Journal
TRANSPORT IN POROUS MEDIA
Volume 60, Issue 1, Pages 89-108Publisher
SPRINGER
DOI: 10.1007/s11242-004-3649-7
Keywords
porous media; flow law; poor separation of scales; Brinkman's law homogenization
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We investigate the validity of Darcy's law when the separation of scales is poor. We use the method of multi-scale asymptotic expansions which gives the macroscopic behaviour from the pore scale description. The first order approximation is the Darcy's law. When the separation of scales is poor, eventual correctors to Darcy's law are obtained by investigating the following orders of approximation, thus enabling us to study its robustness. We investigate the two first correctors. Thus, the accuracy of the macroscopic flow law is improved from O(epsilon) to O(epsilon(3)), where epsilon is the separation of scale parameter. The second corrector shows a Brinkman's term. For macroscopically homogeneous porous media, the first corrector cancels out, that points out the robustness of Darcy's law in this case.
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