How fluid flows influence defect dynamics in active nematic films

Active nematic films are essentially two-dimensional suspensions of active rod-like particles, such as cytoskeleton filaments driven by motor proteins, that locally consume energy and align collectively to generate orientational order. Increasing activity promotes the spontaneous formation of topological defects in the nematic structure and large-scale structures such as kink walls concomitant with inducing self-sustained fluid flows. Using the hydrodynamic description of active nematics, we derive how the defect velocity and the orientational dynamics of the defects depend on both fluid flow and flow-induced alignment. The resultant non-local hydrodynamic interactions between defects are especially important for incompressible flows - the situation relevant to most active cytoskeletal suspensions. We give an analytic treatment of a pair of defects in the overdamped limit. Coarse-graining the defect equations lead to a hydrodynamic model of the binary defect gas, from which we derive the coupling of the fluid flow to both the defect and polarization density.