Modeling flow of nematic liquid crystal down an incline

M. A. Lam*, L. J. Cummings, Te-Sheng Lin, L. Kondic

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


The flow of nematic liquid crystals down an inclined substrate is studied. Under the usual long wave approximation, a fourth-order nonlinear parabolic partial differential equation of the diffusion type is derived for the free surface height. The model accounts for elastic distortions of the director field due to different anchoring conditions at the substrate and the free surface. The partial differential equation we derive admits 2D traveling-wave solutions, which may translate stably or exhibit instabilities in the flat film behind the traveling front. These instabilities, which are distinct from the usual transverse instability of downslope flow, may be analyzed and explained by linear stability analysis of a flat translating film. Intriguing parallels are found with the instabilities exhibited by Newtonian fluid flowing on an inverted substrate and Newtonian fluid flow outside a vertical cylinder.

Original languageEnglish
Pages (from-to)97-113
Number of pages17
JournalJournal of Engineering Mathematics
Issue number1
StatePublished - 29 Oct 2015


  • Inclined plane
  • Liquid crystal
  • Nematic
  • Thin film


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