Batchelor (1), in a review article, proposed a unified The effect of particle surface conditions on the effective conducframework for the very diverse field. Many problems, altivity of spherical dispersions is investigated. The spherical partithough different in appearance, possess identical mathematicles can be either coated with multiple layers or possessive of a cal description. For example, both of the effective thermal certain amount of contact resistance, and can be either randomly conductivity and the effective electric conductivity problems distributed or arranged in simple cubic arrays. The effective coninvolve solution of the Laplace equation, and results can be ductivity of the dispersion is found to be a function of the particle translated from one to the other with appropriate physical volume fraction and the dimensionless multipole polarizability.
quantity substitution. For effective thermal conductivity
Expressions for the dimensionless multipole polarizability for both problems, one deals with temperature, heat flux, and thermal multiply coated sphere and contact resistance problems are derived. The effect of particle surface conditions is realized through conductivity, while for effective electric conductivity probtheir influence on the magnitude of the multipole polarizability, lems the corresponding physical quantities are electric potenand the effect of the multipole polarizability on the effective contial, electric current density, and electric conductivity, reductivity is carefully examined. It is further found that, for random spectively. When dealing with suspensions, this corresponarrays, all members of the multipole polarizability are involved in dence exists, however, only for no or very thin double-layer the evaluation of the effective conductivity, but only half of them situations.
are involved for simple cubic arrays. In addition, the contact resis-Quite often, the dispersed phase of inhomogeneous systance problem has a narrower polarizability variation range than tems is in the form of particulate that may be conveniently that of the multiply coated sphere problem. These two factors modeled as spherical particles. Furthermore, these particles profoundly contribute to the differing effect of multipole polarizcan be either randomly distributed or regularly arranged in abilities on the effective conductivity of the dispersion with respect space. The surface of the particle can be either coated with to the dispersion microstructure and particle surface conditions.