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Microstructure - acoustic properties relationships: Application to membrane and bimodal pore-size distribution effects

This paper presents recent developments in the field of multi-scale acoustics of real porous media. The fundamental idea of the proposed approach is that it is possible to get insight into the microstructure of real porous media and how it collectively dictates their acoustical properties, from the three dimensional implementation of micro-acoustics based scaling relations on idealized unit-cells. The homogenization procedure is applied to the problem of long-wavelength wave propagation in rigid porous media saturated with a Newtonian and thermally conducting fluid. The local problems corresponding to the fluid phase have been solved for the three-dimensional tetrakaidecahedronal model. The geometry of the foam is determined based on two measured macroscopic parameters: 1) the porosity and 2) the hydraulic permeability. The complete set of transport phenomena characterizing the asymptotic behavior of the frequency dependant viscous and thermal dissipation functions are systematically determined. The results of this technique are compared to standing wave tube and micrographs measurements for three real samples of predominately open-celled foams, giving evidences of membrane and bimodal pore-size distribution effects.