.1387 �C + 40 kHz 100 W 138.78 6.76 0.9942 5.7587 �C + 25 kHz 300 W 150.63 9.77 0.9937 4.1892 �C 139.70 7.49 0.9908 6.3692 �C + 25 kHz 100 W 149.74 8.54 0.9935 5.0092 �C + 40 kHz 100 W 139.67 7.40 0.9925 5.7392 �C + 25 kHz 300 W 151.37 11.20 0.9948 9.8597 �C 150.05 7.72 0.9959 2.5197 �C + 25 kHz 100 W 157.88 9.23 0.9974 2.0297 �C + 40 kHz 100 W 150.32 7.53 0.9954 5.2997 �C + 25 kHz 300 W 159.75 11.90 0.9960 2.55

RMSE (%) = Root mean square error: 100�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1n

P1n ½ðMexp �Mpre=MexpÞ

q�2.


irreversible changes of the seeds, such as chemical and structuraldegradation. It was reported that the rate of water absorption bylegumes increased with increase in time and temperature of thesoaking water. As the process continued, water absorption rate de-

creased steadily due to water filling into the free capillary andintermicellar spaces, and increasing the extraction rates of solublesolids from grains (Quast and Silva, 1977; Tang et al., 1994; Sopadeand Obekpa, 1990; Abu-Ghannam and McKenna, 1997).


3.3. A general model to describe the water diffusion as a function ofsoaking time and temperature

Previous studies showed that temperature is one of the mostimportant factors affecting the water diffusivity and water absorp-tion of agricultural products (Kashaninejad et al., 2007; Turhanet al., 2002). An Arrhenius type equation (Eq. (3)), which had beenused previously to describe the temperature dependant hydrationkinetics of legumes (Abu-Ghannam and McKenna, 1997; Turhanet al., 2002), were used to evaluate temperature dependency of dif-fusion coefficients (Deff) and gelatinization temperature:

lnðDeffÞ ¼ lnðDrefÞ �Ea

R

� �1T

� �ð3Þ

where Deff, T, Ea and R are effective diffusion coefficient of theFick’s model, soaking temperature (in K), activation energy forthe hydration process in kJ mol�1 and ideal gas constant in8.314 � 10�3 kJ mol�1 K�1, respectively. Dref is reference diffusionrate constant for the Fick’s model. The rate of water transfer and/or starch gelatinization in whole cereal and legume grains werefound to be changing linearly with temperature and every curvebrake at a specific temperature which is close to gelatinizationtemperature (Bakshi and Singh, 1980; Sayar et al., 2001; Sagolet al., 2006). Arrhenius plots of the natural logarithm of rate con-stants versus the inverse of T (K) for chickpeas are superposed inFig. 5. The activation energy, Ea, is related to the slope of this graph,and shows the temperature dependence of Deff. To locate the tem-perature at which the break in the Arrhenius curve for soakedchickpeas occurred, the estimated natural log of rate constants(Deff) was fitted to a linear model with break point and the breaktemperature was estimated to be 61.47 �C (R2 = 0.9349–0.9954)for the model (Muggeo, 2003). Such a discontinuity in the Arrhe-nius curve has been observed during the soaking of rice (Bakshiand Singh, 1980) and chickpeas (Sayar et al., 2001), and it has beensuggested that the break is linked to the early onset of starch gela-tinization. The process of gelatinization is generally thought to oc-cur between 63 and 70 �C for chickpeas (Fernandez and Berry,1989). However, it has been suggested (Sayar et al., 2001; Turhanet al., 2002) that chickpea gelatinization may actually begin be-tween the lower temperatures of 55 and 60 �C. Starch granules ofthe chickpeas used in this study kept the integrity of Maltesecrosses till 61 �C (Fig. 6). They noticeably started to decrease innumber and distort in shape between 60 and 70 �C (Fig. 6) pointingthat gelatinization temperature of chickpeas starts between 60 and

1/T (1/K)0.0026 0.0028 0.0030 0.0032 0.0034 0.0036

ln (

Def

f, m

2 s-1)

-23.0

-22.5

-22.0

-21.5

-21.0

-20.5

Experimental (20-60 oC)Experimental (60-97 oC)y= -10.9844- 3450.7955*x (R2=0.9756) (20-60 oC)y= -17.9424-1123.565*x (R2 =0.9954) (60- 97 oC)

Fig. 5. Arrhenius plot of Fick’s law model of diffusion constant, Deff, of chickpea overthe soaking temperature range of 20–97 �C.

70 �C. This observed temperature range is fairly close to the re-ported gelatinization temperature of 63–70 �C for chickpea (Fer-nandez and Berry, 1989). It is possible that the break in theArrhenius curve for soaked chickpeas was due to partial gelatiniza-tion and/or structural changes, promoted soaking at temperaturesabove 60 �C.

Incorporating the temperature break at 61.47 �C for the Fick’smodel, time and temperature dependence of moisture contentfor soaked chickpeas, and dependence of initial and equilibriummoisture contents, the following general models were derived todescribe the water absorption kinetics of chickpeas:

M ¼ Me þ ðMo �MeÞ6p2

� exp �p2

r2 1:696� 10�5 exp�345079

T

� �t

� �ð6 60�CÞ ð4Þ

M ¼ Me þ ðMo �MeÞ6p2

� exp �p2

r2 1:613� 10�8 exp�112356

T

� �t

� �ð6 60�CÞ ð5Þ

Eqs. (4) and (5) can be used to find the moisture content ofchickpea during soaking/cooking at any time (seconds) and tem-perature (K) providing that Mo and Me are known.

