Document type
ArticleVersion
Published versionPublication date
All rights reserved
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/18700
Diffusion in spatially and temporarily inhomogeneous media
Journal Title
Director/Tutor
Journal ISSN
Volume Title
Related resource
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 (English)
Citation
Citation
LEHR, Heiner, SAGUÉS I MESTRE, Francesc and SANCHO, José M. Diffusion in spatially and temporarily inhomogeneous media. Physical Review e. 1996. Vol. 54, num. 5, pags. 5028-5036. ISSN 1539-3755. [consulted: 18 of June of 2026]. Available at: https://hdl.handle.net/2445/18700