Water effective diffusion coefficient of sardine sheets during osmotic dehydration at different brine concentrations and temperatures

Journal of Food Engineering 80 (2007) 497–502 www.elsevier.com/locate/jfoodeng

Water effective diffusion coefficient of sardine sheets during osmotic dehydration at different brine concentrations and temperatures Otoniel Corzo a

a,*

, Nelson Bracho

b

Department of Food Technology, Universidad de Oriente, Guatamare, Venezuela b Department of Statistics, Universidad de Oriente, Guatamare, Venezuela Received 25 November 2005; accepted 6 June 2006 Available online 16 November 2006

Abstract The water effective diffusion coefficient of sardine sheets during osmotic dehydration was determined, assuming this process to be governed by Fickian diffusion. Osmotic dehydration of sardine sheets (20.1 · 15.0 · 6.4 mm3) was carried out over five concentrations (0.15, 0.18. 0.21, 0.24 and 0.27 kg NaCl/kg) and temperatures between 30 and 38 C of osmotic solution. The water effective diffusion coefficient ranged approximately from 2.084 · 1012 to 3.015 · 1012 m2/s. Temperature sensitivity of water diffusion coefficient increased (p < 0.05) with increasing brine concentration below 0.24 kg NaCl/kg. This temperature sensitivity was changed, decreased (p < 0.05) at brine concentrations equal or higher than 0.24 kg NaCl/kg. The water effective diffusion coefficient was empirically correlated with concentration and temperature of osmotic solution. A high degree of correlation was observed between predicted and experimental values of the water effective diffusion coefficient (R2 = 0.909).  2006 Elsevier Ltd. All rights reserved. Keywords: Effective diffusion coefficient; Osmotic dehydration; Sardine sheets

1. Introduction Osmotic dehydration removes water partially from fruits or vegetables immersed in a hypertonic solution. During osmotic processing, water flows from the product into the osmotic solution, whereas osmotic solute is transferred from the solution into the product. The rate of diffusion of water from any material made up of such tissue depends upon factors such as temperature and concentration of the osmotic solution, the size and geometry of the material, the solution to material mass ratio, and the level of agitation of the solution (Raoult-Wack, Lafont, Rios, & Guilbert, 1989; Raoult-Wack, 1994; Rastogi & Niranjan, 1998; Rastogi, Eshtisghi, & Knorr, 1999). Fick’s law of dif-

*

Corresponding author. Tel.: +58 295 2631 230; fax: +58 295 2656 545. E-mail address: [email protected] (O. Corzo).

0260-8774/$ - see front matter  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2006.06.008

fusion, based on effective diffusivity approach, has been used to describe the moisture diffusion process for food products by many researchers (Ade-Omowaye, Rastogi, Angersbach, & Knorr, 2002; Azzouz, Guizani, Jomaa, & Belghith, 2002; Fasina, Fleming, & Thompson, 2002; Kang & Delwiche, 2000; McCarthy, Gonzalez, & McCarthy, 2002; Rastogi, Angersbach, Niranjan, & Knorr, 2000; Roberts & Tong, 2003; Telis, Murari, & Yamashita, 2004). There are two parameters required in Fick’s law, these are sample dimensions and effective diffusion coefficient. Effective diffusion coefficient can be obtained from experimental drying data using methods as an analytical solution (Nguyen, Verboven, Scheerlinck, Vandewalle, & Nicolaı, 2006; Park, Yado, & Brod, 2001), the relation between slope of theoretical diffusion curve and slope of experimental mass transfer (Ade-Omowaye et al., 2002; Rastogi & Raghavarao, 2004; Rastogi et al., 2000), and nonlinear regression (Roberts & Tong, 2003; Tungsangpa-

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O. Corzo, N. Bracho / Journal of Food Engineering 80 (2007) 497–502

