Structure of Saturn ring defects for two small spherical colloidal particles

We study the small particle limit of the Landau–de Gennes model around two spherical colloids with strong homeotropic anchoring. We obtain an explicit representation of the minimizing $Q$ -tensor. We then investigate the structure of defect lines and its dependence on the particle distance and orientation. In particular, for certain orientations and for small distances, we observe a line singularity disconnected from the singular line surrounding both particles, similar to the entangled hyperbolic defect configuration observed in experiments, while for larger distances, the two lines merge and eventually the inner singular line disappears.