Equilibrium distribution coefficients during osmotic dehydration of apricot

f o o d a n d b i o p r o d u c t s p r o c e s s i n g 8 6 ( 2 0 0 8 ) 254–267

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Equilibrium distribution coefficients during osmotic dehydration of apricot a,∗ ¨ Togrul ˘ , Ays¸e I˙spir b I˙nci Turk a b

Afyon Kocatepe University, Engineering Faculty, Chemical Engineering Department, 03200 Afyonkarahisar, Turkey ˘ Turkey Firat University, Engineering Faculty, Chemical Engineering Department, 23279 Elazig,

a r t i c l e

i n f o

Article history:

a b s t r a c t The effect of initial osmotic solution concentration (40–70%, w/w), solution temperature

Received 18 October 2007

(25–45 ◦ C), pretreatment before osmotic dehydration (by using chemicals such as K2 S2 O5 ,

Accepted 7 March 2008

Na2 S2 O5 , ethyl oleat + K2 S2 O5 , ethyl oleat + Na2 S2 O5 and ethyl oleat + K2 CO3 ) and the ratio of the sample to solution (1/4–1/25) on equilibrium distribution coefficients of apricot were investigated during osmotic dehydration. The various osmotic agents such as sucrose, fruc-

Keywords:

tose, glucose, maltodextrin and sorbitol were used in osmotic dehydration of apricot. The

Apricot

distribution coefficients of water ranged from 1.893 to 0.822 g g−1 for various concentrations,

Equilibrium distribution coefficient

1.302–0.651 g g−1 for different temperatures, 2.013–0.560 g g−1 for application of pretreatment

Osmotic dehydration

and 1.126–0.822 g g−1 for the ratio of the sample to solution, respectively, while the dis-

Mass transfer

tribution coefficient for solid varied from 1.473 to 0.719 g g−1 for various concentrations, 0.933–0.719 g g−1 for various temperatures, 1.427–0.453 g g−1 for application of pretreatment and 0.916–0.718 g g−1 for sample to solution ratio, respectively. The distribution coefficient for water decreased with increasing temperature and decreasing sample to solution ratio, and with the increase in syrup concentration it increased or decreased with respect to osmotic agent type. The distribution coefficient for the solid was increased with both an increase in temperature and a decrease in the sample to solution ratio, though it decreases with an increase in syrup concentration. A nonlinear regression of experimental data was carried out to correlate the cumulative relationship between distribution coefficient and syrup concentration. In addition to modeling of the effect of the sample to solution ratio on distribution coefficients of apricots, whole developed models have been tested by using statistical analyses such as 2 , mean bias error (MBE) and root mean square error (RMSE). © 2008 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

1.

Introduction

In simple terms, osmosis is a process in which solvents flow from a diluted solution to a concentrated one through a semipermeable membrane to equalize the chemical potential of solute (Aguilera and Stanley, 1999). In foods, osmotic dehydration involves partial dehydration of water-containing cellular solids, which are immersed in hypertonic aqueous solution of various edible solutes (syrup or brine). The driving force for water removal is the chemical potential between the solution and the intercellular fluid. If the membrane is perfectly semipermeable (i.e., water-permeable, solute-repellant)

∗

solute is unable to diffuse through the membrane into the cells. However, due to absence of semipermeable membrane in food, there is always some solute diffusion into the food and leak of the food’s own solute. Thus, mass transport in osmotic dehydration is actually a combination of simultaneous water and solute transfer processes (Panagiotou et al., 1998; Rahman and Perera, 1999; Rault-Wack, 1994). The osmotic dehydration process can be characterized by equilibrium and dynamic periods (Rahman, 1992). In the dynamic period, the mass transfer rates are increased or decreased until equilibrium is reached. Equilibrium is the end of osmotic process, i.e., the net rate of mass transport

Corresponding author. Tel.: +90 272 228 12 13/287; fax: +90 272 228 14 17. ˘ E-mail addresses: [email protected], [email protected] (I˙.T. Togrul). 0960-3085/$ – see front matter © 2008 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.fbp.2008.03.001

f o o d a n d b i o p r o d u c t s p r o c e s s i n g 8 6 ( 2 0 0 8 ) 254–267

255

as: Nomenclature C D MBE R RMSE T Xse Xso Xwe Xwo Xse e Xw

Yso o Yw

WL∞ SG∞

ew =

osmotic solution concentration (%, w/w) relative percentage deviation mean bias error correlation coefficient root mean square error osmotic medium temperature (◦ C) equilibrium salt content initial solid concentration equilibrium water content initial water concentration the mass fractions (wet basis) of the water in food product at equilibrium the mass fractions (wet basis) of the water in food product at equilibrium the mass fractions (wet basis) of the solid in the initial osmotic syrup the mass fractions (wet basis) of the water in the initial osmotic syrup equilibrium water loss equilibrium solid gain

es =

Xie

Xse Yso

(3)

Making use of overall solids to evaluate equilibrium values turns the system food product to a binary system (i.e., water and overall solids), and similarly the solution of sugar (or salt) is also a binary system. Consequently, there is an explicit relationship between ew and es . Once ew is known es can be calculated using the following relationship: es =

o 1 − ew Yw o 1 − Yw

(4)

Parjoko et al. (1996) proposed the following equations to estimate the equilibrium water content (Xwe ) and equilibrium salt content (Xse ): e Xw =

Xse =

is zero. The study of the equilibrium state is necessary for the modeling of the osmotic process as unit operation and also important for a good understanding of the mass transfer mechanisms involved in this system (Barat et al., 1998). Kinetics of osmotic dehydration of potato (Lenart and Flink, 1984; Biswal and Bozprgmehr, 1991), fish tilapia (Medina-Vivanen et al., 1998), apples (Mosalve-Gonzalez et al., 1993; Ertekin and ˘ Sultanoglu, 2000), peas (Ertekin and C¸akaloz, 1996a, 1996b), banana and kiwi fruit (Panagiotou et al., 1998) were studied, but there are a little of study on apricot (Forni et al., 1997; Khoyi and Hesari, 2007; Riva et al., 2005). However, the equilibrium distribution coefficients in these studies were not calculated. Distribution coefficient for salt is defined as the ratio of salt concentration in fish muscle and brine at equilibrium (Del Valle and Nickerson, 1967; Favetto et al., 1981). Since this approach needs the value of salt concentration in brine at equilibrium, Rahman (1992) used initial syrup concentration instead of the equilibrium concentration of the syrup. This assumption is valid when value of ratio R (ratio of mass of solution to the mass of the product) is very high. For the other cases the distribution coefficient is a function ratio R, in addition to other process parameters. This approach becomes practical when equilibrium concentration is difficult to predict. The equilibrium distribution coefficients for the ith component can be defined as (Rahman, 1992);