The Arrhenius equation has been previously used to describethe temperature dependent hydration kinetics of other grainsand seeds (Maskan, 2002; Turhan et al., 2002). The Deff values de-creased as temperature increased suggesting a corresponding in-crease in the initial water absorption rate. As it is evident fromFig. 5, the linearity of the curves indicates an Arrhenius relation-ship for model.

When the Arrhenius equation (3) was applied to the Deff valuesfor temperatures below and above break point (61.47 �C) sepa-rately, the activation energy values of 28.69 (R2 = 0.9756) and9.34 (R2 = 0.9954) kJ mol�1 were calculated, respectively. This va-lue agrees well with the literature value of 19.50 kJ mol�1 for theactivation energy of osmotic hydration of chickpeas at 5–50 �C(Pinto and Esin, 2004). The activation energies of chickpea werefound as 41.79 and 8 kJ mol�1 for 25–37 �C and 37–60 �C tempera-ture ranges by Gowen et al. (2007). In another study, the activationenergy for chickpea was 48 and 18 kJ mol�1 for temperature bel-low and above 55 �C, respectively (Sayar et al., 2001). The loweractivation energy for the rate of water transfer above the gelatini-zation temperature implies that water travels faster in gelatinizedchickpea than in ungelatinized chickpea.

3.4. Effect of ultrasounds on water diffusion during soaking ofchickpeas

One emergent application of power ultrasound in food industryis the enhancement of mass transfer in processes where diffusiontakes place. Power ultrasound introduces that pressure variationat solid/liquid interfaces, and therefore increases the moistureabsorption rate. Acoustic energy also causes oscillating velocitiesand micro streaming at the interfaces which may affect the diffu-sion boundary layer (Gallego-Juarez, 1998). Furthermore, ultra-sonic waves also produce rapid series of alternative contractionsand expansions (sponge effect) of the material in which they aretraveling; this alternating stress creates microscopic channelswhich may make the moisture gain easier. In addition, acousticwaves may produce cavitations of water molecules inside the solidmatrix, which may be beneficial for the gain of strongly attachedmoisture (Gallego-Juarez, 1998; Mulet et al., 2003).

The effects of ultrasounds on water absorption of chickpeaswere illustrated in Figs. 2–4. The statistical analysis of moisture

Fig. 6. Effect of soaking temperature on the birefringence of chickpea starch at 40, 50, 60 and 70 �C.


contents were tabulated in Tables 1–4. Application of 25 kHz100 W ultrasound significantly (P < 0.05) increased the waterabsorption of chickpea for all temperatures (20–97 �C). The mois-ture content (%, d.b.) values of chickpea were found to be increasedfrom 76.91% to 85.14% (d.b.), when the 25 kHz 100 W ultrasoundwas applied at 20 �C and 180 min soaking. Increase in power ofultrasounds (from 100 to 300 W) also further significantly (P <0.05) increased the moisture content (from 85.14% to 91.89%) ofchickpea during 20 �C and 180 min soaking. Similarly, increase inpower (100–300 W) increased the moisture content of soakedchickpea at all other temperatures for a given soaking time. How-ever, 40 kHz 100 W ultrasound applications resulted in slightchanges (mostly increases) in moisture values. Increase in ultra-sound frequency from 25 to 40 kHz insignificantly (P > 0.05) de-creased the moisture content (%, d.b.) from 76.91% to 76.55% atthe same soaking temperature and time (Table 2).

Deff of the Fick’s law model was main parameter for the ultra-sonic assisted process of diffusion which was compared with theconventional soaking. At all temperatures, Deff values found fromthe Fick’s model were significantly increased when 25 kHz 100 Wultrasound treatment applied and also when ultrasound power in-creased to 300 W (Table 5). For soaking at 20 �C, Deff values chan-ged from 1.40 � 10�10 to 1.70 � 10�10 and to 2.01 � 10�10 m2 s�1

for non-ultrasound, 25 kHz 100 W and 25 kHz 300 W ultrasoundtreatments, respectively. Deff changes at all temperatures were sig-nificant (P < 0.05) (Table 5). The ultrasound treatment increased

the water diffusion of chickpea during soaking due to increasingof mass diffusion rate (Fuente et al., 2004). However, applicationof high frequency ultrasonic (40 kHz) for all soaking temperaturesdid not significantly (P > 0.05) affect or/and decreased thewater absorption rate and the diffusion coefficient of chickpea(Tables 2–5 and Figs. 2–4). Change of ultrasound frequency from25 to 40 kHz decrease Deff value from 1.40 � 10�10 to 1.28 �10�10 m2 s�1 (20 �C soaking).

4. Conclusion

Water diffusion rates of chickpea significantly increased(P < 0.05) with increasing of soaking time, temperature and powerof ultrasound (100–300 W). High ultrasound frequencies such as40 kHz did not significantly (P > 0.05) affect the water diffusionof chickpea during soaking. Fick’s diffusion constant (Deff) for atemperature range of 20–97 �C increased from 1.40 � 10�10 to11.9 � 10�10 m2 s�1 with ultrasound application.

Fick’s second law model where Arrhenius relationship insertedfor Deff can be used to determine moisture content of chickpeas as afunction of soaking time and temperature. Average gelatinizationtemperature of chickpea from the water absorption model wasfound as 61.47 �C. Activation energy (Ea) values of chickpea for be-low and above gelatinization temperature of 61.47 �C were foundto be 28.69 and 9.34 kJ mol�1, respectively. Ultrasound treatmentsdecreased the soaking time of chickpea.


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Documents

Fitting Fick’s model to analyze water diffusion into chickpeas during soaking with ultrasound treatment