Spontaneous rotation of active droplets in two and three dimensions

TL;DR

This paper investigates how active nematic droplets spontaneously rotate in two and three dimensions, revealing the mechanisms behind rotation and deformation driven by activity, with implications for biological systems and experiments.

Contribution

The study combines numerical simulations and linear stability analysis to uncover the mechanisms of spontaneous rotation in active nematic droplets in 2D and 3D, including defect formation and droplet deformation.

Findings

Rotation in 2D caused by a central chiral +1 defect.

Droplet deformation transitions from circular to elliptical to rotating annulus with activity.

Critical radius for transition to turbulence is around 700 μm, matching experimental observations.

Abstract

We use numerical simulations and linear stability analysis to study active nematic droplets, in the regime where the passive phase is isotropic. We show that activity leads to the emergence of nematic order and of spontaneous rotation in both two and three dimensions. In 2D the rotation is caused by the formation of a chiral $+1$ defect at the center of the drop. With increasing activity the droplet deforms to an ellipse, and then to a rotating annulus. Growing droplets form extended active arms which loop around to produce holes. In 3D the rotation is due to a disclination which loops away from and back to the surface, defining the rotation axis. In the bulk the disclination loop ends at a skyrmion. Active extensile flows deform the droplet to an oblate ellipsoid, contractile flows elongate it along the rotation axis. We compare our results on rotation in two-dimensional droplets with experiments on microtubule and motor protein suspensions and find a critical radius $\sim 700 \mu m$ above which the spontaneous rotation gives way to active turbulence. Comparing the simulation parameters with experiments on epithelial cell colonies shows that the crossover radius for cell colonies could be as large as $2 mm$, in agreement with experiments.