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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.
2011-07-26
Òptica geomètrica
Materials inhomogenis
Geometrical optics
Inhomogeneous materials
(c) The American Physical Society, 1996
Article
The American Physical Society
         

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