Bubble Pinch-Off in a Rotating Flow

Abstract

We create air bubbles at the tip of a “bathtub vortex” which reaches to a finite depth. The bathtub vortex is formed by letting water drain through a small hole at the bottom of a rotating cylindrical container. The tip of the needlelike surface dip is unstable at high rotation rates and releases bubbles which are carried down by the flow. Using high-speed imaging we find that the minimal neck radius of the unstable tip decreases in time as a power law with an exponent close to $1/3$. This exponent was found by Gordillo et al. [ Phys. Rev. Lett. 95, 194501 (2005)] to govern gas flow driven pinch-off, and indeed we find that the volume oscillations of the tip creates a considerable air flow through the neck. We argue that the Bernoulli pressure reduction caused by this air flow can become sufficient to overcome the centrifugal forces and cause the final pinch-off.