Vortex formation and dynamics of defects in shells of active nematics

Abstract

We present a hydrodynamic model for a thin spherical shell of active nematic liquid crystal with an arbitrary configuration of defects. The active flows generated by defects in the director lead to the formation of stable vortices, analogous to those seen in confined systems in flat geometries, which generate an effective dynamics for four +1/2 defects that reproduces the tetrahedral to planar oscillations observed in experiments. As the activity is increased and the vortices become stronger, the defects are drawn more tightly into pairs, rotating about antipodal points. We extend this situation to also describe the dynamics of other configurations of defects. For example, two +1 defects are found to attract or repel according to the local geometric character of the director field around them, while additional pairs of opposite charge defects can give rise to flow states containing more than two vortices. Finally, we describe the generic relationship between defects in the orientation and singular points of the flow, and suggest implications for the three-dimensional nature of the flow and deformation in the shape of the shell.

arXiv comment10 pages, 6 figures

References in corpus (23)

• The Mechanics and Statistics of Active Matter
• Spontaneous motion in hierarchically assembled active matter
• Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles
• Topology and Dynamics of Active Nematic Vesicles
• Fluid dynamics of bacterial turbulence
• Confinement Stabilizes a Bacterial Suspension into a Spiral Vortex
• Towards a Tetravalent Chemistry of Colloids
• Defect dynamics in active nematics
• Spontaneous symmetry breaking in active droplets provides a generic route to motility
• Ferromagnetic and antiferromagnetic order in bacterial vortex lattices
• Nematic textures in spherical shells
• Stabilization of active matter by flow-vortex lattices and defect ordering
• Defect-mediated morphologies in growing cell colonies
• Spontaneous Circulation of Confined Active Suspensions
• A minimal physical model captures the shapes of crawling cells
• Emergence and Persistence of Collective Cell Migration on Small Circular Micropatterns
• Stable nematic droplets with handles
• Dynamics of defects in active nematics
• Active swarms on a sphere
• A Drop of Active Matter
• Instabilities and waves in thin films of living fluids
• Active polar fluid flow in finite droplets
• Motility of active fluid drops on surfaces

Cited by in corpus (23)

• Topological active matter
• Topology and morphology of self-deforming active shells
• Dynamical patterns in active nematics on a sphere
• Contractile and chiral activities co-determine the helicity of swimming droplet trajectories
• Aging and rejuvenation of active matter under topological constraints
• Three-Dimensional Active Defect Loops
• Geometrical control of active turbulence in curved topographies
• Design of nematic liquid crystals to control microscale dynamics
• Active crystals on a sphere
• Topology of three-dimensional active nematic turbulence confined to droplets
• Anomalous chained turbulence in actively driven flows on spheres
• Dynamics of active nematic defects on the surface of a sphere
• Defect Spirograph: Dynamical Behavior of Defects in Spatially Patterned Active Nematics
• Orientational correlations in active and passive nematic defects
• Morphodynamics of Active Nematic Fluid Surfaces
• Defect order in active nematics on a curved surface
• Helical Flow States in Active Nematics
• Defect Loops in Three-Dimensional Active Nematics as Active Multipoles
• Tuneable defect-curvature coupling and topological transitions in active shells
• Orientational ordering of point dipoles on a sphere
• Active Nematic Multipoles: Flow Responses and the Dynamics of Defects and Colloids
• Elasticity tunes mechanical stress localization around active topological defects
• Motility and self propulsion of active droplets