Damage Potential of the Shock-Induced Collapse of a Gas Bubble

Numerical simulations are used to evaluate the damage potential of the shock-induced collapse of a pre-existing gas bubble near a rigid surface. In the context of shock wave lithotripsy, a medical procedure where focused shock waves are used to pulverize kidney stones, shock-induced bubble collapse represents a potential mechanism by which the shock energy directed at the stone may be amplified and concentrated. First the bubble dynamics of shock-induced collapse are discussed. As an indication of the damage potential, the wall pressure is considered. It is found that, for bubbles initially close to the wall, local pressures greater than 1 GPa are achieved. For larger stand-off distances, the wall pressure is inversely proportional to the location of bubble collapse. From this relationship, it is found that bubbles within a certain initial stand-off distance from the wall amplify the pressure of the incoming shock. Furthermore, the extent along the wall over which the pressure due to bubble collapse is higher than that of the pulse is estimated. In addition, the present computational fluid dynamics simulations are used as input into an elastic waves propagation code, in order to investigate the stresses generated within kidney stone in the context of shock wave lithotripsy. The present work shows that the shock-induced collapse of a gas bubble has potential not only for erosion along the stone surface, but also for structural damage within the stone due to internal wave reflection and interference.