Spontaneous flow created by active topological defects

TL;DR

This paper analytically investigates the flow and stress patterns around topological defects in two-dimensional active nematics, revealing how defect dynamics influence cellular behaviors and providing a framework for understanding active matter systems.

Contribution

It derives analytical expressions for defect velocities and forces in active nematics, linking defect behavior to biological processes like cell extrusion.

Findings

Analytical formulas for defect velocity and stall force.

Non-conservation of cell number affects defect self-advection.

Numerical analysis of Ericksen stress influence.

Abstract

Topological defects are at the root of the large-scale organization of liquid crystals. In two-dimensional active nematics, two classes of topological defects of charges $\pm 1/2$ are known to play a major role due to active stresses. Despite this importance, few analytical results have been obtained on the flow-field and active-stress patterns around active topological defects. Using the generic hydrodynamic theory of active systems, we investigate the flow and stress patterns around these topological defects in unbounded, two-dimensional active nematics. Under generic assumptions, we derive analytically the spontaneous velocity and stall force of self-advected defects in the presence of both shear and rotational viscosities. Applying our formalism to the dynamics of monolayers of elongated cells at confluence, we show that the non-conservation of cell number generically increases the self-advection velocity and could provide an explanation for their observed role in cellular extrusion and multilayering. We finally investigate numerically the influence of the Ericksen stress. Our work paves the way to a generic study of the role of topological defects in active nematics, and in particular in monolayers of elongated cells.