Effect of syrup concentration, temperature and sample geometry on equilibrium distribution coefficients during osmotic dehydration of mango

Food Research International 36 (2003) 65–71 www.elsevier.com/locate/foodres

Effect of syrup concentration, temperature and sample geometry on equilibrium distribution coefficients during osmotic dehydration of mango Shyam S. Sablani*, M. Shafiur Rahman Department of Bioresource and Agricultural Engineering, College of Agriculture, Sultan Qaboos University, PO Box 34, Al Khod 34, Muscat, Sultanate of Oman Received 24 October 2001; accepted 19 March 2002

Abstract The effect of initial sucrose concentration (30–70%), solution temperature (22–90
C) and sample geometry (cube, slice and wedges) on equilibrium distribution coefficients of mango was investigated during osmotic dehydration. The distribution coefficients for water ranged from 0.908 to 2.12 for cubes, 0.919 to 1.74 for slices and 0.915 to 1.95 for wedges, respectively, while the distribution coefficients for solids varied from 0.520 to 1.183 for cubes, 0.683 to 1.13 for slices and 0.592 to 1.17 for wedges, respectively. The distribution coefficient for water decreased with increasing temperature and surface area, and it increased with the increase in syrup concentration and thickness of the minimum geometric dimension. The distribution coefficient for solids increased with the increase in temperature, and surface area, while it decreased with the increase in syrup concentration, and thickness of minimum geometric dimension. A multiple regression analysis of experimental data was carried out to correlate distribution coefficients with dimensionless temperature, syrup concentration and geometric shape parameters. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: Equilibrium distribution coefficient; Moisture transfer; Solute transport; Sugar syrup

1. Introduction Osmotic dehydration is one of the important pretreatments used for dried mango strips consumed as snacks, mango pickle, or mango chutney. The process involves removal of water by immersing them in concentrated aqueous solutions, mainly sugar, salt and spices. In osmotic dehydration, three types of counter-current mass transfer occur: (1) water flows from the product to the solution, (2) a solute transfer from solution to the product and (3) a leaching out of the product’s own solutes (sugars, organic acids, minerals, vitamins, etc.; Panagiotou, Karathanos, & Maroulis, 1998; Rahman & Perera, 1999; Raoult-Wack, 1994a, 1994b). This process offers several advantages by improving quality characteristics of the final product, and improving process efficiency. Solutes and spices incorporation in the syrup makes it possible to introduce the desired amount of an * Corresponding author. Tel.: +968-515-289; fax: +968-513-418. E-mail address: [email protected] (S.S. Sablani).

active component, such as preservative agents, nutrients, flavor, test or texture enhancer for the product. The energy saving may also be achieved as the water from the product is removed without phase change, which is different from conventional air-drying (Rahman & Perera, 1999). 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, Chiralt, & Fito, 1999). Moreover knowledge of the end-point criteria can allow development of theoretical models allowing calculation of the process parameters (Lenart & Flink, 1984). Kinetics of osmotic dehydration of potato was studied by Lenart and Flink (1984), and Lombardi and

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Zaritzky (1996). Equilibrium kinetics was studied by Medina-Vivanco, Sobral, and Hubinger (1998), and Biswal and Bozorgmehr (1991) for fish tilapia and potato, respectively. Mosalve-Gonzalez, Barbosa-Canavos, and Cavalieri (1993) studied the mass transfer and textural changes of apple during osmotic dehydration in sugar syrup. They developed a model for osmotic dehydration kinetics from Fick’s law of diffusion, which also needs the equilibrium kinetics data for water and solids. Martinez-Monzo, Martinez-Navarrette, Chiratt, and Fito (1998) studied the mechanical and structural changes in apple during vacuum osmotic dehydration. Panagiotou et al. (1998) developed an empirical model based on first order kinetics to predict the water loss and solid gain during osmotic dehydration of apple, banana and kiwi fruit. Later they also studied the influence of osmotic agent on dehydration rate of few fruits (Panagiotou, Karathanos, & Maroulis, 1999). The distribution coefficient for salt is defined as the ratio of the salt concentration in fish muscle and brine at equilibrium (Del Valle & Nickerson, 1967; Favetto, Chirife, & Bartholomai, 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 R (ratio of mass of solution to the mass of the product) is very high. In other cases the distribution coefficient is a function of ratio R in addition to other process parameters. This approach makes easy to use most of the practical cases when equilibrium concentration is difficult to predict. The equilibrium distribution coefficients for the ith component can be defined as: lei ¼

