Superfluid Drops: Dynamics of Pinch-Off and Sliding Motion

Abstract

We present high resolution and high speed (5 µs) photographs of ⁴He drops undergoing pinch-off and sliding down a cesiated inclined plane. When a fluid drop is stretched and pulled apart by gravity, a balance of surface tension and inertia resugts in a striking icicle-shaped column of fluid which connects the two separating parts. The narrowest point of the icicle is an example of a finite-time singularity in the equations of motion. The tip radius of the icicle L obeys a power law L∼τ ^2/3, where τ is the time before the moment of pinch-off. We have verified this for both superfluid and normal drops. Because of the boundary condition requiring zero velocity at a solid wall, sliding and rolling motion of drops on a substrate is a subtle issue even for conventional fluids. For example, calculations of the dissipation yields nonphysical infinities. We have analyzed video images of sliding superfluid drop motion and measured the acceleration of ⁴He droplets on a Cesium substrate.