Linear analysis of sound velocity and attenuation in bubbly liquids

Owing to a dispersion effect induced by bubble oscillations, the change of phase velocity and attenuation of waves in bubbly liquids is important. Based on a set of volumetric averaged equations in a two-fluid model with bubble dynamics equation and temperature gradient models, we theoretically investigate linear propagation of pressure (or ultrasonic) waves in mono- and poly-disperse bubbly liquids. By incorporating the dissipation effects, the stop band (i.e., frequency range where the waves cannot propagate) appears a moderate high frequency region in a linear dispersion relation. From the comparison of sound velocity and attenuation with previous experimental data, the effect of acoustic radiation and thermal conduction is discussed. We found that, when using a two-fluid model, even if dissipation effects are considered, the inconvenience of infinite divergence of wave numbers at resonant frequency cannot be solved. However, based on the classical dispersion relation, we discuss how to solve this problem. Furthermore, thermal conduction and acoustic radiation should be appropriately set up to accurately predict the sound velocity and attenuation except in the high-frequency region, the sound velocity in the resonant frequency region, and the attenuation in the high-frequency region.