Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-13T11:28:44.422Z Has data issue: false hasContentIssue false
  • English
  • Français

Modelling spreading dynamics of nematic liquid crystals in three spatial dimensions

Published online by Cambridge University Press:  16 July 2013

T.-S. Lin ,
L. Kondic ,
U. Thiele  and
L. J. Cummings
T.-S. Lin*
Affiliation:
Department of Mathematical Sciences, Loughborough University, Leicestershire LE11 3TU, UK
L. Kondic
Affiliation:
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA
U. Thiele
Affiliation:
Department of Mathematical Sciences, Loughborough University, Leicestershire LE11 3TU, UK
L. J. Cummings
Affiliation:
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We study spreading dynamics of nematic liquid crystal droplets within the framework of the long-wave approximation. A fourth-order nonlinear parabolic partial differential equation governing the free surface evolution is derived. The influence of elastic distortion energy and of imposed anchoring variations at the substrate are explored through linear stability analysis and scaling arguments, which yield useful insight and predictions for the behaviour of spreading droplets. This behaviour is captured by fully nonlinear time-dependent simulations of three-dimensional droplets spreading in the presence of anchoring variations that model simple defects in the nematic orientation at the substrate.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Complex Fluids: Liquid crystals Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 729 , 25 August 2013 , pp. 214 - 230
Copyright
©2013 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barbero, G. & Berberi, R. 1983 Critical thickness of a hybrid aligned nematic liquid crystal cell. J. Phys. (Paris) 44, 609.Google Scholar
Ben Amar, M. & Cummings, L. J. 2001 Fingering instabilities in driven thin nematic films. Phys. Fluids 13, 1160.Google Scholar
Blossey, R., Münch, A., Rauscher, M. & Wagner, B. A. 2006 Slip vs. viscoelasticity in dewetting thin films. Eur. Phys. J. E 20, 267.CrossRefGoogle ScholarPubMed
Carou, J. Q., Mottram, N. J., Wilson, S. K. & Duffy, B. R. 2007 A mathematical model for blade coating of a nematic liquid crystal. Liq. Cryst. 34, 621.Google Scholar
Cummings, L. J. 2004 Evolution of a thin film of nematic liquid crystal with anisotropic surface energy. Eur. J. Appl. Maths 15, 651.Google Scholar
Cummings, L. J., Lin, T.-S. & Kondic, L. 2011 Modeling and simulations of the spreading and destabilization of nematic droplets. Phys. Fluids 23, 043102.Google Scholar
De Gennes, P. G. & Prost, J. 1995 The Physics of Liquid Crystals. Oxford University Press.Google Scholar
Delabre, U., Richard, C. & Cazabat, A. M. 2009 Thin nematic films on liquid substrates. J. Phys. Chem. B 13, 3647.Google Scholar
Lavrentovich, O. D. & Pergamenshchik, V. M. 1994 Stripe domain phase of a thin nematic film and the K13 divergence term. Phys. Rev. Lett. 73, 979.Google Scholar
Leslie, F. M. 1979 Theory of flow phenomena in liquid crystals. Adv. Liq. Cryst. 4, 1.Google Scholar
Lin, T.-S., Cummings, L. J., Archer, A. J., Kondic, L. & Thiele, U. 2013 Note on the hydrodynamic description of thin nematic films: strong anchoring model. http://arxiv.org/abs/1301.4110.CrossRefGoogle Scholar
Lin, T.-S., Kondic, L. & Cummings, L. J. 2012a Defect modeling in spreading nematic droplets. Phys. Rev. E 85, 012702.Google Scholar
Lin, T.-S., Kondic, L. & Filippov, A. 2012b Thin films flowing down inverted substrates: three-dimensional flow. Phys. Fluids 24, 022105.Google Scholar
Manyuhina, O. V. & Ben Amar, M. 2013 Thin nematic films: anchoring effects and stripe instability revisited. Phys. Lett. A 377, 1003.Google Scholar
Manyuhina, O. V., Cazabat, A. M. & Ben Amar, M. 2010 Instability patterns in ultrathin nematic films: comparison between theory and experiment. Europhys. Lett. 92, 16005.Google Scholar
Mechkov, S., Cazabat, A. M. & Oshanin, G. 2009 Post-Tanner spreading of nematic droplets. J. Phys.: Condens. Matter 21, 464134.Google Scholar
Mitlin, V. S. 1993 Dewetting of solid surface: analogy with spinodal decomposition. J. Colloid Interface Sci. 156, 491.Google Scholar
Münch, A., Wagner, B. A., Rauscher, M. & Blossey, R. 2006 A thin film model for corota- tional Jeffreys fluids under strong slip. Eur. Phys. J. E 20, 365.Google Scholar
Myers, T. G. 2005 Application of non-Newtonian models to thin film flow. Phys. Rev. E 72, 066302.Google Scholar
Poulard, C. & Cazabat, A. M. 2005 Spontaneous spreading of nematic liquid crystals. Langmuir 21, 6270.Google Scholar
Sparavigna, A., Lavrentovich, O. D. & Strigazzi, A. 1994 Periodic stripe domains and hybrid-alignment regime in nematic liquid crystals: threshold analysis. Phys. Rev. E 49, 1344.Google Scholar
Thiele, U. 2010 Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth. J. Phys.: Condens. Matter 22, 084019.Google Scholar
Thiele, U. 2011 Note on thin film equations for solutions and suspensions. Eur. Phys. J. Special Topics 197, 213.Google Scholar
Thiele, U., Archer, A. J. & Plapp, M. 2012 Thermodynamically consistent description of the hydrodynamics of free surfaces covered by insoluble surfactants of high concentration. Phys. Fluids 24, 102107.Google Scholar
Witelski, T. P. & Bowen, M. 2003 ADI schemes for higher-order nonlinear diffusion equations. Appl. Numer. Maths 45, 331.Google Scholar