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

Abstract

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 $\mu \mathrm{m}$. 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.

accepted for publication at PRL

References in corpus (5)

• Coalescence of Liquid Drops
• Air entrainment through free-surface cusps
• Scaling at the selective withdrawal transition
• Fracture of a viscous liquid
• Scaling dependence on the fluid viscosity ratio in the selective withdrawal transition

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• Self-Similar Cusp Formation in Thin Liquid Films By Runaway Thermocapillary Forces
• Viscous Withdrawal of Miscible Liquid Layers
• Taylor-Culick retractions and the influence of the surroundings