Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session D8: Patterns and Instabilities I |
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Sponsoring Units: DFD GSNP Chair: Brian Hunt, University of Maryland Room: Baltimore Convention Center 314 |
Monday, March 13, 2006 2:30PM - 2:42PM |
D8.00001: Nonlinear Analysis of the Self-assembly of Nanostructures Shaowen Hu, Girish Nathan, Gemunu Gunaratne, Donald Kouri We investigate properties of a model of nanoscale pattern formation on a uniform substrate. The coefficients of the Ginzburg-Landau equations are concentration dependent. We find that, above the threshold, there are two branches of solutions corresponding to the up and down hexagonal structures; their appearance is related to the initial concentration of the system. The stability of such structures is confirmed by the analysis of the phase dynamics. When system is away from the threshold, the theory predicts a competition of stripe and hexagonal structures. The predicted stability domain of the stripe structures is consistent with numerical simulations. This provides a framework to understand the guided self-assembly technology, e.g., by the photolithography, at a coarse scale. The possible interaction of a large scale mode with the pattern mode is also discussed. [Preview Abstract] |
Monday, March 13, 2006 2:42PM - 2:54PM |
D8.00002: Shear band instability in the presence of convection Sebastien Aumaitre, J.P. Gollub One of the main features of the atmospheric motion of giant gas planets, like Jupiter and Saturn, is their remarkably stable shear band structure. The stability and internal structure of this flow, and the consequences for the internal heat transport, are not fully understood. Here we present a flexible device to study in a laboratory experiment the stability of a shear band flow in the presence of convective heat transport. The shear band flow is generated in layer of conductive fluid by spatially periodic Lorentz forces resulting from an electric current passing through the fluid in the presence of a network of magnets placed under the cell. Moreover, a convective flow is created by an imposed temperature gradient across the fluid layer. By changing the current through the fluid, and the temperature difference across the layer, we are able to adjust independently the velocity fields resulting from the shear and thermal forcing. Heat transport, flow patterns, and velocity fields are monitored. Initial results on the threshold for the instability of the shear band flow, and the resulting flow patterns, will be presented. [Preview Abstract] |
Monday, March 13, 2006 2:54PM - 3:06PM |
D8.00003: Surfactant-enhanced thermocapillary flow in two-dimensional slots. Ram Hanumanthu, Kathleen Stebe An insoluble surfactant at an aqueous-gas interface can assume a variety of surface states including gaseous (G), liquid expanded (LE), and liquid condensed (LC) states. The surface pressure-surface area isotherm for such monolayers is well established; however, their thermocapillary behavior has received less attention. Recently, Nguyen {\&} Stebe reported surfactant-enhanced Marangoni-Benard flows in evaporating aqueous drops, created by the strong dependence of surface tension on temperature in LE-LC co-existence. In this work, flow in a two-dimensional slot in the presence of insoluble surfactant is modeled. The time-dependent, incompressible Navier-Stokes equations, coupled with energy conservation and surface convection-diffusion equations are solved using Galerkin's method of weighted residuals on a finite element mesh. The model is verified against the results of Sen {\&} Davis for steady thermocapillary flows in two-dimensional slots; and of Homsy {\&} Meiburg for surfactant effects in a linear limit. Finally, both steady-state and dynamic flow patterns are presented that evolve when a constitutive equation that captures the full, non-linear, concentration- and temperature-dependent phase-change behavior is used. Predicted flow patterns are compared qualitatively to the experimental observations. [Preview Abstract] |
Monday, March 13, 2006 3:06PM - 3:18PM |
D8.00004: Weakly nonlinear dynamics of the longwave Marangoni instability in a binary-mixture layer in the presence of the Soret effect. Alexander Oron, Alla Podolny, Alexander A. Nepomnyashchy We consider a system consisting of a layer of an incompressible binary liquid with a deformable free surface. We investigate the long-wave Marangoni instability in the case of small Lewis and Galileo numbers for finite capillary and Biot numbers in the case of a specified heat flux at the solid substrate. The Soret effect is taken into account. Both long-wave monotonic and oscillatory modes of instability are found in various parameter domains of the Biot and Soret numbers. We have derived a set of strongly nonlinear evolution equations describing the spatio-temporal dynamics of the layer in three dimensions in the case of the oscillatory instability. The weakly nonlinear analysis based on these equations demonstrates the presence of several kinds of stable supercritical standing and travelling waves. [Preview Abstract] |
