An effective medium treatment of the transport properties of a Voronoi tesselated network

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Abstract
The present work stresses the significance of the effective medium theory in the computation of the macroscopic transport coefficients from the microgeometry of porous media. The porous ‘‘material’’ is simulated as a two-dimensional network of interconnected slits of irregular shape and a random distribution using the Voronoi–Delaunay tesselation technique. The calculation procedure for the macroscopic transport coefficients is based on two concepts, the first one being the approximation of the microscopic field by a smooth field (SFA), and the second one being the average of the network random parameters to a mean/effective value by the effective medium theory (EMT). For the latter we apply an improved version of the EM equation derived for regular lattices by Kirkpatrick [Rev. Mod. Phys. 45, 4 (1973)]. This equation takes into account the irregularity in the slit-length distribution and is applicable on both regular and irregular lattices. The EMT/SFA results of the improved version for ordinary diffusion (apparent diffusivity) are in very good agreement with the numerical ones.

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