Paper detail

Azimuthal Asymmetries and Vibrational Modes in Bubble Pinch-off

The pressure-driven inertial collapse of a cylindrical void in an inviscid liquid is an integrable, Hamiltonian system that forms a finite-time singularity as the radius of the void collapses to zero. Here it is shown that when the natural cylindrical symmetry of the void is perturbed azimuthally, the perturbation modes neither grow nor decay, but instead cause constant amplitude vibrations about the leading-order symmetric collapse. Though the amplitudes are frozen in time, they grow relative to the mean radius which is collapsing to zero, eventually overtaking the leading-order symmetric implosion. Including weak viscous dissipation destroys the integrability of the underlying symmetric implosion, and the effect on the stability spectrum is that short-wavelength disturbances are now erased as the implosion proceeds. Introducing a weak rotational flow component to the symmetric implosion dynamics causes the vibrating shapes to spin as the mean radius collapses. The above theoretical scenario is compared to a closely related experimental realization of void implosion: the disconnection of an air bubble from an underwater nozzle. There, the thin neck connecting the bubble to the nozzle implodes primarily radially inward and disconnects. Recent experiments were able to induce vibrations of the neck shape by releasing the bubble from a slot-shaped nozzle. The frequency and amplitude of the observed vibrations are consistent with the theoretical prediction once surface tension effects are taken into account.