Flow around topological defects in active nematic films

TL;DR

This paper investigates how active nematic films with defects generate flow and how their self-propulsion depends on system size and dissipation mechanisms, revealing a transition from size-dependent to size-independent velocities.

Contribution

It introduces a model incorporating viscous and frictional dissipation, showing how the hydrodynamic length scale controls defect flow and propulsion in active nematic films.

Findings

Vorticity around defects is limited by the hydrodynamic length scale.

Self-propulsion velocity depends on system size relative to the dissipation length.

Velocity saturates in large systems where system size exceeds the dissipation length.

Abstract

We study the active flow around isolated defects and the self-propulsion velocity of $+1/2$ defects in an active nematic film with both viscous dissipation (with viscosity $\eta$) and frictional damping $\Gamma$ with a substrate. The interplay between these two dissipation mechanisms is controlled by the hydrodynamic dissipation length $\ell_d=\sqrt{\eta/\Gamma}$ that screens the flows. For an isolated defect, in the absence of screening from other defects, the size of the vortical flows around the defect is controlled by the system size $R$. In the presence of friction that leads to a finite value of $\ell_d$, the vorticity field decays to zero on the lengthscales larger than $\ell_d$. We show that the self-propulsion velocity of $+1/2$ defects grows with $R$ in small systems where $R<\ell_d$, while in the infinite system limit or when $R\gg \ell_d$, it approaches a constant value determined by $\ell_d$.