Search Advanced

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.

    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:

    [1] Leda Bucciantini, Angiolo Farina, Antonio Fasano . Flows in porous media with erosion of the solid matrix. Networks and Heterogeneous Media, 2010, 5(1): 63-95. doi: 10.3934/nhm.2010.5.63
    [2] Alexei Heintz, Andrey Piatnitski . Osmosis for non-electrolyte solvents in permeable periodic porous media. Networks and Heterogeneous Media, 2016, 11(3): 471-499. doi: 10.3934/nhm.2016005
    [3] Mohamed Belhadj, Eric Cancès, Jean-Frédéric Gerbeau, Andro Mikelić . Homogenization approach to filtration through a fibrous medium. Networks and Heterogeneous Media, 2007, 2(3): 529-550. doi: 10.3934/nhm.2007.2.529
    [4] Brahim Amaziane, Leonid Pankratov, Andrey Piatnitski . An improved homogenization result for immiscible compressible two-phase flow in porous media. Networks and Heterogeneous Media, 2017, 12(1): 147-171. doi: 10.3934/nhm.2017006
    [5] María Anguiano, Renata Bunoiu . Homogenization of Bingham flow in thin porous media. Networks and Heterogeneous Media, 2020, 15(1): 87-110. doi: 10.3934/nhm.2020004
    [6] Martin Gugat, Alexander Keimer, Günter Leugering, Zhiqiang Wang . Analysis of a system of nonlocal conservation laws for multi-commodity flow on networks. Networks and Heterogeneous Media, 2015, 10(4): 749-785. doi: 10.3934/nhm.2015.10.749
    [7] Frederike Kissling, Christian Rohde . The computation of nonclassical shock waves with a heterogeneous multiscale method. Networks and Heterogeneous Media, 2010, 5(3): 661-674. doi: 10.3934/nhm.2010.5.661
    [8] Jinhu Zhao . Natural convection flow and heat transfer of generalized Maxwell fluid with distributed order time fractional derivatives embedded in the porous medium. Networks and Heterogeneous Media, 2024, 19(2): 753-770. doi: 10.3934/nhm.2024034
    [9] Pedro Aceves-Sanchez, Benjamin Aymard, Diane Peurichard, Pol Kennel, Anne Lorsignol, Franck Plouraboué, Louis Casteilla, Pierre Degond . A new model for the emergence of blood capillary networks. Networks and Heterogeneous Media, 2021, 16(1): 91-138. doi: 10.3934/nhm.2021001
    [10] Catherine Choquet, Ali Sili . Homogenization of a model of displacement with unbounded viscosity. Networks and Heterogeneous Media, 2009, 4(4): 649-666. doi: 10.3934/nhm.2009.4.649
  • 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.


  • This article has been cited by:

    1. Q. Xu, T.S. Zhao, Fundamental models for flow batteries, 2015, 49, 03601285, 40, 10.1016/j.pecs.2015.02.001
  • Reader Comments
  • © 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)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Networks and Heterogeneous Media
1.2 1.8

Metrics

Article views(4092) PDF downloads(77) Cited by(1)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog