Orientational instability and spontaneous rotation of active nematic droplets

TL;DR

This paper presents a minimal model explaining how active nematic droplets can spontaneously rotate and switch between different self-propulsion trajectories, revealing a new orientational instability mechanism.

Contribution

The study introduces a reduced-order model capturing the orientational instability and spontaneous rotation of active nematic droplets, linking internal reorientation mechanisms to complex trajectories.

Findings

Spontaneous rotation causes helical trajectories.

Competition of reorientation mechanisms leads to orientational instability.

Transition to chaos explains random trajectories.

Abstract

In experiments, an individual chemically active liquid crystal (LC) droplet submerged in the bulk of a surfactant solution may self-propel along a straight, helical, or random trajectory. In this paper, we develop a minimal model capturing all three types of self-propulsion trajectories of a drop in the case of a nematic LC with homeotropic anchoring at LC-fluid interface. We emulate the director field within the drop by a single preferred polarization vector that is subject of two reorientation mechanisms, namely, the internal flow-induced displacement of the hedgehog defect and the droplet's rotation. Within this reduced-order model, the coupling between the nematic ordering of the drop and the surfactant transport is represented by variations of the droplet's interfacial properties with nematic polarization. Our analysis reveals that a novel mode of orientational instability emerges from the competition of the two reorientation mechanisms and is characterized by a spontaneous rotation of the self-propelling drop responsible for helical self-propulsion trajectories. In turn, we also show that random trajectories in isotropic and nematic drops alike stem from the advection-driven transition to chaos. The succession of the different propulsion modes is consistent with experimentally-reported transitions in the shape of droplet trajectories as the drop size is varied.