Dynamics of bubbles near a rigid surface subjected to a lithotripter shock wave. Part 2. Reflected shock intensifies non-spherical cavitation collapse

Abstract

In this paper we use the boundary integral method to model the non-spherical collapse of bubbles excited by lithotripter shock waves near a rigid boundary. The waves we consider are representative of those developed by shock wave lithotripsy or shock wave therapy devices, and the rigid boundaries we consider are representative of kidney stones and reflective bony tissue. This study differs from previous studies in that we account for the reflection of the incident wave and also the asymmetry of the collapse caused by the presence of the rigid surface. The presence of the boundary causes interference between reflected and incident waves. Quantities such as kinetic energy, Kelvin impulse and centroid translation are calculated in order to illuminate the physics of the collapse process. The main finding is that the dynamics of the bubble collapse depend strongly on the distance of the bubble relative to the wall when reflection is taken into account, but much less so when reflection is omitted from the model. The reflection enhances the expansion and subsequent collapse of bubbles located near the boundary owing to constructive interference between incident and reflected waves; however, further from the boundary, the dynamics of collapse are suppressed owing to destructive interference of these two waves. This result holds regardless of the initial radius of the bubble or its initial state at the time of impact with the lithotripter shock wave. Also, the work done by the lithotripter shock wave on the bubble is shown to predict strongly the maximum bubble volume regardless of the standoff distance and the presence or absence of reflection; furthermore, allowing for non-sphericity, these predictions match almost exactly those of a previously developed spherical model.