Nonstationary flow of a viscous fluid through a porous elastic medium: Asymptotic analysis and two-scale convergence

Allaire and Mikelic studied nonstationary flows of Stokesian fluids through undeformed microperiodic media. The first of these authors assumed the scaling of the viscosity while the second author scaled the liquid density. After homogenization they arrived at different Darcy's laws. Darcy's law derived by Allaire is nonlocal in time while that obtained by Mikelic coincides with the well known Darcy's law derived by many authors for stationary flow. In this context, the nonstationary flows of Stokesian fluids through a linear elastic porous medium are investigated to derive macroscopic equations of Biot type.