Superfluid drops: Dynamics of pinch-off and sliding motion

We present high resolution and high speed (5 mus) photographs of He-4 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 results 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 similar to tau(2/3), where tau 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 He-4 droplets on a Cesium substrate.