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arXiv · 2301.10924

A nematic liquid crystal with an immersed body: equilibrium, stress, and paradox

Thomas G. J. Chandler·Saverio E. Spagnolie
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Abstract

We examine the equilibrium configurations of a nematic liquid crystal with an immersed body in two-dimensions. A complex variables formulation provides a means for finding analytical solutions in the case of strong anchoring. Local tractions, forces, and torques on the body are discussed in a general setting. For weak (finite) anchoring strengths, an effective boundary technique is proposed which is used to determine asymptotic solutions. The energy-minimizing locations of topological defects on the body surface are also discussed. A number of examples are provided, including circular and triangular bodies, and a Janus particle with hybrid anchoring conditions. Analogues to classical results in fluid dynamics are identified, including d'Alembert's paradox, Stokes' paradox, and the Kutta condition for circulation selection.

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Thomas G. J. Chandler, Saverio E. Spagnolie. 2023-01-26. A nematic liquid crystal with an immersed body: equilibrium, stress, and paradox. https://doi.org/10.1017/jfm.2023.488

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