Modeling Acoustically Driven Microbubbles by Macroscopic Discrete-Mechanical Analogues

Abstract

The dynamics of continuous systems that exhibit circular or spherical symmetry like drops, bubbles or some macromolecules, under the influence of some external excitation, develop surface patters that are hard to predict in most practical situations. In the particular case of acoustically driven microbubbles (ultrasound contrast agent), the study of the behavior of the bubble shell requires complex modeling even for describe the most simple oscillation patterns. Furthermore, due to the smallness of the spatio-temporal scale of the problem, an experimental approach requires expensive hardware setup. Despite the complexity of the particular physical problem, the basic dynamical features of some continuous physical systems can be captured by simple models of coupled oscillators. In this work we consider an analogy between a shelled-gas bubble cavitating under the action of an acoustic field and a discrete mechanical system. Thus, we present a theoretical and experimental study of the spatial instabilities of a circular ring of coupled pendulums parametrically driven by a vertical harmonic force. The system is capable of wave propagation and exhibit nonlinearities and dispersion, so manifest rich dynamics: normal oscillation modes (breathing, dipole, quadrupole...) and localized patterns of different types (breathers and kinks) witch are predicted by finite-differences numerical solutions and observed experimentally. On the basis of this analogy, the oscillation patterns and localized modes observed experimentally in acoustically driven bubbles are interpreted and discussed.