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Lattice Boltzmann algorithm for three-dimensional liquid-crystal hydrodynamics.

C Denniston1, D Marenduzzo, E Orlandini

  • 1Department of Applied Mathematics, The University of Western Ontario, London, Ontario N6A 5B8, Canada.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|August 13, 2004
PubMed
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We present a novel lattice Boltzmann algorithm for simulating 3D liquid-crystal hydrodynamics, incorporating viscoelastic effects and topological defects. This method accurately models complex behaviors in nematic liquid crystals.

Area of Science:

  • Physics
  • Materials Science
  • Computational Science

Background:

  • Liquid crystals exhibit complex hydrodynamic behaviors crucial for display technologies.
  • Simulating these behaviors, including viscoelasticity and defects, is computationally challenging.

Purpose of the Study:

  • To develop a versatile 3D lattice Boltzmann algorithm for simulating liquid-crystal hydrodynamics.
  • To incorporate tensor order parameters for modeling both isotropic and nematic phases.
  • To naturally include backflow, topological defects, and viscoelastic effects.

Main Methods:

  • Developed a 3D lattice Boltzmann algorithm.
  • Utilized a tensor order parameter to describe liquid crystal phases.
  • Implemented velocity boundary conditions for simulations.

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Main Results:

  • The algorithm successfully simulates liquid-crystal hydrodynamics in three dimensions.
  • It naturally incorporates backflow effects, hydrodynamics of topological defects, and viscoelastic phenomena like shear-thinning and shear-banding.
  • Demonstrated accurate simulation of optical bounce in twisted nematic devices and secondary flow in sheared nematics.

Conclusions:

  • The lattice Boltzmann algorithm provides a robust framework for simulating complex liquid-crystal hydrodynamics.
  • This method is capable of modeling diverse phenomena relevant to liquid crystal devices and materials science.
  • The algorithm's ability to include various physical effects enhances its applicability in research and development.