Breakup of Air Bubbles in Water: Memory and Breakdown of Cylindrical Symmetry

Using high-speed video, we have studied air bubbles detaching from an underwater nozzle. As a bubble distorts, it forms a thin neck which develops a singular shape as it pinches off. As in other singularities, the minimum neck radius scales with the time until the breakup. However, because the air-water interfacial tension does not drive the breakup, even small initial cylindrical asymmetries are preserved throughout the collapse. This novel, nonuniversal singularity retains a memory of the nozzle shape, size, and tilt angle. In the last stages, the air appears to tear instead of pinch.

Figure 1

Pinch-off of an air bubble from a level underwater, circular nozzle with radius $R_N=4.1\mathrm{mm}$. (a) The bubble appears dark, except for bright optical artifacts. (b) A magnified sequence of pinch-off. In the last frame, the single $\sim 5\mu \mathrm{m}$ satellite bubble is circled. $\Delta t$ gives the time between frames.

Figure 2

Scaling of $h_{\min }$ versus $\tau$ for bubbles released quasistatically in water from circular nozzles of $R_N=1.5\mathrm{mm}$ (open circles) and 4.1 mm (solid circles). The Reynolds numbers in water at the beginning of detachment are approximately 0.6 and 4, respectively. The solid lines show power-law fits with exponent ${\alpha }_h=0.56$, and the dashed lines show fits with logarithmic corrections [14, 24]. Data are taken from multiple pinch-offs, and only data for $\tau \le 230\mu \mathrm{s}$ are used for fitting. Inset: For the tilted-nozzle image sequences shown in Fig. 3a, the radial size of the neck scales differently in the front ($h_{\mathrm{front}}$) and side ($h_{\mathrm{side}}$) directions.

Figure 3

Front and side views of pinch-off from an $R_N=4.1\mathrm{mm}$ nozzle tilted by 2°. The nozzle’s tilt is indicated in the bottom-left frame; in the front images, it is tilted away from the camera. Front and side images are from separate sequences but were selected to match length scales closely. (a) The neck is broadened before the breakup, resembling a crimped and bent double cone. A pair of satellite bubbles $\sim 15\mu \mathrm{m}$ in diameter is produced. Afterward, the tip of each interface is bifurcated. (b) In these $2\mu \mathrm{s}$ exposures, the final form of the neck is captured along with the initial positions of the satellite bubbles. The neck reaches zero thickness while it is still $\sim 20\mu \mathrm{m}$ wide, resulting in what appears to be a rupture instead of a smooth, symmetric pinch-off.

Figure 4

Pinch-off of a burst of air from a slot-shaped nozzle, displaying strong cylindrical asymmetry. (a) For slower bursts, the neck is broadened with a scalloped profile. In a series of discrete events, it tears iteratively from one or both sides. (b) For faster bursts, the neck is more ribbonlike. The ribbon thins until coalescence is initiated, creating a hole in the center of the neck. The remaining two columns of air quickly break. Each of the topological transitions creates one or more satellite bubbles. (c) Under the conditions for (b), we also see off-center tearing that combines aspects of (a) and (b).