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Exuding porous media: deviations from Darcy's law

Published online by Cambridge University Press:  01 February 2021

Didier Lasseux Open the ORCID record for Didier Lasseux [Opens in a new window] ,
Francisco J. Valdés-Parada Open the ORCID record for Francisco J. Valdés-Parada [Opens in a new window] ,
Jean-François Thovert Open the ORCID record for Jean-François Thovert [Opens in a new window]  and
Valeri Mourzenko Open the ORCID record for Valeri Mourzenko [Opens in a new window]
Didier Lasseux*
Affiliation:
I2M, UMR 5295, CNRS, Université Bordeaux, Esplanade des Arts et Métiers, 33405Talence CEDEX, France
Francisco J. Valdés-Parada
Affiliation:
Departamento de Ingeniería de Procesos e Hidráulica, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, 09340Ciudad de México, Mexico
Jean-François Thovert
Affiliation:
Institut P′, CNRS, Université de Poitiers, ISAE-ENSMA, 11 bd Marie et Pierre Curie, TSA 41123, 86073Poitiers CEDEX 9, France
Valeri Mourzenko
Affiliation:
Institut P′, CNRS, Université de Poitiers, ISAE-ENSMA, 11 bd Marie et Pierre Curie, TSA 41123, 86073Poitiers CEDEX 9, France
*
†Email address for correspondence: [email protected]
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Abstract

This work addresses the question of a pertinent macroscale model describing creeping, incompressible and single-phase flow of a Newtonian fluid in an exuding, rigid and homogeneous porous medium. The macroscopic model is derived by upscaling the pore-scale Stokes equations considering a normal mass flux at the solid–fluid interface. The upscaled mass equation shows that the average velocity is non-solenoidal. In addition, the macroscopic momentum equation involves a Darcy term with the classical permeability tensor accounting for macroscopic drag and a correction velocity vector which is a signature of the local fluid displacements induced by the exuding phenomenon. This correction is the sum of a term accounting for the local exuding effect and a compensation term associated with the assumption of spatial periodicity. Both the first term and the permeability tensor are obtained from the solution of the same unique and intrinsic closure problem, which corresponds to that involved in the classical Darcy's law. The upscaled model is validated by comparisons with pore-scale numerical simulations in several illustrative examples. The different configurations evidence the richness of the problem, despite the apparent simplicity of its formulation. The results of this work motivate further investigation about the influence of internal flow sources in transport phenomena in porous media.

JFM classification

Low-Reynolds-number flows: Porous media Mathematical Foundations: General fluid mechanics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 911 , 25 March 2021 , A48
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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