Flow near a sharp corner in a nematic liquid crystal

Abstract

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Díez M. and Atkinson C. 2000Flow near a sharp corner in a nematic liquid crystalProc. R. Soc. Lond. A.45663–95http://doi.org/10.1098/rspa.2000.0509SectionRestricted accessFlow near a sharp corner in a nematic liquid crystal M. Díez M. Díez Escuela Superior de Ingenieros Industriales, Universidad de Navarra, P. Manuel Lardizábal 13, 20018 San Sebastián, Spain Google Scholar Find this author on PubMed Search for more papers by this author and C. Atkinson C. Atkinson Department of Mathematics, Imperial College of Science, Technology and Medicine, 180Que en's Gate, London SW7 2BZ, UK Google Scholar Find this author on PubMed Search for more papers by this author M. Díez M. Díez Escuela Superior de Ingenieros Industriales, Universidad de Navarra, P. Manuel Lardizábal 13, 20018 San Sebastián, Spain Google Scholar Find this author on PubMed Search for more papers by this author and C. Atkinson C. Atkinson Department of Mathematics, Imperial College of Science, Technology and Medicine, 180Que en's Gate, London SW7 2BZ, UK Google Scholar Find this author on PubMed Search for more papers by this author Published:08 January 2000https://doi.org/10.1098/rspa.2000.0509AbstractSolutions are presented for the orientation and flow of a positive nematic liquid crystal near a corner between two planes on which a variety of boundary conditions may be imposed.The flow near the corner is induced by a general motion at a large distance from the corner, which can make the flow symmetric or antisymmetric with respect to the bisector of the angle. The real situation may be a combination of both.The viscosity, usually a damping mechanism, may be responsible for the generation of a geometrical progression of eddies. The smaller the angle between plates, the more probable the existence of eddies. The critical wedge angle for the appearance of eddies is also investigated.The conditions considered are rigid walls and no–slip conditions at the boundaries, which have been treated in order to get a perfect alignment of the directors. For the two specific examples analysed, PAA near 125°C and MBBA near 25°C, eddies only appear in MBBA for an angle between plates smaller than 60°, when the flow induced near the corner is antisymmetric with respect to the bisector of the plates. In this case, the flow near the corner consists of a sequence of eddies whose size and intensity fall off in geometric progression with a ratio depending only on the angle between plates.PAA and MBBA present this qualitative change in behaviour because the viscosity coefficients are much smaller in magnitude in PAA than in MBBA. We construct a nematic liquid crystal with Leslie coefficients, which vary monotonically between the two sets of coefficients for PAA and MBBA. Writing the six viscosity coefficients as μ = μiP + (1 − x)μiM, with i = 1, 6, where the superscript ‘M’ is for MBBA and ‘P’ is for PAA, we find that the critical wedge angle at which eddies would appear (in antisymmetric flow) decreases as x increases from zero to one. The critical wedge angle is zero for x > 0.974 approximately, so no eddies exist in these cases. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Walker A and Stewart I (2011) Wave-induced perturbations in cylindrically layered smectic A liquid crystals, Zeitschrift für angewandte Mathematik und Physik, 10.1007/s00033-011-0155-y, 63:2, (357-371), Online publication date: 1-Apr-2012. Walker A and Stewart I (2007) Periodic Disturbances in Cylindrically Layered Smectic A, Molecular Crystals and Liquid Crystals, 10.1080/15421400701731995, 478:1, (33/[789]-43/[799]), Online publication date: 14-Dec-2007. This Issue08 January 2000Volume 456Issue 1993 Article InformationDOI:https://doi.org/10.1098/rspa.2000.0509Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/01/2000Published in print08/01/2000 License: Citations and impact KeywordsPAAcornerviscosity coefficientsMBBAnematicliquid crystal