Sound attenuation by small spheroidal particles due to visco-inertial coupling

Abstract

The sound attenuation at ultrasonic frequencies caused by small spheroidal particles in a fluid is examined with regard to the size parameters that determine the shape of the attenuation spectrum. Our investigations are based on a coupled phase model for spheroids with arbitrary orientation, thus facilitating the calculation of average attenuation for a given orientation distribution. Since the model just considers the visco-inertial coupling, its applicability is restricted to small solid particles with high density contrast. The calculated attenuation spectra of mono-sized, randomly aligned spheroidal particles are compared with the attenuation spectra of mono-sized spheres. When the latter approximate the former to a reasonable degree the size of the spheres is called attenuation equivalent diameter. It is shown that the concept of attenuation equivalent diameter can be applied only to slightly elongated prolates. Oblates and very stretched prolates yield considerably broader attenuation spectra than mono-sized spheres. While for oblates and for slightly elongated prolates the characteristic frequency of the attenuation spectrum is determined by the volume specific surface, no such attenuation determining size parameter could be identified for very stretched prolates.