During the inertial collapse of a cavitation bubble, potential energy is converted into kinetic energy of the liquid drawn by the collapsing bubble. This kinetic energy concentrates into the bubble as internal energy and is eventually redistributed as the bubble rebounds. An important outcome of this process is the shock emitted during collapse. In the incompressible limit, the bubble dynamics and energy transfer during collapse are well understood and effectively governed by a single parameter, the driving pressure ratio. However, inertial collapse is characterized by high bubble-wall velocities and accelerations, and therefore compressibility effects become important when analyzing energy balance. The present article examines the role of compressibility on energy concentration and release during the inertial collapse of a spherical gas cavity from a theoretical standpoint. This work improves both the methods for and the understanding of this problem in several ways. First, a correction is made to the calculation of radiated energy due to compressibility effects, thus enabling more accurate predictions of energy redistribution at high driving pressures than existing methods. Second, closed-form expressions are provided for the energy and size of the bubble at collapse (i.e., at minimum volume) in terms of the parameters governing the problem, which take into account the effects of compressibility. Finally, we develop an analytical expression relating the shock pressure to the parameters governing the problem. Based on this analysis, we find that energy concentration during collapse obeys one of two scenarios: Up to a driving pressure ratio of approximately 100, $70–90\%$ of the initial energy is concentrated into the bubble at the instant of collapse, whereas beyond that pressure ratio, more than 60% of the initial energy is radiated, thus reducing the efficiency of the energy concentration process.

Close

PrevNext

View figure in article

• Cavitation
• Drops & bubbles
• Shock waves