Yio

(2)

Similarly, the distribution coefficient for overall solids can be defined as:

Greek letters ew the distribution coefficient for water es the distribution coefficient for overall solids reduced chi-square 2

ei =

e Xw o Yw

(1)

where ei is the distribution coefficient, and both Yio and Xie are the mass fractions (wet basis) of the ith component in the initial osmotic syrup and food product at equilibrium, respectively. The distribution coefficient for water can be defined

Xwo − WL∞ 1 − (WL∞ + SG∞ )

(5)

Xso + SG∞ 1 − (WL∞ + SG∞ )

(6)

where Xwo and Xso are initial water and solid concentration respectively, WL∞ is the equilibrium water loss and SG∞ is the equilibrium solid gain. The osmotic dehydration process can be characterized by equilibrium and dynamic periods (Rahman, 1992). In the dynamic period, the mass transfer rates are increased or decreased until equilibrium is reached. Equilibrium is the end of osmotic process, i.e. the net rate of mass transport is zero. The study of the equilibrium state is necessary for the modeling of osmotic process as a unit operation and also important for a good understanding of the mass transfer mechanisms involved in this system (Barat et al., 1998). The distribution coefficients for water and solids were determined for osmotic drying of pineapple in sucrose (Parjoko et al., 1996) and palm sugar (Silveira et al., 1996), and potato (Rahman et al., 2001) in sucrose. They also developed models to predict the distribution coefficients as a function of process temperature and syrup concentration. In the literature there is little information available about the distribution coefficients of water and solids for wide number of food products. In addition, there were negligible studies, which had been carried out to find the effect of pretreatment application and sample to solution ratios. The objectives of this study were to measure and model the equilibrium distribution coefficients of water and solids for osmotically dehydrated apricot, and to investigate the effect of both the pretreatment application prior to osmotic dehydration and the sample to solution ratio on the equilibrium distribution coefficient of water.

2.

Marerials and methods

2.1.

Materials

There are various kinds of apricots in nature. The Hacıhalil type of apricot, which has greater importance than the others

256

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as commercially, was used in this study because other types of apricots are generally more suitable for freshly consumption. Hacıhalil type fresh apricots were directly collected from trees and brought to the laboratory in a wood box. The apricots were refrigerated at 5 ◦ C at 80–90% relative humidity until used for experiments. The whole apricots were sorted visually according to their ripeness and size (average weight of 25 g, average diameters of 3 cm). The average initial moisture content was 80.864% (wet basis), gravimetrically measured using an oven at 75 ◦ C for 24 h. Since this is a temperature at which no structural changes occur during drying process this is one of the preferred values in both infrared and oven methods (Doymaz, ˘ 2004; Togrul and Pehlivan, 2002, 2003, 2004).

2.2.

Experiments

Different osmotic agents such as sucrose, glucose, fructose, maltodextrin and sorbitol have been used to determine the equation distribution coefficients of apricot. The initial concentration of solutions varied from 40% to 70% (w/w), and

temperatures varied from 25 to 45 ◦ C. The ratio of fruit to solution was kept at 1/25 to avoid significant dilution of the medium by water removal, which would lead to local reduction of osmotic driving force during the process. The whole apricots with pits were immersed into the osmotic solution of 850 ml glass jars. The glass jars were placed on a water bath to maintain required temperatures of the syrup during the experiment. The jar was covered with a plastic plate to reduce moisture loss from syrup during experiments. All experiments were conducted within 8 days. Apricots were withdrawn at periodic intervals of 2 h, quickly rinsed and gently blotted with tissue paper to remove excess solution from the surface, then weighed and returned to the osmotic solution to continue the drying process. The control treatment was done for understanding to reach the equilibrium point and it was seen that eighth day was the end of osmotic process and after that the net rate of mass transport was zero. After eight days, the moisture content of apricots was determined in an oven at 75 ◦ C for 24 h (Doymaz, 2004;

Table 1 – %Relative deviation (D) of measured values, moisture and solid contents and water loss and solid gain at equilibrium Solution

Concentration (%, w/w)

Temperature (◦ C)

%Relative deviation (D)

WL∞

SG∞

e Xw

Xse

Fructose

40 50 60 70 70 70

25 25 25 25 35 45

3.30 3.94 5.35 4.06 6.49 1.67

0.5120 0.6670 0.7350 0.7460 0.7530 0.7620

0.0343 0.0597 0.1074 0.1128 0.1262 0.1370

1.5502 0.7417 0.3848 0.3273 0.2908 0.2437

1.1795 1.3119 1.5613 1.5895 1.6595 1.7159

Glucose

40 50 60 70 70 70

25 25 25 25 35 45

4.73 2.71 5.62 5.43 5.52 5.93

0.4860 0.5850 0.6470 0.6860 0.6992 0.7136

0.0009 0.0009 0.0011 0.0027 0.0259 0.0496

1.6860 1.1687 0.8457 0.6409 0.5719 0.4967

1.0046 1.0048 1.0058 1.0140 1.1352 1.2594

Sucrose

40 50 60 70 70 70

25 25 25 25 35 45

7.88 6.11 6.03 6.41 8.60 5.79

0.6000 0.6110 0.6523 0.7200 0.7289 0.7613

0.0140 0.0151 0.0161 0.0172 0.0199 0.0140

1.0903 1.0328 0.8170 0.4632 0.4165 0.2474

1.0732 1.0788 1.0843 1.0897 1.1040 1.7290

Maltodextrin

40 50 60 70 70 70

25 25 25 25 35 45

5.90 6.06 4.12 4.10 4.26 3.81

0.5683 0.5873 0.6833 0.7304 0.7532 0.7622

0.0831 0.0850 0.0986 0.1503 0.1623 0.1688

1.2560 1.1567 0.6550 0.4089 0.2897 0.2427

1.4343 1.4442 1.5153 1.7854 1.8481 1.8821

Sorbitol

40 50 60 70

25 25 25 25

2.65 4.19 3.17 5.66

0.3977 0.4699 0.4884 0.5572

0.0118 0.0129 0.0163 0.0203

2.1475 1.7702 1.6892 1.3140

1.0616 1.0674 1.0852 1.1059

2.55 3.49 2.21 5.37 6.55

0.733 0.736 0.738 0.741 0.743

0.0019 0.0226 0.0417 0.0603 0.0813

0.3953 0.3796 0.3692 0.3535 0.3430

1.0100 1.1181 1.2179 1.3151 1.4248

7.45 8.32 8.32 3.15 7.31

0.711 0.714 0.717 0.722 0.726

0.0972 0.1040 0.1180 0.1230 0.1237

0.5102 0.4946 0.4789 0.4528 0.4319

1.5079 1.5435 1.6166 1.6428 1.7193

The ratio of sample to solution Glucose 1/4 1/8 1/12 1/16 1/20 Maltodextrin

1/4 1/8 1/12 1/16 1/20

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Table 2 – %Relative deviation (D) of measured values, moisture and solid contents and water loss and solid gain at equilibrium for pretreatment application before osmotic dehydration Solution

