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

TL;DR

This paper develops a hydrodynamic framework for nematic liquid crystals on curved surfaces, integrating flow, molecular alignment, and substrate curvature, and demonstrates the theory with a shear flow example on a cylindrical shell.

Contribution

It extends the Ericksen-Leslie theory to curved two-dimensional nematics using a variational approach with curvature effects included.

Findings

Coupled equations describe flow, director orientation, and curvature interactions.

Shear flow influences nematic alignment on curved shells.

Framework can predict behavior of nematics on complex geometries.

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.