Title:
|
Diffusion in spatially and temporarily inhomogeneous media
|
Author:
|
Lehr, H.; Sagués i Mestre, Francesc; Sancho, José M.
|
Other authors:
|
Universitat de Barcelona |
Abstract:
|
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. |
Subject(s):
|
-Òptica geomètrica -Materials inhomogenis -Geometrical optics -Inhomogeneous materials |
Rights:
|
(c) The American Physical Society, 1996
|
Document type:
|
Article Article - Published version |
Published by:
|
The American Physical Society
|
Share:
|
|