Effective conductivity of irregular conducting channeling textures in two dimensions

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Abstract
An irregular continuous conducting channel, linkage, or chain is formed in a sedimentary rock. The grain boundary of a polycrystalline and the blood vessel in a biological body shape such channels. In a previous paper we researched the effective conductivities of regular channeling textures by the finite element method (FEM) as a first approach to the problem of random channeling textures. In this paper we form irregular channeling patterns by computer simulation. The models are formed by randomly packing insulator squares into a metal sheet without any contact and overlap. We compute, by the FEM, the effective conductivities and compare them with previous results. It makes clear that the models are less conductive than a composite with a regular conducting channel. The conductivities agree well with the results from the granular effective medium approximation and from the extended Watson–Leath equation except when the metallic volume fraction is small.