title: Steady-state hydrodynamic instabilities of active liquid crystals: hybrid lattice Boltzmann simulations.
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-one-dimensional 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, rearrange 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 behavior 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 behavior of active nematics.
authors.affiliation: SUPA, School of Physics, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, Scotland.
authors.forename: D
authors.initials: D
authors.lastname: Marenduzzo
authors.forename: E
authors.initials: E
authors.lastname: Orlandini
authors.forename: M E
authors.initials: ME
authors.lastname: Cates
authors.forename: J M
authors.initials: JM
authors.lastname: Yeomans