Dynamics of Point Defects in Nematic Liquid Crystals

Abstract

The presence of topological defects in liquid crystals is know since the very discovery of this interesting state of matter. However, the number of studies considering the dynamics of defects started to increase only recently [Ericksen (1996), Guidone Peroli (1998)]. One of the most interesting features of liquid crystal dynamics is the coupling between the director reorientation and the mass flow (“back flow“ effect). It results from the anisotropy of the liquid crystal molecules and leads to complicated viscous phenomena. Even in the case of the simplest liquid crystal phase (uniaxial nematic), there are five independent viscosities, entering the set of nematodynamic equations, described in detail by Ericksen (1960), Leslie (1966), and Parodi (1970). Recently, dynamics of defects in a cylindrical tube filled with a nematic liquid crystal was studied experimentally for the case of homeotropic anchoring (director prefers perpendicular alignment at the cavity wall) [Hillig (1997)]. Unsolved problems in the theory of defect dynamics and new experiments encouraged us to theoretically examine the annihilation of two point defects with opposite topological charge.