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arXiv:2404.13225v1 Announce Type: new
Abstract: The human tear film (TF) is thin multilayer fluid film that is critical for clear vision and ocular surface health. Its dynamics are strongly affected by a floating lipid layer and, in health, that layer slows evaporation and helps create a more uniform tear film over the ocular surface. The tear film lipid layer (LL) may have liquid crystalline characteristics and plays important roles in the health of the tear film. Previous models have treated the lipid layer as a Newtonian fluid in extensional flow. We extend previous models to include extensional flow of a thin nematic liquid crystal atop a Newtonian aqueous layer with insoluble surfactant between them. We derive the resulting system of nonlinear partial differential equations for thickness of the LL and aqueous layers, surfactant transport and velocity in the LL. Evaporation is taken into account, and is affected by the LL thickness, internal arrangement of its rod-like molecules, and external conditions. Despite the complexity, this system still represents a significant reduction of the full system. We solve the system numerically via collocation with finite difference discretization in space together with implicit time stepping. We analyze solutions for different internal LL structures and show significant effect of the orientation. Orienting the molecules close to the normal direction to the TF surface results in slower evaporation, and other orientations have an effect on flow, showing that this type of model has promise for predicting TF dynamics.