Annihilation of point defects in nematic liquid crystals

Point defects are likely to be generated in the process of filling a capillary tube subject to homeotropic conditions on the boundary. There is plenty of experimental evidence to hold that, when two defects with opposite topological charge happen to be closer than a critical distance, they attract each other. At first, they move very slowly; then, as the distance between them becomes less than a diameter, their relative speed increases dramatically, until they annihilate one other. In this paper we describe, by means of a simple dynamical model, the attraction and annihilation of two defects in an infinite tube. We write the balance between the rate of change in the elastic free energy and the energy dissipated in the director motion. Hence, we derive and solve the differential equation that describes the evolution in time of the distance between the defects. The outcomes of our analysis confirm many qualitative aspects of the experimental evidence. {} 1996 The American Physical Society.