Commun. Comput. Phys., 2 (2007), pp. 1184-1198.


Dynamics of Defect Motion in Nematic Liquid Crystal Flow: Modeling and Numerical Simulation

Chun Liu 1, Jie Shen 2*, Xiaofeng Yang 2

1 Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA.
2 Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA.

Received 2 January 2007; Accepted (in revised version) 10 April 2007
Available online 2 August 2007

Abstract

The annihilation of a hedgehog-antihedgehog pair in hydrodynamics of (elastically isotropic) nematic liquid crystal materials is modeled using the Ericksen-Leslie theory which results in a nonlinear system for the flow velocity field and liquid crystal director field coupled through the transport of the directional order parameter and the induced elastic stress. An efficient and accurate numerical scheme is presented and implemented for this coupled nonlinear system in an axi-symmetric domain. Numerical simulations of annihilation of a hedgehog-antihedgehog pair with different types of transport are presented. In particular, it is shown that the stretching parameter in the transport equation contributes to the symmetry breaking of the pair's moving speed during the dynamics of annihilation.

AMS subject classifications: 76T99, 76D05, 65N35

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Key words: Hedgehog-antihedgehog, liquid crystal, Navier-stokes, defect motion, spectral-Galerkin method.

*Corresponding author.
Email: liu@math.psu.edu (C. Liu), shen@math.purdue.edu (J. Shen), xfyang@math.purdue.edu (X. Yang)
 

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