In this paper, we present a mathematical model describing the effect of polar lipids, excreted by glands in the eyelid and present on the surface of the tear film, on the evolution of a pre-corneal tear film. We aim to explain the interesting experimentally observed phenomenon that the tear film continues to move upward even after the upper eyelid has become stationary. The polar lipid is an insoluble surface species that locally alters the surface tension of the tear film. In the lubrication limit, the model reduces to two coupled non-linear partial differential equations for the film thickness and the concentration of lipid. We solve the system numerically and observe that increasing the concentration of the lipid increases the flow of liquid up the eye. We further exploit the size of the parameters in the problem to explain the initial evolution of the system. © 2010 Society for Mathematical Biology.
|Original language||English (US)|
|Number of pages||31|
|Journal||Bulletin of Mathematical Biology|
|State||Published - Jun 17 2010|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: The authors are particularly grateful for extensive dialogue with Prof. Colin Please,useful comments by Dr. Jim Oliver, and for the support and insight provided by their experimental collab-orators, Prof. Anthony Bron and Dr. John Tiffany. This work was partly funded by an EPSRC-funded MScstudentship, is also partially based on work supported by award number KUK-C1-013-04 made by KingAbdullah University of Science and Technology and by NSF DMS CAREER grant 0239125.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.