To access the full text documents, please follow this link:

Diffusion in spatially and temporarily inhomogeneous media
Lehr, H.; Sagués i Mestre, Francesc; Sancho, José M.
Universitat de Barcelona
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-1/3 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.
Òptica geomètrica
Materials inhomogenis
Geometrical optics
Inhomogeneous materials
(c) The American Physical Society, 1996
The American Physical Society

Show full item record