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Non-linear dynamics of a nematic liquid crystal in the presence of a shear flow

Non-linear dynamics of a nematic liquid crystal in the presence of a shear flow
Non-linear dynamics of a nematic liquid crystal in the presence of a shear flow
In this paper we study a Landau-de Gennes model of a nematic liquid crystal in a model shear flow employing a range of analytical and numerical techniques. We use asymptotic methods and numerical bifurcation theory to provide a comprehensive description of the different in-plane modes that exist in terms of the temperature and imposed shear rate, as well as determining their stability to in-plane disturbances. We show that there are two physically distinct solution branches, one of which corresponds to an in-plane director (denoted IPN). The other branch corresponds to the director being aligned perpendicular to the shear plane, i.e. so-called log-rolling states. We find both tumbling and wagging time-dependent modes. The mode structure is organized by a Takens-Bogdanov point, at which a family of Hopf bifurcation points and a family of limit points coincide. At low strain rates tumbling occurs as a transition from the IPN branch. In addition, we show that at larger values of the strain rate the wagging modes emanate from a Hopf bifurcation on the IPN branch and evolve continuously into tumbling modes. Moreover, we show analytically that this boundary between tumbling and wagging corresponds to a state in which the distribution function is cylindrical in the shear plane. This provides confirmation of the tumbling-wagging transition mechanism observed by Tsuji and Rey in numerical calculations relating to a confined geometry.
nematic liquid crystal, shear flow, bifurcation theory, takens-bogdanov point
1364-5021
195-220
Vicente Alonso, E.
6185ff83-c015-46c8-98a1-2696544afd7b
Wheeler, A.A.
eb831100-6e51-4674-878a-a2936ad04d73
Sluckin, T.J.
8dbb6b08-7034-4ae2-aa65-6b80072202f6
Vicente Alonso, E.
6185ff83-c015-46c8-98a1-2696544afd7b
Wheeler, A.A.
eb831100-6e51-4674-878a-a2936ad04d73
Sluckin, T.J.
8dbb6b08-7034-4ae2-aa65-6b80072202f6

Vicente Alonso, E., Wheeler, A.A. and Sluckin, T.J. (2003) Non-linear dynamics of a nematic liquid crystal in the presence of a shear flow. Proceedings of the Royal Society A, 459 (2029), 195-220. (doi:10.1098/rspa.2002.1019).

Record type: Article

Abstract

In this paper we study a Landau-de Gennes model of a nematic liquid crystal in a model shear flow employing a range of analytical and numerical techniques. We use asymptotic methods and numerical bifurcation theory to provide a comprehensive description of the different in-plane modes that exist in terms of the temperature and imposed shear rate, as well as determining their stability to in-plane disturbances. We show that there are two physically distinct solution branches, one of which corresponds to an in-plane director (denoted IPN). The other branch corresponds to the director being aligned perpendicular to the shear plane, i.e. so-called log-rolling states. We find both tumbling and wagging time-dependent modes. The mode structure is organized by a Takens-Bogdanov point, at which a family of Hopf bifurcation points and a family of limit points coincide. At low strain rates tumbling occurs as a transition from the IPN branch. In addition, we show that at larger values of the strain rate the wagging modes emanate from a Hopf bifurcation on the IPN branch and evolve continuously into tumbling modes. Moreover, we show analytically that this boundary between tumbling and wagging corresponds to a state in which the distribution function is cylindrical in the shear plane. This provides confirmation of the tumbling-wagging transition mechanism observed by Tsuji and Rey in numerical calculations relating to a confined geometry.

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More information

Published date: 2003
Keywords: nematic liquid crystal, shear flow, bifurcation theory, takens-bogdanov point

Identifiers

Local EPrints ID: 29594
URI: http://eprints.soton.ac.uk/id/eprint/29594
ISSN: 1364-5021
PURE UUID: faa30ab5-97c1-426b-a895-b0568e968c40
ORCID for T.J. Sluckin: ORCID iD orcid.org/0000-0002-9163-0061

Catalogue record

Date deposited: 12 May 2006
Last modified: 09 Jan 2022 02:32

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Contributors

Author: E. Vicente Alonso
Author: A.A. Wheeler
Author: T.J. Sluckin ORCID iD

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