DIFFUSION OF FINITE-SIZED BROWNIAN PARTICLES IN POROUS-MEDIA

The effective diffusion coefficient D(e) for porous media composed of identical obstacles of radius R in which the diffusing particles have finite radius beta-R (beta greater-than-or-equal-to 0) is determined by an efficient Brownian motion simulation technique. This is accomplished by first computing D(e) for diffusion of "point" Brownian particles in a certain system of interpenetrable spherical obstacles and then employing an isomorphism between D(e) for this interpenetrable sphere system and D(e) for the system of interest, i.e., the one in which the Brownian particles have radius beta-R. [S. Torquato, J. Chem. Phys. 95, 2838 (1991)]. The diffusion coefficient is computed for the cases beta = 1/9 and beta = 1/4 for a wide range of porosities and compared to previous calculations for point Brownian particles (beta = 0). The effect of increasing the size of the Brownian particle is to hinder the diffusion, especially at low porosities. A simple scaling relation enables one to compute the effective diffusion coefficient D(e) for finite beta given the result of D(e) for beta = 0.