teep & Jindal, 2004). Although effective diffusion coefficient should be obtained from drying curves involving only small moisture change, it was determined that those values obtained from drying curves involving large changes in moisture content were also reliable (Waananen, 1989). It is very common in literature to consider any finite food geometry as infinite flat plate configuration, neglecting the diffusion in the other directions and out of these only a few have considered unsteady state mass transfer during osmotic dehydration (Ade-Omowaye et al., 2002; Escriche, Garcı´a-Pinchi, Andre´s, & Fito, 2000; Kayacier & Singh, 2004; Park et al., 2001; Rastogi & Raghavarao, 2004; Roberts, Tong, & Lund, 2002). Several works have been published on mass transfer and salt diffusivities in fish (Chiralt et al., 2001; Gallart-Jornet et al., 2007; Teixeira & Tobinaga, 1998; Wang, Tang, & Correia, 2000). Our objective was to determine the water effective diffusion coefficient of sardine sheets during osmotic dehydration and investigate the effects of concentration and temperature of osmotic solution on water effective diffusion coefficient. 2. Materials and methods 2.1. Sample preparation The fresh sardine (Sardinella aurita) was acquired from same capture zone of Margarita Island, Venezuela, from fishermen who caught them within 1 h of selling them. Sardines were manually filleted, and then the fillets were cut into sheets from the muscle nearest to head. The samples were sheets with an average length of 20.1 ± 0.5 mm, average width of 15.0 ± 0.6 mm, and 6.4 ± 0.1 mm. The moisture and salt contents were determined for fresh sardine by quadruplicate. 2.2. Osmotic dehydration Randomly groups of 4 sheets in each were formed. A basket with four-marked compartment was used to put in it the sheets of each group to avoid interference between them. Four groups were immersed simultaneously into an osmotic solution of a give concentration and temperature. One group was removed at 1, 2, 3 and 4 h. After the removal from brine the dehydrated sheets of each group were drained during 5 min, blotted with absorbent paper to remove the excess solution. The moisture and salt contents were determined in each group. This procedure took place in each experience to the corresponding conditions according to a 5 · 5 · 4 factorial design where the temperature, concentration an dehydration time were 30, 32, 34, 36, and 38 C, 0.15, 0.18, 0.21, 0.24 and 0.27 kg NaCl/kg, and 1, 2, 3 and 4 h, respectively. The osmotic solution was prepared by mixing commercial grade salt with distilled water. The brine to sample ratio was always 20:1 to avoid significant dilution of the medium by water removal, which would lead to local

reduction of the osmotic driving force during the process. The concentration of the brine (kg NaCl/kg) was adjusted initially and thereafter monitored throughout each run by Mohr’s method (AOAC, 1990). The moisture content of fresh and treated sardine sheets was determined by drying under vacuum (1.93 Pa) at 60 C until constant weight (AOAC, 1990). The salt content of fresh and treated sardine sheets was determined by the Mohr method (AOAC, 1990). 2.3. Determination of effective diffusion coefficient In order to establish the equation of mass transfer during osmotic dehydration, the following considerations were taken into account: the process was isothermal, the main mass transfer was caused by a pseudofickian mechanism, the external resistance to mass transfer negligible compared with internal resistance, the initial moisture content was uniforms throughout the sample, the diffusion coefficient is constant and not a function of moisture concentration. The pseudofickian mechanism is driven by activity gradients (Fito & Chiralt, 1997) between the sardine liquid phase and the brine solution. The reduced driving force (Y) in the sardine liquid phase is defined as (Escriche et al., 2000; Fito & Chiralt, 1997; Gallart-Jornet et al., 2007) Y ¼

xw  xwe xw0  xwe

ð1Þ

where xw, xwe, xw0 are final (time t), equilibrium and initial moisture contents of sardine liquid phase. The moisture contents of sardine liquid phase were calculated by the following equation (Fito & Chiralt, 1997): xw ¼

Xw Xw þ Xs

ð2Þ

where Xw and Xs are the water and salt mass fraction of sardine. The solution of Fick’s second law for diffusion from a rectangular parallelepiped of sides 2a, 2b and 2c result in the following equations for the transfer of water (Crank, 1975):  12     1 De t 1 1 1 3 ½1  Y  ¼ 2 ð3Þ p a b c where De is the water effective diffusion coefficient, and t is the dehydration time. 1 1 The plot of ½1  Y 3 vs. t2 for a given condition of brine concentration and temperature would result in a straight  1     line with the slope equal and 2 Dpe 2 1a 1b 1c . The water effective diffusion coefficient was obtained from the slope of straight line. Dependence of the diffusion coefficient on temperature is represented by the Arrhenius equation: lnðDe Þ ¼ lnðDe0 Þ 

