Diffusion in spatially and temporarily inhomogeneous media.

In this paper we consider diffusion of a passive substance C in a temporarily and spatially inhomogeneous two-dimensional medium. As a realization for the latter we choose a phase-separating medium consisting of two substances A and B , whose dynamics is determined by the Cahn-Hilliard equation. Assuming different diffusion coefficients of C in A and B , we find that the variance of the distribution function of the said substance grows less than linearly in time. We derive a simple identity for the variance using a probabilistic ansatz and are then able to identify the interface between A and B as the main cause for this nonlinear dependence. We argue that, finally, for very large times the here temporarily dependent diffusion ‘‘constant’’ goes like t to a constant asymptotic value D` . The latter is calculated approximately by employing the effective-medium approximation and by fitting the simulation data to the said time dependence. @S1063-651X~96!02111-3#