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W. G. Pritchard Lab Seminar: 3:30-4:30 PM, 104 McAllister Building
**Monday February 16, 2004**
Mathematics and fluid materials: from Euler to motor oil
Andrew Belmonte
W. G. Pritchard Laboratories
Department of Mathematics
Penn State University
Abstract:
The development of mathematics and the experimental observation
of fluid flow have had a long and intertwined history together.
While Euler produced the first differential equation for a fluid,
d'Alembert's paradox indicated that a certain material effect was
absent: the viscous stress. However, even the Navier-Stokes equation
is not adequate to describe every fluid, particularly those in which
a complex microstructure, such as a long-chain polymer molecule,
produces an elastic stress component. I will present experimental
observations of the hydrodynamic flow of a fluid comprised of long
surfactant aggregates in water, known as a "wormlike micellar
fluid". Our discovery of several new instabilities, from jumping
bubbles and spheres to ruptured and blistered filaments, leads to
mathematical challenges in treating the coupling of flow with
the micellar aggregation kinetics.
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