Pretreatment

%Relative deviation (D)

WL∞

SG∞

e Xw

Xse

70% Glucose

K2 S2 O5 Na2 S2 O5 EO + K2 S2 O5 EO + Na2 S2 O5 EO + K2 CO3

6.48 7.31 3.32 3.55 4.31

0.7700 0.6750 0.7426 0.7450 0.7615

0.0306 0.0249 0.0123 0.0714 0.0039

0.2019 0.6984 0.3451 0.3326 0.2463

1.1599 1.1300 1.0643 1.3731 1.0205

70% Fructose

K2 S2 O5 Na2 S2 O5 EO + K2 S2 O5 EO + Na2 S2 O5 EO + K2 CO3

4.63 2.78 5.67 5.43 4.52

0.6390 0.6650 0.6624 0.7221 0.6914

0.0400 0.0548 0.0434 0.0410 0.0458

0.8865 0.7506 0.7642 0.4522 0.6127

1.2090 1.2864 1.2269 1.2143 1.2393

70% Sucrose

K2 S2 O5 Na2 S2 O5 EO + K2 S2 O5 EO + Na2 S2 O5 EO + K2 CO3

4.16 3.65 4.69 3.47 5.68

0.6922 0.6799 0.6986 0.6815 0.7079

0.0261 0.0214 0.0224 0.0195 0.0464

0.6085 0.6728 0.5750 0.6644 0.5264

1.1364 1.1118 1.1172 1.1019 1.0464

70% Maltodextrin

K2 S2 O5 Na2 S2 O5 EO + K2 S2 O5 EO + Na2 S2 O5 EO + K2 CO3

3.34 3.74 2.35 4.86 3.49

0.7530 0.7650 0.7664 0.7698 0.7637

0.1270 0.1050 0.1130 0.1211 0.0800

0.2908 0.2281 0.2207 0.2030 0.2348

1.6636 1.5487 1.5905 1.6328 1.4181

70% Sorbitol

K2 S2 O5 Na2 S2 O5 EO + K2 S2 O5 EO + Na2 S2 O5 EO + K2 CO3

1.69 5.92 6.16 4.18 3.16

0.7180 0.5170 0.6750 0.6418 0.6800

0.0628 0.1007 0.0332 0.0593 0.0266

0.4736 1.5240 0.6984 0.8719 0.6722

1.3280 1.5262 1.1735 1.3099 1.1387

˘ Togrul and Pehlivan, 2002, 2003, 2004). The water activity of osmotic mediums was fairly low because of high concentration of solution. Microbial activity was not also observed at least of eighth day. All the experiments were performed in five replicates and average values have been reported. It was determined that shaking during osmotic dehydration would not be practical. Therefore, all experiments were done at static conditions because of length of time of osmotic dehydration. The water loss and solid gain at any time and at equilibrium are determined by the method as defined by Azuara et al. (1998). For providing long time storage of apricot, absorption of SO2 in uncontrolled medium has been applied as traditional method by farmer. Many problems such as high value of absorbed SO2 concentration in dry material and

color defeat have been occurred in trade of apricot sulphured by this way. The use of sulfuric material like sodium bi sulfite gradually has been important as alternative method for investigation and determination of optimum condition. The experiments divided into four groups were carried out, as follows. Group I The effects of osmotic agent and concentration were investigated for sucrose, fructose, glucose, maltodextrin and sorbitol, using sugar concentrations of 40%, 50%, 60% and 70% (w/w). The ratio of sample to solution and temperature were 1/25 and 25 ◦ C in this group experiments, respectively.

Fig. 1 – Plot of equilibrium distribution coefficients of water and solid of apricot in various osmotic agents at different concentrations. (䊉) Glucose, () fructose, () sucrose, () maltodekstrin and () sorbitol.

258

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Fig. 2 – Equilibrium distribution coefficients of apricot at both different temperatures and various osmotic agents. ( ) Glucose, () fructose, () sucrose and (䊉) maltodekstrin.

Group II The effect of process temperature was investigated for solution temperatures of 25, 35 and 45 ◦ C by using sucrose, fructose, glucose and maltodextrin of 70% (w/w) (at the most high concentration). The ratio of sample to solution was 1/25 in this group experiments. Group III To study the effect of the sample to solution ratio, the osmotic process experiments were repeated at various ratios of 1/4, 1/8, 1/12, 1/16, and 1/20 using glucose and maltodextrin of 70% (w/w). The solution temperature was 25 ◦ C in this group experiments. Group IV To study of effect of pretreatment, prior to osmotic dehydration apricots were immersed for 20 min

into various combinations of chemicals such as 5% Na2 S2 O5, 5% K2 S2 O5 , 2% ethyl oleat + 5% Na2 S2 O5, 2% ethyl oleat + 5% K2 S2 O5 , 5% K2 CO3 . They were applied with all osmotic agents at constant osmotic conditions. These chemicals are prevalently used to ˘ drying apricot (Mahmutoglu et al., 1996; Doymaz, ˘ 2004; Togrul and Pehlivan, 2004).

2.3.

Data analysis

The relative percentage deviation (D) between the mean and individual values was determined by the mean described by Yanniotis and Zarmboutis (1996). 100  |xi − x| 5 xi 5

D=

(7)

i=1

where xi is the normalized individual value of mass transfers (weight loss, water loss or solid gain) of the five samples for each time period and x is their arithmetic mean. The correlation coefficient (R) was one of the primary criterions for selecting the best equation to define suitable model. In addition to R, various statistical parameters such as reduced chi-square (2 ), mean bias error (MBE) and root mean square error (RMSE) were used to determine the quality of the fit. These parameters can be calculated as stated below:

n i=1

2

 =

(Xexp,i − Xpre,i )

2

(8)

N−n

1 (Xpre,i − Xexp,i ) N N

MBE =

(9)

i=1

 RMSE =

1 2 (Xpre,i − Xexp,i ) N N

1/2 (10)

i=1

Fig. 3 – Plot of equilibrium distribution coefficients of water and solid vs. different pretreatment solutions at different osmotic agents for apricot. ( ) Fructose, () glucose, ( ) sucrose, ( ) maltodextrin and ( ) sorbitol.

where Xexp,i stands for the experimental values and Xpre,i denotes predicted values, which are calculated using the model for these measurements. N and n are the number of observations and constants, respectively (Yaldiz and Ertekin, 2001; Yaldiz et al., 2001; Ertekin and Yaldiz, 2004; Menges and Ertekin, 2006a, 2006b).

