The effects of coupling and bubble size on the dynamical-systems behaviour of a small cluster of microbubbles

Abstract

This study endeavours to apply a theoretical model for predicting the dynamics of a bubble cluster of various sizes, within which each bubble may assume different initial conditions from other bubbles in the cluster. The resulting system of coupled Keller–Miksis–Parlitz equations are solved numerically, and the effects of coupling and bubble size on bubble cluster dynamics are examined for a given set of ultrasound parameters. It has been found that the effects of coupling are significant, and a bubble cluster's bifurcation characteristics and route to chaos can be altered by inter-bubble interactions. This gives rise to the possibility of suppressing the chaotic oscillations of microbubbles by varying bubble cluster size. Small equilibrium radii bubbles have little influence on the dynamics of neighbouring bubbles in a cluster via coupling. Furthermore, a bubble system consisting of smaller-sized bubbles transitions from order to chaos at lower driving pressure amplitudes.