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Homogenization of a polymer flow through a porous medium. (English) Zbl 0863.76082

The paper is a mathematical derivation of the laws governing polymer flows through porous media using the tools of the homogenization theory. In the case of Newtonian flow, the homogenization leads to the classical Darcy’s law. In this study some non-Newtonian flows are studied. The attention of the authors is focussed on the two most widely used laws in engineering practice: the “power law”, and the “Carreau law”. Depending on the value of the Reynolds number compared to the small parameter of the homogenization procedure, a relation connecting the filtration velocity to the mean pressure gradient is derived, which may be linear, or nonlinear and nonlocal. For each situation the uniqueness theorem is proved.
Reviewer: Th.Lévy (Paris)

MSC:

76S05 Flows in porous media; filtration; seepage
76A05 Non-Newtonian fluids
35Q35 PDEs in connection with fluid mechanics
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
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