Monday, March 13, 2006 3:18PM - 3:30PM |
D8.00005: Convection onset in a supercritical pure fluid Horst Meyer The convection onset of a pure supercritical fluid -$^3$He - in a Rayleigh-B\'{e}nard cell has been investigated along the critical isochore by measuring the temperature drop $\Delta T(t)$ across the fluid layer as a function of time $t$ after starting the heat current $q$. The measurements showed after the initial sharp rise in $\Delta T(t)$ a first maximum at the time $t_p$, which indicates that the convection has developed and that plumes have reached the upper plate. It was found empirically that $t_p$, scaled by the thermal diffusion relaxation time $\tau_D$, could be expressed as $t_p/\tau_D = F ([Ra - Ra_c])$, where $Ra_c$ is the critical Rayleigh number$^ 1$. A model is proposed which reproduces this observed scaled representation. It uses the instability criterion of the bottom (hot) boundary fluid layer and the calculated Nusselt and Ra numbers for the steady-state convection. The perturbations leading to the convection development, after the fluid instability point has been reached, are unknown. Therefore $t_p/ \tau_D$ is determined within a constant multiplicative factor, the only fit parameter of this model. There is then good agreement over more than four orders of magnitude of $[Ra-Ra_c]$ between the calculations and the experiments. The fit parameter is a phenomenological measure for the effectiveness of the perturbations, and will be discussed. 1. A. Furukawa \underline{et al.} Phys. Rev. \bf{E 68}, 056309 (2003), Fig.5a. [Preview Abstract] |
Monday, March 13, 2006 3:30PM - 3:42PM |
D8.00006: The Resolution of the Domain Chaos Puzzle for Rotated Rayleigh-B\'enard Convection Nathan Becker, Guenter Ahlers Due to the K\"uppers-Lortz instability, Rayleigh-B\'enard convection-patterns exhibit spatio-temporal chaos at the onset of convection when the sample rotates fast enough about a vertical axis. Previous work showed that the scaling of the correlation length $\xi$ determined from the experimental chaotic patterns disagreed with the prediction from a Ginzburg-Landau weakly-nonlinear model.\footnote{Y.-C. Hu, R. Ecke, and G. Ahlers, Phys. Rev. Lett. {\bf 74}, 5040 (1995).} Commonly the power spectrum of the pattern images (the structure factor) is used to extract $\xi$ from the half-width of its peak. Past experiments and simulations used standard Fourier techniques to calculate the power spectrum. On the basis of simulations using the Swift-Hohenberg equation, we show that those results are influenced strongly by the finite image-size available from experiment. The disagreement between experiment and theory was resolved by using the maximum-entropy method to calculate the power spectra. The maximum-entropy method is not as sensitive to the finite image-size effect. When applied to new experimental images, it yielded results for $\xi$ that were in agreement with the theory. [Preview Abstract] |
Monday, March 13, 2006 3:42PM - 3:54PM |
D8.00007: Revealing the buidling blocks of chaos: Deviations from extensivity David A. Egolf, Matthew P. Fishman Researchers have made relatively little progress in developing a predictive theory of far-from-equilibrium, spatially-extended chaotic systems. Even descriptions of the fundamental degrees of freedom and the nature of their interactions --- central elements of statistical mechanics --- are lacking. Using high- precision studies of the fractal dimension as a function of system length for the complex Ginzburg-Landau equation, we have uncovered deviations from extensivity on a length scale consistent with the chaotic length scale, indicating that this spatiotemporal chaotic system is composed of weakly-interacting building blocks, each containing about two degrees of freedom. Our results also suggest an explanation of some of the `windows of periodicity' found in spatiotemporal systems of moderate size. [Preview Abstract] |
Monday, March 13, 2006 3:54PM - 4:06PM |
