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Modeling Of Diffusion In Ellipsoidal Solids: A Simplified Approach

Zhanyong Li, J. Ye, N. Kobayashi, M. Hasatani
Published 2004 · Mathematics

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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 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.
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