Flow around topological defects in active nematic films

We study the active flow around isolated defects and the self-propulsion velocity of [Formula: see text] defects in an active nematic film with both viscous dissipation (with viscosity [Formula: see text]) and frictional damping [Formula: see text] with a substrate. The interplay between these two dissipation mechanisms is controlled by the hydrodynamic dissipation length [Formula: see text] that screens the flows. For an isolated defect, in the absence of screening from other defects, the size of the shear vorticity around the defect is controlled by the system size [Formula: see text]. In the presence of friction that leads to a finite value of [Formula: see text] , the vorticity field decays to zero on the lengthscales larger than [Formula: see text]. We show that the self-propulsion velocity of [Formula: see text] defects grows with [Formula: see text] in small systems where [Formula: see text] , while in the infinite system limit or when [Formula: see text] , it approaches a constant value determined by [Formula: see text].