47 research outputs found
Hydrodynamic theory for nematic shells: the interplay among curvature, flow and alignment
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
Influence of the Extrinsic Curvature on 2D Nematic Films
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