Table 3 – The non-linear regression models described between equilibrium distribution coefficients and concentration and temperature we = f(TC)

Constant Glucose

Sucrose

Maltodextrin

Glucose

Fructose

Sucrose

Maltodextrin

1.035 −0.156 −0.483 0.8571 5.60 × 10−3 8.17 × 10−2 3.70 × 10−3

2.884 −0.210 0.408 0.9251 6.01 × 10−4 2.88 × 10−2 1.08 × 10−3

14.854 −0.754 0.406 0.900 7.27 × 10−3 7.25 × 10−2 4.34 × 10−3

11.552 −0.759 0.025 0.9532 1.60 × 10−3 4.44 × 10−2 1.95 × 10−3

0.624 0.026 −0.754 0.9984 1.93 × 10−4 9.81 × 10−3 9.51 × 10−5

0.286 0.175 −0.995 0.9999 −3.64 × 10−5 1.46 × 10−3 1.24 × 10−6

0.369 0.107 −0.994 0.9997 9.17 × 10−5 6.38 × 10−3 2.41 × 10−5

0.502 0.082 −0.877 0.9967 −3.58 × 10−4 1.51 × 10−2 2.43 × 10−4

Model 2: we se = a exp(bT) exp(cC) a 1.527 b −0.005 c −0.849 R 0.8347 MBE 6.24 × 10−3 RMSE 8.66 × 10−2 4.23 × 10−3 2

0.911 −0.005 0.646 0.9431 2.79 × 10−4 2.40 × 10−2 8.28 × 10−4

1.236 −0.023 0.717 0.911 6.31 × 10−3 6.58 × 10−2 3.88 × 10−3

1.738 −0.023 −0.009 0.947 1.69 × 10−3 4.94 × 10−2 2.20 × 10−3

2.270 1.7 × 10−3 −1.427 0.9972 −1.05 × 10−4 1.12 × 10−2 1.65 × 10−4

2.236 6.5 × 10−3 −1.886 0.9968 −6.45 × 10−4 1.63 × 10−2 2.14 × 10−4

2.430 4.6 × 10−3 −1.890 0.9975 −5.92 × 10−4 1.49 × 10−2 1.88 × 10−4

2.561 3.4 × 10−3 −1.648 0.9888 −4.37 × 10−4 2.80 × 10−2 9.03 × 10−4

Model 3: we se = a + bT + cC + dCT a 1.730 b −0.020 c −1.263 d 0.024 R 0.8229 MBE 6.96 × 10−3 RMSE 8.90 × 10−2 4.50 × 10−3 2

2.034 −0.055 −0.800 0.067 0.9487 4.84 × 10−4 2.40 × 10−2 7.49 × 10−4

Model 4: we se = a + bT + cC + dCT + eT2 + fC2 + gT2 C2 a 1.499 2.219 b 0.203 0.036 c −1.635 −1.220 d −0.281 −0.055 e −0.005 −0.003 f 0.854 0.128 g 0.010 0.005 R 0.9763 0.9985 1.34 × 10−4 MBE 2.05 × 10−3 RMSE 3.31 × 10−2 4.30 × 10−3 2 6.54 × 10−4 2.30 × 10−5 −64.087 70.535 −34.087

1.216 −0.176 −1.924 0.341 0.004 0.739 −9.8 × 10−3 0.9965 2.17 × 10−4 1.20 × 10−2 1.59 × 10−4 −227.113 49.356 0.457

6.755 −0.230 −7.628 0.303 0.9395 3.50 × 10−3 5.42 × 10−2 2.50 × 10−3 1.389 −0.170 0.433 0.168 0.004 0.482 −7.4 × 10−3 0.9835 7.26 × 10−4 2.59 × 10−2 6.97 × 10−4 −24.829 26.955 −0.015

−2.307 0.170 4.459 −0.240 0.9933 4.59 × 10−1 4.64 × 10−1 2.13 × 10−1 0.835 0.102 −0.067 −0.146 −1.4 × 10−3 0.173 0.003 0.9980 9.80 × 10−3 1.43 × 10−2 2.14 × 10−4 226.873 −125.054 −2.570

5.733 −0.153 −7.399 0.226 0.9881 4.85 × 10−5 3.04 × 10−2 7.94 × 10−4 1.404 0.110 −1.691 −0.151 −0.002 0.808 0.004 0.9999 −4.73 × 10−5 3.40 × 10−3 9.46 × 10−6 0.558 9 × 10−4 1.198

5.849 −0.155 −7.485 0.227 0.9899 −3.10 × 10−4 2.87 × 10−2 7.64 × 10−4 1.567 0.101 −1.706 −0.152 −0.002 0.913 0.004 0.9999 −1.10 × 10−4 3.56 × 10−3 1.11 × 10−5 1.627 1 × 10−4 1.910

2.413 −0.011 −2.324 0.020 0.9774 6.46 × 10−4 3.83 × 10−2 1.81 × 10−3 1.541 0.167 −1.560 −0.235 −0.003 0.867 6.7 × 10−3 0.9999 −5.65 × 10−3 6.56 × 10−3 4.04 × 10−5 1891.551 0.611 −4.615

259

Model 5: we se = a + bTc + dCe + f(CT)g a −52.233 b 53.568 c −0.003

5.642 −0.202 −5.639 0.256 0.9300 4.02 × 10−3 5.62 × 10−2 3.08 × 10−3

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Model 1: we se = aTb Cc a b c R MBE RMSE 2

Fructose

se = f(TC)

260

Table 3 – (Continued ) we = f(TC)

Constant Glucose

Fructose

se = f(TC) Sucrose

1.636 3.163 65.802 −0.005 0.9946 2.81 × 10−5 7.74 × 10−3 8.08 × 10−5

253.489 0.451 −50.691 0.483 0.9942 1.05 × 10−3 1.53 × 10−2 2.64 × 10−4

Model 6: we se = a + bTc + d exp(eC) a 79.546 b −5 × 10−18 c 9.839 d −78.317 e 0.009 R 0.8367 MBE 5.99 × 10−3 RMSE 8.53 × 10−2 2 4.18 × 10−3

343.032 −8.638 −104.831 −342.221 −0.002 0.7517 −5.84 × 10−1 5.90 × 10−1 4.77 × 10−1

−423.125 195.555 −0.004 230.549 0.003 0.9109 4.77 × 10−3 6.52 × 10−2 1.04 × 10−4

Model 7: we se = a + b exp(cT) + dCe a 0.763 b −3.2 × 10−5 c 0.182 d 0.001 e −6.439 R 0.9315 MBE 3.15 × 10−3 RMSE 5.84 × 10−2 2 1.84 × 10−3

