Acoustic streaming in porous media – homogenization based two-scale modelling

Abstract

A homogenized model of the acoustic streaming (AS) in rigid porous periodic structure is presented. Using the classical perturbation approach, the first and the second order subproblems arising from the N-S equations governing the fluid dynamics in the pores are obtained and further homogenized. The driving force of the permanent flow is obtained due to the time average of the nonlinear advection terms expressed using the first order acoustic harmonic fluctuations. Homogenization of the 1st order problem yields the dynamic Darcy flow mode governing the wave response. This is employed to constitute the streaming source term involved in the 2nd order homogenized problem for time-averaged pressure field. The AS can be observed at both the macroscopic and the microscopic levels. While the acoustics-driven microflows are observed for any microstructure, the macroscopic AS depends on the porous microstructure geometry and boundary conditions. We propose a solution method based on the spectral analysis of the characteristic microscopic dynamic Stokes flow. The AS phenomenon in the homogenized medium is illustrated using 2D examples of periodic porous microstructures.