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Bulletin of Mathematical Biology

, Volume 73, Issue 6, pp 1171–1201 | Cite as

The Effect of Polar Lipids on Tear Film Dynamics

  • E. Aydemir
  • C. J. W. BrewardEmail author
  • T. P. Witelski
Original Article

Abstract

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.

Keywords

Tear films Lipids Blinking Fluid mechanics Lubrication theory 

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Copyright information

© Society for Mathematical Biology 2010

Authors and Affiliations

  • E. Aydemir
    • 1
  • C. J. W. Breward
    • 1
    Email author
  • T. P. Witelski
    • 2
  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK
  2. 2.Mathematics DepartmentDuke UniversityDurhamUSA

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