Bifurcation structure of the ultrasonically excited microbubbles undergoing buckling and rupture

Abstract

Bubbles exposed to ultrasound are long known to exhibit highly nonlinear and chaotic dynamics. Bubbles stabilized by a shell material (MBs) are widely used as contrast agents in diagnostic ultrasound. However, the nonlinear behavior of the shell significantly increases the complexity of the dynamics. In order to realize the full potential of the MBs, better understanding of the MB behavior is necessary. In this study, the bifurcation structure of the MB with nonlinear shell behavior is investigated for the first time. The Marmottant model was numerically solved, and the bifurcation diagrams of the radial oscillations of the MB were plotted versus the control parameters (e.g., buckling radius). In agreement with recent experimental observations, results predict the generation of subharmonics at very low acoustic pressures. In addition, the numerical simulations predict the generation of higher order subharmonics (e.g., period 3) at very low acoustic pressures (<300 kPa and 25 MHz), which contradicts the predictions by free bubble and viscoelastic shell MB models. Results revealed the strong influence of the buckling and rupture radius on the order of the subharmonics. The numerical results were verified by experimental observations of higher order subharmonics in the oscillations of Definity at 25 and 55 MHz.