Drag on a Moving Defect in a 2D Nematic Liquid Crystal

When a topological defect moves through a 2D nematic liquid crystal, its velocity is determined by a balance between elastic forces and viscous drag forces. Here, we develop an analytic theory to calculate the viscous drag in the presence of backflow, i.e. fluid motion in the liquid crystal. In this calculation, we determine the director field and the fluid velocity field as perturbation series in the defect velocity, assuming that the defect velocity is small. We then find the rate of energy dissipation, using the full Rayleigh dissipation function with all independent nematic viscosities. This calculation shows that positive topological charges experience less drag than negative topological charges, and hence move more rapidly. It also shows that certain nematic viscosity terms in the drag depend on defect orientation.