Topology of Three-Dimensional Active Nematic Turbulence Confined to Droplets

Abstract

Active nematics contain topological defects which under sufficient activity move, create and annihilate in a chaotic quasi-steady state, called active turbulence. However, understanding active defects under confinement is an open challenge, especially in three-dimensions. Here, we demonstrate the topology of three-dimensional active nematic turbulence under the spherical confinement, using numerical modelling. In such spherical droplets, we show the three-dimensional structure of the topological defects, which due to closed confinement emerge in the form of closed loops or surface-to-surface spanning line segments. In the turbulent regime, the defects are shown to be strongly spatially and time varying, with ongoing transformations between positive winding, negative winding and twisted profiles, and with defect loops of zero and non-zero topological charge.The timeline of the active turbulence is characterised by four types of bulk topology-linked events -breakup, annihilation, coalescence and cross-over of the defects -which we discuss could be used for the analysis of the active turbulence in different three-dimensional geometries. The turbulent regime is separated by a first order structural transition from a low activity regime of a steady-state vortex structure and an offset single point defect. We also demonstrate coupling of surface and bulk topological defect dynamics by changing from strong perpendicular to inplane surface alignment. More generally, this work is aimed to provide insight into three-dimensional active turbulence, distinctly from the perspective of the topology of the emergent three-dimensional topological defects. * These authors contributed equally to this work.

Topological structure and dynamics of three-dimensional active nematics

“…The same class of loop geometries also dominated the dynamics in our numerical simulations of bulk 3D active nematics and in recently studied confined active nematics(Fig. 4E, F)(30).…”

“…Combined with other emerging theoretical work (30,31), the developed experimental model system offers a powerful platform to investigate the role of topology, dimensionality, and material order in the chaotic internally driven flows of active soft matter. Furthermore, the use of a multiview light-sheet imaging technique demonstrates its potential to unravel dynamical processes in…”

Rotation and propulsion in 3D active chiral droplets

“…For still larger θ, the droplet rotates and moves in a chaotic manner. This regime is the droplet analogue of what is known as active turbulence (25,26)-the chaotic dynamics observed in an active nematic fluid. In the chaotic regime, motion is random, and the cylindrical symmetry of the droplet shape is lost (Fig.…”

Helical Flow States in Active Nematics

“…One reason for this is because much of the theoretical, computational and experimental work on active nematics is on 2D films for which helicity is identically zero. However, the recent advent of experimentally realizable 3D active nematics [46] spurred immediate interest in 3D active liquid crystals [47][48][49][50][51][52][53][54]. Yet, long-lived, non-zero helical active dissipative structures have not to our knowledge been previously been reported.…”

“…Recent work on 3D active nematics [47][48][49][50][51][52][53][54] has shown them to be complicated by their tangle of 3D disclination lines. However, they also possess the potential for an exciting range of possible dissipative structures.…”