Orientational instability of nematics under oscillatory flow

Generalizing a recently introduced approximation scheme valid when the director relaxation time is large compared to the inverse frequency of an oscillatory flow, we derive equations for the time-averaged torques on the director for a prescribed plane shear flow. Whereas for a linear flow field (simple Couette flow) the average torques vanish, one has for Poiseuille flow (and more general flow fields) torques that tend to orient the director essentially perpendicular to the flow plane. For flow-aligning materials the orientation parallel to the flow is also (weakly) stable. Including the effect of homeotropic surface alignment we estimate the threshold of the oscillation amplitude for the out-of-plane transition. The results are essentially recovered (and improved) by direct numerical simulations.

Electrohydrodynamic Convection in Nematics: Hybrid and Tilted Alignment

We calculate the threshold of electrohydrodynamic convection (EHC) for nematic liquid crystals with negative dielectric anisotropy, where one allows for different director orientations at the upper and lower confining plates (hybrid cells). Besides the planar versus homeotropic case we present for the first time an analysis of continuous tilt at one plate. The predistorted ground state strongly influences the EHC character and the roll orientation. One observes a generic nonstationary behaviour and in particular the interesting scenario of drifting oblique rolls

Flow alignment of nematics under oscillatory shear

Using a simple averaging method we show that under plane oscillatory shear a net torque acts on the director of a nematic liquid crystal leading to unexpected flow alignment. Under quite general conditions the usual flow-alignment orientations are unstable, and the orientation parallel to the shear (perpendicular to the velocity) becomes most stable within the shear plane. The effect drops out exactly under (unrealistic) linear shear unless the director has a nontrivial space dependence. An explicit application to plane Poiseuille flow is presented. Preliminary experimental data are shown which demonstrate a transition under planar oscillatory shear from a homeotropically aligned nematic to a spatially homogeneously deformed state