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Tear film dynamics on an eye-shaped domain. Part 2. Flux boundary conditions

Published online by Cambridge University Press:  18 March 2010

K. L. MAKI ,
R. J. BRAUN ,
P. UCCIFERRO ,
W. D. HENSHAW  and
P. E. KING-SMITH
K. L. MAKI
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, DE 19711, USA
R. J. BRAUN*
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, DE 19711, USA
P. UCCIFERRO
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, DE 19711, USA
W. D. HENSHAW
Affiliation:
Lawrence Livermore National Laboratory, Box 808, L-550, Livermore, CA 94551-0808, USA
P. E. KING-SMITH
Affiliation:
College of Optometry, The Ohio State University, Columbus, OH 43218, USA
*
†Email address for correspondence: [email protected]
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Abstract

We model the dynamics of the human tear film during relaxation (after a blink) using lubrication theory and explore the effects of viscosity, surface tension, gravity and boundary conditions that specify the flux of tear fluid into or out of the domain. The governing nonlinear partial differential equation is solved on an overset grid by a method of lines using finite differences in space and an adaptive second-order backward difference formula solver in time. Our simulations in a two-dimensional domain are computed in the Overture computational framework. The flow around the boundary is sensitive to both our choice of flux boundary condition and the presence of gravity. The simulations recover features seen in one-dimensional simulations and capture some experimental observations of tear film dynamics around the lid margins. In some instances, the influx from the lacrimal gland splits with some fluid going along the upper lid towards the nasal canthus and some travelling around the temporal canthus and then along the lower lid. Tear supply can also push through some parts of the black line near the eyelid margins.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 647: Dedicated to Professor S. H. Davis on his 70th birthday , 25 March 2010 , pp. 361 - 390
Copyright
Copyright © Cambridge University Press 2010

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References

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