Nematic topological defects in the presence of axisymmetric fluid flow

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.