Vortex formation and dynamics of defects in shells of active nematics

TL;DR

This paper develops a hydrodynamic model for active nematic shells, revealing how defect configurations generate vortices and complex flow patterns, with implications for understanding active matter on curved surfaces.

Contribution

It introduces a novel hydrodynamic framework for active nematic shells with arbitrary defect configurations, linking defect dynamics to vortex formation and flow states.

Findings

Stable vortices form around defects due to active flows.

Defect interactions depend on local geometry and activity level.

Flow states can contain multiple vortices beyond simple pairs.

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.