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.

Geometry of thresholdless active flow in nematic microfluidics

“…In this paper we describe conditions for active flow that may be realized for systems with length scales less than L inst , which also corresponds to the limit of small activity. Numerical studies of active nematics suggest that some nonuniform director configurations can lead to laminar flow for arbitrarily small activity, i.e., well below the instability threshold [25]. However, no systematic study of the mechanisms and criteria behind such thresholdless active flow has previously been undertaken.…”

“…However, if the activity parameter α (defined later) exceeds a critical threshold α c , the undistorted nematic ground state becomes unstable. Once this instability threshold is passed, the active nematics spontaneously deform their state of alignment, triggering macroscopic turbulent flow [2,18,[25][26][27][28]. For nematics, this activity threshold α c goes to zero as the system size L → ∞, α c ∼ K L 2 , where K is a characteristic Frank elastic constant.…”

The effect of anchoring on the nematic flow in channels

“…(3,4) are iterated using a lattice Boltzmann method and Eqn. (5) by a finite-difference method 36 , a method that has been previously used by our group when considering a nematic liquid crystal in contact with a substrate patterned with rectangular grooves that may fill without the occurrence of complete wetting 37 . In this study this numerical code was used to analyse the dynamical response of the system to an externally-applied electric field so as to identify switching transitions between these filled states.…”

Mechanisms of Cell Motion in Confined Geometries

“…Motion due to polymerisation [2,24] and to contractility [26] have now been observed experimentally and studied theoretically [14,15,16,32,33,35] and numerically [22,23]. In all these models the essential ingredients for motion are an energy input to overcome dissipation and sufficient adhesion or friction with a substrate to transfer momentum.…”