# On the collective behavior of interacting polydisperse microbubbles

## TL;DR

This study investigates the complex collective oscillatory behavior of polydisperse microbubble clusters, revealing how interactions lead to suppression or amplification of smaller bubbles' dynamics, with implications for optimizing microbubble applications.

## Contribution

It introduces a modified Keller-Miksis model for polydisperse microbubbles and uncovers emergent collective behaviors driven by inter-bubble interactions in clusters.

## Key findings

- Smaller bubbles' dynamics are suppressed or amplified by larger bubbles.
- Emergent collective behavior is dominated by the largest microbubble.
- Constructive interactions can induce period doubling and subharmonic oscillations.

## 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.