Guava, Psidium guajava L., is native to the Caribbean and common throughout all warm areas which has great amount of vitamins C (>3 times as much Vitamin C as an orange), A and B. Guava fruit, as other tropical fruits, is highly perishable which needs preservation methods to increase its shelf-life (Andrade et al., 2007). In recent years, osmotic dehydration has received increasing attention in field of fruits and vegetables preservation due to its potential to keep sensory and nutritional properties similar to the fresh fruits (García-Martínez et al., 2002). Osmotic dehydration is a method applied for water removal of fresh foods, by immersing pieces of the food in a concentrated solution of soluble solute. This solution is referred to as a hypertonic solution in the literature. A driving force for water removal is set up because of a difference in osmotic pressure between the food and its surrounding solution (Corzo and Bracho, 2005). The complex cell wall structure acts as a semi-permeable membrane, which is not completely selective, resulting in two major simultaneous counter current types of mass transfer, one diffusion of water from the product to solution followed by uptake of solutes from the solution into the product (Madamba, 2003). There is also a third flow of natural solutes (sugars, organic acids, minerals, salts, etc.) leaking from the food into the solution (Rastogi and Raghavarao, 2004). The rate of mass transfer depends on factors such as temperature, solution concentration, immersion time, size and geometry of sample, sample to solution ratio and type of pretreatment applied (Rastogi et al., 2002; Panades et al., 2008). The knowledge of the kinetics of water and solute transfers during the processing is of great technological importance because it allows an adequate control of composition of dehydrated material and the correct design of the operation. For modelling the mass transfer phenomena during the osmotic dehydration process, different approaches based on Fick's second low have been reported (Chausi et al., 2001). Nevertheless, some of the assumptions are not very realistic (i.e., high viscosity of the hypertonic solution means that mass transfer resistance in the solution could not be negligible) and complex models are necessary to understand mass transfer phenomena but are not very useful for food industry from practical point of view. In this way, some simpler empirical approaches are proposed allowing the modelling of mass transfers kinetics during osmotic dehydration including parameters with physical meaning. Peleg (1988) used a two parameters model to represent the water adsorption by milk powder and whole rice grains. This empirical model has been used to model the sorption curves of different foods (García-Pascual et al., 2006; Schmidt et al., 2009) and the dehydration rates of fruits, vegetables (Khin et al., 2006; Mercali et al., 2010) treated with osmotic solutions. The other empirical model proposed by Azuara et al., (1992), from a simple mass balance, has been used to describe the dehydration rate and to estimate the equilibrium concentration of solutes in apples (Kaymak-Ertekin and Sultanoglu, 2000) and carrots (Singh et al., 2007) submitted to different osmotic solutions. However, in literature, the suitability of these models to the osmotic dehydration of seedless guava is scarce. The objectives of this study were to investigate the effect of temperature and sucrose solution concentration on mass transfer during osmosis process and to examine the predictive capacity of Peleg, Azuara and Page's equations during osmotic dehydration of seedless guava.
Materials and Methods
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Preparation of seedless guava samples
Fresh seedless guava (Psidium guajava L.) fruits were obtained from a local market (Serdang, Malaysia) on daily basis prior to each set of experiments. Fruits were chosen at commercial maturity according to their similarity of color, size, absence of surface defects and ripening grade (around 8 °Brix). Before each experiment fruits were washed, peeled and cut into 20Â±2 mm cubes manually using very sharp stainless steel knife, and gently blotted with tissue paper to remove the excess of surface humidity. Care was exercised to select only cubes that have same size to minimize the effect of sample size on the experimental data. The dimensions of fruit cubes were measured by Mitutoyo digital caliper (Â±0.02 mm) (Mitutoyo, Waterbury, CT, USA).
Osmotic dehydration procedure
Osmotic solution was prepared by mixing commercial grade sucrose with required amount of distilled water. The sucrose solution concentrations were 30, 40 and 50% (w/w). The concentration of the sucrose was monitored throughout each experiment by refractometer (Atago-Master-20 M, Japan). Experiments were carried out at several temperatures (30, 40 and 50 Â°C) using a circulating water bath (Memmert, WNE14. Memmert GmbH Co. KG, Germany) maintained at desired temperatures (Â±0.5Â°C). The temperature of the water bath and osmotic medium was verified with a digital thermometer (Ellab CTD-85, Ellab, Denmark) and a thermocouple (1.2 mm needle diameter constantan type T). The sucrose to sample ratio was always 10:1 to avoid significant dilution of the medium by water removal, which would lead to local reduction of the osmotic driving force during the process. At determined times (15, 30, 45, 60, 90, 120, 150, 180 and 240 min), the samples were removed from the osmotic solutions, rinsed quickly with distilled water (below 30s) to eliminate the solution adhered to the surface and carefully blotted with tissue paper to remove the excess surface water. No shaking was used in any of the assays. All the experiments were carried out in triplicate and the average values are reported.
