Conductivity estimates of spherical-particle suspensions based on triplet structure factors

In this paper, we present an estimation of the conductivity of composites constituted of identical spheres embedded in a host material. A family of polarization integral equations for the localization problem is constructed and the operator is then minimized to yield an optimal integral equation. As a result, the corresponding Neumann series converges with the fastest rate and can be used to estimate the effective conductivity. By combining this series and integral approximation, one can derive explicit expressions for the overall property using expansions in Fourier domain. For random hard-sphere systems, relations to structure factors and triplet structure factors have been made and Kirkwood superposition approximation is used to evaluate the effective conductivity, taking into account third-order correlations. This presents an original means to account for the statistical information up to third-order correlation when determining the effective properties of composite materials.

Figure 1

Integral over a sphere surface.

Figure 2

Radial distribution function of hard sphere in equilibrium at $f=0.4$. The inset is a snapshot of a typical sample.

Figure 3

Comparison the effective conductivity ($k_e/k_m$) of FCC lattice structure between the approximation OS and FFT complete solution with ratio $k_i/k_m=100$.