Ea RT

ð4Þ

O. Corzo, N. Bracho / Journal of Food Engineering 80 (2007) 497–502

where De0 is the frequency factor (min1), Ea is the activation energy (kJ/mol), R the universal gas constant (8.314 J/ mol K) and T is the absolute temperature (K). The plot of the logarithm of the diffusion coefficient vs. 1/T would result in a straight line with the negative of the slope equal Ea/R and intercept equal ln(De0). 2.4. Statistical analysis Statistical evaluation of the results was performed using a 5 · 5 · 4 factorial design (five concentrations, five temperatures, and four times). Analysis of variance was carried out to find effects (p < 0.05) of temperature and concentration brine on the water diffusion coefficient. Multiple comparison tests were performed using LSD’s test at the 95% confidence level. Linear regression was used to fitting experimental data to Eq. (3). Linear regression was used to fitting data of diffusion coefficient to Arrhenius equation (Eq. (4)) in order to estimate dependence of temperature. Multiple linear regression was used to fitting a model of water diffusion coefficient as a function of brine concentration and temperature. All statistical analysis was carried out with a Statgraphics 5.0 statistical software (Statistical Graphics Corp., Rockville, MD, USA). 3. Results and discussion

499

with increasing dehydration time, brine concentration and temperature. The decreases were faster in the initial period of osmosis and then the rate decreased. During osmotic processing, water flows from the product into the osmotic solution, whereas salt is transferred from the solution into the product. The equilibrium point is reached when water activities of brine and sardine liquid phase become equal. Since water activity can be decreased both by water loss or salt uptake, there is a relationship between water loss and solute uptake to reach equilibrium. The properties of the fish muscle change due to changes in water and salt contents. Studies on salting of milkfish (Sannaveerappa, Ammu, & Joseph, 2004), cod and salmon (Gallart-Jornet et al., 2007) found that high salt concentration denatures the proteins and reduces their water holding capacity (WHC) while that for salting of cod with diluted brines, an increase in the WHC was observed (Barat, Rodrı´guez-Barona, Andre´s, & Fito, 2002; Thorarinsdottir, Arason, Geirsdottir, Bogason, & Kristbergsson, 2002). Increased protein denaturation at a high brine concentration compared with at low brine concentrations causes less sample swelling (Barat et al., 2002) and may promote loss of water from the fish (Deng, 1977). The lower WHC at the higher temperature may be due to increased thermal denaturation of proteins at the higher compared with the lower temperature (Birkeland, Sivertsvik, Nielsen, & Ska¨ra, 2005). However, Sankar and Ramachandran (2005)

3.1. Effective diffusion coefficient

xw (g water/g)

The moisture contents of sardine liquid phase during osmotic dehydration at different brine concentrations (0.21 and 0.24 kg NaCl/g) and temperatures are showed in Fig. 1. It can be seen that moisture content decreased

Concentration (kg NaCl/kg)

Temperature (C)

De · 1012 (m2/s)

R2

0.15

30 32 34 36 38

2.084 ± 0.010 2.148 ± 0.011 2.208 ± 0.004 2.224 ± 0.003 2.231 ± 0.002

0.969 0.960 0.959 0.957 0.956

0.18

30 32 34 36 38

2.208 ± 0.014 2.326 ± 0.003 2.368 ± 0.003 2.625 ± 0.002 2.739 ± 0.003

0.965 0.961 0.957 0.958 0.959

0.21

30 32 34 36 38

2.240 ± 0.005 2.470 ± 0.010 2.571 ± 0.003 2.750 ± 0.007 2.953 ± 0.011

0.967 0.967 0.966 0.964 0.961

0.24

30 32 34 36 38

2.475± 0.004 2.515 ± 0.006 2.644 ± 0.005 2.827 ± 0.003 2.992 ± 0.010

0.970 0.969 0.965 0.963 0.962

0.27

30 32 34 36 38

2.614 ± 0.005 2.762 ± 0.005 2.790 ± 0.002 2.975 ± 0.008 3.015 ± 0.017

0.969 0.967 0.961 0.966 0.964

1.07 1.02 0.97 0.92 0.87 0.82 0.77 0.72 0

xw (g water/g)

Table 1 Water effective diffusion coefficient of sardine sheets during osmotic dehydration at different brine concentrations and temperatures

1 2 3 Dehydration time (h)

4

1.07 1.02 0.97 0.92 0.87 0.82 0.77 0.72 0

1 2 3 Dehydration time (h)

4

Fig. 1. Moisture content of sardine liquid phase (xw) during osmotic dehydration of sardine sheets at 0.21 and 0.24 kg NaCl/kg and different temperatures. (–) 30 C; (– –) 32 C; (Æ Æ) 34 C; (– Æ) 36 C; (– Æ Æ) 38 C.

