Boundary layers in pressure-driven flow in smectic A liquid crystals

I. W. Stewart, M. Vynnycky, S. McKee, M. F. Tomé

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.
LanguageEnglish
Pages1817-1851
Number of pages35
JournalSIAM Journal on Applied Mathematics
Volume75
Issue number4
Early online date26 Aug 2015
DOIs
Publication statusPublished - 1 Sep 2015

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Nonlinear equations
Liquid Crystal
Liquid crystals
Boundary Layer
Boundary layers
Nonlinear Equations
Steady flow
Pressure gradient
Length Scale
Geometry
State Equation
Pressure Gradient
Steady Flow
Dynamic Equation
Perpendicular
Nonlinear Dynamics
Asymptotic Properties
Lateral
Arrangement
Numerical Solution

Keywords

  • smectic A liquid crystals
  • flow dynamics
  • continuum theory
  • analytic solution

Cite this

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Boundary layers in pressure-driven flow in smectic A liquid crystals. / Stewart, I. W.; Vynnycky, M.; McKee, S.; Tomé, M. F.

In: SIAM Journal on Applied Mathematics , Vol. 75, No. 4, 01.09.2015, p. 1817-1851.

Research output: Contribution to journalArticle

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AU - McKee, S.

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AB - 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.

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