Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T05:24:32.372Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical Simulations of Hydrodynamics of Nematic Liquid Crystals: Effects of Kinematic Transports

Published online by Cambridge University Press:  20 August 2015

Shupeng Zhang ,
Chun Liu  and
Hui Zhang
Shupeng Zhang*
Affiliation:
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
Chun Liu*
Affiliation:
Department of Mathematics, Pennsylvania State University, University Park, PA 18601, USA
Hui Zhang*
Affiliation:
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
*
Email:shupeng.zhang@gmail.com
Email:liu@math.psu.edu
Corresponding author.Email:hzhang@bnu.edu.cn
Get access

Abstract

In this paper, we investigate the effects of kinematic transports on the nematic liquid crystal system numerically and theoretically. The model we used is a “1+2” elastic continuum model simplified from the Ericksen-Leslie system. The numerical experiments are carried out by using a Legendre-Galerkin spectral method which can preserve the energy law in the discrete form. Based on this highly accurate numerical approach we find some interesting and important relationships between the kinematic transports and the characteristics of the flow. We make some analysis to explain these results. Several significant scaling properties are also verified by our simulations.

Keywords

65M7076A15Nematic liquid crystalskinematic transportsLegendre-Galerkin spectral methodtumblingflow-aligning
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 4 , April 2011 , pp. 974 - 993
Copyright
Copyright © Global Science Press Limited 2011

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

[1]Yu, H. and Zhang, P., A kinetic-hydrodynamic simulation of microstructure of liquid crystal polymers in plane shear flow, J. Non-Newtonian. Fluid. Mech., 141 (2007), 116–227.CrossRefGoogle Scholar
[2]Tsuji, T. and Rey, A. D., Orientation mode selection mechanisms for sheared nematic liquid crystalline materials, Phys. Rev. E., 57(5) (1998), 5610–5625.Google Scholar
[3]Feng, J. J., Tao, J. and Leal, L. G., Roll cells and disclinations in sheared nematic polymers, J. Fluid. Mech., 449 (2001), 179–200.Google Scholar
[4]Wang, Q., A hydrodynamic theory for solutions of nonhomogeneous nematic liquid crystalline polymers of different configurations, J. Chem. Phys., 116(20) (2002), 9120–9136.Google Scholar
[5]Chonoa, S., Tsujia, T. and Denn, M. M., Spatial development of director orientation of tumbling nematic liquid crystals in pressure-driven channel flow, J. Non-Newtonian. Fluid. Mech., 79 (1998), 515–527.CrossRefGoogle Scholar
[6]Lin, F. H. and Liu, C., Existence of solutions for the Ericksen-Leslie system, Arch. Rat. Mech. Anal., 154(2) (2000), 135–156.CrossRefGoogle Scholar
[7]Lin, F. H. and Liu, C., Nonparabolic dissipative systems modeling the flow of liquid crystals, Commun. Pure. Appl. Math., 48(5) (1995), 501–537.Google Scholar
[8]Lin, P., Liu, C. and Zhang, H., An energy law preserving C 0 finite element scheme for simulating the kinematic effects in liquid crystal dynamics, J. Comput. Phys., 227(2) (2007), 1411–1427.Google Scholar
[9]Liu, C., Shen, J. and Yang, X. F., Dynamics of defect motion in nematic liquid crystal flow: modeling and numerical simulation, Commun. Comput. Phys., 2 (2007), 1184–1198.Google Scholar
[10]Liu, C. and Walkington, N. J., Approximation of liquid crystal flows, SIAM J. Numer. Anal., 37(3) (2007), 725–741.Google Scholar
[11]Liu, C. and Walkington, N. J., Mixed methods for the approximation of liquid crystal flows, M2AN, 36(2) (2002), 205–222.CrossRefGoogle Scholar
[12]Lin, P. and Liu, C., Simulations of singularity dynamics in liquid crystal flows: a C 0 finite element approach, J. Comput. Phys., 215(1) (2006), 348–362.CrossRefGoogle Scholar
[13]Du, Q., Guo, B. Y. and Shen, J., Fourier spectral approximation to a dissipative system modeling the flow of liquid crystals, SIAM J. Numer. Anal., 39(3) (2001), 735–762.Google Scholar
[14]Zhang, H. and Bai, Q., Numerical investigation of tumbling phenomena based on a macroscopic model for hydrodynamic nematic liquid crystals, Commun. Comput. Phys., 7(2) (2010), 317–332.Google Scholar
[15]de Gennes, P. G. and Prost, J., The Physics of Liquid Crystals, Second Edition, Oxford Science, 1993.Google Scholar
[16]Ericksen, J. L., Conservation laws for liquid crystals, Trans. Soc. Rheol., 5(1) (1961), 23–34.Google Scholar
[17]Larson, R. G., The Structure and Rheology of Complex Fluids, Oxford Unversity Press, 1999.Google Scholar
[18]Archer, L. A. and Larson, R. G., A molecular theory of flow alignment and tumbling in sheared nematic liquid crystals, J. Chem. Phys., 103 (1995), 3108–3111.Google Scholar
[19]Sun, H. and Liu, C., On energetic variational approaches in modelling the nematic liquid crystal flows, Discrete. Cont. Dyn. S., 23 (2009), 455–475.CrossRefGoogle Scholar
[20]Liu, C. and Shen, J., On liquid crystal flows with free-slip boundary conditions, Discrete. Cont. Dyn. S., 71 (2001), 307–318.Google Scholar
[21]Shen, J. and Tang, T., Spectral and High-Order Methods with Applications, Science Press, 2006.Google Scholar