Theoretical modeling of a cavitating mooney-rivlin microshell, with multiple scale analysis

Abstract

In this paper we propose a mathematical model with tensorial analysis for a single cavitating microshell bubble immersed in a newtonian liquid, excited by an ultrasound field. We obtain a system of nonlinear differential equations Rayleigh-Plesset kind for a thin shell working as a Mooney Rivlin hyperelastic solid. Numerical solutions of the full equation are obtained, for periodic and nonperiodic oscillations, for different values of the elastic parameters. We also present a frequency analysis for the nonlinear behaviour of the system by obtaining an analytical solution with the method of Multiple Scale Analysis. All of these is carried out taking into account the values of the parameters used in the Contrast Agents phenomena.