Granular effective medium approximation

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Abstract
This article analyzes the structure of the so-called self-similar effective medium approximation (SSEMA) which has been proposed for the effective permittivities in multicomponent inhomogeneous materials such as sedimentary rocks. In particular, our interest lies in understanding what kind of geometry is represented by the SSEMA. We show that, in the case of binary disorder, the first constituent is treated in the SSEMA in such a way that its geometrical continuity in space is guaranteed all the way down to the limit of zero proportion while the second constituent remains disjoint. This accounts for the zero percolation thresholds manifest in Archie’s law.