Sink flow deforms the interface between a viscous liquid and air into a tip singularity

Details Sink flow deforms the interface between a viscous liquid and air into a tip singularity Sink flow deforms the interface between a viscous liquid and air into a tip singularity

2005-12-12

arxiv.org/abs/physics/0512095v1

Physics

Fluid Dynamics

accepted for publication at PRL

Scientific paper

10.1103/PhysRevLett.96.034501

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 $\rm{\mu m}$. The curvature at the tip is controlled by the distance $h$ between the tip and the sink. As a critical distance $h^{\star}$ is approached, the curvature diverges like $1/(h-h^{\star})^3$ and the tip becomes cone-shaped. As the distance to the sink is decreased further, the opening angle of the cone vanishes like $h^2$. No evidence for air entrainment was found, except when the tip was inside the orifice.

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