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 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.