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The breakdown of Darcy's law in a soft porous material

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Abstract

We perform direct numerical simulations of the flow through a model of deformable porous medium. Our model is a two-dimensional hexagonal lattice, with defects, of soft elastic cylindrical pillars, with elastic shear modulus G, immersed in a liquid. We use a two-phase approach: the liquid phase is a viscous fluid and the solid phase is modeled as an incompressible viscoelastic material, whose complete nonlinear structural response is considered. We observe that the Darcy flux (q) is a nonlinear function – steeper than linear – of the pressure-difference (ΔP) across the medium. Furthermore, the flux is larger for a softer medium (smaller G). We construct a theory of this super-linear behavior by modelling the channels between the solid cylinders as elastic channels whose walls are made of material with a linear constitutive relation but can undergo large deformation. Our theory further predicts that the flow permeability is an universal function of ΔP/G, which is confirmed by the present simulations.

Graphical abstract: The breakdown of Darcy's law in a soft porous material

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Article information


Submitted
19 Aug 2019
Accepted
09 Dec 2019
First published
17 Dec 2019

This article is Open Access

Soft Matter, 2020, Advance Article
Article type
Paper

The breakdown of Darcy's law in a soft porous material

M. E. Rosti, S. Pramanik, L. Brandt and D. Mitra, Soft Matter, 2020, Advance Article , DOI: 10.1039/C9SM01678C

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