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Nematic liquid crystals in thin geometries

Tuesday, December 8, 2009 - 3:20pm - 4:00pm
EE/CS 3-180
Linda Cummings (New Jersey Institute of Technology)
Keywords: Nematic Liquid Crystal, non-Newtonian, lubrication theory, asymptotics, electric field effects, interfacial instability,
free boundary problem, LCD

Abstract: Nematic liquid crystals are materials intermediate between the liquid and
solid states. They are typically composed of long, rod-like molecules,
which have a tendency to align with their neighbors, imparting a short-range
(but no long-range) orientational order - although nematics flow, like
conventional liquids, they also retain some elastic character. This gives rise
to complex behavior that does not arise in Newtonian liquids. Moreover, their
response to an applied electric field gives
nematics wide application in the electronic display industry.

We consider mathematical models for three different problems.
Two are classical fluid-dynamical setups: a small droplet spreading
on a flat substrate; and a two-dimensional liquid bridge (or liquid sheet)
under tension. These are free boundary problems, and the thin geometry in
each case enables the use of lubrication analysis to systematically derive
reduced mathematical models governing the free surface evolution. The
spreading drop analysis leads to variants of the classical 4th order thin
film equation, which can exhibit instability in certain regimes. The liquid
bridge problem leads to new versions of the so-called Trouton model
for Newtonian viscous sheets.

The third problem arises in
the display industry, and is concerned with manufacturing a bistable
display device, that can exhibit two optically-distinct configurations in the
absence of an electric field. Such a device has the potential for considerably
reducing the power demands of a display, with accompanying benefits for
battery lifetime and device portability.
MSC Code: 
76A05