On Darcy’s law for growing porous media. (English) Zbl 1346.76194

Summary: The flow of a Newtonian fluid in porous media can be described using Darcy’s law when inertial effects and deformations in the solid can be neglected and no mass interchange occur between the solid and the fluid components. Having in mind bio-medical applications, we analyze the correction to be considered when non-negligible mass exchanges between the constituents are present. This is done both on a thermodynamical basis and using a symmetry and frame indifferent argument.


76S05 Flows in porous media; filtration; seepage
74L15 Biomechanical solid mechanics
76Z05 Physiological flows
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