Non-linear Stokes drag of spherical particles in a nematic solvent

We present a numerical calculation for the Stokes drag of a particle in a nematic solvent. Due to the radial anchoring of the molecules at the particle surface and a uniform director field at infinity, the particle is accompanied by a hyperbolic point defect which gives rise to the so-called dipole configuration. We write the Ericksen-Leslie equation in a reduced form emphasizing the importance of the Ericksen number Er. Due to the coupling between director and velocity field, we find a highly non-linear Stokes drag. We discuss it in terms of an effective viscosity and as a function of Er. Director field and stream line patterns add to the understanding of our results. Finally, we suggest that the non-linear Stokes drag should be observable in a falling-ball experiment.