1.483 −0.284 0.018 2.014 5.683 0.9999 1.03 × 10−5 1.08 × 10−3 1.37 × 10−6

−61.355 −0.012 0.086 62.704 0.006 0.9624 1.66 × 10−3 3.91 × 10−2 1.68 × 10−3

Model 8: we se = a + b exp(cTd ) + eCf a −3.341 b 4.250 c −0.001 d 1.262 e 3.74 × 10−4 f −7.078 R 0.9236

0.984 −0.584 −8.438 0.275 0.520 2.372 0.7552

−1469.620 1158.980 −0.004 0.005 312.479 0.001 0.93930

−2.78 × 10−13 −30.154 39.653 −2.029 0.9978 5.77 × 10−4 1.19 × 10−2 9.28 × 10−5

Glucose

Fructose

Sucrose

Maltodextrin

−226.263 0.004 1.009 −257.327 0.9979 2.44 × 10−4 9.73 × 10−3 1.20 × 10−4

0.533 −0.995 −0.826 −0.087 1.000 −1.36 × 10−5 3.32 × 10−4 8.22 × 10−8

0.385 −1.114 −1.255 0.064 1.000 6.18 × 10−4 7.29 × 10−4 3.52 × 10−7

−1891.120 6 × 10−4 0.005 0.957 0.9906 2.57 × 10−4 2.56 × 10−2 7.63 × 10−4

−376.765 431.222 −2.111 377.252 1 × 10−4 0.9554 1.93 × 10−3 4.23 × 10−2 1.14 × 10−4

0.600 −0.109 −5.779 2.629 −3.138 0.9978 1.38 × 10−4 1.17 × 10−2 1.28 × 10−4

12.936 −12.887 −0.010 3.630 −3.844 0.9999 1.87 × 10−5 1.95 × 10−3 1.57 × 10−6

0.586 5.050 −7.967 4.390 −4.558 0.9969 3.95 × 10−4 1.98 × 10−2 2.02 × 10−4

0.817 −2.785 −19.013 7.382 −6.045 0.9994 4.99 × 10−5 6.93 × 10−3 3.40 × 10−4

−9020.473 −35.166 0.001 9057.060 −4.1 × 10−7 0.9389 3.80 × 10−3 5.47 × 10−2 2.52 × 10−3

−0.558 0.006 0.038 1.190 −0.506 0.9985 8.85 × 10−5 8.85 × 10−3 8.46 × 10−5

−6.079 6.046 0.001 0.450 −1.062 0.9999 6.60 × 10−5 9.41 × 10−4 5.55 × 10−7

0.002 0.001 0.093 0.514 −0.998 1.0000 2.72 × 10−6 4.97 × 10−6 1.82 × 10−11

−1.477 2.081 0.001 0.141 −1.952 0.9997 2.83 × 10−5 4.43 × 10−3 2.08 × 10−5

0.602 2.945 −0.204 0.394 −18.084 17.928 0.9578

536.344 314.298 −0.029 −1.44 × 10−4 −850.096 9.8 × 10−4 0.9979

149.832 −0.518 −13.591 0.004 −149.322 0.006 0.9970

306.016 −0.632 −5.108 0.001 −305.108 0.003 0.9975

493.675 −23.968 −16.721 0.015 −493.102 0.002 0.9907

f o o d a n d b i o p r o d u c t s p r o c e s s i n g 8 6 ( 2 0 0 8 ) 254–267

4 × 10−4 −7.071 29.397 −33.165 0.9206 3.82 × 10−3 6.35 × 10−2 2.13 × 10−3

d e f g R MBE RMSE 2

Maltodextrin

−294.456 236.228 280.427 −430.863 58.915 1.87 × 10−3 −2.142 0.9992 −4.01 × 10−4 7.94 × 10−3 6.20 × 10−5

3.

261

Results and discussion

12.598 −12.160 −13.560 −1.753 −6.12 × 10−9 0.006 −8.706 0.9751 1.12 × 10−3 3.16 × 10−2 1.05 × 10−3

−1.164 −0.147 −6.69 × 10−4 1.559 0.257 2.024 −0.155 0.9986 6.00 × 10−5 8.83 × 10−3 8.43 × 10−5

−140.394 145.267 −0.036 −0.029 81.661 −5.641 0.277 0.9999 −5.34 × 10−4 1.82 × 10−3 1.96 × 10−6

0.217 9.390 −111.611 −0.807 78.208 −5.519 0.276 1.0000 3.42 × 10−6 1.99 × 10−4 3.21 × 10−8

3.1. The effect of process parameters on equilibrium distribution coefficient of apricot

Where C is concentration (%) (w/w) and T is temperature in degree centigrade.

−1.95 × 10 2.26 × 10−1 2.78 × 10−2 MBE RMSE 2

−2.070 3.443 −3.14 × 10−4 1.721 −0.293 −273.429 7.869 0.9688 3.33 × 10−3 4.00 × 10−2 1.40 × 10−3

−3.82 × 10 3.85 × 10−1 1.26 × 10−1 2.24 × 10 4.79 × 10−2 3.22 × 10−3

−3

−3.284 1.783 −0.002 1.261 2.739 0.680 5.562 0.9994 6.05 × 10−6 2.51 × 10−3 8.87 × 10−6

Glucose

−9.08 × 10 9.18 × 10−1 8.31 × 10−1 1.23 × 10 1.26 × 10−1 1.12 × 10−1

−1

Maltodextrin

−1

Sucrose Glucose

−1

Fructose

we = f(TC) Constant

Table 3 – (Continued )

Model 9: we se = a + b exp(cTd ) + e exp(fCg ) a −3.475 b 0.007 c 6.468 d −0.007 e 0.443 f 0.001 g −6.373 R 0.9195 MBE 4.11 × 10−3 RMSE 6.40 × 10−2 2 2.15 × 10−3

3.30 × 10−2 4.70 × 10−2 2.64 × 10−3 5.78 × 10 5.86 × 10−1 2.63 × 10−1 1.42 × 10 1.50 × 10−1 1.74 × 10−2

−1

Sucrose Fructose

se = f(TC)

