Hydrodynamic theory for nematic shells: the interplay among curvature, flow and alignment

Abstract

We derive the hydrodynamic equations for nematic liquid crystals lying on curved substrates. We invoke the Lagrange-Rayleigh variational principle to adapt the Ericksen-Leslie theory to two-dimensional nematics in which a degenerate anchoring of the molecules on the substrate is enforced. The only constitutive assumptions in this scheme concern the free-energy density, given by the two-dimensional Frank potential, and the density of dissipation which is required to satisfy appropriate invariance requirements. The resulting equations of motion couple the velocity field, the director alignment and the curvature of the shell. To illustrate our findings, we consider the effect of a simple shear flow on the alignment of a nematic lying on a cylindrical shell.

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Cited by in corpus (16)

• A viscous active shell theory of the cell cortex
• Theory of nematic and polar active fluid surfaces
• Active nematic flows on curved surfaces
• Divergence-free tangential finite element methods for incompressible flows on surfaces
• Newton-Cartan Submanifolds and Fluid Membranes
• Dynamics of active nematic defects on the surface of a sphere
• Liquid Crystals on Deformable Surfaces
• Hydrodynamic theory of $p-$atic liquid crystals
• Morphodynamics of Active Nematic Fluid Surfaces
• Influence of the Extrinsic Curvature on 2D Nematic Films
• Defect order in active nematics on a curved surface
• Stresses in curved nematic membranes
• Membrane stress and torque induced by Frank's nematic textures: A geometric perspective using surface-based constraints
• Model of the dynamics of an interface between a smectic phase and an isotropic phase of different density
• Hydrodynamic interactions in polar liquid crystals on evolving surfaces
• Simultaneous solution of incompressible Navier-Stokes flows on multiple surfaces