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 βR (β≥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 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 D_e for finite β given the result of D_e for β = 0.