Singularity Formation in Free Surface Flows

Several phenomena involving free-surface flows, such as a pinch-off of a pendant liquid drop, possess an uncommon beauty. To a physicist they are also appealing because their mathematical formulation is in many senses unique: it has to self-consistently describe the flow inside each of the fluids (water, air) as well as the motion of their interface. One peculiarity is due to a discontinuous change in the physical properties of the fluids at the interface, which shows up as a mathematical singularity in the equations of fluid motion. Of particular interest to us are flows, which involve changes in topology, such as in a pinch-off process. Such changes are usually associated with the appearance of an additionional singularity - in the curvature of the interface. Dominant force balance near the singularity implies that these phenomena should possess certain universal features. Theoretical understanding of this universality is of great fundamental importance. The theory finds applications in the design of ink-jet printer heads and fuel injectors as well as in microfluidics, fiber spinning, oil extraction, and water treatment.


Selective fluid withdrawal Drop pinch-off Electrostatic cones

(Photographs by Sid Nagel and Itai Cohen)


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