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Pair creation, motion, and annihilation of topological defects in two-dimensional nematic liquid crystals

Dario Cortese, Jens Eggers*, and Tanniemola B. Liverpool†

  • School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom

  • *jens.eggers@bristol.ac.uk
  • †t.liverpool@bristol.ac.uk
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Phys. Rev. E 97, 022704 – Published 20 February, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.022704

Abstract

We present a framework for the study of disclinations in two-dimensional active nematic liquid crystals and topological defects in general. The order tensor formalism is used to calculate exact multiparticle solutions of the linearized static equations inside a planar uniformly aligned state so that the total charge has to vanish. Topological charge conservation then requires that there is always an equal number of q=1/2 and q=−1/2 charges. Starting from a set of hydrodynamic equations, we derive a low-dimensional dynamical system for the parameters of the static solutions, which describes the motion of a half-disclination pair or of several pairs. Within this formalism, we model defect production and annihilation, as observed in experiments. Our dynamics also provide an estimate for the critical density at which production and annihilation rates are balanced.

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Phys. Rev. E 97, 022704– Published 20 February, 2018
  • Received 4 October 2017
  • Revised 16 January 2018
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