Sound propagation in gas-filled rigid-framed porous media: General theory and new experimental and numerical data

Abstract

The acoustic properties of gas-filled porous media have been the subject of extensive theoretical and experimental work. However, even in the simplest case of rigid-framed materials, most of the theoretical developments found in the acoustical literature remain largely empiric or semiphenomenologic. This is due to the complicated microstructure of porous materials in general. Starting with first principles and using a simple two-scale analysis, a general formulation of the problem of (linear) long-wavelength sound propagation in gas-filled media is provided in terms of two independent permeabilities. One of these—the viscous dynamic permeability—is well known. Its thermal analog, the thermal dynamic permeability, is new in the acoustical context. It can be related to a notion of ‘‘mean survival time’’ in diffusion-controlled reactions. The exact connection between the microgeometry and the frequency-dependent dynamic permeabilities is obtained in terms of independent geometrical distribution functions. Useful analogies with the dispersion of electric and magnetic permeabilities are noted. New experimental and numerical data demonstrate the usefulness of the scaling functions proposed by Wilson et al. and Pride et al. Different limitations of the general modeling and the mentioned scaling functions are also noted.