Simulating the time-dependent diffusion coefficient in mixed-pore-size materials

Abstract

Porous media with a wide distribution of pore sizes are quite common. We show that variable-step-size random walk simulations can be used to model the time-dependent diffusion coefficient D(t) in such porous media. The issue to be overcome is that, in variable-step-size walks, each walker carries its own "clock," and its position is known only at a random set of times. Thus, a direct ensemble-average calculation of <Δr(2)(t)> (the mean-square distance traveled at time t) is problematic. We introduce a sequence of approximations that overcome this apparent difficulty. Calculations are carried out on periodic systems that contain pores of quite different sizes. Where possible, our results are compared to those obtained using fixed-step-size random walks.