Abstract
The effect of particle surface conditions on the effective conductivity of spherical dispersions is investigated. The spherical particles can be either coated with multiple layers or possessive of a certain amount of contact resistance, and can be either randomly distributed or arranged in simple cubic arrays. The effective conductivity of the dispersion is found to be a function of the particle volume fraction and the dimensionless multipole polarizability. Expressions for the dimensionless multipole polarizability for both multiply coated sphere and contact resistance problems are derived. The effect of particle surface conditions is realized through their influence on the magnitude of the multipole polarizability, and the effect of the multipole polarizability on the effective conductivity is carefully examined. It is further found that, for random arrays, all members of the multipole polarizability are involved in the evaluation of the effective conductivity, but only half of them are involved for simple cubic arrays. In addition, the contact resistance problem has a narrower polarizability variation range than that of the multiply coated sphere problem. These two factors profoundly contribute to the differing effect of multipole polarizabilities on the effective conductivity of the dispersion with respect to the dispersion microstructure and particle surface conditions.
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