Variational Formulation and Numerical Simulation of Stochastic Rayleigh-Plesset Equation

Abstract

Cavitation is a formation of bubbles due to the phase transition from liquid to gas, which occurs under the condition that the pressure of the liquid falls to below the vapor pressure. It is known that a single bubble in an ultrasound field shows unsteady motions repeating the process of growth and collapse, which can be described by the Rayleigh-Plesset equation. In our previous experimental observations, the dynamics of such a single bubble in an ultrasound field includes some noises which are originated from the microscopic structures. In this study, we show the variational formulation of the stochastic Rayleigh–Plesset equation with a Wiener process. Finally, we perform our numerical simulation based on our model to show the reproducibility of fluctuations in bubble behaviors.