Sound propagation in dilute suspensions of rigid particles

Abstract

This paper considers sound propagation in suspensions of rigid particles, when both heat and momentum are exchanged between the particles and the host fluid. A theory is developed for small-amplitude, single-frequency oscillatory motions, on the assumption that the temperature of each particle is uniform. This theory applies to dilute suspensions that have arbitrary particle and fluid material densities, and yields the attenuation and the speed of sound in the suspension in terms of the particles’ velocity and temperature fluctuations. These quantities are not specified by the theory, but are available for some situations of interest which cover a very wide frequency range. In the particular case when the particle force and the heat transfer rate are not affected by the compressibility of the fluid, the particle’s velocity and temperature are given by closed-form results that are used to obtain explicit formulas for the attenuation and sound speed. For this case, the present theory reproduces all fundamental predictions available in the literature, and yields new basic results where none seem to exist. Results are also shown for the important case when the particle force includes compressibility effects in the fluid. These provide a unified description for the attenuation and the dispersions which covers the viscous and the scattering regions, as well as the transition region between them.