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Modelling spreading dynamics of nematic liquid crystals in three spatial dimensions

Published online by Cambridge University Press:  16 July 2013

T.-S. Lin ,
L. Kondic ,
U. Thiele  and
L. J. Cummings
T.-S. Lin*
Affiliation:
Department of Mathematical Sciences, Loughborough University, Leicestershire LE11 3TU, UK
L. Kondic
Affiliation:
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA
U. Thiele
Affiliation:
Department of Mathematical Sciences, Loughborough University, Leicestershire LE11 3TU, UK
L. J. Cummings
Affiliation:
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA
*
†Email address for correspondence: t.lin@lboro.ac.uk
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Abstract

We study spreading dynamics of nematic liquid crystal droplets within the framework of the long-wave approximation. A fourth-order nonlinear parabolic partial differential equation governing the free surface evolution is derived. The influence of elastic distortion energy and of imposed anchoring variations at the substrate are explored through linear stability analysis and scaling arguments, which yield useful insight and predictions for the behaviour of spreading droplets. This behaviour is captured by fully nonlinear time-dependent simulations of three-dimensional droplets spreading in the presence of anchoring variations that model simple defects in the nematic orientation at the substrate.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Complex Fluids: Liquid crystals Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 729 , 25 August 2013 , pp. 214 - 230
Copyright
©2013 Cambridge University Press 

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