Coupling Fluid and Solute Dynamics Within the Ocular Surface Tear Film: A Modelling Study of Black Line Osmolarity

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

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


We present a mathematical model describing the spatial distribution of tear film osmolarity across the ocular surface of a human eye during one blink cycle, incorporating detailed fluid and solute dynamics. Based on the lubrication approximation, our model comprises three coupled equations tracking the depth of the aqueous layer of the tear film, the concentration of the polar lipid, and the concentration of physiological salts contained in the aqueous layer. Diffusive boundary layers in the salt concentration occur at the thinnest regions of the tear film, the black lines. Thus, despite large Peclet numbers, diffusion ameliorates osmolarity around the black lines, but nonetheless is insufficient to eliminate the build-up of solute in these regions. More generally, a heterogeneous distribution of solute concentration is predicted across the ocular surface, indicating that measurements of lower meniscus osmolarity are not globally representative, especially in the presence of dry eye. Vertical saccadic eyelid motion can reduce osmolarity at the lower black line, raising the prospect that select eyeball motions more generally can assist in alleviating tear film hyperosmolarity. Finally, our results indicate that measured evaporative rates will induce excessive hyperosmolarity at the black lines, even for the healthy eye. This suggests that further evaporative retardation at the black lines, for instance due to the cellular glycocalyx at the ocular surface or increasing concentrations of mucus, will be important for controlling hyperosmolarity as the black line thins. © 2012 Society for Mathematical Biology.
Original languageEnglish (US)
Pages (from-to)2062-2093
Number of pages32
JournalBulletin of Mathematical Biology
Issue number9
StatePublished - Jul 6 2012
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This paper is based on work supported by Award No. KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST). We are grateful to Professor Richard Braun, Professor Anthony Bron, Professor Colin Please, and Dr. John Tiffany for insightful discussions.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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