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Determination of Kinetics parameters
The fresh and dehydrated seedless guava cubes after each contact times were placed in oven (Heraeus Vacutherm VT6025, Germany) at 105 Â°C until constant weight (24 h) in order to measure the moisture and solids content according to Association of Official Analytical Chemists (AOAC) method 931.04 (AOAC, 1990). In order to determine mass change, all samples were weighed before and after treatment using an analytical balance (Mettler AJ 150, Switzerland) with accuracy of Â±0.0001 g. From these data, solid gain (SG) and water loss (WL) were determined in all the cases at different times, t, in agreement with the following expressions (Panagiotou et al., 1999).
where M0 is the initial mass of fresh sample (g), M is the mass of sample after time (t) of osmotic dehydration (g), m is the dry mass of sample (g) after time (t) of osmotic dehydration, m0 is the initial dry mass of sample (g).
Peleg (1988) proposed an equation to describe the kinetics of moisture sorption that approaches equilibrium asymptotically. The adaptation of this equation for the present study is given by Eq. (3).
Where X is dependent variable at time t, X0 is initial dependent variable, K1 is the Peleg rate constant, and K2 is the Peleg capacity constant. In Eq. (3), ''Â±'' becomes ''+'' if the process is hydration and ''-'' if the process is dehydration. The Peleg rate constant K1 relates to dehydration rate at the very beginning, t = t0
The Peleg capacity constant K2 relates to minimum attainable dependent variable. As tâ†’âˆž, Eq. (5) gives the relation between equilibrium content (Xe) and K2
The model proposed by Azuara et al., (1992) is based on the mass balance represented by Eq. (6).
XG = XGâˆž - XG* (6)
where XG* is the mass of solid or water that did not enter (or leave) the sample after an elapsed time t, XGâˆž is the concentration after long immersion times (''equilibrium concentration") that depends on the temperature and solid solution concentration. As XG increases and XG* decreases during the immersion time, these variables can be interrelated by a parameter K, i.e. XG = KXG*. The K parameter depends on the immersion time (t) and on the rate of mass transfer (water or solid), as given by Eq. (7).
The substitution of Eq. (6) into the Eq. (7) leads to an equation that could be used for estimating the mass gain or loss of a component by the sample for a given immersion time (Eq. (8)).
One of the most useful empirical models is Page's Eq. (10) (Page, 1949), which is an empirical modification of the simple exponential model. It was used to fit the experimental dehydration data and it is written in the form:
in which, K is the dehydration constant, n is the Page's parameters; and t is the process time, (min).
Experimental design and statistical analysis
The experimental design applied was a 3 Ã- 3 Ã- 9 factorial design in a frame of Complete Randomized Design (CRD), corresponding to the three solution concentrations, three temperatures and nine immersion time intervals. Analysis of variance (ANOVA) was carried out to find significant effects (p < 0.05) of process parameters using Minitab v.14 (Minitab Inc. State College, PA, USA). Non-Linear regression using Levenberg-Marquardt method was used to fitting database to different models by using the STATISTICA 6.0 software (StatSoft, Inc., USA). The criteria for characterizing the fitting to the model were the determination coefficient (R2), the root mean square error (RMSE) and the mean relative percentage deviation modulus (E). These parameters can be calculated as follows:
where Vexp and Vpre are the experimental and predicted values, respectively, n is the number of experimental data points. A model is considered acceptable if E value is below 10% (Deng and Zhao, 2008). Therefore, the best model was chosen as one with the highest coefficient of correlation (R2), the least RMSE and E values.
