Description of the Osmodehydration
6.3 MATERIALS AND METHODS
Golden Delicious apples were obtained from a local market. The fruits were cut into disk-shaped pieces 46 mm in diameter and 4 mm thick and immediately immersed into a 20 g/l solution of ascorbic acid for 5 min to control browning. In osmotic dehydration, it is necessary to count with reliable kinetics the changes in mass that are attributed to the process and not to variability of the product. To overcome this, a continuous method of evaluation of the kinetics was used. With this method, it is possible to obtain all the kinetics by measuring weight losses in the same sample along the processing time (Azuara et al., 1998). The apple disks were dehydrated by immersing into a 500 g/l sucrose solution set at 30, 40, or 50°C. A food:solution ratio greater than 1:20 was maintained at all times. Samples were withdrawn peri-odically up to a total drying time of 5 h. Immediately after sample withdrawal, the disks were blotted with drying paper to remove excess solution. Each disk was weighed and its thickness measured at at least three different points using a Mitutoyo micrometer. After these measurements, the disks were returned to the osmotic solu-tion to continue the process. At the end of the experiment, moisture content was determined in each sample by placing it into vacuum oven for 24 h at 70°C (AOAC, 1984).
6.4 RESULTS
6.4.1 MATHEMATICAL MODELING
Work on concentration profiles along osmotic dehydration of apples carried out by Salvatori et al. (1997) has shown the existence of a zone in the center of the samples that keeps the initial conditions of the fresh fruit and that decreases in size with time. This experimental evidence may suggest the possibility of developing a kinetic equation based on the shrinking core model (Levenspiel, 1976).
Given that the thickness/diameter ratio of the apple disks was smaller than 0.1 (actual ratio = 0.086), the samples can be considered as semiinfinite plates, in which fluxes of water and soluble solids are unidirectional (Vaccarezza et al., 1974).
According to the shrinking core theory, during the drying process the moist center decreases and a crust is formed. The crust contains less moisture than the initial water content between the surface and the moist core. At all times, core properties are similar to those of the initial stages (Levenspiel, 1976). The shrinking core model
proposes that the total resistance to water transfer from the sample to the osmotic solution can be explained by the existence of two resistances acting in series: an internal one represented by an effective diffusion coefficient through the dried shell, and an external one located in the film of fluid around the particle. The contribution of each resistance towards the total one along OD is different, and the limiting one will be that of higher value (Levenspiel, 1976).
Water loss (WFL) and solids gain (SG) during osmotic dehydration were cal-culated using equations derived from mass balances (Azuara et al., 1992).
(6.1)
(6.2)
Apple samples had different initial moisture and solids content, causing the scatter observed in WFL and SG values (Karathanos et al., 1995). To minimize the variation, constants s1, s2, WFL∞, and SG∞ were calculated with equations developed for a method for continuous evaluation of osmotic dehydration kinetics (Azuara et al., 1998). The rate of water transfer per unit area from the moist core to the surface and through the dehydrated crust is given by:
(6.3)
Azuara et al. (1992) proposed the following equation to calculate the effective diffusion coefficient for foodstuffs having a flat slab geometry:
(6.4)
Figure 6.1 shows that a variable diffusion coefficient such as the one evaluated with Equation (6.4) is a unique function of the Fourier number and thus can be modeled as pure diffusion. The rate of water transfer per unit surface area of the disk, from the food surface to the fluid, is given by:
(6.5)
By manipulating Equations (6.3), (6.4), and (6.5), it is possible to arrive at:
(6.6)
Equation (6.6) shows that total resistance to mass transfer is the algebraic sum of an internal diffusive resistance (shell resistance) plus a solids uptake resistance through the film of solution surrounding the foodstuff. Therefore, the model can be written in the following form:
Total resistance to = shell resistance + film resistance to (6.7) mass transfer to water flow waterflow
Equation (6.6) can be written in its dimensionless form:
(6.8)
Ymod= (πs1lo2/hw(WFL∞ – SG∞))Xmod. – (1 + α) (6.9) The expression to estimate the half thickness of the moist core (lc) is:
(6.10) FIGURE 6.1 Dimensionless water loss vs. Fourier number for different thicknesses of apple disks (T = 30°C).
