Attenuation and dispersion of sound in dilute suspensions of spherical particles

This paper considers sound propagation in dilute suspensions of constant-mass particles that can translate and pulsate under the effects of a small amplitude sound wave. A new theory for sound attenuation and dispersion is developed on the basis of the changes of the suspension's compressibility produced by the relative motions between host fluid and particles. The approach, used earlier to treat propagation in rigid-particle suspensions, decouples the propagation problem from the more difficult problem of obtaining accurate descriptions for the fluid-particle interactions. In this work the role of the pulsational motion is included in the theoretical framework. The resulting theory is thus applicable to aerosols, bubbly liquids, emulsions, and hydrosols composed of elastic particles, and includes, as a special limit, rigid-particle suspensions. The results are expressed in terms of three complex quantities that describe, respectively, the particles' translational velocity, temperature, and pressure, relative to their counterparts in the fluid. Theoretical results for these quantities, applicable in wide frequency ranges, are available from previous studies [Temkin and Leung, J. Sound Vib. 49, 75-92 (1976), Temkin, J. Fluid. Mech. 380, 1-38 (1999)]. Together with the compressibility theory presented here, they provide a more general description of propagation in dilute suspensions than presently available. In the case of aerosols and hydrosols, the theory produces known results for the attenuation and the sound speed. For bubbly liquids and emulsions the new results presented here differ from those available in the literature. The differences are traced to the neglect in the existing theories of the acoustic pressure disturbance produced by the pulsations of the particles.