Acoustic properties of porous metamaterials featured by acoustic streaming, homogenization based modelling

We consider secondary effects induced by acoustic waves in viscous barotropic fluids saturating pores in elastic, or rigid scaffolds with elastically suspended particles. The asymptotic homogenization method is applied to derive models of the acoustic wave propagation and of the related acoustic streaming (AS) as the secondary effect. This phenomenon originating due to the nonlinearity (divergence of the Reynolds stress) in the Navier Stokes equation is retained using the perturbation analysis. This yields the first and the second order sub-problem enabling to linearize the model governing fluid dynamics. The local AS in the microstructure produces forces acting on the suspended particles, transforming the pore geometry, hence, modulating the acoustic properties. As the consequence, the permeability involved in both the subproblems is modified due to the slowly oscillating particles. The sensitivity analysis can be employed to introduce the homogenized coefficients of the model depending on the particle motion.