−1

−1

Maltodextrin

f o o d a n d b i o p r o d u c t s p r o c e s s i n g 8 6 ( 2 0 0 8 ) 254–267

The relative percentage deviations (D) for experimental values and determined values of water loss and solid gain at equilibrium from experimental values, which are determined by using Azuara et al. (1998) models, are given in Tables 1–2. The equilibrium water and solid contents were estimated using Eqs. (5) and (6), and the results were shown in Tables 1–2. At constant temperature, equilibrium water content has been decreased and equilibrium solid content has been increased with the increased solute concentration and decreased sample to solution ratio. At a constant solute concentration, equilibrium water content has been decreased and equilibrium solid content has been increased with the increased temperature. This could be explained by the fact that the process starts by simultaneous transport of water and solid, and reaches an equilibrium point. The equilibrium point is reached when water activities of both solute and product become equal. Since water activity can be decreased both by water loss or solid gain, there is a relationship between water loss and solid gain in reaching to equilibrium. The relative transport of water loss and solid gain to reach equilibrium was identified and explained by Rahman and Lamb (1990) and Parjoko et al. (1996). They have mentioned that water can be diffused through the cell membranes easily compared to solutes. Thus, at higher temperatures the osmotic equilibrium is achieved by more water flow from cells relative to the solid transport, causing less solid gain. The equilibrium distribution coefficients for both water and solid were calculated using Eqs. (2) and (3). The equilibrium distribution coefficients of water and solids varied from 1.473 to 0.719 g g−1 and 1.302–0.651 g g−1 , respectively, within the range of syrup concentration and temperature studied in these works. Typical concentration and temperature effect on equilibrium distribution coefficient of apricot are presented in Figs. 1 and 2, respectively. The effect of syrup concentration on the equilibrium distribution coefficient for water showed different trends related to various osmotic agents. Distribution coefficient of water for sorbitol, fructose and partly sucrose has been increased with increased syrup concentration. But distribution coefficient of water for glucose and maltodextrin showed a decreasing tendency with increasing syrup concentration. As for distribution coefficient of solid, it has been decreased with the increasing solute concentration. (Fig. 1) At a constant syrup concentration, distribution coefficient of water has been decreased and distribution coefficient of solid has been increased with increased temperature of solution (Fig. 2). Temperature had much greater effect on ew than es for glucose, sucrose and maltodextrin solutions. As for fructose, temperature had the same effect both ew and es . Sablani et al. (2002) found that ew is varied from 0.621 to 1.800 g g−1 , and es is varied from 0.466 to 1.460 g g−1 in case of osmotic dehydration of apple cubes, when temperature and syrup concentration varied from 22 to 90 ◦ C and 30% to 70%, respectively. Corzo and Bracho (2004) have found that, equilibrium distribution coefficients of water are varied from 0.501 to 0.625 g g−1 , and distribution coefficients of salt is varied from 0.529 to 0.778 g g−1 in case of an osmotic dehydration of sardine sheets, when temperature and salt concentration varied

262

Table 4 – The non−linear regression models described between equilibrium distribution coefficients and concentration for sorbitol Models

Sorbitol

1

we = a + bCc se = a + bCc

2

we = a + bCc + d exp(eC) se = a + bCc + d exp(eC)

3

b

c

0.940 1536.506

2.704 −1536.120

10.200 19.830

−53.231 −22.784

we = a exp(bC) se = a exp(bC)

2.665 0.542

−1.850 1.779

– –

4

we = aCb se = aCb

2.625 0.529

0.970 −0.968

– –

5

we = a + b exp(cCd ) se = a + b exp(cCd )

0.908 −2.208

3.18 × 10−7 2.206

6

we = aln(C) + b se = aln(C) + b

1.347 −0.962

2.304 0.339

7

we = a exp(bC) + c se = a exp(bC) + c

0.112 3.782

3.398 −3.986

0.692 0.519

8

we = a + bC + cC2 se = a + bC + cC2

1.378 2.959

−2.434 −5.560

4.539 3.439

9

we = a exp(bC) + c exp(dC) se = a exp(bC) + c exp(dC)

4.67 × 107 1.490

−50.427 −1.053

0.484 5.277

Where C is concentration (%), (w/w).

2.911 6.26 × 10−4 0.047 0.086

15.997 0.220 – –

d

e

R

MBE

RMSE

2

− –

0.9986 0.9959

1.26 × 10−4 −3.45 × 10−3

1.12 × 10−2 1.97 × 10−2

2.34 × 10−4 3.40 × 10−4

0.166 0.613

0.9994 0.9999

3.17 × 10−5 6.66 × 10−7

7.30 × 10−3 2.60 × 10−3

1.08 × 10−4 5.82 × 10−6

– –

– –

0.9958 0.9954

4.12 × 10−1 −7.89 × 10−1

4.12 × 10−1 7.89 × 10−1

3.83 × 10−1 6.29 × 10−1

– –

– –

0.9861 0.9999

−7.79 × 10−4 −6.31 × 10−3

3.75 × 10−2 6.84 × 10−3

2.33 × 10−3 5.88 × 10−5

– –

0.9985 1.0000

−2.65 × 10−4 −1.51 × 10−5

1.16 × 10−2 1.81 × 10−4

2.49 × 10−4 2.60 × 10−8

– –

0.9699 0.9959

1.14 × 10−3 −5.31 × 10−2

5.22 × 10−2 5.82 × 10−2

4.98 × 10−3 2.83 × 10−3

0.9983 0.9999

1.45 × 10−4 4.46 × 10−6

1.26 × 10−2 1.79 × 10−3

2.88 × 10−4 2.61 × 10−6

0.9989 0.9997

1.53 × 10−4 −3.40 × 10−5

9.69 × 10−3 4.95 × 10−3

1.84 × 10−4 2.15 × 10−5

0.9998 1.0000

1.22 × 10−4 −3.64 × 10−6

4.11 × 10−3 3.66 × 10−6

3.82 × 10−5 1.25 × 10−11

− – 39.217 1.962

0.190 −0.804 – –

– – 1.953 −7.094

f o o d a n d b i o p r o d u c t s p r o c e s s i n g 8 6 ( 2 0 0 8 ) 254–267

a

f o o d a n d b i o p r o d u c t s p r o c e s s i n g 8 6 ( 2 0 0 8 ) 254–267

263

Fig. 4 – Plot of equilibrium distribution coefficients of apricot vs. the ratio of sample to solution for glucose and maltodextrin. ( ) we and () se .

