Acoustic streaming in homogenized deformable porous media

Abstract

This paper deals with the acoustic streaming (AS) in periodic poroelastic and rigid media. The fluid-structure interaction problem is imposed in elastic scaffolds. The perturbation with respect to a small parameter proportional to the inverse Strouhal number is applied, which leads to the first and the second order sub-problem enabling to linearize the Navier-Stokes equations governing the barotropic viscous fluid dynamics in deforming scaffolds. Subsequent treatment by the asymptotic homogenization leads to a two scale problem where the macroscopic model provides the vibro-acoustic analysis in the Biot-type medium. It yields the AS source term for the second order problem which attains the form of the Darcy flow. The macroscopic and the local microscopic AS effects are examined for different geometries of the suspension particles (inclusions) and frequency of the incident waves.