Shock wave emission upon spherical bubble collapse during cavitation-induced megasonic surface cleaning

When a gas bubble in a liquid interacts with an acoustic wave near a solid surface, the bubble first expands and then collapses. In this paper, a mathematical framework combining the Gilmore model and the method of characteristics is presented to model the shock wave emitted at the end of the bubble collapse. It allows to describe the liquid velocity at the shock front as a function of the radial distance to the bubble center in the case of spherical bubble collapse. Numerical calculations of the liquid velocity at the shock front have shown that this velocity increases with the acoustic amplitude and goes through a maximum as a function of the initial bubble radius. Calculations for different gas state equations inside the bubble show that the Van der Waals law predicts a slightly higher liquid velocity at the shock front than when considering a perfect gas law. Finally, decreasing the value of the surface tension at the bubble/liquid interface results in an increase of the liquid velocity at the shock front. Our calculations indicate that the strength of the shock waves emitted upon spherical bubble collapse can cause delamination of typical device structures used in microelectronics.