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A discrete random walk model for diffusion in media with double diffusivity

Published online by Cambridge University Press:  17 February 2009

James M. Hill
James M. Hill
Affiliation:
Department of Mathematics, University of Wollongong, Wollongong, New South Wales 2500
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Abstract

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Diffusion in the presence of high-diffusivity paths is an important issue of current technology. In metals, high-diffusivity paths are identified with dislocations, grain boundaries, free surfaces and internal microcracks. In pourous media such as rocks, fissures provide a system of high-flow paths. Recently, based on a continuum approach, these phenomena have been modelled, resulting in coupled systems of partial differential equations of parabolic type for the concentrations in bulk and in the high-diffusivity paths. This theory assumes that each point of the medium is simultaneously occupied by more than one diffusion or flow path. Here a simple discrete random walk model of diffusion in a medium with double diffusivity is given.

Type
Research Article
Information
The ANZIAM Journal , Volume 22 , Issue 1 , July 1980 , pp. 58 - 74
Copyright
Copyright © Australian Mathematical Society 1980

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