Speaker:Quan Deng, University of Delaware
Title: Tear film dynamics in a moving domain

Abstract: The ocular tear film is critical for good vision and eye health. We consider model problems for the pre-corneal tear film over multiple blink cycles with evaporation and with heat transfer from a model domain for the eye. The nonlinear PDE for film thickness is coupled with heat transfer under the film; simultaneous solution on a moving domain is via a spectral method. Periodicity in the film and temperature dynamics is explored. The numerical results reveal a similarity to quantitative in vivo observations of the film dynamics and the surface temperature of the film. We also consider a model problem for the tear film on a moving two-dimensional rectangular domain. The problem considers a thin Newtonian layer covered by an insoluble surfactant representing the effect of polar lipids. The goal is to explore the Marangoni effect exerted by surfactant and quantify some aspects of lipid patterns observed experimentally.

Time: Friday, December 7, 2012, 1:30-2:30 p.m.

Place: Planetary Hall (formerly S & T I), Room 242

Department of Mathematical Sciences
George Mason University
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Fairfax, VA 22030-4444
http://math.gmu.edu/
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