Orientational instabilities in nematic liquid crystals with weak anchoring under combined action of steady flow and external fields.

We study the homogeneous and the spatially periodic instabilities in a nematic liquid crystal layer subjected to steady plane Couette or Poiseuille flow. The initial director orientation is perpendicular to the flow plane. Weak anchoring at the confining plates and the influence of the external electric and/or magnetic field are taken into account. Approximate expressions for the critical shear rate are presented and compared with semianalytical solutions in case of Couette flow and numerical solutions of the full set of nematodynamic equations for Poiseuille flow. In particular the dependence of the type of instability and the threshold on the azimuthal and the polar anchoring strength and external fields is analyzed.

Theory of director precession and nonlinear waves in nematic liquid crystals under elliptical shear.

We study theoretically the slow director precession and nonlinear waves observed in homeotropically oriented nematic liquid crystals subjected to circular or elliptical Couette and Poiseuille flow and an electric field. From a linear analysis of the nematodynamic equations it is found that in the presence of the flow the electric bend Fréedericksz transition is transformed into a Hopf-type bifurcation. In the framework of an approximate weakly nonlinear analysis we have calculated the coefficients of the modified complex Ginzburg-Landau equation, which slightly above onset describes nonlinear waves with strong nonlinear dispersion. We also derive the equation describing the precession and waves well above the Fréedericksz transition and for small flow amplitudes. Then the nonlinear waves are of diffusive nature. The results are compared with full numerical simulations and with experimental data.

Pattern-forming instabilities in nematic liquid crystals under oscillatory Couette flow.

We consider instabilities, either homogeneous or periodic in space, which develop in a nematic liquid crystal layer under rectilinear oscillatory Couette flow for planar surface alignment of the director perpendicular to the flow plane. On the basis of a numerical and analytical linear stability analysis we determine the critical amplitude of the oscillatory flow, the wave number, and the symmetry of the destabilizing mode and present a comprehensive phase diagram of the flow instabilities. In particular it is found that by varying the frequency of the Couette flow the instability changes its temporal symmetry. This transition is shown to be related to the inertia effects of the nematic fluid, which become more important with increasing flow frequency. We also show that an electric field applied perpendicularly to the nematic layer can induce an exchange of instabilities with different spatial and temporal symmetries. The theoretical results are compared with experiments, when available.

Phase separation in the presence of spatially periodic forcing.

We have investigated theoretically phase separation in the presence of spatially periodic forcing. From the analytic and numeric study of a suitably generalized Cahn-Hilliard equation in one and two dimensions, we find that the forcing amplitude necessary to generate a periodic kink-type state from small random initial conditions depends weakly on wave number. This amplitude is much larger than the one necessary to stabilize the periodic state, i.e., to prevent late-stage coarsening, once it is established. Surprisingly, the destabilizing mode is of long-wave type, which is in contrast to the well-known most rapidly growing coarsening mode in the unforced system. In the Allen-Cahn equation with nonconserved order parameter the relevant modes are always long wave. It appears feasible to observe these effects by imposing a temperature modulation by optical grating which then couples to concentration modulation via the (Ludwig-)Soret effect.

Dynamics of cholesteric structures in an electric field.

Motivated by Lehmann-like rotation phenomena in cholesteric drops we study the transverse drift of two types of cholesteric fingers, which form rotating spirals in thin layers of cholesteric liquid crystal in an ac or dc electric field. We show that electrohydrodynamic effects induced by Carr-Helfrich charge separation or flexoelectric charge generation can describe the drift of cholesteric fingers. We argue that the observed Lehmann-like phenomena can be understood on the same basis.