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

Abstract

We present a numerical calculation for the Stokes drag of a particlein a nematic solvent. Due to the radial anchoring of the moleculesat the particle surface and a uniform director field at infinity, theparticle is accompanied by a hyperbolic point defect which gives riseto the so-called dipole configuration. We write the Ericksen-Leslieequation in a reduced form emphasizing the importance of the Ericksennumber 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 andstream line patterns add to the understanding of our results.Finally, we suggest that the non-linear Stokes drag should be observablein a falling-ball experiment.