A nematic liquid crystal with an immersed body: equilibrium, stress, and paradox
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914695029456896 |
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| author | Chandler, Thomas G. J. Spagnolie, Saverio E. |
| author_facet | Chandler, Thomas G. J. Spagnolie, Saverio E. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_10924 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A nematic liquid crystal with an immersed body: equilibrium, stress, and paradox Chandler, Thomas G. J. Spagnolie, Saverio E. Soft Condensed Matter Fluid Dynamics 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. |
| title | A nematic liquid crystal with an immersed body: equilibrium, stress, and paradox |
| topic | Soft Condensed Matter Fluid Dynamics |
| url | https://arxiv.org/abs/2301.10924 |