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Main Authors: Chandler, Thomas G. J., Spagnolie, Saverio E.
Format: Preprint
Published: 2023
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Online Access:https://arxiv.org/abs/2311.17708
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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