PARTICLE IRREGULARITY AND AGGREGATION EFFECTS IN AIRBORNE SUSPENSIONS AT AUDIO- AND LOW ULTRASONIC FREQUENCIES

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 non-spherical shapes nor effective radius theories are able to account for these data. Qian [21] 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, τvis the dynamic relaxation time of the particles) as a fractal scale. It requires an empirical determination of the difference between the fractal dimension of the measured suspension and that of a hypothetical suspension of spheres with the same particle size distribution. However, values obtained at a single frequency also enable fits with data at other frequencies. The new fractal modification of scattering theory is found to enable better agreement with measured attenuation as a function of concentration for irregular particles than an effective radius model. Also, the fractal modification is able to predict the observed frequency dependence at a given concentration rather better than effective radius approaches. Moreover, the fractal approach is found to enable discrimination between the effects of particle irregularity and aggregation.