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The effect of weak inertia on flow through a porous medium

Published online by Cambridge University Press:  26 April 2006

C. C. Mei  and
J.-L. Auriault
C. C. Mei
Affiliation:
Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
J.-L. Auriault
Affiliation:
Institut de Mécanique de Grenoble, B.P. 53, Grenoble, France
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Abstract

Using the theory of homogenization we examine the correction to Darcy's law due to weak convective inertia of the pore fluid. General formulae are derived for all constitutive coefficients that can be calculated by numerical solution of certain canonical cell problems. For isotropic and homogeneous media the correction term is found to be cubic in the seepage velocity, hence remains small even for Reynolds numbers which are not very small. This implies that inertia, if it is weak, is of greater importance locally than globally. Existing empirical knowledge is qualitatively consistent with our conclusion since the linear law of Darcy is often accurate for moderate flow rates.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 222 , January 1991 , pp. 647 - 663
Copyright
© 1991 Cambridge University Press

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