Dynamics of nematic point defects in a capillary with tilted boundary conditions

Abstract

The motion of a single point defect in a cylindrical cavity filled with a nematic liquid crystal is described by solving numerically the simplified equations of nematodynamics. Perfect homeotropic anchoring for the director on the lateral boundary would result in the creation of domains with equal elastic energy, escaped upwards or downwards along the cavity axis and separated by point defects of strength ± 1. Defects do not move as long as they are sufficiently far apart. However, small deviations from homeotropic anchoring remove this degeneracy and the energetically favourable domains start to expand at the expense of the others, thus setting the defects in motion along the tube. We present a new numerical approach, which neglects the backflow, for studying the influence of both the pretilt and the elastic anisotropy (K ₃₃ ≠ K ₁₁) on the motion of a defect. We show how even very small pretilt angles (≈1°) result in speeds observed in experiments. For a moderate elastic anisotropy, the velocity of a +1 defect equals the velocity of a -1 defect, whereas for K ₃₃≫K ₁₁ a + 1 defect moves faster than a -1 defect. For small pretilts we confirm a good qualitative agreement with an existing analytical approach, which proves inaccurate for large pretilts.