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Diffusion in spatially and temporarily inhomogeneous media
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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.
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LEHR, Heiner, SAGUÉS I MESTRE, Francesc, SANCHO, José m.. Diffusion in spatially and temporarily inhomogeneous media. _Physical Review e_. 1996. Vol. 54, núm. 5, pàgs. 5028-5036. [consulta: 1 de febrer de 2026]. ISSN: 1539-3755. [Disponible a: https://hdl.handle.net/2445/18700]