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Effective equations for flow in random porous media with a large number of scales

Published online by Cambridge University Press:  21 April 2006

Jacob Rubinstein
Jacob Rubinstein
Affiliation:
Institute for Mathematics and its Applications, 514 Vincent Hall, 206 Church St. S.E., University of Minnesota Minneapolis, MN 55455 and Department of Mathematics, Stanford University, Stanford, CA 94305
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Abstract

We rederive Brinkman's equations for the flow of slow viscous fluid past a random distribution of identical obstacles using the Foldy's approximation. It is shown explicitly that such a derivation is valid for extremely dilute systems. We argue that Brinkman's equation can be used even in systems with lower porosity by proposing a model of porous media that has a very large number of scales.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 170 , September 1986 , pp. 379 - 383
Copyright
© 1986 Cambridge University Press

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