Attenuation and Dispersion of Sound by Particulate-Relaxation Processes

TLDR

In acoustic fields, particle temperature and velocity can lag behind the surrounding fluid, linking particulate relaxation to internal molecular relaxation mechanisms. The study develops a theory of acoustic attenuation and dispersion in aerosols based on particulate‑relaxation processes. The theory models attenuation and dispersion by accounting for lagging particle temperature and velocity relative to the fluid. The theory accurately predicts attenuation and dispersion for small heavy particles and matches experimental data, but the predicted maximum attenuation at ωτd≈1 and maximum dispersion at low frequencies remain untested. Citation: J.

Abstract

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.