Multiscale models of metallic particles in nematic liquid crystals
Multiscale models of metallic particles in nematic liquid crystals
In this paper we use the method of homogenization to derive a set of approximate equations which describe a nematic liquid crystal colloid in which the dopants are freely rotating metallic particles. Previously we have studied the approximate behavior of liquid crystals doped with particles under the assumption that these remain stationary [Bennett et al (2014), Phys Rev E 90, 062595]. This paper builds on Bennett et al (2014) by extending the theory to include rotating particles. We find a set of governing equations for the nematic liquid crystal and for the dopant particles. Effective material parameters are given explicitly in terms of the microscopic particle-liquid crystal interaction parameters by a sequence of cell problems solved on the micro-scale. We validate our model by direct comparison to large scale numerical simulation and find excellent agreement for a variety of dopants shapes.
homogenisation, nematic liquid crystal, colloidal particles, approximation methods, Numerical methods
1228–1255
Bennett, Thomas P.
9a342b50-e08a-47a8-adb2-1d8d51a9604b
D'Alessandro, Giampaolo
bad097e1-9506-4b6e-aa56-3e67a526e83b
Daly, Keith R.
29920932-1779-4d08-81f8-bdd898191e5a
24 April 2018
Bennett, Thomas P.
9a342b50-e08a-47a8-adb2-1d8d51a9604b
D'Alessandro, Giampaolo
bad097e1-9506-4b6e-aa56-3e67a526e83b
Daly, Keith R.
29920932-1779-4d08-81f8-bdd898191e5a
Bennett, Thomas P., D'Alessandro, Giampaolo and Daly, Keith R.
(2018)
Multiscale models of metallic particles in nematic liquid crystals.
SIAM Journal on Applied Mathematics, 78 (2), .
(doi:10.1137/18M1163919).
Abstract
In this paper we use the method of homogenization to derive a set of approximate equations which describe a nematic liquid crystal colloid in which the dopants are freely rotating metallic particles. Previously we have studied the approximate behavior of liquid crystals doped with particles under the assumption that these remain stationary [Bennett et al (2014), Phys Rev E 90, 062595]. This paper builds on Bennett et al (2014) by extending the theory to include rotating particles. We find a set of governing equations for the nematic liquid crystal and for the dopant particles. Effective material parameters are given explicitly in terms of the microscopic particle-liquid crystal interaction parameters by a sequence of cell problems solved on the micro-scale. We validate our model by direct comparison to large scale numerical simulation and find excellent agreement for a variety of dopants shapes.
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Accepted/In Press date: 30 January 2018
e-pub ahead of print date: 24 April 2018
Published date: 24 April 2018
Keywords:
homogenisation, nematic liquid crystal, colloidal particles, approximation methods, Numerical methods
Identifiers
Local EPrints ID: 419329
URI: http://eprints.soton.ac.uk/id/eprint/419329
ISSN: 0036-1399
PURE UUID: ba388d45-80c9-48a3-873e-007097b71103
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Date deposited: 10 Apr 2018 16:30
Last modified: 16 Mar 2024 06:25
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Author:
Thomas P. Bennett
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