The temperature and velocity of a particle suspended in an acoustic field are subject to fluctuations that may lag behind those of the surrounding fluid. A theory for acoustic attenuation and dispersion in an aerosol based on these particulate-relaxation processes is given. The close relationship between particulate relaxation and relaxation mechanisms due to lagging molecular or atomic internal degrees of freedom is displayed. The particulate-relaxation theory predicts attenuation and dispersion by small, heavy particles, in close agreement with existing, more-detailed theories, for values of ωτd, (ω is the circular acoustic frequency, τd is the dynamic relaxation time of the particle) smaller than and including order unity. Comparison with existing experimental data of attenuation and dispersion [J. W. Zink and L. P. Delsasso, J. Acoust. Soc. Am. 30, 765–771 (1958)] shows good agreement. However, the existence of a maximum attenuation per wavelength, when ωτd ≈ 1, that is predicted by the theory is not tested by the above experiments, which were conducted with ωτd > 1. Similarly, the maximum dispersion that occurs at the low-frequency limit was not tested in the previous experiments.

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.

An experimental study of the motion of small water droplets in both accelerating and decelerating conditions is presented. Droplets with diameters in the range 115-187μm were exposed to propagating N-waves having strengths smaller than 0.03. Droplet-displacement data were obtained by single-frame stroboscopic photography, at an equivalent framing rate of 4000 pictures per second. The data were fitted by means of best-fit polynomials in time, which were used to obtain drag coefficients in accelerating and decelerating flow conditions. In addition to providing drag data for impulsive-type motions, these data show that the unsteady drag follows two entirely distinct trends. In one, applicable to decelerating relative flows, the unsteady drag is always larger than the steady drag at the same Reynolds number. In the other, applicable to accelerating relative flows, the unsteady drag is always smaller than the corresponding steady value. These trends have not been previously known. They give some support to a mechanism recently proposed (see Temkin & Kim 1980) to explain departures of the drag coefficient for a sphere from its steady value; namely, the changes in size of the recirculating region behind the sphere, relative to its steady counterpart at the same Reynolds number.

Originally published in 2005, this book is an introduction to the physics of suspensions of bubbles, droplets, and solid particles in both gases and fluids. Rather than treating each combination separately, a unified approach is used that permits most particle-fluid combination types to be discussed together. To do this, the book first presents a detailed discussion of the basic particle motions that small particles can sustain, paying particular attention to translations and pulsations, and to the thermal effects that occur as a result of those motions. The book then introduces the reader to the dynamics and thermodynamics of suspensions, with acoustic motions providing the main focus in the latter part of the book. The important acoustic problems of attenuation and dispersion are discussed from several fundamental perspectives. The book concludes with applications of acoustic techniques to the characterization and modification of suspensions by means of acoustic waves.