Defect Loops in Three-Dimensional Active Nematics as Active Multipoles

We develop a description of defect loops in three-dimensional active nematics based on a multipole expansion of the far-field director and show how this leads to a self-dynamics dependent on the loop's geometric type. The dipole term leads to active stresses that generate a global self-propulsi...

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Bibliographic Details
Published in:arXiv.org 2021-06
Main Authors: Houston, Alexander J H, Alexander, Gareth P
Format: Article
Language:English
Subjects:
Dipoles
Fluid dynamics
Fluid flow
Hydrodynamics
Multipoles
Quadrupoles
Torque
Online Access:Get full text
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Summary:We develop a description of defect loops in three-dimensional active nematics based on a multipole expansion of the far-field director and show how this leads to a self-dynamics dependent on the loop's geometric type. The dipole term leads to active stresses that generate a global self-propulsion for splay and bend loops. The quadrupole moment is non-zero only for non-planar loops and generates a net `active torque', such that defect loops are both self-motile and self-orienting. Our analysis identifies right- and left-handed twist loops as the only force and torque free geometries, suggesting a mechanism for generating an excess of twist loops. Finally, we determine the Stokesian flows created by defect loops and describe qualitatively their hydrodynamics.
ISSN:2331-8422
DOI:10.48550/arxiv.2106.15424