Numerical investigation of liquid crystal colloids using a continuum description

We investigate numerically the configuration of a nematic liquid crystal around two spherical particles. For the description of the orientational order of a nematic liquid crystal, we adopt a Landau-de Gennes continuum theory in terms of a second-rank tensor order parameter Q(ij) together with the use of bispherical coordinates to describe the geometry of the system with two spherical particles. Above but close to the nematic-isotropic transition point, we observe capillary condensation of a nematic liquid crystal between the two particles under appropriate conditions. Below the transition point where liquid crystals possess nematic order, a point-like defect called a hyperbolic hedgehog appears close to a particle when strong normal anchoring is imposed. With the aid of an adaptive mesh refinement scheme to achieve sufficient numerical resolution to describe topological defects, we present our numerical results showing how the orientation profile of a nematic liquid crystal is distorted when the distance between two particles is small enough.