D8.00008: Estimating the State of Large Spatio-Temporally Chaotic Systems: Application to a Rayleigh-Benard Convection Experiment Matthew Cornick, Edward Ott, Brian Hunt Data Assimilation (DA) refers to the estimation of a dynamical system's state from the combined knowledge of past observations (possibly incomplete and noisy) and knowledge of an approximate model for the systems time evolution. Here we consider DA for spatio-temporally chaotic systems, and, in particular, we study the Local Ensemble Kalman Filter DA technique. We have applied this technique to Rayleigh-Benard convection undergoing spiral defect chaos. Using a system model (Boussinesq equations) and time series of noisy shadowgraphs we obtain estimates of the temperature and velocity field everywhere in a convection cell. This technique provides us with an indirect measurement of quantities previously inaccessible such as mean flow. We also demonstrate the utility of this method for forming initial conditions and producing 'forecasts' from the model. [Preview Abstract] |
Monday, March 13, 2006 4:06PM - 4:18PM |
D8.00009: Competition between left and right spiral vortices and their combinations with different or equal amplitudes Manfred L\"{u}cke, Alexander Pinter, Christian Hoffmann Stability, bifurcation properties, and the spatiotemporal behavior of different nonlinear combination structures of spiral vortices in the counter rotating Taylor-Couette system are investigated by full numerical simulations and by coupled amplitude equation approximations. Stable cross-spiral structures with continuously varying content of left and right spiral modes are found. Their solution provides a stability transferring connection between the initially stable, axially counter propagating wave states of pure spirals and the axially standing waves of so-called ribbons that become stable slightly further away from onset of vortex flow. [Preview Abstract] |
Monday, March 13, 2006 4:18PM - 4:30PM |
D8.00010: An Accurate Mode Selection Mechanism for Magnetic Fluids David Jackson, Jos\`{e} Miranda When a ferrofluid is trapped in a Hele-Shaw cell and subjected to a perpendicular magnetic field a fingering instability results in the droplet evolving into a complex branched structure. This fingering instability depends on the magnetic field ramp rate but it also depends critically on the initial state of the droplet. Small perturbations in the initial droplet can have a large influence on the resulting final pattern. By simultaneously applying a stabilizing azimuthal magnetic field, we gain more control over the mode selection mechanism. In fact, a linear stability analysis predicts that any mode can be selected by appropriately adjusting the strengths of the applied fields. We present the results of numerical simulations that demonstrate that this mode-selection mechanism is quite robust and ``overpowers'' any initial perturbations on the droplet. This provides a predicable way to obtain patterns with any number of fingers whatsoever. [Preview Abstract] |
Monday, March 13, 2006 4:30PM - 4:42PM |
D8.00011: Controlling Interfacial Instabilities in Hele-Shaw Cells: Theory Shuwang Li, John Lowengrub, Jake Fontana, Peter Palffy-Muhoray The growth of crystals in an undercooled melt and interface evolution in Hele-Shaw cells are governed by similar underlying mathematics. Hele-Shaw experiments can therefore give valuable insights into crystal growth. In the context of crystal growth, Li, Lowengrub and co-workers have demonstrated (e.g. see J. Crystal Growth, Physica D) that by varying the temperature conditions in the far-field in a prescribed way without feedback, interface instabilities (e.g. Mullins-Sekerka) can be suppressed and crystals may be grown with desired symmetries. Interestingly, at long times nonlinear stabilization is observed and leads to the existence of universal crystal shapes that depend only on the far-field temperature conditions. Here, this work is adapted to interface evolution in Hele-Shaw cells where the control parameter is the injection pressure. Namely, we consider the displacement of oil by air and we demonstrate that by varying the injection pressure in a prescribed, time-dependent way (without feedback) that the Saffman-Taylor instability can be suppressed and controlled such that bubbles of desired symmetries can form. This is in agreement with recent experimental predictions (presented separately in this session). We further predict the existence of universal bubble shapes that depend only on the injection pressure; the experimental confirmation of such universal shapes is the subject of ongoing studies. [Preview Abstract] |
Monday, March 13, 2006 4:42PM - 4:54PM |
