On the developments of Darcy's law to include inertial and slip effects - 06/09/17

Doi : 10.1016/j.crme.2017.06.005

Didier Lasseux ^a,^{^⁎} , Francisco J. Valdés-Parada ^b
^a CNRS, Université de Bordeaux, I2M – UMR 5295, Esplanade des Arts-et-Métiers, 33405 Talence cedex, France
^b Universidad Autónoma Metropolitana-Iztapalapa, Departamento de Ingeniería de Procesos e Hidráulica, Av. San Rafael Atlixco 186, 09340 Mexico, D.F., Mexico

^⁎Corresponding author.

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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.

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