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Bull Math Biol DOI 10.1007/s11538-013-9858-x ORIGINAL ARTICLE Meniscal Tear Film Fluid Dynamics Near Marx’s Line

By V. S. Zubkov, C. J. W. Breward and E. A. Gaffney

Abstract

Abstract Extensive studies have explored the dynamics of the ocular surface fluid, though theoretical investigations are typically limited to the use of the lubrication approximation, which is not guaranteed to be uniformly valid a-priori throughout the tear meniscus. However, resolving tear film behaviour within the meniscus and especially its apices is required to characterise the flow dynamics where the tear film is especially thin, and thus most susceptible to evaporatively induced hyperosmolarity and subsequent epithelial damage. Hence, we have explored the accuracy of the standard lubrication approximation for the tear film by explicit comparisons with the 2D Navier–Stokes model, considering both stationary and moving eyelids. Our results demonstrate that the lubrication model is qualitatively accurate except in the vicinity of the eyelids. In particular, and in contrast to lubrication theory, the solution of the full Navier–Stokes equations predict a distinct absence of fluid flow, and thus convective mixing in the region adjacent to the tear film contact line. These observations not only support emergent hypotheses concerning the formation of Marx’s line, a region of epithelial cell staining adjacent to the contact line on the eyelid, but also enhance our understanding of the pathophysiological consequences of the flow profile near the tear film contact line.

Publisher: 2013-10-01
Year: 2012
OAI identifier: oai:CiteSeerX.psu:10.1.1.360.3674
Provided by: CiteSeerX
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