European Journal of Applied Mathematics

Table of Contents - February 2012 - Volume 23, Special Issue 01 (Liquid Crystals)  

Papers

A perturbative approach to the backflow dynamics of nematic defects

PAOLO BISCARIa1 and TIMOTHY J. SLUCKINa2

a1 Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy email: paolo.biscari@polimi.it

a2 School of Mathematics, University of Southampton, Southampton SO17 1BJ, UK email: t.j.sluckin@soton.ac.uk

Abstract

We present an asymptotic theory that includes in a perturbative expansion the coupling effects between the director dynamics and the velocity field in a nematic liquid crystal. Backflow effects are most significant in the presence of defect motion, since in this case the presence of a velocity field may strongly reduce the total energy dissipation and thus increase the defect velocity. As an example, we illustrate how backflow influences the speeds of opposite-charged defects.

(Received November 18 2010)

(Revised November 23 2010)

(Accepted November 30 2010)

(Online publication January 05 2011)

Key words:

  • Nematic liquid crystals;
  • Perturbations, asymptotics;
  • propagation of defects