Sink Flow Deforms the Interface Between a Viscous Liquid and Air into a Tip Singularity

In our experiment, an interface between a viscous liquid and air is deformed by a sink flow of constant flow rate to form a sharp tip. Using a microscope, the interface shape is recorded down to a tip size of 1 µm. The curvature at the tip is controlled by the distance h between the tip and the sink. As a critical distance h^* is approached, the curvature diverges like 1/(h-h^*)³ and the tip becomes cone shaped. As the distance to the sink is decreased further, the opening angle of the cone vanishes like h². No evidence for air entrainment was found, except when the tip was inside the orifice.

©2006 The American Physical Society