Journal Article

An overset grid method for the study of reflex tearing

K. L. Maki, R. J. Braun, T. A. Driscoll and P. E. King-Smith

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 25, issue 3, pages 187-214
Published in print September 2008 | ISSN: 1477-8599
Published online July 2008 | e-ISSN: 1477-8602 | DOI:
An overset grid method for the study of reflex tearing

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  • Applied Mathematics
  • Biomathematics and Statistics


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We present an overset grid method to simulate the evolution of human tear film thickness subject to reflex tearing. The free-surface evolution is governed by a single fourth-order non-linear equation derived from lubrication theory with specified film thickness and volume flux at each end. The model arises from considering the limiting case where the surfactant is strongly affecting the surface tension. In numerical simulations, the overset grid is composed of fine boundary grids near the upper and lower eyelids to capture localized capillary thinning referred to as ‘black lines’ and a Cartesian grid covers the remaining domain. Numerical studies are performed on a non-linear test problem to confirm the accuracy and convergence of the scheme. The computations on the tear film model show qualitative agreement with in vivo tear film thickness measurements. Furthermore, the role of the black lines in the presence of tear supply from the lid margins, reflex tearing, was found to be more subtle than a barrier to tear fluid flow between the anterior of the eye and the meniscus at the lid margin. During reflex tearing, tears may flow through the region normally containing the black line and drift down over the cornea under the influence of gravity.

Keywords: tear film; reflex tearing; black line; overset grid; lubrication theory

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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