Diffusion of finite-sized Brownian particles in porous media

Abstract

The effective diffusion coefficient De for porous media composed of identical obstacles of radius R in which the diffusing particles have finite radius βR (β≥0) is determined by an efficient Brownian motion simulation technique. This is accomplished by first computing De for diffusion of ‘‘point’’ Brownian particles in a certain system of interpenetrable spherical obstacles and then employing an isomorphism between De for this interpenetrable sphere system and De for the system of interest, i.e., the one in which the Brownian particles have radius βR. [S. Torquato, J. Chem. Phys. 95, 2838 (1991)]. The diffusion coefficient is computed for the cases β=1/9 and β=1/4 for a wide range of porosities and compared to previous calculations for point Brownian particles (β=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 De for finite β given the result of De for β=0.