Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-10T21:00:18.220Z Has data issue: false hasContentIssue false
  • English
  • Français

The Kinematic Effects of the Defects in Liquid Crystal Dynamics

Part of: Foundations, constitutive equations, rheology Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  22 June 2016

Rui Chen ,
Weizhu Bao  and
Hui Zhang
Rui Chen*
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100088, P.R. China
Weizhu Bao*
Affiliation:
Department of Mathematics, National University of Singapore, Singapore, 119076
Hui Zhang*
Affiliation:
School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P.R. China
*
*Corresponding author. Email addresses:ruichenbnu@gmail.com (R. Chen), bao@cz3.nus.edu.sg (W. Z. Bao), hzhang@bnu.edu.cn (H. Zhang)
*Corresponding author. Email addresses:ruichenbnu@gmail.com (R. Chen), bao@cz3.nus.edu.sg (W. Z. Bao), hzhang@bnu.edu.cn (H. Zhang)
*Corresponding author. Email addresses:ruichenbnu@gmail.com (R. Chen), bao@cz3.nus.edu.sg (W. Z. Bao), hzhang@bnu.edu.cn (H. Zhang)
Get access

Abstract

Here we investigate the kinematic transports of the defects in the nematic liquid crystal system by numerical experiments. The model is a shear flow case of the viscoelastic continuummodel simplified fromthe Ericksen-Leslie system. The numerical experiments are carried out by using a difference method. Based on these numerical experiments we find some interesting and important relationships between the kinematic transports and the characteristics of the flow. We present the development and interaction of the defects. These results are partly consistent with the observation from the experiments. Thus this scheme illustrates, to some extent, the kinematic effects of the defects.

Keywords

Nematic liquid crystalskinematic effectsfinite difference methoddefects

MSC classification

Secondary: 65M70: Spectral, collocation and related methods 76A15: Liquid crystals
Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 1 , July 2016 , pp. 234 - 249
Copyright
Copyright © Global-Science Press 2016 

