Modeling flow of nematic liquid crystal down an incline

Document Type

Article

Publication Date

10-29-2015

Abstract

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.

Identifier

84942505809 (Scopus)

Publication Title

Journal of Engineering Mathematics

External Full Text Location

https://doi.org/10.1007/s10665-014-9697-2

e-ISSN

15732703

ISSN

00220833

First Page

97

Last Page

113

Issue

1

Volume

94

Grant

DMS-0908158

Fund Ref

National Science Foundation

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