Darcy's law for two-dimensional flows: Singularities at corners and a new class of models

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As is known, Darcy's model for fluid flows in isotropic homogeneous porous media gives rise to singularities in the velocity field for essentially two-dimensional flow configuration, like flows over corners. Considering this problem from the modelling viewpoint, the present study aims at removing this singularity, which cannot be regularized via conventional generalizations of the Darcy model, like Brinkman's equation, without sacrificing Darcy's law itself for unidirectional flows where its validity is well established experimentally. The key idea is that, as confirmed by a simple analogy, the permeability of a porous matrix with respect to flow is not a constant independent of the flow but a function of the flow field (its scalar invariants), decreasing as the curvature of the streamlines increases. This introduces a completely new class of models where the flow field and the permeability field are linked and, in particular problems, have to be found simultaneously.
Original languageEnglish
Pages (from-to)5207-5214
Number of pages8
JournalAIChE Journal
Issue number11
Early online date22 Jun 2017
Publication statusPublished - 10 Oct 2017


  • mathematical modeling
  • porous media
  • Darcy's law
  • velocity singularity
  • curvature of streamlines


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