On Landau–de Gennes Energy Minimizers Surrounding Generalized Colloid Particles

Abstract

We consider the interaction between a single colloid particle of generalized shape and nematic liquid crystal in the framework of Landau–de Gennes theory. At the particle surface, general strong or weak uniaxial anchoring conditions are applied as well as uniform uniaxial forcing at infinity. In this context, it is found that the field-free Landau–de Gennes functional with surface energy admits uniformly continuous minimizers. We then study two examples of non-spherical colloids in a limiting regime known as the ‘small particle limit’. Explicit solutions to the small particle limit are found in the case of a prolate and oblate spheroidal colloid with ‘almost homeotropic’ strong anchoring. From there, a Saturn ring defect is numerically observed in both cases.