Theoretical derivation of Darcy's law for fluid flow in thin porous media

Francisco J. Suárez‐Grau

Mathematische Nachrichten, 2022, vol. 295, issue 3, 607-623

Abstract: In this paper we study stationary incompressible Newtonian fluid flow in a thin porous media. The media under consideration is a bounded perforated 3D domain confined between two parallel plates. The description of the domain includes two small parameters: ε representing the distance between plates and aε$a_\varepsilon$ connected to the microstructure of the domain such that aε≪ε$a_\varepsilon \ll \varepsilon$. We consider the classical setting of perforated media, i.e. aε$a_\varepsilon$‐periodically distributed solid (not connected) obstacles of size aε$a_\varepsilon$. The goal of this paper is to introduce a version of the unfolding method, depending on both parameters ε and aε$a_\varepsilon$, and then to derive the corresponding 2D Darcy law.

Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.202000184

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:295:y:2022:i:3:p:607-623

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().