Boundary Layers in Pressure-driven Flow in Smectic A Liquid Crystals

Abstract

Abstract. This article examines the steady flow of a smectic A liquid crystal sample that is initially aligned in a classical "bookshelf" geometry confined between parallel plates and is then subjected to a lateral pressure gradient which is perpendicular to the initial local smectic layer arrangement. The nonlinear dynamic equations are derived. These equations can be linearized and solved exactly to reveal two characteristic length scales that can be identified in terms of the material parameters and reflect the boundary layer behavior of the velocity and the director and smectic layer normal orientations. The asymptotic properties of the nonlinear equations are then investigated to find that these length scales apparently manifest themselves in various aspects of the solutions to the nonlinear steady state equations, especially in the separation between the orientations of the director and smectic layer normal. Non-Newtonian plug-like flow occurs and the solutions for the director profile and smectic layer normal share features identified elsewhere in static liquid crystal configurations. Comparisons with numerical solutions of the nonlinear equations are also made.

Two-dimensional flow and linear stability properties of smectic A liquid crystals

“…We first linearised the full system of equations comprising this theory to obtain a simplified set of equations governing the dominant behaviour of the SmA in response to small disturbances around its reference configuration. The resultant system was then used to describe a simple two-dimensional plug-like flow pattern and accompanying director and layer configurations; the solutions were found to be in agreement with the results of Stewart et al [32]. Next, an analysis regarding the stability of an initially planaraligned sample of SmA using this system of equations was found to yield regimes in which one could realistically expect to see instabilities arise, as demonstrated by examination of the three stability criteria (5.15)-(5.17).…”

“…A more detailed account of pressure-driven flow applied perpendicularly to the layered structure may be found in the work of Stewart et al [32], in which the asymptotic properties of the nonlinear system are analysed. However, it is evident that the linear system considered here is sufficient for prediction of the leading-order flow and alignment behaviour, and can be used to study features of a variety of other twodimensional flow patterns and gain insight into dominant modes of SmA behaviour.…”

Configuration of a smectic A liquid crystal due to an isolated edge dislocation

“…3-4 for various values of the relevant elasticity and energy terms. The differences between the predictions of the more general framework of De Vita and Stewart and those of the classical case justify the use of the former as a model for SmA samples in which this separation plays a non-negligible role in determining their behaviour in equilibrium settings such as that considered here and when undergoing motion (see, for instance, reference [23]). Given that significant decoupling between n and a has been demonstrated in previous work [1-3, 7, 19], it is clear that such a model provides valuable insight which is surely necessary for those wishing to fully understand the rich and complex behaviour of the SmA phase.…”