Effective medium approximation of 3-D Voronoi networks

This article deals with the determination of the effective (apparent) diffusivity from the topological characteristics of microscopically inhomogeneous materials. The porous medium is modeled as a three-dimensional network of interconnected pores by means of the Voronoi–Delaunay tesselation. The cal...

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Bibliographic Details
Published in:Journal of applied physics 1990-04, Vol.67 (7), p.3249-3253
Main Authors: VRETTOS, N. A, IMAKOMA, H, OKAZAKI, M
Format: Article
Language:English
Subjects:
Condensed matter: electronic structure, electrical, magnetic, and optical properties
Electronic transport in condensed matter
Exact sciences and technology
Physics
Theory of electronic transport
scattering mechanisms
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Summary:This article deals with the determination of the effective (apparent) diffusivity from the topological characteristics of microscopically inhomogeneous materials. The porous medium is modeled as a three-dimensional network of interconnected pores by means of the Voronoi–Delaunay tesselation. The calculation procedure is based on an improved version of the effective medium theory and the smooth field approximation. We investigate the case where the pores in the effective network are transformed to pores of a uniform cross-sectional area, and the case where the pore conductances are all replaced by an effective one. The results are compared with the numerical network solution. It is shown that the effective cross-section area approach reproduces the ‘‘exact’’ calculated transport coefficient with an error of less than 9%, whereas the effective uniform conductance approach fails considerably, displaying an error of 62%.
ISSN:0021-8979
1089-7550
DOI:10.1063/1.345357