Influence of the Extrinsic Curvature on 2D Nematic Films

Abstract

Nematic interfaces are thin fluid films, ideally two-dimensional, endowed with an in-plane degenerate nematic order. In this letter we examine a generalisation of the classical Plateau problem to an axisymmetric nematic interface bounded by two coaxial parallel rings. The equilibrium interface shape results from the competition between surface tension, which favours the minimization of the interface area, and the nematic elasticity which instead promotes the alignment of the molecules along a common direction. We find two classes of equilibrium solutions with intrinsically uniform alignments: one in which the molecules are aligned along the meridians, the other along parallels. Depending on two parameters, one geometric and the other constitutive, the Gaussian curvature of the equilibrium interface may be negative, vanishing or positive. The stability of these equilibrium configurations is investigated.

References in corpus (4)

• Hydrodynamic theory for nematic shells: the interplay among curvature, flow and alignment
• Nematic Films and Radially Anisotropic Delaunay Surfaces
• Hyperbolic Interfaces
• Curvature-driven stability of defects in nematic textures over spherical disks

Cited by in corpus (7)

• Micromagnetic Theory of Curvilinear Ferromagnetic Shells
• An optical wormhole from hollow disclinations
• Liquid Crystals on Deformable Surfaces
• Defect order in active nematics on a curved surface
• Membrane stress and torque induced by Frank's nematic textures: A geometric perspective using surface-based constraints
• Axisymmetric membranes with edges under external force: buckling, minimal surfaces, and tethers
• Mechanics of nematic membranes: Euler-Lagrange equations, Noether charges, stress, torque and boundary conditions of the surface Frank nematic field