New models and measurements concerning sound attenuation in concentrated airborne suspensions

Abstract

In the inertial regime of frequency-radius space, irregularity and aggregation of particles can result in values of acoustic attenuation that are significantly different from those predicted by assuming separated smooth spherical particles. Data obtained previously from suspensions of alumina particles and olivine sand in air at audio frequencies, together with new data obtained at low ultrasonic frequencies in suspensions of glass beads and silica flour, are compared with predictions. It is shown that neither a coupled-phase theory modified to allow for nonspherical shapes nor effective radius theories are able to account for these data. Qian [Phys. Rev. E 53(3), 2304–2306 (1996)] has suggested that suspensions may be treated as fractal media and used the acoustic Reynolds number as the fractal dimension in modifying scattering theory. A new fractal modification of multiple scattering theory for acoustic attenuation is derived. The theory uses ωτv (ω is the angular acoustic frequency, τv is the dynamic relaxation time of the particles) as a fractal scale. Fitted values of fractal dimension obtained at a single frequency are found to enable fits with data at other frequencies. Moreover, the fractal approach is found to enable discrimination between the effects of particle irregularity and aggregation. [Work supported by EPSRC (UK).]