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.
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Selective fluid withdrawal
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Drop pinch-off
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Electrostatic cones
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(Photographs by Sid Nagel and Itai Cohen)
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