Interaction of Spherical Colloidal Particles in Nematic Media with Degenerate Planar Anchoring

The interaction between two spherical colloidal particles with degenerate planar anchoring in a nematic media is studied by numerically minimizing the bulk Landau-de Gennes and surface energy using a finite element method. We find that the energy achieves its global minimum when the particles are in close contact and making an angle $\theta = 28^\circ \pm 2$ with respect to the bulk nematic director, in agreement with the experiments. Although the quadrupolar structure of the director field is preserved in the majority of configurations, we show that for smaller orientation angles and at smaller inter-particle separations, the axial symmetry of the topological defect-pairs is continuously broken, resulting in the emergence of an attractive interaction.