Nematic liquid crystal models for the lipid layer of the human tear film
Date
2024
Authors
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Publisher
University of Delaware
Abstract
The human tear film is a thin, multilayer fluid film that protects and nourishes the eye and is critical for clear vision and ocular surface health. The tear film’s dynamics are strongly affected by its outermost floating lipid layer. One of the main roles of the lipid layer is to help prevent evaporation of the aqueous layer. The lipid layer’s thickness, composition, and structure all contribute to its barrier function. In this dissertation, we focus on the influence of the lipid layer’s structure on tear film thinning and breakup. ☐ The lipid layer is primarily nonpolar with a layer of polar lipids at the lipid-aqueous interface. There is evidence that the nonpolar region of the lipid layer may have liquid crystalline characteristics; however, previous models treated it as a Newtonian fluid in extensional flow. We investigate the relationship between the structure and function of the lipid layer by developing novel one- and two-layer mathematical models that represent the lipid layer as a thin film of nematic liquid crystal. ☐ Nematic liquid crystals are composed of rod-like molecules that have orientational order, which is described by the director field n. We use the Ericksen-Leslie equations for conservation of energy, mass, and momentum to describe the liquid crystal dynamics. Many variables associated with the lipid layer depend on the orientation of the molecules through the angle θ of the director field, which affects the stresses in the fluid. ☐ We begin by studying the extensional flow of a free film of nematic liquid crystal. The film has free surfaces on both sides, which must be found as part of the solution. We derive a new limit for nematic liquid crystal under moderate elasticity that results in a system of two nonlinear partial differential equations. We analyze solutions arising from applying several different boundary conditions chosen because of the underlying application, with a particular emphasis on dynamics and mechanisms under stretching. The new system has complex dependence on boundary conditions that was explored numerically. At early times and depending on the initial film shape and boundary conditions, pressure either aids or opposes extensional flow. This changes the free surface dynamics of the sheet and can lead to patterns reminiscent of those observed in tear films. ☐ Next, we extend previous two-layer models of the tear film to include flow of a thin nematic liquid crystal in extension atop a shear-dominated Newtonian aqueous layer with insoluble surfactant between them. This new model incorporates nematic molecular orientation into the evaporation resistance. We use perturbation theory to derive a system of nonlinear partial differential equations that model the thickness of the lipid and aqueous layers, surfactant transport, and velocity in the lipid layer. We solve the system numerically and conduct a detailed parameter study. We model the two primary mechanisms for tear breakup, evaporation- and Marangoni-driven flow, and analyze solutions for different internal lipid layer structures. ☐ We believe this model to be the first to combine the flow of liquid crystal and Newtonian layers in this way and to incorporate both thickness and structure of the lipid layer into the evaporation resistance. Our results show significant effect from molecular orientation and are in general agreement with experimental evidence. Incorporating lipid layer structure into models for the tear film has promise for predicting tear film dynamics and can lead to a better understanding of the role of the lipid layer in eye health.
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Keywords
Lipid layer, Nematic liquid crystal, Tear film, Fluid film, Aqueous layer