Radial oscillations of gas bubbles in viscoelastic materials

Most previous studies of acoustic cavitation in biological tissue have treated the material surrounding the bubble as a Newtonian fluid with sometimes increased viscosity. The present work describes the derivation of a generalized Rayleigh-Plesset equation for a gas bubble in a continuous viscoelastic material. Viscoelasticity is modeled to include either stress relaxation (Maxwell fluid) or aftereffect (Voigt fluid). Several cases are considered: (1) a bubble with a (a) viscous shell suspended in a Newtonian fluid, (b) viscoelastic shell suspended in a Newtonian fluid, (c) viscoelastic shell suspended in a viscoelastic fluid; and (2) a “clean” bubble suspended in a (a) viscous or (b) viscoelastic fluid. In general, the effect of viscoelasticity is to decrease the resonance frequency and increase the threshold for transient cavitation. Preliminary measurements of cavitation thresholds in a liquid seeded with Albunex® stabilized microbubbles are presented and interpreted in light of the theory. [Work supported by NIH.]