Multiple scattering of acoustic waves and porous absorbing media

Porous media like air-saturated polymer foams with open cells, have a nontrivial frequency-dependent absorption that arises due to viscous and thermal effects at the scale of the rigid frame microstructure. In order to produce multiple scattering at ultrasonic frequencies, mesoscale scatterers are introduced in the porous medium host. The effective wave number of such a multiscale medium should take into account the peculiar absorption at the microscale and the multiple scattering at the mesoscale to describe precisely the propagation of a coherent acoustic wave. For this purpose, a simple model is developed. First, an equivalent fluid model, derived from a homogenization method, is used to describe the acoustic propagation in the host porous medium itself. Second, the scattering by the inclusions is described with a multiple scattering approximation (independent scattering approximation). This simple model allows to obtain the total effective wave number of the porous medium with mesoscale scatterers. After some validating results on the multiple scattering by an array of rigid cylinders in air, experiments on the multiple scattering by rigid cylinders embedded in a porous medium are presented and compared to the developed simple model. Incidentally, it appears that for the host medium itself, the equivalent fluid model is not capable to describe the high-frequency behavior whilst a multiple scattering approach with (thin) viscous and thermal boundary layers around the scatterers is accurate in the whole frequency range.