Nematic topological defects in the presence of axisymmetric fluid flow

TL;DR

This paper analytically demonstrates how topological defects in nematic liquid crystals are advected and rotate with fluid flow in an axisymmetric system, extending understanding from numerical simulations to exact solutions.

Contribution

It provides an exact solution to the Ericksen-Leslie equations showing defect advection and rotation in axisymmetric flow, simplifying previous complex numerical studies.

Findings

Defects rotate with the fluid vortex at the same angular velocity.

Exact analytical solution for nematodynamic equations in axisymmetric flow.

Defect configurations are advected without deformation by the flow.

Abstract

Recent numerical simulations of lid-driven cavity flow of a nematic liquid crystal have found dynamical behavior where topological defects rotate about the center of the fluid vortex induced by the lid motion. By considering a simpler geometry of an infinite system with axisymmetric fluid flow we show that the Ericksen-Leslie nematodynamic equation for the director can be solved exactly. The solution demonstrates that any configuration of defects will be advected by the fluid flow, with the defects rotating about the center of the fluid vortex with the angular velocity of the fluid.