Interaction between spherical particles in a deformed liquid crystal

We study how the initial deformation of a nematic liquid crystal affects the interaction between particles mediated by the elastic deformation of a nematic liquid crystal. We calculate the interaction energy between particles in a hybrid nematic cell, homeotropic on the surface of one confining plate and tangential (director can rotate freely) on the other. We find an analytic form of the interaction energy in the case of weak anchoring on the surface of the particle. This interaction energy can be non-monotonic and have a minimum in its landscape, which makes a clear contrast to that in a uniform nematic liquid crystal.