Viscous attenuation of sound in dilute suspensions of rigid particles

Abstract

This work considers the attenuation of sound for plane waves traveling in isothermal suspensions of rigid particles, in the limit of small volume concentrations. Two new results for the viscous attenuation coefficient are presented. The first is based on the complete force equation for a sphere in an oscillating, incompressible fluid, and leads to a low-frequency attenuation which differs from existing results, except when the fluid-particle density ratio is small, as is the case in aerosols. The second result is based on an earlier study [S. Temkin and C. M. Leung, J. Sound Vib. 49, 75–92 (1976)] which considered the motion of a sphere in a sound wave in a viscous fluid. This second result includes compressibility effects and merges with the first at low frequencies and with the equivalent result due to scattering alone at high frequencies.