Exact Coherent Structures and Phase Space Geometry of Preturbulent 2D Active Nematic Channel Flow

Abstract

This work is a unified study of stable and unstable steady states of 2D active nematic channel flow using the framework of Exact Coherent Structures (ECS). ECS are stationary, periodic, quasiperiodic, or traveling wave solutions of the governing equations that, together with their invariant manifolds, organize the dynamics of nonlinear continuum systems. We extend our earlier work on ECS in the preturbulent regime by performing a comprehensive study of stable and unstable ECS for a wide range of activity values spanning the preturbulent and turbulent regimes.In the weakly turbulent regime, we compute more than 200 unstable ECS that co-exist at a single set of parameters, and uncover the role of symmetries in organizing the phase space geometry. We provide conclusive numerical evidence that in the preturbulent regime, generic trajectories shadow a series of unstable ECS before settling onto an attractor. Finally, our studies hint at shadowing of quasiperiodic type ECS in the turbulent regime.

From disks to channels: dynamics of active nematics confined to an annulus

“…We also note that the absence of the corotating state at strong anchoring is consistent with the absence of this state in the study of exact coherent structures for active nematics in channels in ref. 58, which was performed with strong homeotropic anchoring conditions. More broadly, the small value of x p for high activities explains the observations from this work and Norton et al 59 that strongly confined active nematics are insensitive to topological constraints, and that the anchoring effects are restricted to a narrow region near the boundary.…”

“…20,39,42,45,49–55 Experiments in the annulus geometry 46,47 and lane configurations 44 demonstrate that confinement can tame this turbulence to generate ordered flows. However, despite these experiments and previous theoretical investigations of active nematics confined in channels, 24,28,37,43,44,56–58 disks, 45,46,59,60 and annulus geometries, 37,46,47,61,62 the influence of channel curvature and finite channel length on emergent behaviors is yet to be studied in detail.…”

Soft confinement of self-propelled rods: simulation and theory

“…One method to study and control active matter is through geometric confinement. [4][5][6][7][8][9][10][11] Confinement introduces additional complexities to the dynamics of active matter, as interactions with boundaries profoundly influence the emergent properties of the system. [12][13][14][15][16][17][18][19][20] For active rods, the proportion of normal and parallel alignment to the confinement direction is set by the competition between activity-induced boundary accumulation (normal alignment) and entropy-mediated reorientation (parallel alignment).…”

Boundaries control active channel flows

“…Polar active fluids, such as dense suspensions of swimming bacteria, transition from laminar to undulating and periodic travelling flows upon increasing the channel width, eventually giving place to turbulent dynamics [21][22][23][24]. In active nematics, both numerical studies [25][26][27][28] and experiments with microtubule-kinesin suspensions [29] with strong anchoring to the channel walls have revealed a transition from laminar to oscillatory flows to a lattice of counter-rotating flow vortices with associated order of disclinations in the nematic texture. Similar flow states and transitions are also reported in other geometries, such as in circular confinement [15,19,30].…”