The half thickness of the apple disk at time t (lt) was adjusted with the following equation:
(6.11) Activation energy (Ea) can be estimated using an Arrhenius-type equation of the following form:
(6.12) Goodness of fit was estimated with the mean relative deviation modulus (P%) between the experimental and predicted values:
(6.13)
6.5 DISCUSSION
Figure 6.2 shows the volume change of the apple disks (Vt/Vo) vs. moisture content at 30°C. Three stages during the osmotic dehydration can be observed. The same behavior was obtained when the drying process was carried out at 40 and 50°C.
These experimental results obtained using macroscopic measurements are in agreement
FIGURE 6.2 Changes in volume and total resistance during osmotic dehydration of apple disks.
l l l l l
Vt/Vo Total resistance x 10 -4 (min/cm)
Moisture (g water/g wet solid)
Stage 1 Stage 2
Stage 3
with the three stages theory proposed at the microscopic level by Toupin et al. (1989) and Le Maguer and Yao (1995).
The mathematical model based on the shrinking core theory also predicted three stages as a function of the total resistance to water flow (Figure 6.2). In the model, α is a dimensionless parameter that is characteristic for each stage and that increases with the amount of impregnated solids into the apple disk, which decreases as the amount of washed solids by water flow increases. The parameters of each stage are reported inTable 6.1. It can be observed that α increased as the osmotic dehydration took place. A similar effect was observed when the temperature was increased. In addition, the mass transfer coefficient for water (hw) had an opposite behavior as compared with that of α. This may be due to the fact that impregnation on the surface raised the film resistance to water flow.
InFigure 6.3 (dimensionless form of Equation (6.9)), the presence of the three stages of osmodehydration at 40 and 50°C can be observed. At the end of each stage and the beginning of the next one, an increment of (1 + α) and a decrease of hw are observed. As seen in Figure 6.4, the diffusion coefficient of water (Dw) decreased as the moisture content decreased. On the other hand, Dw increased with tempera-ture. However, it should be noted that there is a zone of high moisture where Dw increased as the moisture content decreased (Figure 6.4). In this zone, the osmotic solution penetrates into the apple tissue to expel the trapped air from intercellular spaces, facilitating the diffusion of water contained in the superficial cells. As a consequence, the apple–solution interface increases and Dw also increases. At the beginning of the second stage, an increase in the length of the water diffusion path around the cells on the surface and the cells in the moist core occurs, which leads to a decrease of Dw. The third stage is beyond collapse and Dw diminishes as moisture content decreases.
Figure 6.5 depicts the variation of lt and lc with time. It can be seen that lt and lc diminish faster along the first stage than in the second and third stages. Moreover, in the third stage, the half thickness of the moist core (lc) is close to zero because the equilibrium has almost been reached.
TABLE 6.1
Parameters of the Model
Temperature
30 0.7156 0.1476 0.0317 1st
2nd
40 0.7505 0.1747 0.0531 1st
2nd
50 0.7602 0.2354 0.0903 1st
2nd
FIGURE 6.3 Stages of osmotic dehydration (OD) obtained with Equation (6.9).
FIGURE 6.4 Variation in the diffusion coefficient during osmotic dehydration of apple disks.
-9 -8 -7 -6 -5 -4 -3 -2 -1
-14 -12 -10 -8 -6 -4 -2 0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
40°C 50°C
Ymod (40°C) Ymod (50°C)
Xmod
Stage 1 Stage 2
Stage 3
0 2 4 6 8 10 12 14
0.3 0.4 0.5 0.6 0.7 0.8 0.9
30°C 40°C 50°C
Dw× 10 10 (m2 /s)
Moisture (g water/g wet solid)
Stage 1
Stage 2
Stage 3
As shown inTable 6.2, lt can be calculated as a function of lc and the half-thickness of the apple disk at equilibrium (le). A good fit was obtained with P values≤1.952%.
Also, as the increment of temperature favors solids entrance and diminishes shrinkage, correction factor c is less negative.
Activation energy (Ea) for water diffusion increased as the moisture content of the apple disks decreased. For stage 1, the moisture content varied from 0.83 to 0.78 g water/g wet solid, and Ea was in the range of 8.6 to 10.5 kcal/mol. For stage 2, the moisture content varied from 0.78 to 0.56 g water/g wet solid, and Ea was in the range of 10.5 to 13.0 kcal/mol. For stage 3, the moisture content varied from 0.56 to 0.50 g water/g wet solid, and Ea was in the range of 13.0 to 17.7 kcal/mol.
FIGURE 6.5 Variation of lc and lt with time during osmotic dehydration of apple disks.
