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

Published online by Cambridge University Press:  22 April 2015

M. A. LAM ,
L. J. CUMMINGS ,
T.-S. LIN  and
L. KONDIC
M. A. LAM
Affiliation:
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ, 07102 email: mal37@njit.edu, Linda.Cummings@njit.edu, kondic@njit.edu
L. J. CUMMINGS
Affiliation:
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ, 07102 email: mal37@njit.edu, Linda.Cummings@njit.edu, kondic@njit.edu
T.-S. LIN
Affiliation:
Department of Applied Mathematics, National Chiao Tung University, 1001 Ta Heueh Road, Hsinchu 300, Taiwan email: tslin@math.nctu.edu.tw
L. KONDIC
Affiliation:
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ, 07102 email: mal37@njit.edu, Linda.Cummings@njit.edu, kondic@njit.edu
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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.

Keywords

Thin filmsliquid crystalscontact linesand gravity driven flow
Type
Papers
Information
European Journal of Applied Mathematics , Volume 26 , Special Anniversay Issue 5: Celebrating 75 years , October 2015 , pp. 647 - 669
Copyright
Copyright © Cambridge University Press 2015 

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Footnotes

†

This work was supported by NSF grant DMS-1211713.

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