Xie Yio

ð1Þ

where lei is the distribution coefficient, and 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 as: lew ¼

Xwe Ywo

ð2Þ

Similarly, the distribution coefficient for total solids can be defined as: les ¼

Xse Yso

ð3Þ

Use of total solids to evaluate equilibrium values makes the system food product a binary system (i.e. water and total solids) and in the same way the solution of sugar (or salt) is also a binary system. Consequently

there is an explicit relationship between the lew and les. Once lew is known les can be calculated using the following relationship: les ¼

1  lew Ywo 1  Ywo

ð4Þ

The distribution coefficients for water and solids were determined in case of osmotic drying of pineapple in sucrose (Parjoko, Rahman, Buckle, & Perera, 1996) and palm sugar (Silveira, Rahman, & Buckle, 1996), and potato (Rahman, Sablani, & Al-Ibrahim, 2001) in sucrose. They also developed models to predict the distribution coefficients as a function of processing 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 is very little study carried out to find the effect of surface area on the distribution coefficients. The objective of this study was to measure and model the equilibrium distribution coefficients of water and solids for mango of different geometric shapes as a function of syrup concentration and temperature.

2. Materials and methods 2.1. Materials A batch of mature totapuri variety mangoes of medium size was obtained from local supermarket of Muscat, Oman. The fruits were refrigerated at 10
C and at 95% relative humidity until used for experiments. All experiments were conducted within 4 days of purchase when skin color was a little yellow. Mangoes were handpeeled and cut into three different shapes: cubes (2.0 cm side), slices (3.51.81.0 cm) and wedges (length 5.5 cm and side triangle 2.02.51.5 cm). The surface area was estimated from the geometric dimensions of the samples. In the case of wedge, surface area was estimated from the sum of the areas of four triangles comprising the surface. The mango pieces were immersed into a sucrose–water solution into a bath of size 15 cm diameter and 22.5 cm height. The container was made of stainless steel and insulated with paperboard of 1 cm thickness. The containers were placed on hot plates to maintain required temperatures of the syrup during the experiment. The container was covered with a plastic plate to reduce moisture loss from syrup during experiments. The osmotic medium was agitated continuously with a magnetic stirrer to maintain a uniform temperature throughout the experiment, thus enhancing equilibrium condition. The temperatures were also monitored using digital thermometers within the accuracy of  0.1
C. The initial concentration of sucrose varied

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from 30 to 70% (kg sugar/100 kg syrup), and temperatures varied from 22 to 90
C. The syrup–fruit mass ratio (R) was kept very high (  22.0 kg syrup/kg sample) to reduce the effect of syrup and fruit mass ratio on the process.

MRE ¼

N 1X lR N i¼1

ð7Þ

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uN 2 uP u lR  lR ti¼1

2.2. Equilibration distribution coefficients

STDR ¼

The set of the experiment was conducted for the determination of distribution coefficients under different processing conditions. The mango pieces of different shapes were immersed in syrup for a period of 24 h. This time was considered to be sufficient for mango pieces to reach equilibrium with a sugar–water solution as identified by Rahman et al. (2001), Parjoko et al. (1996), and Silveira et al. (1996) for other plant materials. Samples were then quickly rinsed and gently blotted with tissue paper to remove surface water before analysis. The water content and total solids were measured gravimetrically from the samples. Three replicates for each geometrical shape were used in this study. The distribution coefficients for water and solids were estimated using Eqs. (2) and (3).

where lA ¼ lp lE ; lR ¼ ðlP lE Þ=lE . The parameters lP and lE are predicted and experimental values of distribution coefficients.