O. Corzo, N. Bracho / Journal of Food Engineering 80 (2007) 497–502

observed that proteins from Indian carp appeared labile to denaturation at relatively low temperatures (20 C). The moisture contents of sardine liquid phase at the different conditions of osmotic dehydration were converted to the reduced driving force (Y) (Eq. (1)). The coefficient of determination (R2 > 0.95), and no pattern evident with the residuals across the range of diffusion coefficients indi1 cated the goodness of fit of experimental ½1  Y 3 data to Eq. (3) (Table 1). Plots of fitted experimental data to Eq. (3) for five given conditions of brine concentration and temperature (Fig. 2) are shown as an example. The water effective diffusion coefficient of sardine sheets at different brine concentrations and temperatures are summarized in Table 1. The De values ranged approximately from 2.084 · 1012 to 3.015 · 1012 m2/s. These values fell within the normally expected range of De for dehydrated foods (Ade-Omowaye et al., 2002; Chenlo, Moreira, Ferna´ndez-Herrero, & Va´squez, 2006a, Chenlo, Moreira, Ferna´ndez-Herrero, & Va´squez, 2006b; Medina-Vivanco, Sobral, & Hubinger, 2002; Rastogi & Raghavarao, 2004; Zogzas, Maroulis, & Marinos-Kouris, 2000; Zogzas et al., 1996), for salting cod and salmon (Gallart-Jornet et al., 2007) or obtained with other technical for different

a

foods (Nguyen et al., 2006; Veraverbeke, Verboven, Scheerlinck, Hoang, & Nicolaı, 2003). Analysis of variance showed that there were significant differences (p < 0.05) in the water diffusion coefficient affected by brine concentration, temperature, and their interactions (Fig. 3). At a constant brine concentration, water diffusion coefficient increased with increasing temperature. At a constant brine temperature, water diffusion

De x1012 (m2/s)

500

2.8 2.6 2.4 2.2 2 0.15 0.18 0.21 0.24 0.27 Brine concentration (kg NaCl/kg)

Fig. 3. Multiple comparison of means of water effective diffusion coefficient at different temperatures and brine concentrations. (–) 0.15 kg NaCl/kg; (– –) 0.18 kg NaCl/kg; (Æ Æ) 0.21 kg NaCl/kg; (– Æ) 0.24 kg NaCl/ kg; (– Æ Æ) 0.27 kg NaCl/kg.

b

0.7

3.4 3.2 3

0.72 0.7

0.66

(1-Y)1/3

(1-Y)1/3

0.68

0.64 0.62

0.66

0.6 0.58 1

c

0.68

1.2

1.4 1.6 t 0.5(h0.5)

1.8

2

0.64 1

d

0.77

1.4 1.6 t 0.5 (h0.5)

1.8

2

1.8

2

0.8 0.78

(1-Y)1/3

(1-Y)1/3

0.75

1.2

0.73 0.71

0.76 0.74

0.69 0.72

0.67

0.7

0.65 1

1.2

1.4 1.6 t 0.5 (h0.5)

1.8

1

2

1.2

1.4 1.6 t 0.5 (h0.5)

e 0.83 (1-Y)1/3

0.81 0.79 0.77 0.75 0.73 0.71 1 1

1.2

1.4 1.6 t 0.5 (h 0.5)

1.8

2

Fig. 2. Plot of fitted experimental ½1  Y 3 data to Eq. (3) for a given condition of brine concentration and temperature. (a) 15 g NaCl/g and 30 C; (b) 18 g NaCl/g and 32 C; (c) 21 g NaCl/g and 34 C; (d) 24 g NaCl/g and 36 C; (e) 27 g NaCl/g and 38 C.

O. Corzo, N. Bracho / Journal of Food Engineering 80 (2007) 497–502

501

Table 2 Activation energy (Ea) and frequency factor ln(De0) values for water diffusion coefficient of sardine sheets during osmotic dehydration at different brine concentrations Parameter

