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

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.
Comment: 30 pages, 16 figures, submitted to Journal of Fluid Mechanics