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| Format: | Preprint |
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2023
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| Online Access: | https://arxiv.org/abs/2311.17708 |
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| _version_ | 1866909445033820160 |
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| author | Chandler, Thomas G. J. Spagnolie, Saverio E. |
| author_facet | Chandler, Thomas G. J. Spagnolie, Saverio E. |
| contents | Anisotropic fluids appear in a diverse array of systems, from liquid-crystal displays to bacterial swarms, and are characterized by orientational order. Large colloidal particles immersed in such environments disturb the medium's orientational order, however, resulting in a stored elastic energy within the bulk. As a consequence, multiple immersed bodies interact at equilibrium through fluid-mediated forces and torques, which depend on the bodies' positions, orientations, and shapes. We provide the equilibrium configuration of a model nematic liquid crystal with multiple immersed bodies or inclusions in two-dimensions, as well as the associated body forces, torques, and surface tractions. A complex variables approach is taken which leans on previous work by Crowdy (2020) for describing solutions with multiply-connected domains. Free periods of a complex director field, which correspond to topological defect positioning and net topological charge, are determined numerically to minimize a global stored elastic energy, including a contribution of a weak (finite) anchoring strength on the body surfaces. Finally, a general, analytical description of two-body far-field interactions is provided, along with examples using two cylindrical inclusions of arbitrary position and size, and two triangles of arbitrary position and orientation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_17708 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Exact and approximate solutions for elastic interactions in a nematic liquid crystal Chandler, Thomas G. J. Spagnolie, Saverio E. Soft Condensed Matter Fluid Dynamics Anisotropic fluids appear in a diverse array of systems, from liquid-crystal displays to bacterial swarms, and are characterized by orientational order. Large colloidal particles immersed in such environments disturb the medium's orientational order, however, resulting in a stored elastic energy within the bulk. As a consequence, multiple immersed bodies interact at equilibrium through fluid-mediated forces and torques, which depend on the bodies' positions, orientations, and shapes. We provide the equilibrium configuration of a model nematic liquid crystal with multiple immersed bodies or inclusions in two-dimensions, as well as the associated body forces, torques, and surface tractions. A complex variables approach is taken which leans on previous work by Crowdy (2020) for describing solutions with multiply-connected domains. Free periods of a complex director field, which correspond to topological defect positioning and net topological charge, are determined numerically to minimize a global stored elastic energy, including a contribution of a weak (finite) anchoring strength on the body surfaces. Finally, a general, analytical description of two-body far-field interactions is provided, along with examples using two cylindrical inclusions of arbitrary position and size, and two triangles of arbitrary position and orientation. |
| title | Exact and approximate solutions for elastic interactions in a nematic liquid crystal |
| topic | Soft Condensed Matter Fluid Dynamics |
| url | https://arxiv.org/abs/2311.17708 |