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Homogenization approach to filtration through a fibrous medium

Mohamed Belhadj 1 Eric Cancès 2, 3 Jean-Frédéric Gerbeau 4 Andro Mikelić 5
1 BANG - Nonlinear Analysis for Biology and Geophysical flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt
3 MICMAC - Methods and engineering of multiscale computing from atom to continuum
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
4 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6
Abstract : We study the flow through fibrous media using homogenization techniques. The fibre network under study is the one already used by M. Briane in the context of heat conduction of biological tissues. We derive and justify the effective Darcy equation and the permeability tensor for such fibrous media. The theoretical results on the permeability are illustrated by some numerical simulations. Finally, the low solid fraction limit is considered. Applying results by G. Allaire to our setting, we justify rigorously the leading order term in the empirical formulas for the effective permeability used in engineering. The results are also confirmed by a direct numerical calculation of the permeability, in which the small diameter of the fibres requires high accuracy approximations.
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Submitted on : Saturday, May 26, 2012 - 3:01:00 PM
Last modification on : Wednesday, July 8, 2020 - 12:43:12 PM

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Mohamed Belhadj, Eric Cancès, Jean-Frédéric Gerbeau, Andro Mikelić. Homogenization approach to filtration through a fibrous medium. Networks and Heterogeneous Media, AIMS-American Institute of Mathematical Sciences, 2007, 2 (3), pp.529-550. ⟨10.3934/nhm.2007.2.529⟩. ⟨hal-00701778⟩



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