D8.00012: Controlling Interfacial Instabilities in Hele-Shaw Cells: Experiments Jake Fontana, Peter Palffy-Muhoray, Shuwang Li, John Lowengrub The growth of crystals in an undercooled melt and interface evolution in Hele-Shaw cells are governed by similar underlying mathematics. Hele-Shaw experiments can therefore give valuable insights into crystal growth. We have constructed radial Hele-Shaw cells where oil between parallel glass plates could be displaced by air whose injection pressure is a function of time. Here we describe our experimental apparatus and present results for the interface evolution for different driving schemes. We have found that, in agreement with recent theoretical predictions (presented separately in this session), we can prevent the onset of the Saffman-Taylor instability, or we can select and grow a particular unstable mode and drive the interface towards a corresponding universal shape. Varying the injection pressure during growth thus allows control over interfacial instabilities. [Preview Abstract] |
Monday, March 13, 2006 4:54PM - 5:06PM |
D8.00013: Liquid manipulation via morphological transitions Ralf Seemann, Martin Brinkmann, Evgeny Gurevich, Stephan Herminghaus, Jean-Christophe Baret, Michel Decre Liquid deposited on rectangular grooves, has a variety of possible liquid morphologies determined by the contact angle, $\theta$, and the exact channel geometry. In our experiments, electrowetting is used to tune $\theta$ reversibly from 100 to 50 $^{\circ}$, leading to a reversible transition between a drop- like morphology at large $\theta$ and extended liquid filaments for small $\theta$. The transition is capillarity-driven but the behavior of the liquid above the transition is influenced by the electrical properties of the liquid. The static length of the liquid filament is a function of the applied Voltage and is in perfect agreement with a simple transmission-line model. Emphasis is put on the dynamic aspects of the filling and the draining behavior that follow a modified Washburn law. In case of thin and elastic ridges separating two grooves the cross talk of the liquid morphologies with the elastic substrate has an ordering effect on the position of the droplets. [Preview Abstract] |
Monday, March 13, 2006 5:06PM - 5:18PM |
D8.00014: Diffusion-induced spontaneous pattern formation on gelation surfaces Hiroaki Katsuragi Polymer gels make various kinds of surface patterns, which are typical non-equilibrium phenomena, under the volume phase transition. Mechanical instabilities due to swelling or shrinking of polymer gels play an essential role in such pattern formations. However, there is no report on diffusion-induced spontaneous pattern formation in polymer gels. Here we report the diffusion-induced (not caused by the mechanical instability) macroscopic pattern formation on gelation surfaces. We experimented on two-dimensional poly-acrylamide gelation that is governed by free radical polymerization. Gel slabs were made on Petri-dishes with free upper surface boundary condition. Then, random and straight stripe patterns (surface deformations) were observed, depending on gelation conditions. We consider a reaction-diffusion dynamics to describe this pattern formation. Acrylamide is considered as an activator and oxygen works as an inhibitor in the gelation reaction-diffusion system. We found the scaling relation between the characteristic wavelength and the gelation time. This scaling is consistent with the reaction-diffusion dynamics. [Preview Abstract] |
Monday, March 13, 2006 5:18PM - 5:30PM |
D8.00015: Using Capillary Flows to Pattern Lines Saurabh Vyawahare, Kate Craig, Axel Scherer One can appreciate how capillary forces cause unexpected patterns and shapes by looking at a soap bubble. Pattern formation by surface tension is seen in ring patterns of coffee stains, fingering patterns in Hele-Shaw cells, ordering of two dimensional micro-sphere crystals, combing of DNA and skeleton formation in marine creatures called radiolarians. Though comman, problems involving the understanding and control of the self-assembly mechanism need to be resolved before using capillary forces as a practical lithographic tool. Here, we report capillary flows create line patterns in evaporating liquids between closely spaced parallel plates. The widths of these lines range from a few microns to a few nanometers. Deliberate patterning of such lines requires pinning of the contact line and the presence of foaming surfactants. The position and type of line can be controlled with artificial pinning points and varying solutes respectively, and large-scale photolithography can be used to guide and control the definition of nanostructures. We provide ``proof of principle'' demonstrations of this method's application by creating lines of colloidal quantum dots and micro-spheres. This represents the first step in using capillary phenomena to create controlled, self--assembling, one-dimensional wire-like structures [Preview Abstract] |
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