TABLE 6.2
Parameters for Equation (6.11)
Temperature (ºC) le (cm) c (cm) P (%)
30 0.14057 −0.04205 1.952
40 0.13079 −0.01848 1.755
50 0.13740 +0.02926 0.657
0 0.05 0.1 0.15 0.2
0 50 100 150 200 250 300 350
lt 40°C lt 50°C
lc 40°C lc 50°C lt 30°C
lc 30°C
lt or lc (cm)
Time (min)
6.6 CONCLUSIONS
To model osmotic dehydration as a pure diffusion process, it is necessary to account for a nonconstant diffusion coefficient (Dw), which varies in such a way that the dimensionless variation of mass can be represented as a unique function of the Fourier number. It is possible to determine macroscopically the stages of the process by measuring volume changes of a sample during the process. The shrinking core model applied to this operation predicts the same stages as volume change measure-ments do. This model takes into account water losses, solids entrance, weight losses, and variation of sample thickness. The greater the impregnation, the lower the water flux from the product to the solution. This may be due to the fact that impregnated sugar molecules on the surface of the slices interact with water molecules, creating an additional resistance to water flux from the sample to the medium. Shrinkage of the discs decreases with impregnation and temperature. It was possible to predict the change in sample thickness along the OD process, considering initial thickness and size of the wet core.
NOMENCLATURE
c Constant for correction of thickness for solids gained and temperature (cm)
Cintsol Interfacial solids concentration (g/cm3)
Cso Volumetric concentration of sucrose in the solution (g/cm3) Cw Volumetric concentration of water in the apple (g/cm3) Cwi Volumetric concentration of water inside the apple disk at
time 0 (g/cm3)
Cwo Volumetric concentration of water inside the osmotic solution (g/cm3)
do Initial diameter of the apple disk (cm)
Do Frequency factor (m2/sec)
Dw Effective diffusion coefficient of water (m2/sec)
Ea Activation energy (kcal/mol)
Fo = Dw t/lt
2 Fourier number
F= WFLmod∞
/WFL∞exp Correction factor
hw Mass transfer coefficient of water based on the concentration of osmotic solution (g of water–m/g of solids–sec)
lo Half-thickness of the apple disk at time 0 (cm) lt Half-thickness of the apple disk at time t (cm) lc Half-thickness of the moist core (cm)
le Half-thickness of the apple disk at equilibrium (cm)
Mi Experimental values
Mo Initial weight of the apple disk (g)
Mpi Predicted values
ML Weight lost by the food at time t (g)
N Number of experimental data
P Mean relative deviation modulus between the experimental and predicted values (%)
R Universal gas constant (1.987 cal/mol K) s1 Constant related to water loss (min–1) s2 Constant related to solids gain (min–1)
SG Amount of solids gained by the apple disk at time t (g) SG∞ Amount of solids gained by the apple disk at equilibrium (g)
t Time (min, sec)
T Absolute temperature (K)
Vo Volume of the apple disk at time 0 (cm3) Vt Volume of the apple disk at time t (cm3)
WFL Amount of water lost by the apple disk at time t (g) WFL∞ Amount of water lost by the apple disk at equilibrium (g) WFLmod∞ Value for WFL∞ obtained from Equation (1)
WFLexp∞ Value for WFL∞ obtained experimentally
WFS Amount of water that remains in the apple disk at time t, but that could leave the disk by diffusion (g)
x Position of a point in the circular plate in Cartesian coordinates, measured in axial direction (cm)
α Unidimensional characteristic parameter for each stage
ACKNOWLEDGMENTS
To CYTED Project XI.13, IPN–México and Universidad Veracruzana–México for support.
REFERENCES
AOAC, Official Methods of Analysis, Association of Official Analytical Chemists, Washington, DC, 1984.
Azuara, E., Beristain, C.I., and Gutiérrez, G.F., A method for continuous kinetic evaluation of osmotic dehydration, Lebensm.-Wiss. Technol., 31, 317–321, 1998.
Azuara, E., Cortés, R., Garcia, H.S., and Beristain, C.I., Kinetic model for osmotic dehydration and its relationship with Fick’s second law, Int. J. Food Sci. Technol., 27, 409–418, 1992.
Beristain, C.I., Azuara, E., Cortes, R., and Garcia, H.S., Mass transfer during the osmotic dehydration of pineapple rings, Int. J. Food Sci. Technol., 25, 576–582, 1990.
Conway, J., Castaigne, F., Picard, G., and Vovan, X., Mass transfer considerations in the osmotic dehydration of apple, Can. Inst. Food Sci. Technol. J., 16, 25–29, 1983.
