Evolution of spherical cavitation bubbles: parametric and closed-form solutions
arXiv:1508.01157 · doi:10.1063/1.4942237
Abstract
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
9 pages, 5 figures, 14 references, version accepted for publication at Phys. Fluids
References in corpus (5)
- Cavitation Bubble Dynamics inside Liquid Drops in Microgravity
- Analytical solutions for problems of bubble dynamics
- Analytical Approximations for the Collapse of an Empty Spherical Bubble
- Analytical solutions of the Rayleigh equation for empty and gas--filled bubble
- Integrable Abel equations and Vein's Abel equation