Note on the hydrodynamic description of thin nematic films: Strong anchoring model

Handle URI:
http://hdl.handle.net/10754/599006
Title:
Note on the hydrodynamic description of thin nematic films: Strong anchoring model
Authors:
Lin, Te-Sheng; Cummings, Linda J.; Archer, Andrew J.; Kondic, Lou; Thiele, Uwe
Abstract:
We discuss the long-wave hydrodynamic model for a thin film of nematic liquid crystal in the limit of strong anchoring at the free surface and at the substrate. We rigorously clarify how the elastic energy enters the evolution equation for the film thickness in order to provide a solid basis for further investigation: several conflicting models exist in the literature that predict qualitatively different behaviour. We consolidate the various approaches and show that the long-wave model derived through an asymptotic expansion of the full nemato-hydrodynamic equations with consistent boundary conditions agrees with the model one obtains by employing a thermodynamically motivated gradient dynamics formulation based on an underlying free energy functional. As a result, we find that in the case of strong anchoring the elastic distortion energy is always stabilising. To support the discussion in the main part of the paper, an appendix gives the full derivation of the evolution equation for the film thickness via asymptotic expansion. © 2013 AIP Publishing LLC.
Citation:
Lin T-S, Cummings LJ, Archer AJ, Kondic L, Thiele U (2013) Note on the hydrodynamic description of thin nematic films: Strong anchoring model. Phys Fluids 25: 082102. Available: http://dx.doi.org/10.1063/1.4816508.
Publisher:
AIP Publishing
Journal:
Physics of Fluids
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
2013
DOI:
10.1063/1.4816508
Type:
Article
ISSN:
1070-6631
Sponsors:
T.L. and U.T. acknowledge support from the European Union (EU) under Grant No. MRTN-CT-2004-005728 (MULTIFLOW). U.T. would like to thank Gunter Grun for an invitation to Bonn in October 2004 where they did a derivation similar to that in the appendix and discussed the sign of the elasticity term in the resulting evolution equation. L.J.C. and L.K. acknowledge support from the National Science Foundation (NSF) under Award Nos. DMS-0908158 and DMS-1211713, and L.J.C. also acknowledges support from KAUST under Award No. KUK-C1-013-04.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorLin, Te-Shengen
dc.contributor.authorCummings, Linda J.en
dc.contributor.authorArcher, Andrew J.en
dc.contributor.authorKondic, Louen
dc.contributor.authorThiele, Uween
dc.date.accessioned2016-02-25T13:51:03Zen
dc.date.available2016-02-25T13:51:03Zen
dc.date.issued2013en
dc.identifier.citationLin T-S, Cummings LJ, Archer AJ, Kondic L, Thiele U (2013) Note on the hydrodynamic description of thin nematic films: Strong anchoring model. Phys Fluids 25: 082102. Available: http://dx.doi.org/10.1063/1.4816508.en
dc.identifier.issn1070-6631en
dc.identifier.doi10.1063/1.4816508en
dc.identifier.urihttp://hdl.handle.net/10754/599006en
dc.description.abstractWe discuss the long-wave hydrodynamic model for a thin film of nematic liquid crystal in the limit of strong anchoring at the free surface and at the substrate. We rigorously clarify how the elastic energy enters the evolution equation for the film thickness in order to provide a solid basis for further investigation: several conflicting models exist in the literature that predict qualitatively different behaviour. We consolidate the various approaches and show that the long-wave model derived through an asymptotic expansion of the full nemato-hydrodynamic equations with consistent boundary conditions agrees with the model one obtains by employing a thermodynamically motivated gradient dynamics formulation based on an underlying free energy functional. As a result, we find that in the case of strong anchoring the elastic distortion energy is always stabilising. To support the discussion in the main part of the paper, an appendix gives the full derivation of the evolution equation for the film thickness via asymptotic expansion. © 2013 AIP Publishing LLC.en
dc.description.sponsorshipT.L. and U.T. acknowledge support from the European Union (EU) under Grant No. MRTN-CT-2004-005728 (MULTIFLOW). U.T. would like to thank Gunter Grun for an invitation to Bonn in October 2004 where they did a derivation similar to that in the appendix and discussed the sign of the elasticity term in the resulting evolution equation. L.J.C. and L.K. acknowledge support from the National Science Foundation (NSF) under Award Nos. DMS-0908158 and DMS-1211713, and L.J.C. also acknowledges support from KAUST under Award No. KUK-C1-013-04.en
dc.publisherAIP Publishingen
dc.titleNote on the hydrodynamic description of thin nematic films: Strong anchoring modelen
dc.typeArticleen
dc.identifier.journalPhysics of Fluidsen
dc.contributor.institutionLoughborough University, Loughborough,en
dc.contributor.institutionNew Jersey Institute of Technology, Newark, United Statesen
kaust.grant.numberKUK-C1-013-04en
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