Director structure around a colloid particle suspended in a nematic liquid crystal

We analyze the director field around a spherical colloid particle with radial (homeotropic) anchoring on its surface. Depending on the relative strength of anchoring W, controlled by the parameter WR/K with K the Frank constant and R the particle radius, the director distribution may possess a singular ring of a -1/2 disclination the equatorial plane. The equilibrium radius of this ring, at rigid radial anchoring, is a*approximate to 1.25R and only weakly depends on the disclination core energy. At small anchoring the director field is regular and weakly disturbed by the particle, there is a characteristic crossover W* between thr two regimes. We obtain the analytical expression for n(r), which decays as r(-3) sin 2 theta away from the particle, and compare it with the exact numerical solution in the highly distorted nonlinear regime.