Defect Loops in Three-Dimensional Active Nematics as Active Multipoles

Abstract

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.

arXiv comment6 pages, 3 figures

References in corpus (27)

• The Mechanics and Statistics of Active Matter
• Spontaneous motion in hierarchically assembled active matter
• Meso-scale turbulence in living fluids
• Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles
• Topological Defects and Interactions in Nematic Emulsions
• Living Liquid Crystals
• Defect annihilation and proliferation in active nematics
• Defect dynamics in active nematics
• Topological structure and dynamics of three dimensional active nematics
• Universal scaling of active nematic turbulence
• No many-scallop theorem: Collective locomotion of reciprocal swimmers
• Rotation and propulsion in 3d active chiral droplets
• Confinement controlled bend instability of three-dimensional active fluids
• Hydrodynamics of Active Defects: from order to chaos to defect ordering
• Dumb-bell swimmers
• Three-Dimensional Active Defect Loops
• Vortex formation and dynamics of defects in shells of active nematics
• Flow states and transitions of an active nematic in a three dimensional channel
• Twist-induced crossover from 2D to 3D turbulence in active nematics
• Global Defect Topology in Nematic Liquid Crystals
• Topology of three-dimensional active nematic turbulence confined to droplets
• Active cholesterics: odder than odd elasticity
• Morphology of active deformable 3D droplets
• Pair creation, motion, and annihilation of topological defects in 2D nematics
• The role of fluid flow in the dynamics of active nematic defects
• Spectral energy analysis of bulk three-dimensional active nematic turbulence
• Maxwell's Theory of Solid Angle and the Construction of Knotted Fields

Cited by in corpus (7)

• Singularity identification for the characterization of topology, geometry, and motion of nematic disclination lines
• Kinematics and dynamics of disclination lines in three-dimensional nematics
• Helical Flow States in Active Nematics
• Chirality, anisotropic viscosity and elastic anisotropy in three-dimensional active nematic turbulence
• Coexistence of defect morphologies in three dimensional active nematics
• Active Nematic Multipoles: Flow Responses and the Dynamics of Defects and Colloids
• Analytical model for the motion and interaction of two-dimensional active nematic defects