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 a, of heterogeneous media composed of regular and random distributions of hard spheres of conductivity a, in a matrix of conductivity (pi for virtually the entire volume fraction range and for several values of the conductivity ratio a = ~~/a,, including superconducting spheres (a = CO ) and perfectly insulating spheres (a = 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 u, accurately with a comparatively fast execution time. The microstructure-sensitive analytical approximation of o, for dispersions derived by Torquato [J. Appl. Phys. 58,379O (1985) ] is shown to be in excellent agreement with our data for random suspensions for the wide range of conditions reported here.