Pressure Field Generated by Nonspherical Bubble Collapse

Abstract

The method of matched asymptotic expansions is used to investigate the behavior of a collapsing bubble near a solid wall. Cases are studied in which the ratio ε between the initial spherical bubble radius and its distance from the wall is small. Expansions in powers of ε lead to a simple system of differential equations which is solved numerically. The bubble shape, the velocity potential and the pressure field are determined as functions of time. The deformation of the bubble is a singular perturbation of the pressure field around it. An increase in the value of ε augments the pressure on the solid wall by orders of magnitude. The influence of surface tension and the proximity of the wall, gas content and its law of compression, are investigated. The results are compared to previous investigations. One advantage of the method employed is the fact that it leads to a numerical solution which costs very little computer time. In addition, it can be extended very easily to more complex cases such as multibubble configurations or to walls coated with elastomeric coatings.