Analytical solution for the collapse motion of an empty hyper-spherical bubble in N dimensions

Abstract

The Rayleigh-Plesset equation including the surface tension for the collapse motion of an empty hyper-spherical bubble is considered. Firstly, the collapse time is derived. Secondly, a direct approach based on polynomial function is proposed and employed to construct the analytical solution for this case. It is shown that, when the surface tension is zero, the obtained analytical solution is equivalent to the known one but in a different form. In addition, we also discuss the influences of the relevant physical parameters on the collapse motion.