from 32 to 38 ◦ C and 0.150 to 0.270 g g−1 , respectively. The values of distribution coefficients for mangos were (Sablani and Rahman, 2003) in the range reported earlier for different food products (Parjoko et al., 1996; Silveira et al., 1996) Barat et al. (1998) studied the mechanism of equilibrium kinetics during osmosis. They have identified two points in equilibration: first compositional equilibrium was achieved in a relatively short time, depending on conditions. Then a bulk flux of osmotic solution into the fruit tissue occurred due to relaxation of previously shrunken cellular structure. The equilibrium estimated here is the initial equilibrium stage without structure relaxation. The initial equilibration period is necessary for ultimate mass transport of solutes and water. The effect of using a pretreatment prior to osmotic dehydration about the equilibrium distribution coefficients of apricot is shown in Fig. 3. In making use of the pretreatment, different effects were observed for each pretreatment chemical and osmotic agent. In fructose, the application of K2 S2 O5 , Na2 S2 O5 and EO + K2 S2 O5 enhanced the equilibrium distribution coefficient of water while the whole pretreatment had increased the equilibrium distribution coefficient of solid. In glucose, Na2 S2 O5 increased ew while the whole pretreatment was decreasing es . In sucrose, each pretreatment application increased ew while the application of K2 S2 O5 , Na2 S2 O5 and EO + K2 S2 O5 was increasing es . In maltodextrin, any pretreatment application decreased the equilibrium distribution

coefficients for water and solid. In sorbitol, Na2 S2 O5 increased ew , while each pretreatment was also increasing es . These different effects may be a cause of collaboration or conflict in between pretreatment chemicals and osmotic agents. The effect of sample to solution ratio on the equilibrium distribution coefficients of apricot is given in Fig. 4 by using glucose and maltodextrin solution. The effect of sample to solution ratio on distribution coefficients showed opposite trends, i.e., decreasing the sample to solution ratio has decreased distribution coefficient of water, but it also increased the distribution coefficient of solid. The same effect was also seen in the effect of concentration on the equilibrium content of water and solid. As mentioned above, at a constant temperature, equilibrium water content has been decreased and equilibrium solid content has been increased with the increased solute concentration.

3.2.

Modeling of distribution coefficients

The equilibrium distribution coefficient of apricot has been obtained for different combinations of concentration and temperature of osmotic solution has been modeled by using nine nonlinear regression models. Regression has been calculated by using the statistical package Statistica 5.0 (Statistica, 1995). The models’ results are given in Table 3 for sucrose, glucose, fructose and maltodextrin and also in Table 4 for sorbitol. As it

Fig. 5 – Comparison of measured and predicted values from model 4, include both concentration and temperature term.

264

f o o d a n d b i o p r o d u c t s p r o c e s s i n g 8 6 ( 2 0 0 8 ) 254–267

Table 5 – The non-linear regression models described between equilibrium distribution coefficients and the ratio of sample to solution Constant

Glucose ␭we

Model 1: we se = a + bRatioc a b c R MBE RMSE 2

Maltodextrin se

we

se

0.971 −0.007 −0.931 0.9990 −7.07 × 10−7 2.04 × 10−3 3.32 × 10−6

145.085 −144.496 5.81 × 10−4 0.9746 5.05 × 10−4 1.47 × 10−2 1.39 × 10−4

−188.061 189.326 4.5 × 10−4 0.9437 4.91 × 10−4 1.74 × 10−2 3.35 × 10−4

61.885 −61.075 4.97 × 10−4 0.9554 1.17 × 10−4 6.49 × 10−3 3.30 × 10−5

Model 2: we se = a + bRatioc + d exp(eRatio) a 3.265 b −2.149 c −0.083 d 0.471 e −6.678 R 0.9993 MBE 1.46 × 10−6 RMSE 1.78 × 10−3 2 2.44 × 10−6

12.513 −12.097 0.028 −0.760 −6.133 0.9997 −1.19 × 10−5 1.50 × 10−3 1.47 × 10−6

10.325 −9.171 −0.002 −0.476 −34.034 0.9993 2.69 × 10−6 1.88 × 10−3 4.03 × 10−6

13.354 0.005 −0.843 −12.521 −0.0028 0.9956 −3.95 × 10−5 2.05 × 10−3 3.30 × 10−6

Model 3: we se = a exp(bRatio) a b R MBE RMSE 2

0.836 0.545 0.873 5.71 × 10−4 2.30 × 10−2 3.99 × 10−4

0.869 −0.873 0.900 6.50 × 10−4 2.85 × 10−2 5.26 × 10−4

0.992 0.582 0.825 9.76 × 10−4 3.02 × 10−2 9.78 × 10−4

0.910 −0.267 0.859 1.20 × 10−4 1.12 × 10−2 9.90 × 10−5

Model 4: we se = aRatiob a b R MBE RMSE 2

1.055 0.071 0.964 1.95 × 10−4 1.25 × 10−2 1.19 × 10−4

0.607 −0.109 0.981 6.42 × 10−5 1.29 × 10−2 1.06 × 10−4

1.279 0.078 0.937 4.16 × 10−4 1.85 × 10−2 3.76 × 10−4

0.812 −0.035 0.958 3.55 × 10−5 6.30 × 10−3 3.11 × 10−5

188.436 −78.278 0.875 5.1 × 10−4 0.9746 3.76 × 10−5 1.47 × 10−2 1.39 × 10−4

−8.878 0.003 7.992 1.07 × 10−3 0.9429 −4.39 × 10−4 1.75 × 10−2 3.40 × 10−4

10.364 −0.815 2.462 0.001 0.9551 4.08 × 10−5 6.51 × 10−3 3.32 × 10−5

−0.058 0.589 0.975 −7.92 × 10−2 8.14 × 10−2 4.48 × 10−3

0.059 1.265 0.944 6.30 × 10−2 6.85 × 10−2 4.83 × 10−3

−0.021 0.810 0.955 −2.60 × 10−2 2.73 × 10−2 6.01 × 10−4

−0.058 1.096 0.597 0.975 −7.62 × 10−2 7.86 × 10−2 4.19 × 10−3

0.059 7.323 1.096 0.944 1.35 × 10−2 2.80 × 10−2 7.61 × 10−4

−0.021 2.527 0.838 0.955 −1.62 × 10−2 1.84 × 10−2 2.77 × 10−4

Model 5: we se = a + b exp(cRatiod ) a 0.966 b −48709.8 c −16.186 d 0.0745 R 0.9989 MBE 1.14 × 10−5 RMSE 2.07 × 10−3 2 3.43 × 10−6 Model 6: we se = aln(Ratio) + b a 0.045 b 1.045 R 0.969 MBE 5.68 × 10−2 RMSE 6.05 × 10−2 2 2.69 × 10−3 Model 7: we se = aln(bRatio) + c a b c R MBE RMSE 2

0.045 2.442 0.987 0.969 3.67 × 10−2 4.18 × 10−2 1.25 × 10−3

Model 8: we se = a exp(bRatio) + c a 1.885 b 0.254 c −1.050 R 0.876

0.336 −19.756 0.719 0.996

946.934 6.78 × 10−4 −945.946 0.833

0.141 −23.339 0.859 0.994

265

f o o d a n d b i o p r o d u c t s p r o c e s s i n g 8 6 ( 2 0 0 8 ) 254–267

Table 5 – (Continued ) Constant

Glucose ␭we

Maltodextrin se

we

se

5.49 × 10 2.27 × 10−2 3.89 × 10−4

−5

3.06 × 10 5.98 × 10−3 2.28 × 10−5

−3

1.00 × 10 2.9 × 10−2 9.37 × 10−4

6.07 × 10−6 2.44 × 10−3 4.68 × 10−6

Model 9: we se = a exp(bRatio) + c exp(dRatio) a 0.899 b 0.193 c −0.357 d −36.068 R 0.9993 MBE 2.68 × 10−6 RMSE 1.77 × 10−3 2 2.40 × 10−6

