Granular materials have been conventionally used for acoustic treatment due to their sound absorptive and sound insulating properties. An emerging field is the study of the acoustical properties of multiscale porous materials. An example of these is a granular material in which the particles are porous. In this paper, analytical and hybrid analytical-numerical models describing the acoustical properties of these materials are introduced. Image processing techniques have been employed to estimate characteristic dimensions of the materials. The model predictions are compared with measurements on expanded perlite and activated carbon showing satisfactory agreement. It is concluded that a double porosity granular material exhibits greater low-frequency sound absorption at reduced weight compared to a solid-grain granular material with similar mesoscopic characteristics.

A variety of new porous materials with unusually small pores have been manufactured in the past decades. To predict their acoustical properties, the conventional models need to be modified. When pore size becomes comparable to the molecular mean free path of a saturating fluid, the no-slip conditions on the pore surface are no longer accurate and hence the slip effects have to be taken into account. In this paper, sound propagation in microfibrous materials is modeled analytically, approximating the geometry by a regular array of rigid parallel cylinders. It has been shown that velocity and thermal slip on a cylinder surface significantly changes the model predictions leading to lower attenuation coefficient and higher sound speed values. The influence of material porosity, fiber orientation, and size on these effects is investigated. Finite element method is used to numerically solve the oscillatory flow and heat transfer problems in a square array of cylindrical fibres. Numerical results are compared with predictions of the analytical model and the range of its validity is identified.

This paper investigates sound propagation in multiscale rigid-frame porous materials that support mass transfer processes, such as sorption and different types of diffusion, in addition to the usual visco-thermo-inertial interactions. The two-scale asymptotic method of homogenization for periodic media is successively used to derive the macroscopic equations describing sound propagation through the material. This allowed us to conclude that the macroscopic mass balance is significantly modified by sorption, inter-scale (micro- to/from nanopore scales) mass diffusion, and inter-scale (pore to/from micro- and nanopore scales) pressure diffusion. This modification is accounted for by the dynamic compressibility of the effective saturating fluid that presents atypical properties that lead to slower speed of sound and higher sound attenuation, particularly at low frequencies. In contrast, it is shown that the physical processes occurring at the micro-nano-scale do not affect the macroscopic fluid flow through the material. The developed theory is exemplified by introducing an analytical model for multiscale sorptive granular materials, which is experimentally validated by comparing its predictions with acoustic measurements on granular activated carbons. Furthermore, we provide empirical evidence supporting an alternative method for measuring sorption and mass diffusion properties of multiscale sorptive materials using sound waves.

An omnidirectional sound absorber based on the acoustic analogy of the electromagnetic metamaterial “black hole” has been developed and tested. The resulting structure is composed of a hollow cylindrical porous absorbing core and a graded index matching layer which employs multiple rods of varying size and spacing to gradually adjust the impedance of the air to that of the porous absorbing core. A semi-analytical model is developed, and the practical challenges and their implications with respect to performance are considered. A full size device is built and tested in an anechoic chamber and the semi-analytical model used in the design process is validated. Finally, the theory is extended to allow for losses in the metamaterial matching layer, and it is shown that improved performance may be achieved with a dual purpose layer which acts as an absorber whilst also providing the required impedance matching condition.