Model for interaction of bubbles in a cloud near a rigid surface

Abstract

Bubble clouds produced during lithotripsy undergo complicated motions including bubble interactions that may inhibit kidney stone comminution. Our study of bubble interactions is motivated by high-speed photographs reported by Pishchalnikov et al. [J. Acoust. Soc. Am. 114, 2386 (2003)]. In the work reported here, we simulated the observed bubble motion with a model based on the equations derived by Zabolotskaya [Sov. Phys. Acoust. 30, 365 (1984)]. The equations for interaction of two bubbles were generalized and solved numerically for a cluster of n bubbles near a rigid boundary, which represents the stone. The initial spatial distribution of bubbles in three dimensions was assumed to be random. When a short negative pressure pulse was applied, the simulated bubbles grew in size. When two bubbles touched each other, they were merged into a single bubble that conserved mass of the gas. Results are presented in selected planes intersecting the bubble cloud for different instants of time. Bubble interaction was found to reduce the maximum sizes to which the bubbles grow. The bubbles near the rigid boundary are constrained by neighboring bubbles and grow less rapidly, and to smaller sizes, than other bubbles. Interactions within the cloud thus suppress bubble growth and cavitation. [Work supported by ARL:UT IR&D.]