Experiments on bubble pinch-off

A bubble is slowly grown from a vertical nozzle until it becomes unstable and pinches off. We use ultra-high-speed video imaging, at frame-rates up to 1millionfps, to study the dynamics and shape of the pinch-off neck region. For bubbles in water (Bo ≃ 1.0) the radius of the neck reduces with a power law behavior R∼t^α, over more than 2 decades, with an exponent in the range α=0.57 ± 0.03, in good agreement with other available studies, but which is slightly larger than 1/2 predicted by Rayleigh-Plesset theory. The vertical curvature in the neck increases more slowly than the azimuthal curvature, making the neck profiles more slender as pinch-off is approached. Self-similar shapes are recovered by normalizing the axial coordinate by a separate length scale which follows a different power law, L_z∼t^γ, where γ=0.49 ± 0.03. Results for air, He, and SF₆ gas are identical, suggesting that the gas density plays a minimal role in the dynamics. The pinch-off in water leaves behind a tiny satellite bubble, around 5 uml;m in diameter and the flow-field inside the liquid is shown to be consistent with simple sink flow. The effects of liquid viscosity on the pinch-off speed and neck shapes, are also characterized. The speed starts to slow down at a viscosity of about 10 times that of water, which corresponds to Re_μ ≃ 2000. This also changes the power law, increasing the exponent to α ≃ 1 for viscosities above 70cP (Re_μ ≃ 40). For surrounding liquid of viscosity above 10cP, we observe just before pinch-off, that the neck is stretched into a thin filament of air, which then breaks into a stream of microbubbles. In some cases we observe a cascade of bubble sizes. While some of the details differ, our results are in overall agreement with those of Burton, Waldrep, and Taborek [Phys. Rev. Lett. 94, 184502 (2005)], except we do not observe the rupture of the air cylinder as it reduces to 50 μm size. For water we observe a continuous necking down to the pixel-resolution of our optical system, which at the largest frame-rates is ∼10 μm.