What is it about?

This work develops a mathematical model of the extensional flow of a liquid crystal. Extensional flow is like pulling taffy; the fluid is suspended in air as a film and then stretched. The air is assumed to have no effect on the flow, and the fluid is assumed symmetric about its straight midline. The liquid crystal material is a fluid that flows yet has internal structure; the molecules inside are assumed to be like rods that are roughly lined up in the same direction. The nematic liquid crystal has the least amount of ordering of the possible liquid crystal phases. Despite all of these simplifications, the mathematics of deriving the models are complicated. One of the two models presented is new, to our knowledge: the case with modeerate elasticity. The conditions applied at the start of the simulations and on the ends of the fluid make a difference to what outcomes happen during stretching. We examine a number of cases and present results for those. Various patterns and changes in patterns occur that may turn out to be relevant to application to the tear film on the eye.

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Why is it important?

The tear film on the eye is a multilayer fluid that is painted onto the eye with each blink of the upper eyelid. This outermost layer of the tear film, the lipid layer, The lipid layer is an oily layer that floats on an aqueous layer that is primarily water; that aqueous layer is primarily what is thought of as tears. As a start, this paper neglects that water layer and only studies the lipid layer. The patterns seen with this greatly simplified model show some similarity to patterns seen in vivo with complex optical systems. Because of that similarity, we are encouraged to put this model together with an aqueous layer and continue to try to explain the patterns seen on the human eye. We hope to explain the patterns seen in the failure of the tear film, often called tear breakup, and to predict the conditions there. Those conditions include hyperosmolarity (or high saltiness), that is thought to be an important contributor to dry eye disease (DED). DED affects millions of people worldwide, and its symptoms may include sensations of grittiness, burning, itching, dryness, and poor focus. A basic science understanding of the causes of DED may lead to better treatments of this common ailment.

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This page is a summary of: Extensional flow of a free film of nematic liquid crystal with moderate elasticity, Physics of Fluids, June 2023, American Institute of Physics, DOI: 10.1063/5.0151809.
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