Flows in porous media with erosion of the solid matrix

Leda Bucciantini; Angiolo Farina; Antonio Fasano; Leda Bucciantini; Angiolo Farina; Antonio Fasano

doi:10.3934/nhm.2010.5.63

Networks and Heterogeneous Media

2010, Volume 5, Issue 1: 63-95. doi: 10.3934/nhm.2010.5.63

Previous Article Next Article

Flows in porous media with erosion of the solid matrix

1.
Università degli Studi di Firenze, Dipartimento di Fisica, Via Sansone 1, I-50019 Sesto Fiorentino (FI)
2.
Università degli Studi di Firenze, Dipartimento di Matematica "Ulisse Dini”, Viale Morgagni 67/A, I-50134 Firenze

Received: 01 July 2009 Revised: 01 October 2009
Primary: 76S05; Secondary: 35R35.

We consider the flow of an incompressible Newtonian fluid through an idealized porous medium consisting of an array of identical solid symmetric lamellae, whose profile varies in space and time due to a stress induced erosion process. The focus is on the influence of mass exchange between solid and fluid on the macroscopic flow. By means of the upscaling procedure illustrated in [6] we derive the governing system of equations for the macroscopic flow, encompassing various physical situations. We show that Darcy's law no longer applies in the classical sense. The corresponding mathematical problem turns out to be surprisingly complicated. Existence and uniqueness are proved. Numerical simulations are presented.
- Darcy's law,
- homogenization,
- PDE's,
- free boundary problems
Citation: Leda Bucciantini, Angiolo Farina, Antonio Fasano. Flows in porous media with erosion of the solid matrix[J]. Networks and Heterogeneous Media, 2010, 5(1): 63-95. doi: 10.3934/nhm.2010.5.63

Related Papers:
Abstract

We consider the flow of an incompressible Newtonian fluid through an idealized porous medium consisting of an array of identical solid symmetric lamellae, whose profile varies in space and time due to a stress induced erosion process. The focus is on the influence of mass exchange between solid and fluid on the macroscopic flow. By means of the upscaling procedure illustrated in [6] we derive the governing system of equations for the macroscopic flow, encompassing various physical situations. We show that Darcy's law no longer applies in the classical sense. The corresponding mathematical problem turns out to be surprisingly complicated. Existence and uniqueness are proved. Numerical simulations are presented.
Reader Comments

Your name:*

Email:*
© 2010 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)