Nonlinear corrections to Darcy's law at low Reynolds numbers

Under fairly general assumptions, this paper shows that for periodic porous media, whose period is of the same order as that of the inclusion, the nonlinear correction to Darcy's law is quadratic in terms of the Reynolds number, i.e. cubic with respect to the seepage velocity. This claim is sub...

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Bibliographic Details
Published in:Journal of fluid mechanics 1997-07, Vol.343, p.331-350
Main Authors: FIRDAOUSS, MOUAOUIA, GUERMOND, JEAN-LUC, LE QUÉRÉ, PATRICK
Format: Article
Language:English
Subjects:
Exact sciences and technology
Flows through porous media
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Nonhomogeneous flows
Physics
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Summary:Under fairly general assumptions, this paper shows that for periodic porous media, whose period is of the same order as that of the inclusion, the nonlinear correction to Darcy's law is quadratic in terms of the Reynolds number, i.e. cubic with respect to the seepage velocity. This claim is substantiated by reinspection of well-known experimental results, a mathematical proof (restricted to periodic porous media), and numerical calculations.
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112097005843