In the preceding paper, we have established an interface equation for directional solidification under the influence of a shear flow parallel to the interface. This equation is asymptotically valid near the absolute stability limit. The flow, described by a nonlocal term, induces a lateral drift of the whole pattern due to its symmetry-breaking properties. We find that at not-too-large flow strengths, the transcritical nature of the transition to hexagonal patterns shows up via a hexagonal modulation of the stripe pattern even when the linear instability threshold of the flowless case has not yet been attained. When the flow term is large, the linear description of the drift velocity breaks down and transitions to flow-dominated morphologies take place. The competition between flow-induced and diffusion-induced patterns (controlled by the temperature gradient) leads to new phenomena such as the transition to a different lattice structure in an array of hexagonal cells. Several methods to characterize the morphologies and their transitions are investigated and compared. In particular, we consider two different ways of defining topological defects useful in the description of patterns and we discuss how they are related to each other.

PACS. 61.30.Gd -Orientational order of liquid crystals; electric and magnetic field effects on order. PACS. 61.72.Cc -Kinetics of defect formation and annealing. PACS. 61.72.Ff -Direct observation of dislocations and other defects (etch pits, decoration, electron microscopy, X-ray topography, etc.).Abstract. -In homeotropically aligned nematics with negative dielectric anisotropy the electrohydrodynamic instability occurs above a bend Fréedericksz transition. In the presence of a magnetic field H parallel to the liquid crystal slab, ordered roll patterns with a welldefined uniform wave vector k id appear above the onset of convection. By rotating the cell around an axis perpendicular to the slab by a small angle α, one can manipulate the system into a state with wave vector k = k id + ∆ k, where ∆ k is roughly perpendicular to k id . We have studied experimentally the motion of defects, which then move essentially perpendicular to the rolls. The direction as well as the magnitude of the velocity as a function of ∆ k agrees with predictions of the weakly nonlinear theory. In particular, we obtain evidence for the nonanalyticity for ∆ k → 0.

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In electroconvection experiments with planarly aligned nematic liquid crystals the director orientation is, conventionally, fixed through a mechanical treatment (rubbing) of the polymer-coated electrodes. Without rubbing, on the other hand, the flow direction during sample filling imposes the director orientation. We report atomic force microscopy and x-ray measurements that show an anisotropy in the polymer surface structure on several scales as a result of the rubbing. In particular we observe a fish-bone structure on a 10 nm scale. We visualize the orientation of the director both during and after filling the system using the electroconvection pattern. This is a convenient tool for exploring new director configurations. We confirm for the observed surface structure that when flow and surface designate different orientations, the mechanical surface treatment dominates. We have been able to obtain regions with radial director orientation of millimeter size. Such an alignment renders possible new types of electroconvection experiments.

An asymptotic interface equation for directional solidification near the absolute stability limit is extended by a nonlocal term describing a shear flow parallel to the interface. In the long-wave limit considered, the flow acts destabilizing on a planar interface. Moreover, linear stability analysis suggests that the morphology diagram is modified by the flow near onset of the Mullins-Sekerka instability. Via numerical analysis, the bifurcation structure of the system is shown to change. Besides the known hexagonal cells, structures consisting of stripes arise. Due to its symmetry-breaking properties, the flow term induces a lateral drift of the whole pattern, once the instability has become active. The drift velocity is measured numerically and described analytically in the framework of a linear analysis. At large flow strength, the linear description breaks down, which is accompanied by a transition to flow-dominated morphologies which is described in the following paper. Small and intermediate flows lead to increased order in the lattice structure of the pattern, facilitating the elimination of defects. Locally oscillating structures appear closer to the instability threshold with flow than without.