Scaling at the selective withdrawal transition

Abstract

In the selective withdrawal experiment fluid is withdrawn through a tube with its tip suspended a distance S above an unperturbed two-fluid interface. At low withdrawal rates, Q, the interface forms a steady state hump and only the upper fluid is withdrawn. When Q is increased (or S decreased), the interface undergoes a transition so that the lower fluid is entrained with the upper one, forming a thin steady-state spout. Near this discontinuous transition the hump curvature becomes very large and displays power-law scaling behavior. This scaling is used to show that steady-state profiles for humps at different flow rates and tube heights can all be scaled onto a single similarity profile.

11 pages, 4 figures

Cited by in corpus (11)

• Free surface flows with large slopes: beyond lubrication theory
• Fracture of a viscous liquid
• Sink flow deforms the interface between a viscous liquid and air into a tip singularity
• Scaling dependence on the fluid viscosity ratio in the selective withdrawal transition
• Stretching and squeezing of sessile dielectric drops by the optical radiation pressure
• Self-Similar Cusp Formation in Thin Liquid Films By Runaway Thermocapillary Forces
• Viscous Withdrawal of Miscible Liquid Layers
• Opposed flow focusing: evidence of a second order jetting transition
• Self-similar dynamics of air film entrained by a solid disk in confined space: a simple prototype of topological transitions
• Liquid interfaces in viscous straining flows: Numerical studies of the selective withdrawal transition
• Taylor-Culick retractions and the influence of the surroundings