Pressure-driven changes to spontaneous flow in active nematic liquid crystals

Joshua Walton,Nigel J Mottram,Michael Grinfeld,Geoffrey Mckay

doi:10.1140/epje/i2020-11973-8

Joshua Walton, Nigel J Mottram + Show 2 more

Open Access

https://doi.org/10.1140/epje/i2020-11973-8

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Abstract

.We consider the effects of a pressure gradient on the spontaneous flow of an active nematic liquid crystal in a channel, subject to planar anchoring and no-slip conditions on the boundaries of the channel. We employ a model based on the Ericksen-Leslie theory of nematics, with an additional active stress accounting for the activity of the fluid. By directly solving the flow equation, we consider an asymptotic solution for the director angle equation for large activity parameter values and predict the possible values of the director angle in the bulk of the channel. Through a numerical solution of the full nonlinear equations, we examine the effects of pressure on the branches of stable and unstable equilibria, some of which are disconnected from the no-flow state. In the absence of a pressure gradient, solutions are either symmetric or antisymmetric about the channel midpoint; these symmetries are changed by the pressure gradient. Considering the activity-pressure state space allows us to predict qualitatively the extent of each solution type and to show, for large enough pressure gradients, that a branch of non-trivial director angle solutions exists for all activity values.Graphical abstract

Highlights

The similarities between the macroscopic symmetries, flow and defect patterns generated in active fluids and those of elongated rod-like molecules in liquid crystals mean that continuum hydrodynamic models of nematic liquid crystals have commonly been adopted in the theoretical modelling of active fluids [2, 3]
We investigate the pressure-driven states in active nematics where we show how the stability of equilibria, in particular those of a certain symmetry, can be promoted through an applied pressure gradient, which, given the one-dimensional nature of the system, is constant
Poiseuille flow would be the result of applying a pressure gradient to the trivial state in the absence of activity, leading to a symmetric velocity and an antisymmetric director angle solution which vanishes in the centre of the channel

Summary

Introduction

The similarities between the macroscopic symmetries, flow and defect patterns generated in active fluids and those of elongated rod-like molecules in liquid crystals mean that continuum hydrodynamic models of nematic liquid crystals have commonly been adopted in the theoretical modelling of active fluids [2, 3]. Yang and Wang [39] consider the influence of active viscous stress tensor and self-propelling speed terms for channel flows of active polar liquid crystals The former is added to the stress tensor, whereas the latter enters the governing equation for the polar director field. We consider an active nematic liquid crystal, confined between two parallel plates at z = 0 and z = d, and subject to a pressure gradient parallel to the x-direction The dynamics of the fluid velocity and director angle can be modelled by the balance of linear and angular momentum through the Ericksen-Leslie equations for nematic liquid crystals [33, 34, 44], with the inclusion of the active stress term introduced in eq (1):. It is possible to decouple eqs. (2) and (3) using the same approach considered in Mottram et al [46], leading to a single, non-local, dynamic equation for the director angle, namely γ1

A B ζ sin θ cos θ

Extensile active nematic

Conclusions