Lesson 10. Mass Transfer Kinetics During Osmotic Dehydration

  • The osmotic dehydration process different than other drying processes as mass transfer takes place in liquid form (water comes out of product without phase change). Therefore, different models are available for the process.

  • During osmotic dehydration, two resistances oppose mass transfer, one internal and the other external.

  • The fluid dynamics of the solid fluid interface governs the external resistance whereas, the much more complex internal resistance is influenced by cell tissue structure, cellular membrane permeability, deformation of vegetable/fruit pieces and the interaction between the different mass fluxes.

  • Under the usual treatment conditions, the external resistance is negligible compared to the internal one. Variability in biological product characteristics produces major difficulties regarding process modeling and optimization.

    Mass transfer is affected by variety, maturity level and composition of product.

  • The complex non-homogenous structure of natural tissues complicates any effort to study and understand the mass transport mechanisms of several interacting counter current flows (water, osmotic solute, soluble product solids).

  • A mathematical model developed by Azuara et al. (1992) was used to study the mass transfer in osmotic dehydration of carrot slices. The various parameters considered for the model were moisture loss at any time (MLt), moisture loss at equilibrium

    (\[M{L_\infty }\]), solid gained at any time (SGt), solids gained at equilibrium (\[S{G_\infty }\]) and the time of osmotic dehydration (t). The models are as follows:

For moisture loss:

\[M{L_t}=\frac{{{S_1}t\,(M{L_\infty})}}{{1+{S_1}t}}=\frac{{(M{L_\infty})t}}{{\frac{1}{{{S_1}}}+t}}\].................(1)

\[\frac{t}{{M{L_t}}}=\frac{1}{{{S_1}(M{L_\infty})}}+\frac{t}{{M{L_\infty}}}\]..................(2)

For solid gain:

\[SGt=\frac{{{S_2}t\,(S{G_\infty })}}{{1+{S_2}t}}=\frac{{(S{G_\infty })t}}{{\frac{1}{{{S_2}}}+t}}\]..........(3)

\[\frac{t}{{S{G_t}}} = \frac{1}{{{S_2}(S{G_\infty })}} + \frac{t}{{S{G_\infty }}}{\rm{}}\]....................(4)

  • The plots of \[\frac{t}{{M{L_t}}}\] vs. t and \[\frac{t}{{S{G_t}}}\]  vs. t would be linear, the parameters could be determined from the intercept and slope. The Eqns. 1 and 3 could then be used to predict the mass transfer kinetics. S1 and S2 are the constants related to the rates of water and solid diffusion, respectively.

  • The terms indicate that \[\frac{1}{{{S_1}}}\] or \[\frac{1}{{{S_2}}}\] represent the time required for half of the diffusible matter (water or solids) to diffuse out or enter in the product, respectively. Further, as the time t becomes much longer (that is, t→∞) than the values of \[\frac{1}{{{S_1}}}\] or \[\frac{1}{{{S_2}}}\] , the water loss or the solid gain, MLt or SGt, approaches equilibrium value, ML∞ or SG∞, asymptotically.

  • In above equations, the values of parameters S1, ML∞, S2 and SG∞ can be estimated from short duration osmotic kinetic data by performing linear regression or graphical plotting of the above equations in the linearized form.

Last modified: Monday, 30 September 2013, 4:28 AM