Theoretical Investigation of Spherical Bubble Dynamics in High Mach Number Regimes

Abstract

The compressibility of fluids has a profound influence on oscillating bubble dynamics, as characterized by the Mach number. However, current theoretical frameworks for bubbles, whether at the first or second order of the Mach number, are primarily confined to scenarios characterized by weak compressibility. Thus, a critical need to elucidate the precise range of applicability for both first- and second-order bubble theories arises. Herein, we investigate the suitability and constraints of bubble theories with different orders through a comparative analysis involving experimental data and numerical simulations. The focal point of our investigation encompasses theories such as the Rayleigh–Plesset, Keller, Herring, and second-order bubble equations. Furthermore, the impact of parameters inherent in the second-order equations is examined. For spherical oscillating bubble dynamics in a free field, our findings reveal that the first- and second-order bubble theories are applicable when Ma⩽0.3 and 0.4, respectively. For a single sonoluminescence bubble, we define an instantaneous Mach number, Ma _i. The second-order theory shows abnormal sensibility when Ma _i is high, which is negligible when Ma _i⩽0.4. The results of this study can serve as a valuable reference for studying compressible bubble dynamics.

Keywords

Bubble dynamics / Spherical bubble / Cavitation / Compressibility / Mach number