2.3. Data analysis Analysis of variance (ANOVA) was carried out to identify the influence of the significant (P < 0.05) process variables on the distribution coefficients for solids and water. The dimensionless parameters considered were T/Tr, Yos , As/l 2, where T is the process temperature (K), Tr is the reference temperature (273 K), As is surface area of the sample (m2), and l is smallest geometric dimension of the sample (m). Multiple regression analysis was also conducted to develop empirical correlations between distribution coefficients and parameters significantly affecting the process. The performance of the dimensionless prediction equations were compared using mean relative error (MRE), mean absolute error (MAE), standard deviations in relative error (STDR) and absolute error (STDA). The coefficient of determination, R2, of the linear regression line between the values predicted from the dimensionless equations and the experimental was also used as measure of performance. The four error measures used to compare the performance of the various dimensionless equations were: MAE ¼

STDA ¼

N 1X lA N i¼1

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uN 2 uP u lA  lA ti¼1 N1

ð5Þ

ð6Þ

ð8Þ

N1

3. Results and discussion Moisture content of fresh mango was 88.7% (wet basis). The equilibrium distribution coefficients for solids water were calculated using Eqs. (2) and (3). For simplicity only water equilibrium distribution coefficients under various conditions are presented in Table 1. The equilibrium distribution coefficients for solids can simply be obtained from Eq. (4). Distribution coefficients of water and solids varied from 0.908 to 2.12 and from 0.520 to 1.183, respectively, within the range of syrup concentration, temperature, size and shape of the samples studied in this work. At a constant syrup Table 1 Water equilibrium coefficients (lew) for mango pieces of different geometries at various experimental conditions lew Temperature Sucrose
concentration ( C) (fraction) Cubes

Slices

Wedges

22 22 22 22 22 40 40 40 40 40 60 60 60 60 60 90 90 90 90 90

1.07 (0.049) 1.14 (0.028) 1.30 (0.106) 1.46 (0.139) 1.74 (0.109) 0.97 (0.003) 1.03 (0.011) 1.06 (0.007) 1.14 (0.006) 1.31 (0.063) 0.97 (0.006) 0.98 (0.003) 1.06 (0.038) 1.11 (0.034) 1.26 (0.923) 0.94 (0.008) 0.92 (0.017) 0.98 (0.029) 1.03 (0.040) 1.3 (0.065)

1.07 (0.030) 1.15 (0.050) 1.29 (0.113) 1.63 (0.179) 1.95 (0.289) 0.97 (0.006) 1.03 (0.014) 1.08 (0.013) 1.19 (0.003) 1.41 (0.084) 0.96 (0.012) 0.97 (0.007) 1.02 (0.006) 1.1 (0.019) 1.15 (0.053) 0.93 (0.002) 0.92 (0.015) 0.96 (0.017) 1.01 (0.027) 1.07(0.055)

0.3 0.4 0.5 0.6 0.7 0.3 0.4 0.5 0.6 0.7 0.3 0.4 0.5 0.6 0.7 0.3 0.4 0.5 0.6 0.7

1.09 (0.025) 1.18 (0.067) 1.39 (0.137) 1.72 (0.067) 2.12 (0.043) 1.00 (0.008) 1.06 (0.013) 1.09 (0.025) 1.23 (0.033) 1.52 (0.094) 0.97 (0.023) 0.97 (0.005) 1.04 (0.042) 1.09 (0.013) 1.11 (0.086) 0.92 (0.006) 0.91 (0.014) 0.93 (0.017) 0.97 (0.009) 1.1(0.053)

Values in parentheses are standard deviations. Surface area (As) in m2: 24106 for cube; 23.2106 for Slice; 18106 for wedges. Minimum length (l ) in m: 0.02 for cubes; 0.01 for slices; 0.015 for wedges.

