Before the Dark Ages of dry eye in the nineties and the Age of Restasis in the noughties, some of the best dry eye science... like Dr. Holly's in the eighties... was more inclined to work in that direction.
Tear film dynamics on an eye-shaped domain I: pressure boundary conditions.
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.
Math Med Biol. 2010 Sep;27(3):227-54. Epub 2010 Jan 11.
Maki KL, Braun RJ, Henshaw WD, King-Smith PE.
Department of Mathematical Sciences, University of Delaware, Newark, DE 19711, USA.