Effects of liquid compressibility on coupled radial and translational motion of a bubble

Abstract

In shock wave lithotripsy, explosive bubble growth is followed by a collapse phase during which bubble wall velocities can approach the speed of sound in the liquid. If the bubble is simultaneously in translation, the velocity of translation can also exhibit a very large spike during rebound. The velocity spike corresponds to conservation of translational momentum as the bubble radius, and thus entrained mass, become very small. It can then be important to include effects of compressibility on both the radial and translational motion. This presentation discusses corrections to the coupled equations for radial and translational motion when compressibility, and therefore acoustic radiation, are taken into account. For pure radial motion, compressibility introduces a radiation term proportional to the third time derivative of bubble volume, and inversely proportional to sound speed. For pure dipole motion, linear theory predicts a radiation force proportional to the second time derivative of the translational velocity, also inversely proportional to sound speed [Morse and Ingard, Theoretical Acoustics (1968)]. Numerical simulations will be presented that illustrate the magnitudes of compressibility effects on solutions of the coupled equations for radial and translational motion. [Work supported by the NSF Graduate Research Fellowship.]