Numerical estimation of the effective conductivity of heterogeneous media with a 2D cellular automaton fluid

Abstract

A 2D cellular automaton fluid is used to estimate the effective transport properties of macroscopically homogeneous and isotropic two-phase mixtures. The method is applied to the determination of the electrical conductivity of two-phases agregates. The effective conductivity is calculated as a function of the relative concentration and for different values of the conductivity ratio between the constituting phases. Numerical results agree well with theoretical bounds in the case of alternating layers parallel or perpendicular to the direction of flow. For random isotropic distribution of the inclusion phase, the conductivity estimated by the cellular automaton falls between the theoretical Hashin-Shtrikman (H-S) bounds. The results presented are very close to experimental data, such as conductivity measurements on Al-Bi mixtures. Copyright 1997 by the American Geophysical Union.