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concentration, distribution coefficient of water decreased and distribution coefficient of solids increased with the increasing temperature (Figs. 1–6). The influence of syrup concentration on distribution coefficients showed opposite trends, i.e. Increasing syrup concentration increased distribution coefficient of water but

decreased the distribution coefficient of solids (Figs. 1–6). Rahman et al. (2001) found that lew varied from 0.700 to 1.05 and les varied from 0.840 to 1.55 in case of osmotic dehydration of potato when temperature and syrup concentration varied from 22 to 80
C and 30 to 65%, respectively. The values of distribution coefficients

Fig. 1. Plot of experimental lew vs. syrup concentration at various temperatures for mango cubes.

Fig. 3. Plot of experimental lew vs. syrup concentration at various temperatures for mango slices.

Fig. 2. Plot of experimental les vs. syrup concentration at various temperatures for mango cubes.

Fig. 4. Plot of experimental les vs. syrup concentration at various temperatures for mango slices.

S.S. Sablani, M. Shafiur Rahman / Food Research International 36 (2003) 65–71

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time (usually within 24 h), depending on conditions. Then a bulk flux of osmotic solution into the fruit tissue occurred due to the 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 estimating the time of osmotic process, and ultimate mass transport of solutes and water. 3.1. Modeling of distribution coefficients Analysis of variance showed that the influence of T/ Tr, YoS , and As/l 2 on both distribution coefficients for solids and water was significant (P < 0.05). As a first attempt, equations were developed for individual geometries using experimental data for the distribution coefficients for solids and water: 3.1.1. Cubes lew ¼ 2:214 Fig. 5. Plot of experimental lew vs. syrup concentration at various temperatures for mango wedges.

les ¼ 0:421



T Tr



T Tr

1:99

2:62





0:419

ð9Þ

0:355

ð10Þ

0:395

ð11Þ

0:290

ð12Þ

0:377

ð13Þ

0:306

ð14Þ

Yso

Yso

3.1.2. Slices lew



T ¼ 1:876 Tr

les ¼ 0:551



T Tr

1:25

1:61





Yso

Yso

3.1.3. Wedges lew ¼ 1:937

les

Fig. 6. Plot of experimental les vs. syrup concentration at various temperatures for mango wedges.

obtained for mango pieces are 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 identified two periods in equilibration: first compositional equilibrium was achieved in a relatively short





T Tr

T ¼ 0:519 Tr

1:57

1:90





Yso

Yso

The dimensionless Eqs. (9)–(14) are valid for temperature ratios in the range 1.08–1.33 (22–90
C) and syrup concentration in the range 0.30–0.70 kg sugar/kg solution. The error parameters such as mean absolute error (MAE) and mean relative error (MRE) with standard deviations in absolute errors (STDA) and relative errors (STDR), and coefficient of regression (R2) are given in Table 2. Sopade (2001) considered the coefficient of regression, standard error and mean relative error to identify criteria in accepting the best isotherm model. No one parameter was found to solely indicate a perfect fit, and models could be better assessed on more than one statistical parameter. Thus, different criteria

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Table 2 Error parameters in the prediction of distribution coefficients Geometry MAE

