Modeling of Diffusion in Ellipsoidal Solids: A Simplified Approach

Abstract

A three-dimensional model was applied to rigorously interpret the diffusion phenomena in ellipsoidal solids. The numerical solution of the diffusion equation was obtained by the finite difference method for ellipsoids of various shape factors. Due to its complexity for practical use, the spheroidal model (two-dimensional model) was utilized as a better alternative. In comparison with the numerical results generated by the three-dimensional model, the spheroidal model still fails to give good predictions in some cases, although it was assumed to have the same volume and surface area (i.e., same ORDER REPRINTS shape factor) as that of the ellipsoidal model. Consequently, a simplified approach was developed with satisfactory predictions, that is to apply a one-dimensional model to solve the diffusion problem with equivalent diameter as well as equivalent liquid diffusivity, which is a function of the intrinsic diffusivity and geometry factor.

Model-Based Estimate for Time-Dependent Apparent Diffusivity

“…Such a dramatic decay may be ascribed to the structural changes in the endosperm during parboiling, such as gelatinization of starch and disintegration of proteins. [16] The good match of experimental and simulated values for rice validates the conclusion by Li and coworkers [5] regarding credible modeling of ellipsoids using the respective equations for spheres of equivalent volume. …”

“…Interestingly, the simulation results for ellipsoids coincide well (5-9%) with the ones for spheres of the same volume. [5] Therefore, Eq. (4) can also be used to simulate diffusion in ellipsoidal particles such as rice, wheat, barley, and the like.…”