On modeling tear breakup dynamics with a nematic lipid layer

One of the main roles of the lipid layer (LL) of the tear film (TF) is to help prevent evaporation of the aqueous layer (AL). The LL thickness, composition, and structure all contribute to its barrier function. It is believed that the lipid layer is primarily nonpolar with a layer of polar lipids at...

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Bibliographic Details
Published inJournal of engineering mathematics Vol. 147; no. 1
Main Authors Taranchuk, M. J., Braun, R. J.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.08.2024
Springer Nature B.V
Subjects
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Crystal structure
Evaporation
Lipids
Liquid crystals
Mathematical and Computational Engineering
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Molecular structure
Nematic crystals
Parameters
Theoretical and Applied Mechanics
Thickness
Tear film
Lipid layer
Nematic liquid crystal
Marangoni effect
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Summary:One of the main roles of the lipid layer (LL) of the tear film (TF) is to help prevent evaporation of the aqueous layer (AL). The LL thickness, composition, and structure all contribute to its barrier function. It is believed that the lipid layer is primarily nonpolar with a layer of polar lipids at the LL/AL interface. There is evidence that the nonpolar region of the LL may have liquid crystalline characteristics. We investigate the structure and function of the LL via a model of the tear film with two layers, using extensional flow of a nematic liquid crystal for the LL and shear-dominated flow of a Newtonian AL. Evaporation is taken into account and is affected by the LL thickness, internal arrangement of its rod-like molecules, and external conditions. We conduct a detailed parameter study with a focus on the evaporative resistance parameter, the Marangoni number, and primary liquid crystal parameters including the Leslie viscosities and director angle. This new model responds similarly to previous Newtonian models in some respects; however, incorporating internal structure via the orientation of the liquid crystal molecules affects both evaporation and flow. As a result, we see new effects on TF dynamics and breakup.
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ISSN:0022-0833
1573-2703
DOI:10.1007/s10665-024-10385-9