title: 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.
authors.affiliation: Dipartimento di Ingegneria dell'Innovazione, Università del Salento, via per Monteroni, Edificio "Corpo O", 73100 Lecce, Italy.
authors.forename: Gaetano
authors.initials: G
authors.lastname: Napoli
authors.affiliation: School of Mathematics and Statistics, University of Glasgow, University Gardens 15, G12 8QW Glasgow, United Kingdom.
authors.forename: Luigi
authors.initials: L
authors.lastname: Vergori