Cube Slice Wedge All data

STDA

MRE

STDR

R2

lew

les

lew

les

7.18 6.58 6.14 5.78

9.80 7.67 9.57 6.65

0.720 0.659 0.710 0.708

0.720 0.665 0.690 0.732

lew

les

lew

les

lew

les

0.119 0.098 0.094 0.105

0.089 0.067 0.069 0.095

0.151 0.123 0.117 0.094

0.019 0.050 0.050 0.053

8.88 11.4 7.56 8.08 7.45 8.45 8.74 10.8

were presented for the models used in this study. The relative errors in the prediction of lew and les for the above equations were in the range of 7–11%. This prediction accuracy is usually acceptable for most engineering design. In Eqs. (9)–(14), the power constant of temperature ratio (T/Tr) is much higher than that of syrup concentration. This indicated that the temperature influence was more pronounced than that of syrup concentration. The influence of temperature and sucrose on distribution coefficients was highest on cube shaped geometry. In Eqs. (9), (11) and (13) the power constants of (T/Tr) are negative and that of Yso are positive. This indicated that increasing temperature decreased lew, and increasing Yso increased lew. Opposite trends were observed in the Eqs. (10), (12) and (14). This could be explained by the equilibrium reached by counter flow of water and solids. The reverse trend of water loss and solid gain can also be explained by the fact that the process starts by simultaneous transport of water and solute, and reaches equilibrium point. The equilibrium point is reached when water activities (i.e. chemical potential) of syrup and product become equal. Since water activity can be decreased both by water loss or solute gain, there is a relationship between water loss and solid gain to reach equilibrium, i.e. If water loss is higher, then solids gain must be lower, and if solids gain is higher then water loss must be lower (Parjoko et al., 1996). The relative transport of water loss and solids gain to reach equilibrium was also identified and explained by Rahman and Lamb (1990). They mentioned that water can diffuse easily compared to solutes through the cell membrane, thus at higher temperatures the approach to osmotic equilibrium is achieved more by flow of water from cell compared to the solids transport, thus less solid gain. A similar phenomenon was also observed earlier. Marcotte, Toupin and Le Maguer (1991) developed a mathematical model for kinetics of equilibrium of a cellular structure during osmotic dehydration. The model was based on the internal cellular structure of plant materials. The simulation confirmed that the cell membrane represents the major resistance to mass transfer in such systems (Toupin, Marcotte, & Le Maguer, 1989). The water coming out particularly from the surface cells through membrane restricted the sugar

penetration into the cellular material (Marcotte & Le Maguer, 1992). It is known that apart from syrup concentration and temperature, rate of mass transfer during osmotic concentration depends on many other variables, such as structure (or porosity) of food material, specific surface area of food pieces, composition of the solution (i.e. solute molecular weight and nature, presence of ions), pressure (vacuum or high pressure), pretreatment of product, solution-product ratio. These variables may also influence distribution coefficients for water and solids. Thus attempts were made to develop prediction equations by combing all geometry by including the shape parameter As/l 2 (varied from 6.0 to 23.2) in the prediction. The correlations developed are: lew



T ¼ 2:05 Tr

les ¼ 0:468



1:60

T Tr

2:04





0:007 As l2

ð15Þ

 0:317 As 0:023 l2

ð16Þ

0:397 Yso

Yso

The mean relative error for Eqs. (15) and (16) were 8.74 and 10.8, respectively (Table 2). The prediction of distribution coefficients improved significantly when surface area and minimum geometric dimension was included (P < 0.05; Table 2). Eqs. (15) and (16) show the powers of shape factor is very low compared to the temperature and concentration, thus indicating the effect of shape factor (studied in this study) on the process is much lower than the concentration and temperature effect. Including the geometric factor makes the prediction models more generic compared to earlier Eqs. (9)–(14). In the literature negligible attempt was found to include the shape factor in the prediction model, thus it is one step forward compared to earlier models.

4. Conclusions Equilibrium distribution coefficients of water and solids during osmotic dehydration of mango pieces were influenced by temperature, syrup concentration and sample geometry. Dimensionless relationships were developed for the prediction of distribution coefficients for mango during osmotic dehydration in sucrose–water solution. The influence of temperature on the process was the maximum and shape factor was minimum. The temperature and syrup concentration showed opposite trends in terms of their influence on distribution coefficients. The correlation of distribution coefficients developed in this study can be useful in the design of osmotic drying equipment for mango. The total water removal can be predicted from the distribution coefficients and

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the requirement of syrup for specific process conditions can be estimated. Further studies are needed to quantify the influence of other variables, such as types of solutes, pretreatment, structure, and operating pressure.

Acknowledgements Funding from the Sultan Qaboos University research projects (IG/AGR/BIOR/02/02 and IG/AGR/BIOR/ 02/03) is gratefully acknowledged.

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