On the effective conductivity of flat random two-phase models

S. A. Bulgadaev

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On the effective conductivity of flat random two-phase models

S. A. Bulgadaev

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Abstract

An approximate equation for the effective conductivity sigma_eff of systems with a finite maximal scale of inhomogeneities is deduced. An exact solution of this equation is found and its physical meaning is discussed. A two-phase randomly inhomogeneous model is constructed by a hierarchical method and its effective conductivity at arbitrary phase concentrations is found in the mean-field-like approximation. These expressions satisfy all the necessary symmetries, reproduce the known formulas for sigma_eff in the weakly inhomogeneous case and coincide with two recently found partial solutions of the duality relation. It means that sigma_eff even of two-phase randomly inhomogeneous system may be a nonuniversal function and can depend on some details of the structure of the inhomogeneous regions. The percolation limit is briefly discussed.

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S. A. Bulgadaev. 2004-03-09. On the effective conductivity of flat random two-phase models. https://arxiv.org/abs/cond-mat/0403256

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