Crank, J., The Mathematics of Diffusion, 2nd ed., Clarendon Press, Oxford, 1975.
Hough, G., Chirife, J., and Marini, C., A simple model for osmotic dehydration of apples, Lebensm.-Wiss. Technol., 26, 151–156, 1993.
Karathanos, V.T., Kostaropoulos, A.E., and Saravacos, G.D., Air-drying kinetics of osmoti-cally dehydrated fruits, Drying Technol., 13, 1503–1521, 1995.
Le Maguer, M., Osmotic dehydration: review and future directions, in Proc. Int. Symposium Progress in Food Preservation Process, CERIA, Brussels, vol. 1, 1988, pp. 283–309.
Le Maguer, M. and Yao, Z.-M., Mass transfer during osmotic dehydration at the cellular level, in Food Preservation by Moisture Control, Fundamentals and Applications, Barbosa-Cánovas, G.V. and Welti-Chanes, J., Eds., 1995, pp. 325–350.
Levenspiel, O., Solid-fluid reactions, in Chemical Reaction Engineering, 2nd. ed., Wiley, New York, 1976, p. 357–377.
Marcotte, M. and Le Maguer, M., Mass transfer in cellular tissues. II: Computer simulation vs. experimental data, J. Food Eng., 17, 177–199, 1992.
Marcotte, M., Toupin, C.J., and Le Maguer, M., Mass transfer in cellular tissues. I: The mathematical model, J. Food Eng., 13, 199–220, 1991.
Mujaffar, S. and Sankat, C.K., The osmotic dehydration of shark fillets, Proceedings of the 11th International Drying Symposium, Akritidis, C.B., Marinos-Kouris D., and Saravakos, G.D., Eds., ZITI Editions, Thessaloniki, Greece, 19–22, vol. A, 1998, pp. 911–921.
Nobel, P.S., Biophysical Plant Physiology and Ecology, W.H. Freeman and Company, New York, 1983.
Parjoko, Rahman, M.S., Buckle, K.A., and Perera, C.O., Osmotic dehydration kinetics of pineapple wedges using palm sugar, Lebensm.-Wiss. Technol., 29, 452–459, 1996.
Raoult-Wack, A.L., Petitdemange, F., Giroux, F., Ríos, G., Guilbert, S., and Lebert, A., Simultaneous water and solute transport in shrinking media. 2: A compartmental model for the control of dewatering and impregnation soaking process, Drying Tech-nol., 9, 613–630, 1991.
Salvatori, D., Andrés, A., Chiralt, A., and Fito, P., Concentration profiles in apple tissue during osmotic dehydration, Proceedings of the Seventh International Congress on Engi-neering and Food, Jowitt, R., Ed., Shefield Academic Press, Brighton, U.K., 1997.
Saurel, R., Raoult-Wack, A.L., Rios, G., and Guilbert. S., Mass transfer phenomena during osmotic dehydration of apple. I. Fresh plant tissue, Int. J. Food Sci. Technol., 29, 531–542, 1994.
Soddu. A. and Gioia, F., Diffusion through living systems: sugar loss from sugar beets, Chem.
Eng. Sci., 34, 763–773, 1979.
Stahl, R. and Loncin, M., Prediction of diffusion in solid foodstuffs, J. Food Process. Preserv., 3, 213–223, 1979.
Toupin, C.J. and Le Maguer, M., Osmotically induced mass transfer in plant storage tissues:
a mathematical model—Part 2, J. Food Eng., 10, 97–121, 1989.
Toupin, C.J., Marcotte, M., and Le Maguer, M., Osmotically induced mass transfer in plant storage tissues: a mathematical model—Part 1, J. Food Eng., 10, 13–38, 1989.
Vaccarezza, L.M., Lombardi, J.L., and Chirife, J., Kinetics of moisture movement during air drying of sugar beet root, J. Food Technol., 9, 317–327, 1974.
Vial, C., Guilbert, S., and Cuq, J., Osmotic dehydration of kiwifruits: influence of process variables on the color and ascorbic acid content, Sci. Aliment., 11, 63–84, 1991.
Yao, Z. and Le Maguer, M., Mathematical modelling and simulation of mass transfer in osmotic dehydration processes. I: Conceptual and mathematical models, J. Food Eng.
29, 349–360, 1996.
Yao, Z. and Le Maguer, M., Osmotic dehydration: an analysis of fluxes and shrinkage in cellular structure, Trans. ASAE, 39, 2211–2216, 1997.