Effective conductivity of suspensions of hard spheres by Brownian motion simulation

A generalized Brownian motion simulation technique developed by Kim and Torquato [J. Appl. Phys. 68, 3892 (1990)] is applied to compute ‘‘exactly’’ the effective conductivity σe of heterogeneous media composed of regular and random distributions of hard spheres of conductivity σ2 in a matrix of conductivity σ1 for virtually the entire volume fraction range and for several values of the conductivity ratio α=σ2/σ1, including superconducting spheres (α=∞) and perfectly insulating spheres (α=0). A key feature of the procedure is the use of first-passage-time equations in the two homogeneous phases and at the two-phase interface. The method is shown to yield σe accurately with a comparatively fast execution time. The microstructure-sensitive analytical approximation of σe for dispersions derived by Torquato [J. Appl. Phys. 58, 3790 (1985)] is shown to be in excellent agreement with our data for random suspensions for the wide range of conditions reported here.