ln(De0) Ea (kJ/mol) R2

Concentration (kg NaCl/kg) 0.15

0.18

0.21

0.24

0.27

24.23 ± 0.24 6.692 ± 0.614 0.868

18.26 ± 0.44 21.633 ± 0.113 0.954

16.54 ± 0.30 25.877 ± 0.773 0.984

19.04 ± 0.36 19.415 ± 0.913 0.962

21.06 ± 0.30 14.107 ± 0.775 0.949

coefficient increased with increasing brine concentration. An increase in the concentration results in an increase in osmotic pressure gradient, increasing the driving force for water removal between solution and food, and thereby higher mass transfer rates and water effective diffusion coefficient. The results are in agreement with the results for osmotic dehydration of carrots (Rastogi & Raghavarao, 1997), pineapple (Rastogi & Raghavarao, 2004), coated potato (Khin, Zhou, & Perera, 2006) and chestnut (Chenlo et al., 2006a, 2006b). 3.2. Modeling effects of temperature and concentration on the diffusion coefficient The linearity of the data (R2 > 0.86) indicates that the water diffusion coefficient as a function of temperature followed an Arrhenius relationship, regardless of concentration (Table 2). The computed values of activation energy (Ea) and natural logarithm of frequency factor (ln(De0)) are reported in Table 2. Higher Ea value indicated greatest temperature sensitivity of diffusion coefficient. Temperature sensitivity of water diffusion coefficient increased (p < 0.05) with increasing brine concentration below 0.24 kg NaCl/kg. This temperature sensitivity was changed, decreased (p < 0.05) at brine concentrations equal or higher than 0.24 kg NaCl/kg. Multiple linear regression (Table 3) fitted data of diffusion coefficient as a function of absolute temperature (1/ T) and brine concentration (C). The models as fitted correspond to ln De ¼ 20:257 þ 2:049ðCÞ  2110:29ð1=T Þ

ð5Þ

The model as fitted explained the 90.9 % of the variability in De at the 99% confidence level (Table 3). With this model the water diffusion coefficient can be calculated when the sardine sheets are osmotic dehydrated in brines in the range 0.15–0.27 kg NaCl/g and temperatures in the range 30–38 C. In Eq. (5) the coefficient for brine concenTable 3 Multiple linear regression for water effective diffusion coefficient as a function of temperature and brine concentration Parameter

Estimate

Standard error

Statistic t

p-Value

Constant C 1/T

20.257 2.049 2110.29

0.375 0.081 115.04

53.99 25.28 18.39

<0.0001 <0.0001 <0.0001

R2

0.909

tration is positive and for temperature is negative. This indicates that water diffusion coefficient increased with increasing both brine concentration and temperature. 4. Conclusions In this study, the simplified solution of Fick’s second law, and considering the sardine sheets as a flat plate, was used to calculate the water effective diffusion coefficient of sardine sheets during osmotic dehydration at different brine concentrations and temperatures. The values found were comparable with those in literature obtained with other techniques and for other dehydrated foods. The temperature dependence of the water and salt diffusion coefficients indicated an Arrhenius relationship. Model of diffusion coefficient as a function of absolute temperature and brine concentration was found. References Ade-Omowaye, B. I. O., Rastogi, N. K., Angersbach, A., & Knorr, D. (2002). Osmotic dehydration behavior of red paprika (Capsicum annnum L.). Journal of Food Science, 67(5), 1790–1796. AOAC (1990). Official methods of analysis (15th ed.). Washington, DC: Association of Official Analytical Chemists. Azzouz, S., Guizani, A., Jomaa, W., & Belghith, A. (2002). Moisture diffusivity and drying kinetic equation of convective drying of grapes. Journal of Food Engineering, 5(4), 323–330. Barat, J. M., Rodrı´guez-Barona, S., Andre´s, A., & Fito, P. (2002). Influence of increasing brine concentration in the cod salting process. Journal of Food Science, 65(7), 1922–1925. Birkeland, S., Sivertsvik, M., Nielsen, H. H., & Ska¨ra, T. (2005). Effects of brining conditions on weight gain in herring (Clupea harengus) fillets. Journal of Food Science, 70(7), E418–E424. Chenlo, F., Moreira, R., Ferna´ndez-Herrero, G., & Va´squez, G. (2006a). Mass transfer during osmotic dehydration of chestnut using sodium chloride solutions. Journal of Food Engineering, 73, 164–173. Chenlo, F., Moreira, R., Ferna´ndez-Herrero, G., & Va´squez, G. (2006b). Experimental results and modeling of the osmotic dehydration kinetics of chestnut with glucose solutions. Journal of Food Engineering, 74, 324–334. Chiralt, A., Fito, P., Barat, J. M., Andre´s, A., Gonza´lez-Martı´nez, C., Escriche, I., et al. (2001). Use of vacuum impregnation in food salting process. Journal of Food Engineering, 49, 141–151. Crank, J. (1975). The mathematics of diffusion (2nd ed.). Oxford: Clarendon Press (pp. 24–25). Deng, J. C. (1977). Effect of freezing and frozen storage on salt penetration into fish muscle immersed in brine. Journal of Food Science, 42, 348–351. Escriche, I., Garcı´a-Pinchi, R., Andre´s, A., & Fito, P. (2000). Osmotic dehydration of kiwifruit (Actinidis chinensis): Fluxes and mass transfer kinetics. Journal of Food Process Engineering, 23, 191–205.

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