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The breakdown of Darcy's law in a soft porous material
KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-9004-2292
KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.ORCID iD: 0000-0001-8487-3551
KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-4346-4732
KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, SE-10691 Stockholm, Sweden.ORCID iD: 0000-0001-6162-7112
2020 (English)In: Soft Matter, ISSN 1744-683X, E-ISSN 1744-6848, Vol. 16, no 4, p. 939-944Article in journal (Refereed) Published
Abstract [en]

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 (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 material with a linear constitutive relation but can undergo large deformation. Our theory further predicts that the flow permeability is an universal function of Delta P/G, which is confirmed by the present simulations.

Place, publisher, year, edition, pages
Royal Society of Chemistry, 2020. Vol. 16, no 4, p. 939-944
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-268803DOI: 10.1039/c9sm01678cISI: 000510894800006PubMedID: 31845717Scopus ID: 2-s2.0-85078684721OAI: oai:DiVA.org:kth-268803DiVA, id: diva2:1395970
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QC 20200225

Available from: 2020-02-25 Created: 2020-02-25 Last updated: 2020-05-11Bibliographically approved

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