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The influence of non-polar lipids on tear film dynamics

Published online by Cambridge University Press:  04 April 2014

M. Bruna  and
C. J. W. Breward
M. Bruna*
Affiliation:
Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
C. J. W. Breward
Affiliation:
Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
*
†Email address for correspondence: bruna@maths.ox.ac.uk
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Abstract

In this paper we examine the effect that physiological non-polar lipids, residing on the surface of an aqueous tear film, have on the film evolution. In our model we track the evolution of the thickness of the non-polar lipid layer, the thickness of the aqueous layer and the concentration of polar lipids which reside at the interface between the two. We also utilise a force balance in the non-polar lipid layer in order to determine its velocity. We show how to obtain previous models in the literature from our model by making particular choices of the parameters. We see the formation of boundary layers in some of these submodels, across which the concentration of polar lipid and the non-polar lipid velocity and film thickness vary. We solve our model numerically for physically realistic parameter values, and we find that the evolution of the aqueous layer and the polar lipid layer are similar to that described by previous authors. However, there are interesting dynamics for the non-polar lipid layer. The effects of altering the key parameters are highlighted and discussed. In particular, we see that the Marangoni number plays a key role in determining how far over the eye the non-polar lipid spreads.

JFM classification

Biological Fluid Dynamics: Biomedical flows Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 746 , 10 May 2014 , pp. 565 - 605
Copyright
© 2014 Cambridge University Press 

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