Effective conductivity of suspensions of hard spheres by Brownian motion simulation

摘要

A generalized Brownian motion simulation technique developed by Kim and Torquato lsqb;J. Appl. Phys.68, 3892 (1990)rsqb; is applied to compute lsquo;lsquo;exactlyrsquo;rsquo; the effective conductivity sgr;eof heterogeneous media composed of regular and random distributions of hard spheres of conductivity sgr;2in a matrix of conductivity sgr;1for virtually the entire volume fraction range and for several values of the conductivity ratio agr;=sgr;2/sgr;1, including superconducting spheres (agr;=infin;) and perfectly insulating spheres (agr;=0). A key feature of the procedure is the use offirsthyphen;passagehyphen;timeequations in the two homogeneous phases and at the twohyphen;phase interface. The method is shown to yield sgr;eaccurately with a comparatively fast execution time. The microstructurehyphen;sensitive analytical approximation of sgr;efor dispersions derived by Torquato lsqb;J. Appl. Phys.58, 3790 (1985)rsqb; is shown to be in excellent agreement with our data for random suspensions for the wide range of conditions reported here.