Effective conductivity of dispersions: The effect of resistance at the particle surfaces

Abstract

The effective thermal or electrical conductivity of a suspension of monodisperse spherical particles embedded in a matrix of different conductivity is computed for the case when there exists a finite resistance at the particle-matrix interface. The calculation is carried out to second order in the volume fraction θ of the particle phase for a dispersion having the structure of equilibrium hard spheres. Both the first-order (Maxwell) and the second-order approximations are found to represent experimental data reasonably well for dispersions of low to moderate concentration. To first order in θ, the calculation of the conductivity of a dispersion with surface resistance is equivalent to the calculation of the conductivity of another dispersion with no surface resistance, but with a different particle conductivity. In the case of polydisperse systems, the effective conductivity is found to be sensitive to the particle size distribution.