Insensitivity of active nematic liquid crystal dynamics to topological constraints

Abstract

Confining a liquid crystal imposes topological constraints on the orientational order, allowing global control of equilibrium systems by manipulation of anchoring boundary conditions. In this article, we investigate whether a similar strategy allows control of active liquid crystals. We study a hydrodynamic model of an extensile active nematic confined in containers, with different anchoring conditions that impose different net topological charges on the nematic director. We show that the dynamics are controlled by a complex interplay between topological defects in the director and their induced vortical flows. We find three distinct states by varying confinement and the strength of the active stress: a topologically minimal state, a circulating defect state, and a turbulent state. In contrast to equilibrium systems, we find that anchoring conditions are screened by the active flow, preserving system behavior across different topological constraints. This observation identifies a fundamental difference between active and equilibrium materials.

Self-organized dynamics and the transition to turbulence of confined active nematics

“…Existing continuum theories of active nematics predict suppression of spontaneous flows below a critical length scale and activity threshold, density flux from high to low director curvature, chaotic dynamics at high activity and large length scales; and regular circulating flows in the intermediate regime [7,[21][22][23][24][25][26]43]. While these models are not identical, nor are the applied boundary conditions, they all fail to predict both the doubly-periodic dynamics at intermediate confinement and the two-step route to bulk-like turbulence.…”

“…However, the full extent to which the dynamics of active liquid crystals can be prescribed through control of the boundaries remains an open question. For example, recent theoretical work suggests that circular confinement generate robust circular flows that are largely independent of the details of the director boundary conditions [21].…”

Reconfigurable flows and defect landscape of confined active nematics

“…This results in bend instabilities that grow perpendicular to the walls with the weak strength of the anchoring allowing the director to deviate from a planar configuration at the positions where the bend instability is developed. Previous simulations that assumed no-slip velocity and strong alignment conditions on the confinement did not observe defect nucleation at the boundaries [30,45], and showed insensitivity of the active nematic patterns to the boundary conditions [45]. This is because the strong anchoring used in these works prevented defects forming at the walls.…”

Active matter invasion

“…In addition to the bulk dynamics, the interaction with walls or obstacles of different shape can add further complexity. Theoretically, using the active nematohydrodynamics framework, a transition to spontaneous flows in channels has been predicted [49,50], as well as more complex states with intricate interplay of defects and vortices, and a transition to active turbulence [51,52,53].…”