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We derive the hydrodynamic equations for nematic liquid crystals lying oncurved substrates. We invoke the Lagrange-Rayleigh variational principle toadapt the Ericksen-Leslie theory to two-dimensional nematics in which adegenerate anchoring of the molecules on the substrate is enforced. The onlyconstitutive assumptions in this scheme concern the free-energy density, givenby the two-dimensional Frank potential, and the density of dissipation which isrequired to satisfy appropriate invariance requirements. The resultingequations of motion couple the velocity field, the director alignment and thecurvature of the shell. To illustrate our findings, we consider the effect of asimple shear flow on the alignment of a nematic lying on a cylindrical shell.

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