Evolution of spherical cavitation bubbles: parametric and closed-form solutions
Abstract
The study connects the Rayleigh-Plesset equation to Abel's equation to derive periodic Weierstrass solutions for bubbles with surface tension and numerically treats the nonintegrable viscous case.
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
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