A single oscillating bubble in liquids with high Mach number.

The oscillation characteristics of a single bubble and its induced radiation pressure and the dissipated power are essential for a wide range of applications. For bubble oscillations with high Mach number, the influence of the liquid compressibility is significantly strong and should be fully considered. In the present paper, the bubble wall motion equation with the second-order Mach number is employed for investigating a free oscillating bubble in the liquid with numerical and experimental verifications. For the purpose of comparisons, the revised Keller-Miksis equation up to the first-order Mach number is solved with the same conditions (e.g. the initial conditions and the ambient pressure). Through our simulations, comparing with the predictions by the first-order equation, we find that: (1) The bubble radius, the bubble wall radial velocity and the bubble wall radial acceleration predicted by the second-order equation with high Mach number are significantly different respectively, and the dimensionless differences increase with the increase of the Mach number. (2) The valid prediction range of the second-order equation is much larger. (3) The dissipated power predicted by the second-order equation with high Mach number is smaller.