1.313 −0.873 −0.443 −0.873 0.9002 6.50 × 10−4 2.85 × 10−2 5.26 × 10−4

1.100 0.092 −0.514 −32.894 0.9994 2.69 × 10−6 1.80 × 10−3 3.69 × 10−6

1.086 −0.267 −0.176 −0.267 0.8591 1.19 × 10−4 1.12 × 10−2 9.90 × 10−5

MBE RMSE 2

−4

can be seen in Table 3, the equilibrium distribution coefficients for water and solid are depended on the concentration and temperature of the osmotic solution, in addition to combined effect of these parameters. The relationship between sample-to-solution-ratio and equilibrium distribution coefficients of apricot has also been modeled by using nine nonlinear models. The models’ results are given in Table 5. To find the best models explaining the variations, a huge variety of empirical correlation were used. The best models, which have the highest correlation coefficient (R) and statistical analysis results, are summarized in Table 6. The proposed models in Table 6 can confidently be used for explaining the effect of concentration, temperature and sample to solution ratio, used experimental range because of high correlation coefficient, low 2 , MBE and RMSE. The values calculated from model 4, include both concentration and temperature term, which give almost good results for all agents, from model 9 for sorbitol and from model 2 for the ratio of sample to solution were plotted vs. measured values to simply compare predicted and measured values. The results given in Figs. 5–7 can be considerable as brief of all the modeling studies.

Fig. 6 – Comparison of measured and predicted values from model 9 for sorbitol.

Fig. 7 – Comparison of measured and predicted value from model 2 for effect of the sample to solution ratio.

266

f o o d a n d b i o p r o d u c t s p r o c e s s i n g 8 6 ( 2 0 0 8 ) 254–267

3.69 × 10−6 3.30 × 10−6 1.80 × 10−3 2.05 × 10−3 2.69 × 10−6 −3.95 × 10−5

2.40 × 10−6 1.47 × 10−6 1.77 × 10−3 1.50 × 10−3 2.68 × 10−6 −1.19 × 10−5

3.82 × 10−5 2.60 × 10−8 1.25 × 10−11 4.11 × 10−3 1.81 × 10−4 3.66 × 10−6 1.22 × 10−4 −1.51 × 10−5 −3.64 × 10−6

9.28 × 10−5 4.04 × 10−5 1.19 × 10−2 6.56 × 10−3 5.77 × 10−4 −5.65 × 10−3 we = −24.829 + 26.955T−0.015 − 2.78 × 10−13 C−30.154 + 39.653(CT)−2.029 se = 1.541 + 0.167T − 1.560 C − 0.235CT − 0.003T2 + 0.867 C2 + 6.7 × 10−3 T2 C2

1.59 × 10−4 3.52 × 10−7 1.82 × 10−11 3.21 × 10−8

Conclusions

The equilibrium distribution coefficients of water and solids during osmotic dehydration of apricot have been affected by temperature, syrup concentration, various osmotic agents, pretreatment application before osmotic dehydration, and the sample to solution ratio. The temperature, syrup concentration, type of osmotic agents and sample to solution ratio showed opposite trends in terms of their effect on distribution coefficients. The pretreatment application prior to osmotic dehydration has shown different effects for various osmotic agents and chemical solution. Relationships been the function of concentration of osmotic agent, temperature and the sample to solution ratio, were developed for predicted distribution coefficients of apricot during osmotic dehydration in sugar solutions. The chosen models can confidently be used for explaining the effect of concentration, temperature and sample to solution ratio, used experimental range because of high correlation coefficient, low 2 , MBE and RMSE. The correlation of distribution coefficients developed in this study can be beneficial for the design of osmotic drying equipment for apricot. The total water removal can be predicted from the distribution coefficients and the syrup requirement for specific process conditions can be estimated.

we = 0.899 exp(0.193Ratio) −0.357 exp(−36.068Ratio) se = 12.513 − 12.097Ratio0.028 − 0.760 exp(−6.133Ratio)

we = 1.1 exp(0.092Ratio) − 0.514exp(−32.894Ratio) se = 13.354 + 0.005Ratio−0.843 − 12.521 exp(−0.0028Ratio) Ratio 1/4–1/25 Maltodextrin

C (40–70%) Sorbitol

The ratio of sample to solution Glucose Ratio 1/4–1/25

we = 4.67 × 107 exp(−50.427C) + 0.484 exp(1.953C) se = −2.208 + 2.206 exp(0.220 C−0.804 ) se = 1.490 exp(−1.053C) + 5.277 exp(−7.094C)

Acknowledgment

C (40–70%) T (25–45 ◦ C) Maltodextrin

1.20 × 10−2 7.29 × 10−4 4.97 × 10−6 1.99 × 10−4 2.17 × 10−4 6.18 × 10−4 2.72 × 10−6 3.42 × 10−6 we = 1.216 − 0.176T − 1.924C + 0.341CT + 0.004T2 + 0.739C2 − 9.8 × 10−3 T2 C2 se = 1.627 + 1 × 10−4 T1.91 + 0.385C−1.114 − 1.255(CT)0.064 se = 0.002 + 0.001 exp(0.093T) + 0.514C−0.998 se = 0.217 + 9.39 exp(−111.61T−0.81 ) + 78.208 exp(−5.519C0.276 ) C (40–70%) T (25–45 ◦ C) Sucrose

1.37 × 10−6 8.22 × 10−8 1.08 × 10−3 3.32 × 10−4 C (40–70%) T (25–45 ◦ C) Fructose

we = 1.483 − 0.284 exp(0.018T) + 2.014C5.683 se = 0.558 + 9 × 10−4 T1.198 + 0.533C−0.995 − 0.826(CT)−0.087

1.03 × 10−5 −1.36 × 10−5

6.54 × 10−4 8.43 × 10−5 3.31 × 10−2 8.83 × 10−3 2.05 × 10−3 6.00 × 10−5 C (40–70%) T (25–45 ◦ C) Glucose

we = 1.499 + 0.203T − 1.635C − 0.281CT − 0.005T2 + 0.854C2 + 0.010T2 C2 se = −1.164 − 0.147 exp(−6.69 × 10−4 T1.56 ) + 0.257 exp(2.024C−0.155 )

RMSE Osmosis conditions Solution

Table 6 – Statistical analyses results of the best models

Model

MBE

2

4.

This study was supported by the Research Foundation of Firat University (project no: FUBAP-1145).

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