Session A28 - Interfacial Instability and Pattern Formation.
FOCUS session, Monday morning, March 18
208, Indiana Convention Center

[A28.001] Wax tectonics: from deep rifts to ridges

We report experiments using paraffin wax to model oceanic ridge dynamics. In our experiment, two freezing wax plates float on melted wax and are pulled apart with constant velocity, forming a spreading rift. Using synthetic Shellwax Callista we observe behavior very similar to that of the Earth: microplates, transform faults, and ridge topography. For different spreading velocities the wax forms deep rifts (low speeds, < 25 \mum/s), flat topography (intermediate speeds, (25 - 35 \mum/s), and shallow ridges (high speeds, > 35 \mum/s). We report quantitative observations on this transition and investigate dynamic similarity and scaling between the wax and the Earth. This work is supported by the Cornell Presidential Research Scholars Program and the National Science Foundation under grant DMR-0072077.

[A28.002] Solidification of a Supercooled Liquid in a Narrow Channel

We simulate solidification in a narrow channel through the use ofa phase-field model simulated on an adaptive grid. At high undercooling,we find that the solid can grow in fingerlike steady-states whose shape we derive based on simple physical arguments. At low undercooling, fingers become unstable, exhibiting unsteady growth. In this regime we findwe find good agreement between our results and experiment, as well as with previously untested theoretical predictions regarding Hele Shaw fingers.

[A28.003] The role of sidebranches in the stability of dendritic array

The role of sidebranches of dendrites in pattern formation during the directional solidification of binary alloys is investigated experimentally. In standard experiments sidebranches in a dendritic array grow toward each other, which may influence the stability of the array. Here we decrease the interactions of sidebranches by carrying out the experiments with an array of dendrites rotated by 45 degrees around the growth direction forcing the side branches to grow into the wall rather than toward each other. We observe that the preferred primary spacings for this array are smaller than for the standard array under the same growth condition, indicating that the direct interaction between sidebranches stabilizes the array of large spacing. We also found that it is the tip splitting instability that sets the upper limit of primary spacing for the array of rotated dendrites, while for the standard array it is mainly the sidebranching instability. At the cell-dendrite transition no increase in spacing is observed for the array of rotated dendrites, in contrast to the standard arrays.

[A28.004] Grain Boundary Formation in Polymer Blend Thin Films

The solidification microstructures of thin-film polymers are studied. The mixture of crystallizing polymer PEO and glassy polymer PMMA displays a compact dense branching (or seaweed) morphology, a four fold symmetric dendrite, diffusion limited aggregation, and spherulitic growth. Crystal growth is nucleated at arbitrary points through small perturbations in the film. We focus on seaweed and dendritic microstructures which can coexist for the same polymer mixing ratio. Competitive growth is observed for crystal nucleation in a square and hexagonal lattice and is characterized by measuring the volume fraction of the crystal and interfacial orientation. Nucleation geometry, crystal orientation and morphology all play a role.

[A28.005] Diverse Patterns Induced by Constant Electric-Field in Colloid

A surprisingly diverse set of interesting patterns are formed by micron-size charge-stabilized colloidal particles subjected to a constant vertical electric field. Increasing the applied voltage just beyond the decomposition potential for water creates highly organized microscopic patterns with spatial period ranging from 20 to 200 micrometers. Higher voltages yield different macroscopic patterns with larger spatial periods extending to 2 mm. The patterns including toroids, flowers with convective coronas, tumbling blobs, labyrinths and complicate transient patterns etc., are located in the bulk or on the electrodes. It is a coupled system of hydrodynamic flows and reaction-diffusion of ions and charged colloid in the DC electric field. We introduce a general set of equations describing such systems and demonstrate its similarity to Rayleigh-Benard convection. Our experiments also showed that the electroneutrality breaks down in pure water electrolysis.

[A28.006] Universality classes in anisotropic non-equilibrium growth models

We study the effect of generic spatial anisotropies on the scaling behavior in the Kardar-Parisi-Zhang equation. In contrast to its ``conserved'' variants, anisotropic perturbations are found to be relevant in d>2 dimensions, leading to rich phenomena that include novel universality classes and the possibility of first-order phase transitions and multicritical behavior. These results question the presumed scaling universality in the strong-coupling rough phase, and shed further light on the connection with generalized driven diffusive systems.

[A28.007] Damping the Fingering Instability in Rotating Magnetic Fluids

A fingering instability occurs when a drop of liquid in a Hele-Shaw cell is rotated at a constant angular velocity. If this liquid is a ferrofluid, this fingering instability can be suppressed by the application of an azimuthally applied magnetic field. We have studied this situation analytically and computationally and have observed a number of interesting behaviors, including what we refer to as a ``diamond ring'' instability. This magnetic damping can also be used to reduce the instabilities in other systems, such as the fingering that results when a ferrofluid drop in a Hele-Shaw cell is subjected to a transverse magnetic field.

[A28.008] Computational solution of liquid-gas interface shapes from the refractions of a defocused grid

We have observed unusual surface film distortions on two parallel sapphire walls close together and wetted by liquid. The closed and constant volume cell is filled with carbon dioxide close to its liquid-gas critical point in weightless conditions (Mir station). The two-phase fluid consists of a flat gas bubble surrounded by liquid, creating a significant area of wetting film on the sapphire. By ray tracing the shadow of a defocused grid through the cell and the film, we determined the shape of the liquid-gas interface. This numerical method finds the surface shape by comparing the resultant shadow displacements found in the experimental images with an assumed shape in the simulation. Based on the solution of this inverse problem, we found very large local curvatures. The film thickness changes were also much larger than films typically found on Earth by close to an order of magnitude. These film distortions are created from the thick uniform wetting film by heating the cell wall and the fluid far from thermodynamic equilibrium. Temperature data during the heating revealed a gas temperature exceeding both the liquid and the wall temperature. This large film thickness allows an explanation of this overheating that is consistent with a previous explanation.

