Steady-state hydrodynamic instabilities of active liquid crystals: Hybrid lattice Boltzmann simulations

TL;DR

This paper uses hybrid lattice Boltzmann simulations to explore the complex steady-state hydrodynamic instabilities of active nematic liquid crystals, revealing phase transitions, hysteresis, and spontaneous flow patterns driven by activity and anchoring conditions.

Contribution

It introduces a robust hybrid simulation method to analyze steady-state behaviors and instabilities in active nematics, highlighting phenomena absent in passive systems.

Findings

Existence of a transition from passive to active phase with spontaneous flow.

Hysteresis and history-dependent steady states in flow-aligning active nematics.

Spontaneous flow patterns such as convection rolls and banded flows.

Abstract

We report hybrid lattice Boltzmann (HLB) simulations of the hydrodynamics of an active nematic liquid crystal sandwiched between confining walls with various anchoring conditions. We confirm the existence of a transition between a passive phase and an active phase, in which there is spontaneous flow in the steady state. This transition is attained for sufficiently ``extensile'' rods, in the case of flow-aligning liquid crystals, and for sufficiently ``contractile'' ones for flow-tumbling materials. In a quasi-1D geometry, deep in the active phase of flow-aligning materials, our simulations give evidence of hysteresis and history-dependent steady states, as well as of spontaneous banded flow. Flow-tumbling materials, in contrast, re-arrange themselves so that only the two boundary layers flow in steady state. Two-dimensional simulations, with periodic boundary conditions, show additional instabilities, with the spontaneous flow appearing as patterns made up of ``convection rolls''. These results demonstrate a remarkable richness (including dependence on anchoring conditions) in the steady-state phase behaviour of active materials, even in the absence of external forcing; they have no counterpart for passive nematics. Our HLB methodology, which combines lattice Boltzmann for momentum transport with a finite difference scheme for the order parameter dynamics, offers a robust and efficient method for probing the complex hydrodynamic behaviour of active nematics.