Dynamics of finite-size air filaments in a static liquid

Abstract

This study undertakes a numerical investigation of the dynamics of a finite-size air filament surrounded by a denser fluid medium with a range of viscosity. The two edges of the filament retract due to its surface tension effects. It is shown that if the aspect ratio is small, the filament recoils in a single bubble while for large aspect ratios, the filament ruptures at its two ends. Between these two limits, the filament can escape from pinch-off through the reopening of the neck and/or breakup in the middle region. The air filament pinch-off is accompanied by the formation of a thin air thread, which subsequently breaks up into microbubbles. Viscous effects of the external fluid do not show a significant impact on the fate of large or small aspect ratio filaments but instead control the shape of the bulge and the neck region close to breakup. Before breakup, the bulge adopts a prolate shape for Ohnesorge numbers smaller than 0.01, while an oblate shape is obtained for Ohnesorge numbers larger than 1. A spherical shape is obtained between these two limits. For small Ohnesorge numbers, the neck region exhibits a reflection symmetry perpendicular to the filament axis while for large Ohnesorge numbers, a thread of air forms and connects the bulge to the filament. The radius of the neck is shown to decrease as a power-law function of the time before breakup with the exponent of 0.5 for small Ohnesorge numbers and 1 for large Ohnesorge numbers.