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. Analogies to classical results in fluid dynamics are identified, including d'Alembert's paradox, Stokes’ paradox and the Kutta condition for circulation selection.
Funder
Division of Materials Research
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics,Applied Mathematics