Modelling the capillary locking of point defects in nematic liquid crystals

It has long been known that the equilibrium configuration with minimum energy of a nematic liquid crystal within a cylinder subject to homeotropic conditions on the lateral boundary is escaped along the axis of the cylinder, and there is no singularity of the orientation field. So problems of explaining the presence of point defects in capillary tubes and of exploring their stability arise. There is enough evidence to believe that the menisci play a central role in preventing the orientation field around a point defect from unwinding towards the escaped configuration. We propose a variational model which describes how a point defect interacts with a meniscus. This interaction fades away at a finite distance. When active, it is two-sided, being repulsive at first and then attractive when the defect comes closer to the centre of curvature of the meniscus. Thus, when a defect is enclosed between two menisci they can become antagonists, so that there is a metastable equilibrium position where the defect could be locked in.