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-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.

18 eps figures, accepted for publication in Phys. Rev. E

References in corpus (5)

• Generic phase diagram of active polar films
• Rheology of Active Filament Solutions
• Dynamic regimes of hydrodynamically coupled self-propelling particles
• A Lattice-Boltzmann model for suspensions of self-propelling colloidal particles
• Internal Motility in Stiffening Actin-Myosin Networks

Cited by in corpus (16)

• Topology and Dynamics of Active Nematic Vesicles
• Pushing off the walls: a mechanism of cell motility in confinement
• Shearing active gels close to the isotropic-nematic transition
• Biphasic, Lyotropic, Active Nematics
• Spontaneous flow states in active nematics: a unified picture
• Sheared active fluids: thickening, thinning and vanishing viscosity
• Excitable Patterns in Active Nematics
• Complex Spontaneous Flows and Concentration Banding in Active Polar Films
• Minimal continuum theories of structure formation in dense active fluids
• Colloids in Cholesterics: Size-Dependent Defects and Non-Stokesian Microrheology
• Active nematic materials with substrate friction
• The effect of anchoring on nematic flow in channels
• Stress reorganisation and response in active solids
• Driven active and passive nematics
• The need for inertia in nonequilibrium steady states of sheared binary fluids
• Flexoelectric switching in cholesteric blue phases