Journal Article

Tear film dynamics on an eye-shaped domain I: pressure boundary conditions

Kara L. Maki, Richard J. Braun, William D. Henshaw and P. Ewen King-Smith

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 27, issue 3, pages 227-254
Published in print September 2010 | ISSN: 1477-8599
Published online January 2010 | e-ISSN: 1477-8602 | DOI: http://dx.doi.org/10.1093/imammb/dqp023
Tear film dynamics on an eye-shaped domain I: pressure boundary conditions

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We study the relaxation of a model for the human tear film after a blink on a stationary eye-shaped domain corresponding to a fully open eye using lubrication theory and explore the effects of viscosity, surface tension, gravity and boundary conditions that specify the pressure. The governing non-linear partial differential equation is solved on an overset grid by a method of lines using a finite-difference discretization in space and an adaptive second-order backward-difference formula solver in time. Our 2D simulations are calculated in the Overture computational framework. The computed flows show sensitivity to both our choices between two different pressure boundary conditions and the presence of gravity; this is particularly true around the boundary. The simulations recover features seen in 1D simulations and capture some experimental observations including hydraulic connectivity around the lid margins.

Keywords: lubrication theory; overset grid; tear film; thin film

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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