Spherical particle in a nematic liquid crystal under an external field: the Saturn ring regime

TL;DR

This paper investigates the behavior of nematic liquid crystals around a spherical particle under a strong external field, revealing a boundary layer and Saturn ring defect formation predicted by a Landau-de Gennes model.

Contribution

It provides a scaling law for the energy and predicts Saturn ring defects as a stable configuration under high external fields.

Findings

Energy concentrates in a boundary layer around the particle.

Presence of quadrupolar symmetry in the energy distribution.

Formation of Saturn ring defect instead of a dipolar defect.

Abstract

We consider a nematic liquid crystal occupying the exterior region in R^3 outside of a spherical particle, with radial strong anchoring. Within the context of the Landau-de Gennes theory, we study minimizers subject to a strong external field, modelled by an additional term which favors nematic alignment parallel to the field. When the external field is high enough we obtain a scaling law for the energy. The energy scale corresponds to minimizers concentrating their energy in a boundary layer around the particle, with quadrupolar symmetry. This suggests the presence of a Saturn ring defect around the particle, rather than a dipolar director field typical of a point defect.