Collective nonlinear behavior of interacting polydisperse microbubble clusters

Abstract

Exploiting the full potential of MBs for applications requires a good understanding of their complex dynamics. Improved understanding of MB oscillations can lead to further enhancement in optimizing their efficacy in many applications and also invent new ones. Previous studies have predominantly addressed the behavior of a single isolated MB in an infinite liquid domain, whereas most applications employ MBs in clusters. Oscillating MBs have been shown to generate secondary pressure waves that modify the dynamics of the MBs in their proximity. A modified Keller-Miksis equation is used to account for inter-bubble interactions. The oscillatory dynamics of each MB within clusters was computed by numerically solving the resulting system of coupled nonlinear second order differential equations. Frequency response analysis and bifurcation diagrams were employed to track the dynamics of interacting MBs. Here we investigate the dynamics of polydisperse MB clusters over a wide range of acoustic and geometric parameters. An emergent collective behavior within bubble clusters was observed whereby individual dynamics of smaller bubbles were suppressed resulting in a collective behavior dominated by the dynamics of the largest MB within the cluster. The emergent dynamics of smaller MBs within bubble clusters can be characterized by constructive and destructive inter-bubble interactions. In constructive interactions, the radial oscillations of smaller bubbles matched those of the largest MB and their oscillations are amplified. In destructive interactions, the oscillations of smaller bubbles are suppressed so that their oscillations match those of the largest MB. Furthermore, a special case of constructive interactions is presented where dominant MB (largest) can force smaller MBs into period doubling and subharmonic oscillations.

Nonlinear dynamics and bifurcation structure of ultrasonically excited lipid coated microbubbles

“…Effects of coupling, bubble size, and spatial arrangement have been studied in [102] and effects of boundary proximity on the dynamics of a bubble cluster is investigated in [103] . We have shown in [105] that the bubble cluster may exhibit collective behavior dominated by the response of the larger bubbles. Future studies need to look into the effect of the interaction of lipid coated MBs and potential collective behavior of the lipid coated bubbles at lower excitation pressure amplitudes.…”

“…Bubble–bubble interaction should also be considered as in applications bubbles exist in poly-disperse clouds. The bifurcation structure of the interacting bubbles has been studied extensively in [99] , [100] , [101] , [102] , [103] , [104] , [105] . These studies have shown that the bubble–bubble interaction significantly influences the dynamics of each bubble.…”

Investigation of the 1/2 order subharmonic emissions of the period-2 oscillations of an ultrasonically excited bubble

“…However, non-spherical oscillations, especially in larger bubbles can significantly influence the bubble behavior [4,63,64,65] and threshold of SH emissions [31,32]. Bubble-bubble interaction is another important factor that changes the threshold of SH emissions in mono-disperse bubble clouds [40] as well as poly-disperse bubble clouds [66,67,68]. Interaction with a boundary also influences the pressure threshold of SH emissions [68].…”

Nonlinear dynamics and acoustic emissions of interacting cavitation bubbles in viscoelastic tissues

“…to describe the cavitation bubble dynamics in soft tissues and to analyze the resultant acoustic emissions, but only focusing on a single bubble for simplicity [24] , [25] , [26] , [27] . For the bubble–bubble interactions, many researches have been focused on the translational motions or radial pulsations of bubbles in Newtonian fluids [28] , [29] , [30] , [31] , [32] , [33] , [34] , [35] , [36] , [37] , [38] , [39] , [40] . It has demonstrated that the bubble–bubble interactions make them behave very differently from individual bubbles.…”