Three-dimensional coating flow of nematic liquid crystal on an inclined substrate

M. A. Lam, L. J. Cummings, T. S. Lin, L. Kondic

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We consider a coating flow of nematic liquid crystal (NLC) fluid film on an inclined substrate. Exploiting the small aspect ratio in the geometry of interest, a fourth-order nonlinear partial differential equation is used to model the free surface evolution. Particular attention is paid to the interplay between the bulk elasticity and the anchoring conditions at the substrate and free surface. Previous results have shown that there exist two-dimensional travelling wave solutions that translate down the substrate. In contrast to the analogous Newtonian flow, such solutions may be unstable to streamwise perturbations. Extending well-known results for Newtonian flow, we analyse the stability of the front with respect to transverse perturbations. Using full numerical simulations, we validate the linear stability theory and present examples of downslope flow of nematic liquid crystal in the presence of both transverse and streamwise instabilities.

Original languageEnglish (US)
Pages (from-to)647-669
Number of pages23
JournalEuropean Journal of Applied Mathematics
Volume26
Issue number5
DOIs
StatePublished - Oct 1 2015

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Keywords

  • Thin films
  • contact lines
  • gravity driven flow
  • liquid crystals

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