Dynamics of a nematic liquid crystal around a spherical particle

We present the results of our numerical calculations that focus on the dynamics of a nematic liquid crystal around a spherical particle imposing strong homeotropic anchoring at the surface. The first part of this article is devoted to the discussion of the effect of an external magnetic or electric field on the director configuration of a nematic liquid crystal. With the aid of an adaptive mesh refinement scheme, together with the tensor description of the orientational order, for the first time in numerical calculations we successfully reproduce the transition from a hyperbolic hedgehog defect to a Saturn ring defect, which was observed in a recent experiment. We also find that the trajectories of the defect core sensitively depend on the field strength. In the second part we investigate how a hydrodynamic flow influences the orientational order of a nematic liquid crystal around a particle carrying a hyperbolic hedgehog defect. We observe that for an intermediate Ericksen number, which characterizes the ratio of the viscous force to the elastic force of a nematic liquid crystal, the liquid crystal is strongly convected by the flow, which results in a considerable elastic distortion.