Electrical conductivity of inhomogeneous two component media in two dimensions

TL;DR

This paper derives a general expression for the electrical conductivity of inhomogeneous two-component media in two dimensions, considering various arrangements and shapes of inclusions, with relevance to temperature-dependent systems.

Contribution

It provides a versatile formula for effective conductivity in two-dimensional inhomogeneous media with variable component proportions and geometries.

Findings

Effective conductivity depends on spatial arrangement and inclusion shape.

The formula applies to systems with temperature-dependent component ratios.

Useful for modeling inhomogeneous materials in various physical contexts.

Abstract

The electrical conductivity is calculated for regular inhomogeneous two component isotropic medium in which droplets of one phase with conductivity sigma_2 are embedded in another, with conductivity sigma_1. An expression is formulated which can be used in many different situations, and is of particular relevance in the case where the relative proportion of the components is temperature dependent and varies over a wide range. The behavior of effective conductivity depends on the spatial arrangements and the shape of the inclusions.