The Electrical Conductivity of Composite Media

Abstract

A general theory is given of the gross electrical conductivity (or thermal conductivity, dielectric constant or magnetic permeability) of a composite medium having its isotropic granular components distributed spatially in a disordered way. It is shown that the gross conductivity is a weighted superposition of the component conductivities with weights containing the volume fractions of the components and an intensity factor depending on the average electric field for the whole medium and for each component. By introducing a suitably defined `average electrostatic problem', the case of grains spherical in the mean and suspended in a uniform medium is examined in detail, and the gross conductivity explicitly found. The limiting case in which the suspending fluid is withdrawn and the grains coalesce is shown to give rise to a discontinuity in the gross conductivity. Coated grains, e.g. oxide-coated metallic grains, are also treated.