Model for the oscillations of the shell of a contrast agent, liquid and solid cases

Abstract

In the present theoretical formulation we study the oscillations of a solid bubble (shell), surrounding a perfect gas, under an ultrasound drive pressure. The model comprehends a Rayleigh-Plesset kind equation for the liquid radius that surrounds the shell together with an equation for the oscillating pressure in the liquid and the exact solution for an elastic solid that represents the shell. We state as main parameters b which represent the quasi steady state deformation of the solid, pX is the ratio of the ambient pressure and the elasticity modulus, and bA which represents the ratio of the driving pressure and the dynamic pressure. As main results we give the oscillations of the liquid in time and the pressure also. For the solid we obtained a weak oscillatory and irregular behavior which predicts the final collapse of the solid.