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Q-tensor model for electrokinetics in nematic liquid crystals

O. M. Tovkach1,2,*, Christopher Conklin3,†, M. Carme Calderer4,‡, Dmitry Golovaty1,§, Oleg D. Lavrentovich5,∥, Jorge Viñals3,¶, and Noel J. Walkington6,#

  • 1Department of Mathematics, The University of Akron, Akron, Ohio 44325, USA
  • 2Bogolyubov Institute for Theoretical Physics, NAS of Ukraine, Metrologichna 14-b, Kyiv 03680, Ukraine
  • 3School of Physics and Astronomy and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA
  • 4School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA
  • 5Liquid Crystal Institute, Kent State University, Kent, Ohio 44242, USA
  • 6Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

  • *Present address: Department of Physics, University of Massachusetts, Amherst, MA 01003; otovkach@umass.edu
  • †conk0044@umn.edu
  • ‡calde014@umn.edu
  • §dmitry@uakron.edu
  • ∥olavrent@kent.edu
  • vinals@umn.edu
  • #noelw@andrew.cmu.edu
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Phys. Rev. Fluids 2, 053302 – Published 5 May, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.053302

Abstract

We use a variational principle to derive a mathematical model for a nematic electrolyte in which the liquid crystalline component is described in terms of a second-rank order parameter tensor. The model extends the previously developed director-based theory and accounts for the presence of disclinations and possible biaxiality. We verify the model by considering a simple but illustrative example of liquid crystal-enabled electro-osmotic flow around a stationary dielectric spherical particle placed at the center of a large cylindrical container filled with a nematic electrolyte. Assuming homeotropic anchoring of the nematic on the surface of the particle and uniform distribution of the director on the surface of the container, we consider two configurations with a disclination equatorial ring and with a hyperbolic hedgehog, respectively. The computed electro-osmotic flows show a strong dependence on the director configurations and on the anisotropies of dielectric permittivity and electric conductivity of the nematic, characteristic of liquid crystal-enabled electrokinetics. Further, the simulations demonstrate space charge separation around the dielectric sphere, even in the case of isotropic permittivity and conductivity. This is in agreement with the induced-charge electroosmotic effect that occurs in an isotropic electrolyte when an applied field acts on the ionic charge it induces near a polarizable surface.

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Phys. Rev. Fluids 2, 053302– Published 5 May, 2017
  • Received 11 December 2016
Article part of CHORUS

©2017 American Physical Society

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