Effect of a hydrodynamic flow on the orientation profiles of a nematic liquid crystal around a spherical particle

We study the effect of a hydrodynamic flow on the orientational configuration of a nematic liquid crystal around a spherical particle imposing rigid normal anchoring. We discuss the cases of large Ericksen numbers (characterizing the ratio of viscous force to the elastic force), where strong elastic deformation by the flow is expected. We assume the Stokes flow profile and deal with a simplified dynamic equation of the orientational order parameter of a second-rank tensor Q_αβ. We consider the cases where a particle accompanying a hyperbolic hedgehog or a Saturn ring is subjected to a flow along the axis of rotational symmetry. In both cases the orientation profiles exhibit considerable deformation by a flow.