Results and Discussions
The changes in the experimental data of solid and water contents during osmotic treatments are presented in Figures 1-2. As expected, SG and WL increased with immersion time. A high initial rate of SG and WL, followed by a slower gain (and loss) in the later stages was observed. Several research groups have published similar curves for osmotic dehydration of foods (Eren and Kaymak-Ertekin, 2007; Schmidt et al., 2009; Corrêa et al., 2010). Increase in solution concentration resulted in an increase in the osmotic pressure gradients and, hence, higher WL (and SG) values throughout the osmosis period were obtained. These results indicate that by choosing a higher concentration medium, some benefits in terms of faster water loss could be achieved. However, a much greater gain of solids is observed (Ito et al., 2007; Ispir and Togrul, 2009). It has been pointed out that an increase of the osmotic pressure gradient cause a loss of functionality of the cell plasmatic membrane that allows solute entrance (Antonio et al., 2008). On the other hand, high temperatures of osmotic media also cause accelerated mass transfer as shown in Figures 1-2. This behavior was observed for all the assayed concentrations, although the intensity of the effect was higher with the most concentrated solutions. Increase in kinetics of mass transfer when samples were immersed into a high temperature solution is due to increase in rate of diffusion in this condition. Higher temperatures seem to promote faster water loss through swelling and plasticizing of cell membranes as well as the better water transfer characteristics on the product surface due to lower viscosity of the osmotic medium (Uddin et al., 2004; Singh et al., 2007). Also, higher solid gains at higher temperatures may be due the destruction to cell membrane structure (Le Maguer, 1988). Such effects have also been reported in other fruits and vegetables (Tortoe et al., 2007; Corrêa et al., 2010).
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Peleg, Azuara and Page's equations were used to fit the experimental data. Peleg parameters obtained from the non-linear regression analysis are shown in Table 1. The k1 parameter of the Peleg's model, representative of the initial mass transfer rate (Eq. (4)), decreased with the increase of solution concentration and temperature. When analysing these results, it was observed that the value of initial mass transfer coefficients for SG and WL were found to be significantly (p < 0.05) dependent on the concentration and temperature of the osmotic. This behavior could be due to a cellular response to the osmotic pressure and temperature increment, as observed by Sachetti et al. (2001) and Corzo and Bracho (2006) in the osmotic dehydration process of apple and sardine sheets. The parameter k2 describes the rate of SG and WL at the equilibrium stage of osmotic dehydration process. A significant
(p < 0.05) relationship between k2Â and solution concentration observed, i.e., an increase in osmotic concentration caused a decrease in the value of k2 for SG and WL.
Azuara's equation parameter obtained for SG and WL are shown in Table 2. In Eq. (8) K represent the time required for half of the diffusible matter (water or solid) to diffuse out or enter in the product respectively. Azuara's equation parameter (K) for SG followed the same tendency regarding the k1 parameter that decreased with the increase of concentration and temperature (p < 0.05) whereas K did not show a clear pattern for WL with sucrose concentration and temperature (p > 0.05).
Page's parameters obtained for SG and WL are presented in Table 3. For SG it can be observed that parameter K decreased with solution concentration and temperature, while the parameter n did not show a clear pattern with temperature. For WL, the parameter K did not show any trend with solution concentration and temperature. The parameter n increased at higher concentrations and temperature. Similar results about page model were reported by
Azoubel and Murr (2004) and Vega- Gálvez et al. (2009).
The statistical parameters that qualify the goodness of fit (R2, RMSE and E) indicated that the experimental values of SG and WL estimated by the Peleg model are more reliable due to high R2 values and small values of RMSE and E (Table 1-3).
The effects of osmotic solution concentration and temperature on the kinetics of mass transfer in terms of SG and WL were investigated. The rate of SG and WL of seedless guava was directly related to the concentration and temperature of solution. The experimental values of SG and WL during the osmotic dehydration of seedless guava cubes were fitted to Peleg, Azuara and Page's equations. Peleg's equation presented the best adjustment of the experimental data. The SG and WL at any sucrose solution and temperature during the course of osmotic dehydration of seedless guava could be predicted with sufficient accuracy by using the Peleg equation. Peleg's parameters k1 and k2 for SG were from 939.09Â±78.39 to 148.43Â±27.85 and from 16.32Â±0.43 to 11.67Â±0.58, respectively, and for WL varied from 257.49Â±43.08 to 125.27Â±15.88 and 3.85Â±0.22 to 2.06Â±0.08, respectively. In this way, the Peleg model allows the simulation of mass transfer processes during osmotic dehydration, and consequently it can be used as a useful tool in the design and control of the corresponding industrial operation.