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] Berrenman, D. W. and Meiboom, S., Tensor representation of Oseen-Frank strain energy in uniaxial cholesterics, Phys. Rev. A, 30 (1984), 1955–1959.Google Scholar
[2] Bao, W. Z. and Zhang, Y. Z., Dynamics of the ground state and central vortex states in Bose-Einstein condensation, M3AS, 15 (2005), 1863–1896.Google Scholar
[3] 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.Google Scholar
[4] Chandrasekhar, S., Liquid Crystals, Cambridge University Press, Chapter 3, 1977.Google Scholar
[5] Denniston, C., Disclination dynamics in nematic liquid crystals, Phys. Rev. B, 54 (1996), 6272–6275.Google Scholar
[6] Doi, M. and Edwards, S. F., The Theory of Polymer Dynamics, Oxford University Press, New York, 1986.Google Scholar
[7] 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 (2001), 735–762.Google Scholar
[8] Ericksen, J. L., Conservation laws for liquid crystals, Trans. Soc. Rheol., 5 (1961), 23–34.CrossRefGoogle Scholar
[9] Feng, J. J., Tao, J. and Leal, L. G., Roll cells and disclinations in sheared nematic polymers, J. Fluid Mech., 449 (2001), 179–200.CrossRefGoogle Scholar
[10] de Gennes, P. G. and Prost, J., The Physics of Liquid Crystals, second edition, Oxford Science, 1993.CrossRefGoogle Scholar
[11] Grecov, D. and Rey, A. D., Shear-induced textural transitions in flow-aligning liquid crystal polymers, Phys. Rev. E, 68 (2003), 061704.Google Scholar
[12] Hess, S. Z., Fokker-Planck-equation approach to flow alignment in liquid crystals, Z. Naturforsch, 31A (1976), 1034–1037.CrossRefGoogle Scholar
[13] Kleman, M., Defects in liquid crysrals, Rep. Prog. Phys., 52 (1989), 555–654.Google Scholar
[14] Kurik, M. V. and Lavrentovich, O. D., Defects in liquid crysrals: homotopy theory and experimental studies, Sov. Phys. Usp. 31 (1988), 196–224.Google Scholar
[15] Larson, R. G., The Structure and Rheology of Complex Fluids, Oxford Unversity Press, 1999.Google Scholar
[16] Lin, F. H. and Liu, C., Global existence of solutions for Ericksen-Leslie system, Arch. Rat. Mech. Anal., 154 (2001), 135–156.CrossRefGoogle Scholar
[17] Lin, P. and Liu, C., Simulations of singularity dynamics in liquid crystal flows: A C 0 finite element approach, J. Comput. Phys., 215 (2006), 348–362.Google Scholar
[18] Lin, F. H., Liu, C. and Zhang, P., On hydrodynamics of viscoelastic fluids, Commun. Pure Appl. Math., 58 (2005), 1–35.Google Scholar
[19] 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 (2007), 1411–1427.Google Scholar
[20] 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
[21] Liu, C. and Sun, H., On energetic variational approaches in modeling the nematic liquid crystal flows, Discrete and Continuous Dynamical Systems, 23 (2009), 455–475.Google Scholar
[22] Liu, C. and Walkington, N. J., Approximation of liquid crystal flows, SIAM J. Numer. Anal., 37 (2000), 725–741.CrossRefGoogle Scholar
[23] Liu, C. and Walkington, N. J., Mixed methods for the approximation of liquid crystal flows, M2AN, 36 (2002), 205–222.Google Scholar
[24] Mori, H., Gartland, E.C., Kelly, J.R. and Bos, P.J., Multidimensional directormodeling using the Q tensor representation in a liquid crystal cell and its application to the π cell with patterned electrodes, Jpn. J. Appl. Phys. 38 (1999), 135–146.CrossRefGoogle Scholar
[25] Mottram, N. and Newton, C., Introduction to Q-tensor theory, University of Strathclyde Mathematics, Research Report, 2004, No.10, http://www.mathstat.strath.ac.uk/people/academic/nigel-mottram Google Scholar
[26] Nazarenko, V.G. and Lavrentovich, O.D., Archoring transition in a nematic liquid crystal composed of centrsymmetric molecules, Phys. Rev. E, 49 (1994), 990–994.Google Scholar
[27] Ranganath, G. S., Defects in liquid crystals, Current Science, 59 (1990), 1106–1124.Google Scholar
[28] Rey, A. D., Theory of linear viscoelasticity of chiral liquid crystals, Rheol Acta, 35 (1996), 400–409.Google Scholar
[29] Rey, A. D. and Denn, M. M., Dynamical phenomena in liquid-crystalline matericals, Annu. Rev. Fluids Mech., 34 (2002), 233–266.Google Scholar
[30] Rey, A. D., Capillary models for liquid crystal fibers, membranes, films, and drops, Soft Matter, 3 (2007), 1349–1368.Google Scholar
[31] Rey, A. D. and Tsuji, T., Recent advances in theoretical liquid crystal rheology, 7 (1998), 623–639.Google Scholar
[32] Satiro, C. and Moraes, F., Lensing effects in a nematic liquid crystal with topological defects, Eur. Phys. J. E, 20 (2006), 173–178.Google Scholar
[33] Tsuji, T. and Rey, A. D., Effect of long range order on sheared liquid crystalline materials: Part 1: compatibility between tumbling behavior and fixed anchoring, J. Non-Newtonian Fluid Mech., 73 (1997), 127–152.Google Scholar
[34] Tsuji, T. and Rey, A. D., Orientation mode selection mechanisms for sheared nematic liquid crystalline materials, Phys. Rev. E, 57 (1998) 5609–5627.CrossRefGoogle Scholar
[35] Toch, G., Denniston, C. and Yeomanns, J.M., Hydrodynamics of topological defects in nematic liquid crystals, Phys. Rev. Lett., 88 (2002), 105504.Google Scholar
[36] Wang, Q., Forest, M. G. and Zhou, R., A kinetic theory for solutions of nonhomogeneous nematic liquid crystalline polymers with density variations, J. Fluids Eng., 126 (2004), 180–188.Google Scholar
[37] Wang, Q., A hydrodynamic theory for solutions of nonhomogeneous nematic liquid crystalline polymers of different configurations, J. Chem. Phys., 116 (2002), 9120–9136.CrossRefGoogle Scholar
[38] Yang, X. F., Forest, M. G., Mullins, W. and Wang, Q., Quench sensitivity to defects and shear banding in nematic polymer film flows, J. Non-Newtonian Fluid Mech., 159 (2009), 115–129.Google Scholar
[39] 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.Google Scholar
[40] Zhang, H. and Bai, Q., Numerical investigation of tumbling phenomena based on a macroscopic model for hydrodynamic nematic liquid crystals, Commun. Comput. Phys., 7 (2010), 317–332.Google Scholar
[41] Zhang, S., Liu, C. and Zhang, H., Numerical simulations of hydrodynamics of nematic liquid crystals:effects of kinematic transports, Commun. Comput. Phys., 9 (2011), 974–993.CrossRefGoogle Scholar