On the developments of Darcy's law to include inertial and slip effects

Didier Lasseux; Francisco J. Valdés-Parada

doi:10.1016/j.crme.2017.06.005

On the developments of Darcy's law to include inertial and slip effects

Didier Lasseux ¹ ; Francisco J. Valdés-Parada ²

¹ CNRS, Université de Bordeaux, I2M – UMR 5295, Esplanade des Arts-et-Métiers, 33405 Talence cedex, France
² Universidad Autónoma Metropolitana-Iztapalapa, Departamento de Ingeniería de Procesos e Hidráulica, Av. San Rafael Atlixco 186, 09340 Mexico, D.F., Mexico

Comptes Rendus. Mécanique, A century of fluid mechanics: 1870–1970, Volume 345 (2017) no. 9, pp. 660-669.

Abstract

The empirical Darcy law describing flow in porous media, whose convincing theoretical justification was proposed almost 130 years after its original publication in 1856, has however been extended to account for particular flow conditions. This article reviews historical developments aimed at including inertial and slip effects (respectively, when the Reynolds and Knudsen numbers are not exceedingly small compared to unity). Despite the early empirical extensions to include inertia and slip effects, it is striking to observe that clear formal derivations of physical models to account for these effects were reported only recently.

Received: 2016-12-04
Accepted: 2017-03-26
Published online: 2017-07-12

DOI: 10.1016/j.crme.2017.06.005

Keywords: Porous media, Inertial flow, Slip flow, Darcy's law, Forchheimer correction, Klinkenberg correction

Author's affiliations:

Didier Lasseux ¹; Francisco J. Valdés-Parada ²

¹ CNRS, Université de Bordeaux, I2M – UMR 5295, Esplanade des Arts-et-Métiers, 33405 Talence cedex, France
² Universidad Autónoma Metropolitana-Iztapalapa, Departamento de Ingeniería de Procesos e Hidráulica, Av. San Rafael Atlixco 186, 09340 Mexico, D.F., Mexico

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Didier Lasseux; Francisco J. Valdés-Parada. On the developments of Darcy's law to include inertial and slip effects. Comptes Rendus. Mécanique, A century of fluid mechanics: 1870–1970, Volume 345 (2017) no. 9, pp. 660-669. doi : 10.1016/j.crme.2017.06.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.06.005/

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