Acoustic waves in homogenized fluid-saturated deforming periodic scaffolds under permanent flow

Acoustic waves in a poroelastic medium with periodic structure are studied with respect to permanent seepage flow which modifies the wave propagation. The homogenization method provides the macroscopic equations governing the dynamic response of an effective medium. whose the properties are determined by the characteristic responses. We consider a Newtonian slightly compressible fluid under the barotropic acoustic approximation. In contrast with usual simplifications, the advection phenomenon of the Navier-Stokes equations is accounted for. The homogenization results are based on the periodic unfolding method combined with the asymptotic expansion technique. The dynamic permeability depends on the fluid flow properties including the advection effects associated with an assumed stationary perfusion of the porous structure. Numerical results show influence of the advection velocity on the strong dispersion of the quasi-shear mode