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Darcy's law for flow in a periodic thin porous medium confined between two parallel plates
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
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Number of Authors: 5
2016 (English)In: Transport in Porous Media, ISSN 0169-3913, E-ISSN 1573-1634, Vol. 115, no 3, 473-493 p.Article in journal (Refereed) Published
Abstract [en]

We study stationary incompressible fluid flow in a thin periodic porous medium. The medium under consideration is a bounded perforated 3D-domain confined between two parallel plates. The distance between the plates is \(\delta \), and the perforation consists of \(\varepsilon \)-periodically distributed solid cylinders which connect the plates in perpendicular direction. Both parameters \(\varepsilon \), \(\delta \) are assumed to be small in comparison with the planar dimensions of the plates. By constructing asymptotic expansions, three cases are analysed: (1) \(\varepsilon \ll \delta \), (2) \(\delta /\varepsilon \sim \text {constant}\) and (3) \(\varepsilon \gg \delta \). For each case, a permeability tensor is obtained by solving local problems. In the intermediate case, the cell problems are 3D, whereas they are 2D in the other cases, which is a considerable simplification. The dimensional reduction can be used for a wide range of \(\varepsilon \) and \(\delta \) with maintained accuracy. This is illustrated by some numerical examples.

Place, publisher, year, edition, pages
2016. Vol. 115, no 3, 473-493 p.
Keyword [en]
Thin porous media · Asymptotic analysis · Homogenization · Darcy’s law · Mixed boundary condition · Stress boundary condition · Permeability
National Category
Engineering and Technology
Research subject
Fluid Mechanics; Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-8685DOI: 10.1007/s11242-016-0702-2Local ID: 7396f0ae-22ce-48c1-b5d8-eaeed32c8ba5OAI: oai:DiVA.org:ltu-8685DiVA: diva2:981623
Funder
Swedish Research Council
Note

Validerad; 2016; Nivå 2; 2016-11-25 (andbra)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2016-12-02Bibliographically approved

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Fabricius, JohnHellström, GunnarLundström, StaffanMiroshnikova, ElenaWall, Peter
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