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

Document Type

Article

Publication Date

10-1-2015

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.

Identifier

84948099698 (Scopus)

Publication Title

European Journal of Applied Mathematics

External Full Text Location

https://doi.org/10.1017/S0956792515000091

e-ISSN

14694425

ISSN

09567925

First Page

647

Last Page

669

Issue

5

Volume

26

Grant

DMS-1211713

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