Vibration and Nonlinear Resonance in the Break-up of an Underwater Bubble

TL;DR

This study combines high-speed imaging, nonlinear analysis, and simulations to investigate the complex dynamics of underwater bubble break-up, revealing how initial shape perturbations influence the pinch-off process and resulting shapes.

Contribution

It introduces a combined experimental, analytical, and numerical approach to understand nonlinear resonance effects in underwater bubble break-up.

Findings

Oscillations lead to shape distortions and coalescence-like pinch-off.

Constructive interference of shape modes causes coalescence-like break-up.

Destructive interference results in sharply curved bubble neck profiles.

Abstract

We use high-speed X-ray phase-contrast imaging, weakly nonlinear analysis and boundary integral simulations to characterize the final stage of underwater bubble break-up. The X-ray imaging study shows that an initial azimuthal perturbation to the shape of the bubble neck gives rise to oscillations that increasingly distort the cross-section shape. These oscillations terminate in a pinch-off where the bubble surface develops concave regions that contact similar to what occurs when two liquid drops coalesce. We also present a weakly nonlinear analysis that shows that this coalescence-like mode of pinch-off occurs when the initial shape oscillation interferes constructively with the higher harmonics it generates and thus reinforce each other's effects in bringing about bubble break-up. Finally we present numerical results that confirm the weakly nonlinear analysis scenario as well as provide insight into observed shape reversals. They demonstrate that when the oscillations interfere destructively, a qualitatively different mode of pinch-off results where the cross-section profile of the bubble neck develops sharply-curved regions.