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Flow in random porous media: mathematical formulation, variational principles, and rigorous bounds

Published online by Cambridge University Press:  26 April 2006

Jacob Rubinstein  and
S. Torquato
Jacob Rubinstein
Affiliation:
Department of Mathematics, Stanford University, Stanford, CA 94305-2125, USA Present address: Department of Mathematics, Technion-I.I.T. Haifa 32000, Israel.
S. Torquato
Affiliation:
Department of Mechanical and Aerospace Engineering and Department of Chemical Engineering, North Carolina State University, Raleigh, NC 27695-7910, USA
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Abstract

The problem of the slow viscous flow of a fluid through a random porous medium is considered. The macroscopic Darcy's law, which defines the fluid permeability k, is first derived in an ensemble-average formulation using the method of homogenization. The fluid permeability is given explicitly in terms of a random boundary-value problem. General variational principles, different to ones suggested earlier, are then formulated in order to obtain rigorous upper and lower bounds on k. These variational principles are applied by evaluating them for four different types of admissible fields. Each bound is generally given in terms of various kinds of correlation functions which statistically characterize the microstructure of the medium. The upper and lower bounds are computed for flow interior and exterior to distributions of spheres.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 206 , September 1989 , pp. 25 - 46
Copyright
© 1989 Cambridge University Press

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