A nematic liquid crystal with an immersed body: equilibrium, stress, and paradox

TL;DR

This paper analyzes equilibrium states, stresses, and paradoxes in a 2D nematic liquid crystal with an immersed body, using complex variables and boundary techniques to explore defect locations and classical fluid dynamics analogues.

Contribution

It introduces an effective boundary method for weak anchoring and provides analytical solutions for various body shapes, advancing understanding of nematic-liquid crystal interactions.

Findings

Analytical solutions for strong anchoring cases.

Asymptotic solutions for weak anchoring.

Identification of classical fluid dynamics analogues.

Abstract

We examine the equilibrium configurations of a nematic liquid crystal with an immersed body in two-dimensions. A complex variables formulation provides a means for finding analytical solutions in the case of strong anchoring. Local tractions, forces, and torques on the body are discussed in a general setting. For weak (finite) anchoring strengths, an effective boundary technique is proposed which is used to determine asymptotic solutions. The energy-minimizing locations of topological defects on the body surface are also discussed. A number of examples are provided, including circular and triangular bodies, and a Janus particle with hybrid anchoring conditions. Analogues to classical results in fluid dynamics are identified, including d'Alembert's paradox, Stokes' paradox, and the Kutta condition for circulation selection.