[A28.009] Transverse Bursts in Inclined Layer Convection: Experiment

We report experimental results on inclined layer convection in a fluid of Prandtl number \sigma \approx 1. A codimension-two point divides regions of buoyancy-driven convection (longitudinal rolls) at lower angles from shear-driven convection (transverse rolls) at higher angles (Daniels et al. PRL 84: 5320, 2000). In the region of buoyancy-driven convection, near the codimension-two point, we observe longitudinal rolls with intermittent, localized, subharmonic transverse bursts. The patterns are spatiotemporally chaotic. With increasing temperature difference the bursts increase in duration and number. We examine the details of the bursting process (e.g. the energy of longitudinal, transverse, and mixed modes) and compare our results to bursting processes in other systems. This work is supported by the National Science Foundation under grant DMR-0072077 and the IGERT program in nonlinear systems, grant DGE-9870631.

[A28.010] Transverse Bursts in Inclined Layer Convection: Theory

We report theoretical and computational results on thermally driven inclined layer convection. For small Prandtl number fluids, experiments have reported bursting phenomena at both small angles, strong driving and high angles, weak driving (Daniels et al. PRL 84: 5320, 2000). Theoretically, the small angle, strong driving case was described by Clever and Busse (Physics of Fluids 12: 2137, 2000) and was connected to a subharmonic instability. At large angles, close to the codimension-two point, intermittent, localized, transverse subharmonic bursts occur at weak driving. Qualitatively, the bursts draw energy from the roll modes, exhaust them while growing, and die out when they are unable to find a new attractor. We investigate a connection between the small- and large-angle bursts. Using Galerkin methods and direct simulations of the underlying Boussinesq equations, we examine the extent to which they are related to a linear instability of the roll pattern. We address a possible connection to the shear flow turbulent bursts observed in Taylor-Couette flow. In addition, we present a theoretical analysis of the small Prandtl number case, for which the codimension-two point moves to zero angle. This work is supported by a Cornell Graduate Student Fellowship and by the National Science Foundation under grant DMR-0072077.

[A28.011] Phase diagram of the liquid crystal N4 in electroconvection

We study different patterns in electroconvection in N4 liquid crystal cell as a function of two parameters : the applied frequency and the applied voltage. An electroconvection cell consists of two conductive glass plates. The liquid crystal is placed between the gap (of 24�E in our case) of these two plates. Rubbing the inner surface of the glass plates orients the molecules of the liquid crystal along a direction called the director. Convection rolls appear above a critical value of an AC voltage of a defined frequency. An optical system of polarizer/analyzer, and sometimes a quarter wave plate, allows a visual observation of the patterns. Patterns observed in electroconvection for N4 are very similar to those observed in thermoconvection for the same liquid crystal (Plaut et al. 1998). Below the Lifschitz frequency (2500Hz in our case), zig and zag patterns are obtained at the onset. Above the Lifschitz point, normal rolls are obtained at the onset. We will report more on the various patterns and transition that are observed.

[A28.012] Random-walk simulations of Hele-Shaw viscous flows: From unstable fractals to steady-state Saffman-Taylor fingers

I adapt a mean-field ��density�� formalism to study and describe phenomena of viscous fingering taking place between two immiscible fluids in a Hele-Shaw cell, i.e. the Saffman-Taylor problem. For that purpose I explore an alternative approach to the viscous fingering, whose basic concepts have been originally introduced by Witten and Sander in their paradigm of diffusion-limited aggregation (DLA) [Phys. Rev. Lett. 47, 1400 (1981)]. Advancing the original DLA algorithm, I formulate its mean-field generalization in stochastic and deterministic terms. The stochastic model proposed simulates patterns which demonstrate a striking resemblance to natural Hele-Shaw shapes and, for steady-state regimes, follow precisely Saffman-Taylor hydrodynamic solutions known for channel and sector geometries; the relevant deterministic theory is derived from that stochastic model. As a principal conclusion, I prove asymptotic equivalency of both the stochastic and deterministic mean-field DLA formulations to the Saffman-Taylor hydrodynamics in terms of an interface evolution.

[A28.013] Reconstruction of Process Pathways from Computational Time-Series

In 1995, Arkin et al. (J. Phys. Chem. 99) introduced a technique for reconstructing chemical reaction pathways from concentration data. This was experimentally tested two years later (Science 277) to a subset of the reactants of the glycolytic pathway, kept far from equilibrium in a continuous-flow, stirred-tank reactor. We here report an application of and extentions to this technique in a real-world system in which the number of reactants is large and the experimental data readily available. Connections may be made with dynamic data from DNA microarrays (eg., S. Chu et al. Science 282, 1998), in which the number of relevant reactants (i.e., genes) can number in the thousands or tens of thousands.

[A28.014] Spatio-Temporal instabilities and an Intrinsic Feedback-like Mechanism in Nonlinear LiNbO3 crystals

We have measured and analyzed the spatio-temporal behavior of the electro-optic (EO) responsivity of LiNbO3 single crystals. While there is no apparent feedback-loop circuit involved in the sensor system, very strong spatio-temporal instabilities appear in the EO responsivity of some LiNbO3 crystals. The temporal instability exhibits an intermittent bursting pattern, which is similar in nature to the results obtained by Grebogi et al (Phys. Rev A 36 , 5365, 1987) from numerical simulations using the Ikeda map. This intermittent bursting in our experiment is due to the interplay between the external fields and the screening fields, and stems from strong nonlinear photorefractive effects. These effects establish an intrinsic feedback-like mechanism in nonlinear LiNbO3 crystals.

Part A of program listing