Cavitation of spherical bubbles: closed-form, parametric, and numerical solutions

We present an analysis of the Rayleigh-Plesset equation for a three dimensional vacuous bubble in water. When the effects of surface tension are neglected we find the radius and time of the evolution of the bubble as parametric closed-form solutions in terms of hypergeometric functions. A simple novel particular solution is obtained by integration of Rayleigh-Plesset equation and we also find the collapsing time of the bubble. By including capillarity we show the connection between the Rayleigh-Plesset equation and Abel's equation, and we present parametric rational Weierstrass periodic solutions for nonzero surface tension. In the same Abel approach, we also provide a discussion of the nonintegrable case of nonzero viscosity for which we perform a numerical integration