A modified Rayleigh–Plesset model for a non-spherically symmetric oscillating bubble with applications to boundary integral methods

In this article the analytical solution to the Rayleigh–Plesset equation for a spherically symmetric oscillating bubble is extended to apply to the much more general (non-spherically symmetric) bubble configuration. An equivalent bubble radius and an equivalent bubble wall velocity are introduced in order to do so. The influence of gravity, surface tension, nearby solid walls, vapor bubbles, bubbles filled with adiabatic or isothermal gas have been considered in the model. An interesting outcome is that the equivalent bubble wall velocity is no longer the time derivative of the equivalent bubble radius. This observation can possibly explain why in various numerical and experimental observations the oscillation time of a bubble changes when compared to that of a standalone bubble; near a solid surface it increases while it decreases when the bubble is placed near a free surface. The current developed theory can be further employed to ascertain the accuracy of a numerical scheme simulating bubble dynamics in an incompressible surrounding flow approximation. An often used numerical technique to simulate such bubble dynamics is the boundary integral method (BIM).