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The breakdown of Darcy's law in a soft porous material
- Source :
- Soft Matter, 2020, 16, 939-944
- Publication Year :
- 2019
-
Abstract
- We perform direct numerical simulations of the flow through a model of a 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 ($\Delta P$) 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 a material with a linear constitutive relation but can undergo large deformation. Our theory further predicts that the flow permeability is a universal function of $\Delta P/G$, which is confirmed by the present simulations.<br />Comment: 6 pages, 3 figures, Some minor changes (including the title) from the previous submission
- Subjects :
- Physics - Fluid Dynamics
Subjects
Details
- Database :
- arXiv
- Journal :
- Soft Matter, 2020, 16, 939-944
- Publication Type :
- Report
- Accession number :
- edsarx.1902.02505
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1039/C9SM01678C