Valid Regions of Formulas of Sound Speed in Bubbly Liquids**Supported by the National Natural Science Foundation of China under Grant No 51506051, the National Basic Research Program of China under Grant No 2015CB251503, and the Fundamental Research Funds for the Central Universities under Grant No JB2015RCY04.

Abstract

There are numerous formulae relating to the predictions of sound wave in the cavitating and bubbly flows. However, the valid regions of those formulae are rather unclear from the view point of physics. In this work, the validity of the existing formulae is discussed in terms of three regions by employing the analysis of three typical lengths involved (viscous length, thermal diffusion length and bubble radius). In our discussions, viscosity and thermal diffusion are both considered together with the effects of relative motion between bubbles and liquids. The importance of relative motion and thermal diffusion are quantitatively discussed in a wide range of parameter zones (including bubble radius and acoustic frequency). The results show that for large bubbles, the effects of relative motion will be prominent in a wide region.