Surface Instability of Icicles

Quantitatively-unexplained stationary waves or ridges often encircle icicles. Such waves form when roughly 0.1 mm-thick layers of water flow down the icicle. These waves typically have a wavelength of 1cm approximately independent of external temperature, icicle thickness, and the volumetric rate of water flow. In this paper we show that these waves can not be obtained by naive Mullins-Sekerka instability, but are caused by a quite new surface instability related to the thermal diffusion and hydrodynamic effect of thin water flow.Comment: 11 pages, 5 figures, Late

Dynamics of a faceted nematic-smectic B front in thin-sample directional solidification

We present an experimental study of the directional-solidification patterns of a nematic - smectic B front. The chosen system is C_4H_9-(C_6H_{10})_2CN (in short, CCH4) in 12 \mu m-thick samples, and in the planar configuration (director parallel to the plane of the sample). The nematic - smectic B interface presents a facet in one direction -- the direction parallel to the smectic layers -- and is otherwise rough, and devoid of forbidden directions. We measure the Mullins-Sekerka instability threshold and establish the morphology diagram of the system as a function of the solidification rate V and the angle theta_{0} between the facet and the isotherms. We focus on the phenomena occurring immediately above the instability threshold when theta_{0} is neither very small nor close to 90^{o}. Under these conditions we observe drifting shallow cells and a new type of solitary wave, called "faceton", which consists essentially of an isolated macroscopic facet traveling laterally at such a velocity that its growth rate with respect to the liquid is small. Facetons may propagate either in a stationary, or an oscillatory way. The detailed study of their dynamics casts light on the microscopic growth mechanisms of the facets in this system.Comment: 12 pages, 19 figures, submitted to Phys. Rev.

Pattern formation in directional solidification under shear flow. I: Linear stability analysis and basic patterns

An asymptotic interface equation for directional solidification near the absolute stabiliy 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 the 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, described in a companion 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.Comment: 20 pages, Latex, accepted for Physical Review

Surface effects in nucleation and growth of smectic B crystals in thin samples

We present an experimental study of the surface effects (interactions with the container walls) during the nucleation and growth of smectic B crystals from the nematic in free growth and directional solidification of a mesogenic molecule ($C_4H_9-(C_6H_{10})_2CN$) called CCH4 in thin (of thickness in the 10 $\mu$m range) samples. We follow the dynamics of the system in real time with a polarizing microscope. The inner surfaces of the glass-plate samples are coated with polymeric films, either rubbed polyimid (PI) films or monooriented poly(tetrafluoroethylene) (PTFE) films deposited by friction at high temperature. The orientation of the nematic and the smectic B is planar. In PI-coated samples, the orientation effect of SmB crystals is mediated by the nematic, whereas, in PTFE-coated samples, it results from a homoepitaxy phenomenon occurring for two degenerate orientations. A recrystallization phenomenon partly destroys the initial distribution of crystal orientations. In directional solidification of polycrystals in PTFE-coated samples, a particular dynamics of faceted grain boundary grooves is at the origin of a dynamical mechanism of grain selection. Surface effects also are responsible for the nucleation of misoriented terraces on facets and the generation of lattice defects in the solid.Comment: 15 pages, 24 figures, submitted to PR

The Effect of Convection on Disorder in Primary Cellular and Dendritic Arrays

Directional solidification studies have been carried out to characterize the spatial disorder in the arrays of cells and dendrites. Different factors that cause array disorder are investigated experimentally and analyzed numerically. In addition to the disorder resulting from the fundamental selection of a range of primary spacings under given experimental conditions, a significant variation in primary spacings is shown to occur in bulk samples due to convection effects, especially at low growth velocities. The effect of convection on array disorder is examined through directional solidification studies in two different alloy systems, Pb-Sn and Al-Cu. A detailed analysis of the spacing distribution is carried out, which shows that the disorder in the spacing distribution is greater in the Al-Cu system than in Pb-Sn system. Numerical models are developed which show that fluid motion can occur in both these systems due to the negative axial density gradient or due the radial temperature gradient which is always present in Bridgman growth. The modes of convection have been found to be significantly different in these systems, due to the solute being heavier than the solvent in the Al-Cu system and lighter than it in the Pb-Sn system. The results of the model have been shown to explain experimental observations of higher disorder and greater solute segregation in a weakly convective Al-Cu system than those in a highly convective Pb-Sn system

The effect of an electric field on the morphological stability of the crystal-melt interface of a binary alloy

We perform a fully time-dependent linear stability analysis of the morphological stability of a planar interface during directional solidification of a binary alloy at constant velocity in the presence of an electric field. We take account of the electromigration of solute and the differing electrical conductivities of solid and liquid for a model in which the temperature gradient is constant. We compare our results with the constitutional supercooling criterion and show there may be substantial differences. We derive a modified constitutional supercooling criterion which is valid over a large range of conditions. We also find under certain conditions that the onset of instability may be time dependent

The effect of an electric field on the morphological stability of the crystal-melt interface of a binary alloy II. Joule heating and thermoelectric effects

We perform a fully time-dependent linear stability analysis of the morphological stability of a planar interface during directional solidification of a binary alloy at constant velocity in the presence of an electric field. We take into account electromigration of solute, Joule heating, and thermoelectric effects. This represents an extension of the simple model of Wheeler et al. in which the latter two effects were neglected. We find that for tin–bismuth and germanium–gallium alloys the influence of electromigration and differing electrical conductivities in each phase are the most important in determining the linear stability of the system, with the Peltier heat and Thomson effect the most significant of the thermoelectric effects, particularly at low velocities where an additional long wavelength instability may arise. Joule heating and Seebeck effects appear to be of lesser importance

Convective stability in the Rayleigh-Benard and directional solidification problems - high-frequency gravity modulation

The effect of vertical, sinusoidal, time-dependent gravitational acceleration on the onset of solutal convection during directional solidification is analyzed in the limit of large modulation frequency-OMEGA. When the unmodulated state is unstable, the modulation amplitude required to stabilize the system is determined by the method of averaging, and is O(OMEGA). Comparison of the results from the averaged equations with numerical solutions of the full linear stability equations (based on Floquet theory) show that the difference is O(OMEGA-1/2). When the unmodulated state is stable, resonant modes of instability occur at large modulation amplitude. These are analyzed using matched asymptotic expansions to elucidate the boundary-layer structure for both the Rayleigh-Benard and directional solidification configurations. The leading-order term for the modulation amplitude is of O(OMEGA-2); the first-order correction of O(OMEGA-3/2) is calculated, and the results are compared with numerical solutions of the full linear stability equations. Based on these analyses, a thorough examination of the dependence of the stability criteria on the unmodulated Rayleigh number, Schmidt number, and distribution coefficient, is carried out