Seminars & Events

Computations In Science Seminar
"Numerical Analysis of Tip Singularities in Viscous Flow"

DATE: September 5, 2007
TIME: 12:30 p.m.
SPEAKER: Jens Eggers
LOCATION: KPTC 206, University of Chicago

Description:
When a bubble (or drop) is placed in a strong viscous flow (e.g. a shear flow), it develops very sharp tips at its ends. Similarly sharp structures occur when a viscous fluid is sucked away from its interface with the ambient air (selective withdrawal). We have constructed a code to solve for stationary solutions of the flow equations for arbitrary viscosity ratios, both for the drop and the selective withdrawal geometry. The code resolves tip curvatures of more than $108$ times the bubble radius. We compare the shape and stability of drops to an earlier theory by Taylor (1964). We then focus on the highly curved tip region, not considered by Taylor. We find that the shape near the tip is universal, i.e. independent of the driving flow and of the geometry of the interface. A similar statement applies to the stability of solutions, which is controlled by the
viscosity ratio. This leaves open major questions as to the proper interpretation of recent experiments in the selective withdrawal geometry.

More Information:
Discussion over bag-lunch at 12:15 p.m.
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