Azarpazhooh, Ramaswamy - Osmotic Dehydrationstructure approach that assumes water transport as a trans-membrane movement or
Fick's second law with estimation of diffusion coefficients for both water loss and sugar
gain (Azuara et al., 1992; Fito et al., 1996; Yao and LeMaguer, 1996) also including hy-
drodynamic mechanisms (Fito et al., 1996; Salvatori, 1998). In addition, empirical and
semi-empirical models are often applied (Barat et al., 2001b).
A number of investigators have used Fick’s unsteady state law of diffusion to esti-
mate the water or solute diffusivity, simulating the experiments with boundary condi-
tions to overcome the assumptions involved in Fick’s law (Barat et al., 2001b; Fasina et
al., 2002). There are two parameters required in Fick's law; these are sample dimen-
sions and the effective diffusion coefficient. The effective diffusion coefficient can be ob-
tained by finding numerical or analytical solutions to experimental data, calculating the
relation between the slope of theoretical diffusion curve and the slope of experimental
mass transfer ratio (Rastogi et al., 2000a; Rastogi et al., 2002), and applying linear and
nonlinear regressions (Akpinar, 2006). Much of the literature considers any finite food
geometry as infinite flat plate configuration, neglecting the diffusion in the other direc-
tions. Of these studies, only a few have considered unsteady state mass transfer during
osmotic dehydration (Escriche et al., 2000; Rastogi and Raghavarao 2004).
Modeling of diffusion is a combination of physical and empirical approach. Mass
transfer studies in food rehydration are typically founded on Fick's 1st and 2nd laws:
22x
D W
t
V W
∂
= ∂
∂
∂ (3)^
dx
dW
Jx=−D^
(4)where: Jx, flux (g H2O/m^2 s); W, moisture content (g H 2 O/m^3 ); x, spatial coordinate
(m); t, time (s); D, diffusion coefficient (m^2 /s); V, volume (m^3 ).
This allows the estimation of the diffusion coefficients for both water loss and solids
gain individually or simultaneously. The mass transfer is assumed to be unidirectional
and the interactions of the other components on the diffusion of the solute are negligible.
Analytical solutions of the equation are available for idealized geometries, i.e. spheres,
infinite cylinders, infinite slabs, and semi-infinite medium. For these analytical solutions
of the unsteady state diffusion model to exactly apply, it is necessary either to keep the
external solution concentration constant or to have a fixed volume of solution. The resis-
tance at the surface of the solids is assumed to be negligible compared to the internal
diffusion resistance in the solids. Biswal et al. (1991) and Ramaswamy and Van Nieu-
wenhuijzen (2002) used a rate parameter to model osmotic dehydration of green beans
as a function of solution concentration and process temperature. The parameter was
calculated from the slope of the straight line obtained from bean moisture loss and solid
gain vs. the square root of time (Biswal et al., 1991).
Azuara et al. (1992) developed a model based on mass balances of water and sugar
to predict the kinetics of water loss and solids gain during osmotic dehydration. The
model is related to Fick’s second law of unsteady state one-dimensional diffusion
through a thin slab in order to calculate the apparent diffusion coefficients for each con-