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On a hierarchy of approximate models for flows of incompressible fluids through porous solids. (English) Zbl 1123.76066
This review article reproduces the basics and balance equations of mixture theory of Truesdell. It is shown in which way Darcy equation, Brinkman equations and Biot model, which all describe the flow through porous media, are connected with the mixture theory. Several problems are considered: e.g. the flow of fluids with shear rate dependent viscosity through a rigid porous solid, flows wherein inertial effects in the fluid cannot be ignored, the effect of pressure on flows through porous media, and the effect of compressibility of the fluid or the flow through solids undergoing small and large deformations. Finally, one section is devoted to the choice of boundary conditions for problems in the mechanics of mixtures.

##### MSC:
 76S05 Flows in porous media; filtration; seepage 76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
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