Acoustics of sorptive porous materials

Abstract

Sound propagation in conventional rigid-frame porous materials is affected by the viscosity of the saturating gas and the heat transfer between the gas and the solid frame. This paper investigates the acoustical properties of hierarchical porous materials that support mass transfer processes, such as sorption and different types of diffusion, in addition to the previously mentioned effects. The two-scale asymptotic expansion method of homogenisation for periodic media is used to derive the macroscopic acoustic description. This description allowed to conclude that, at the leading order, neither sorption nor diffusion affects the macroscopic fluid flow through the material. However, the effective compressibility is significantly modified by these physical phenomena. Specifically, the real part of the low-frequency bulk modulus can take values much smaller than those found in conventional materials while its imaginary part is increased around the characteristic frequency associated with diffusion. As a consequence, the sound waves are slowed down and more attenuated at low frequencies. The results are exemplified for sorptive porous, fibrous, and granular materials and the influence of their microstructural descriptors on their effective acoustical properties is discussed.