Stokes drag of spherical particles in a nematic environment at low Ericksen numbers

As a first approach to the motion of particles in anisotropic liquids, we study the Stokes drag of spherical particles in three different nematic environments: a uniform director field, the Saturn-ring configuration, and the dipole configuration. Two independent friction coefficients for the respective motion parallel and perpendicular to the overall symmetry axis exist. We determine these coefficients by solving the Ericksen-Leslie equations for low Ericksen numbers, i.e., when the director field is not influenced by the flow of the liquid crystal around the particle. We present streamline patterns and interpret them. Compared to the uniform director field and the Saturn-ring configuration, the dipolar configuration lacks a mirror plane as a symmetry element whose consequences we illustrate.