We present an analysis of the Rayleigh-Plesset equation for a three dimensional vacuous bubble in water. In the simplest case when the effects of surface tension are neglected, the known parametric solutions for the radius and time evolution of the bubble in terms of a hypergeometric function are briefly reviewed. By including the surface tension, we show the connection between the Rayleigh-Plesset equation and Abel’s equation, and obtain the parametric rational Weierstrass periodic solutions following the Abel route. In the same Abel approach, we also provide a discussion of the nonintegrable case of nonzero viscosity for which we perform a numerical integration.
Physics of Fluids
American Institute of Physics
Scholarly Commons Citation
Mancas, S., & Rosu, H. C. (2016). Evolution of Spherical Cavitation Bubbles: Parametric and Closed-Form Solutions. Physics of Fluids, 28(2). https://doi.org/10.1063/1.4942237
Dr. Mancas was on leave from Embry-Riddle Aeronautical University on a research fellowship at Hochschule München at the time this paper was published.