Thermal convection in a planar nematic liquid crystal with a stabilizing magnetic field

Hydrodynamic instabilities in ferronematics

In the hydrodynamic description of ferronematics there are various dynamic magnetic-field effects, linear in the field strength, that are negligible in usual nematics, but can play a role in ferronematics. Here, we investigate theoretically the influence of these new terms on the thermal convection (Rayleigh-Bénard) and the viscous fingering (Saffman-Taylor) instability in ferronematics in the presence of a strong magnetic field. We find that the instabilities are qualitatively changed due to the occurrence of a finite vorticity component--a feature that is known from simple liquids in the case of a superimposed mechanical rotation. We suggest to use the additional effects (cross-flow within convection rolls, oblique rolls, rotating fingers) for measuring the phenomenological coefficients involved.

Low symmetry patterns on magnetic fluids

The pattern formation on the free surface of a magnetic fluid subjected simultaneously to a vertical and a horizontal magnetic field is investigated theoretically. In this anisotropic system planforms less symmetric then squares and hexagons arise. The relative stability of parallel ridges and asymmetric patterns, periodic on a rectangular or a rhombic lattice, is studied using a perturbative energy minimization procedure. Moreover, the interplay between the anisotropy and the broken up-down symmetry of the system is quantitatively analyzed.

Rayleigh-Bénard convection in elliptic and stadium-shaped containers

We report on defect formation in convection patterns of stadium-shaped and elliptical horizontal layers of fluid heated from below (Rayleigh-Bénard convection). The fluid was ethanol with a Prandtl number sigma=14.2. The outermost convection roll was forced to be parallel to the sidewall by a supplementary wall heater. The major- and minor-axis aspect ratios Gamma(i)=D(i)/2d, i=1, 2 (D(i) are the major and minor diameter and d the thickness) were 19.4 and 13.0, respectively. For the stadium shape, we found a stable pattern that was reflection-symmetric about the major diameter and had a downflow roll of length L(s) along a large part of this diameter. This roll terminated in two convex disclinations, as expected from theory. No other patterns with the outermost roll parallel to the sidewall were found. The wave numbers of the rolls in the curved sections and L(s) decreased with increasing epsilon identical with DeltaT/DeltaT(c)-1, consistent with a prediction for wave-number selection by curved rolls in an infinite system. At large epsilon, the roll adjacent to the sidewall became unstable due to the cross-roll instability. For the elliptical shape, wave-director frustration yielded a new defect structure predicted by Ercolani et al. Depending on the sample history, three different patterns with the outermost roll parallel to the wall were found. For one, the central downflow roll seen in the stadium was shortened to the point where it resembled a single convection cell. Along much of the major diameter there existed an upflow roll. The new defect structure occurred where the two downflow rolls surrounding the central upflow roll joined. This joint, instead of being smooth as in the stadium case, was angular and created a protuberance pointing outward along the major diameter. We also found a pattern with an upflow roll along the major diameter without the central downflow cell. A third pattern contained a downflow cell, but this cell was displaced by a roll width from the center along a minor diameter. As epsilon increased, the length L(e) between the two protuberances and the wave numbers along the outer parts of the major diameter decreased for all three patterns, analogous to what was found for the stadium. The upper stability limit of these patterns was also set by the cross-roll instability.

Competition of periodic and homogeneous modes in extended dynamical systems

Despite their simple structure, spatially homogeneous modes can participate directly in pattern-formation processes. This is demonstrated by new experimental and theoretical results for thermo- and electroconvection in planar nematic liquid crystals, where two distinct homogeneous modes, twist and splay distortions of the director field, emerge. Their nonlinear excitation is due to certain spontaneous symmetry-breaking bifurcations.

Convection in the presence of a first-order phase change

We report experimental and theoretical results for two-phase convection in a thin horizontal layer of a fluid with a first-order phase change and heated from below. A top layer of the nematic phase of a liquid crystal is located above the bottom layer of the isotropic phase of the same substance. A horizontal field of 1000 G is applied in order to align the director of the nematic phase. Over some ranges of the thickness of the isotropic phase, and in sufficiently large thermal gradients, the more dense nematic phase can be stably stratified above the less dense isotropic one, with a stable interface between them. Based on the equations of motion derived for this problem by Busse and Schubert [J. Fluid Mech. 46, 801 (1971)], we evaluate the bifurcation lines between the quiescent and convecting states and the corresponding critical wave vectors as a function of the interface position. We report experimental measurements based on Nusselt-number determinations for the locations of the bifurcation lines. They are in good agreement with the theoretical results. We also report approximate determinations of the critical wave numbers which are semiquantitatively consistent with the theory. A great diversity of patterns is observed in the convecting states, including normal and parallel rolls, rolls with defects and disorder, target patterns and spirals, and cellular flow with upflow or downflow at the cell center. These patterns are discussed in terms of the breaking of the mirror symmetry at the horizontal midplane by the interface, and in terms of the orienting effects of the magnetic field.