Young and Young–Laplace equations for a static ridge of nematic liquid crystal, and transitions between equilibrium states

Cousins, J. R.L. , Duffy, B. R., Wilson, S. K. and Mottram, N. J. (2022) Young and Young–Laplace equations for a static ridge of nematic liquid crystal, and transitions between equilibrium states. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 478(2259), 20210849. (doi: 10.1098/rspa.2021.0849) (PMID:35370444) (PMCID:PMC8966048)

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Abstract

Motivated by the need for greater understanding of systems that involve interfaces between a nematic liquid crystal, a solid substrate and a passive gas that include nematic–substrate–gas three-phase contact lines, we analyse a two-dimensional static ridge of nematic resting on a solid substrate in an atmosphere of passive gas. Specifically, we obtain the first complete theoretical description for this system, including nematic Young and Young–Laplace equations, and then, making the assumption that anchoring breaking occurs in regions adjacent to the contact lines, we use the nematic Young equations to determine the continuous and discontinuous transitions that occur between the equilibrium states of complete wetting, partial wetting and complete dewetting. In particular, in addition to continuous transitions analogous to those that occur in the classical case of an isotropic liquid, we find a variety of discontinuous transitions, as well as contact-angle hysteresis, and regions of parameter space in which there exist multiple partial wetting states that do not occur in the classical case.

Item Type:Articles
Keywords:Nematic liquid crystals, wetting, dewetting, Young equation, Young–Laplace equation.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Mottram, Professor Nigel and Cousins, Dr Joseph
Authors: Cousins, J. R.L., Duffy, B. R., Wilson, S. K., and Mottram, N. J.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences
Publisher:The Royal Society
ISSN:1364-5021
ISSN (Online):1471-2946
Copyright Holders:Copyright © 2022 The Authors
First Published:First published in Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences: 478(2259): 20210849
Publisher Policy:Reproduced under a Creative Commons licence

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
311131Control of free-surface flow morphologies in anisotropic liquidsNigel MottramEngineering and Physical Sciences Research Council (EPSRC)EP/T012501/2M&S - Mathematics