Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session H9: Instabilities and Fluid Dynamics |
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Sponsoring Units: DFD Chair: Jerzy Blawzdziewicz, Yale University Room: Morial Convention Center RO7 |
Tuesday, March 11, 2008 8:00AM - 8:12AM |
H9.00001: Low Frequency Oscillations in the Upper Atmosphere Sudip Sen No definitive theory exists which explains the origin of various low frequency oscillations observed in the ionosphere. Various authors, over the course of time, have put forward various explanations of this important phenomenon. Most recently it has been proposed that the spatial transverse shear in the parallel flow destabilizes many low frequency oscillations and this may be the origin of low frequency oscillations in the ionosphere [V V Gavrishchaka et al., Phys. Rev. Lett. {\bf 80}, 728 (1998) and Phys. Rev. Lett. {\bf 85}, 4285 (2000)]. In this article we review the various theories proposed till date to explain the origin of low frequency oscillations. We address the most recent theories in more detail. We show that the recent proposition of the spatial transverse shear might excite many instabilities may not be so obvious. Parallel flow curvature when taken into account might actually act to stabilize various instabilities [S. Sen et al. Phys. Rev. Lett. {\bf 88}, 185001 (2002)]. This article therefore concludes while much work has been done on the ionospheric oscillations much more work possibly remains to be done in this important area of space physics. [Preview Abstract] |
Tuesday, March 11, 2008 8:12AM - 8:24AM |
H9.00002: Capillary-controlled instability in immiscible, parallel flow in porous media Thomas Ramstad, Alex Hansen When two immiscible fluids flow in parallel in a strongly wetted porous medium the global interface separating them tend to be kept in place by local capillary barriers. However, above a certain threshold in the flow rate, the separating interface may become unstable and mobilized. We study this instability theoretically by using a two-dimensional network as a model for porous media in a flow regime where capillary forces cannot be neglected. It is found that a boundary zone with a sharp saturation profile occurs between the regions originally saturated with either a wetting or a non-wetting phase. This zone has a well defined width and moves with constant speed towards the non-wetting region. In the opposite direction, a current of non-wetting bubbles is set up, but wetting bubbles into the non-wetting region are absent. This behavior is genuinely different from shear-induced Kelvin-Helmholtz instabilities. [Preview Abstract] |
Tuesday, March 11, 2008 8:24AM - 8:36AM |
H9.00003: Stability of multi-layer Hele-Shaw flows with and without diffusion Prabir Daripa In this talk, we will provide some results in the context of multi-layer Hele-Shaw flows. We will address issues related to collective effects of individually unstable interfaces on the overall stability of multi-layer Hele-Shaw flows in the presence of interfacial surface tensions. We will also discuss complications in the analysis resulting from making, in the above set-up, individual layers also unstable. We obtain some sufficient conditions for suppressing instability of two-layer flows by introducing arbitrary number of constant viscosity fluid layers in between. For stabilization purposes, this condition allows selection of fluids in internal layers based on interfacial surface tensions and viscosities of fluids. Time permitting, we also examine the effects of species diffusion on the stability of the three-layer Hele-Shaw flows. This has relevance to enhanced oil recovery by polymer flooding. Analytically, we will prove the diffusive slow-down of unstable waves. It will be shown that a strong enough diffusion can almost stabilize the flow, though the magnitude of this diffusion coefficient required to completely stabilize the flow will depend on the magnitude of interfacial viscosity jumps and the viscosity gradient of the basic viscous profile of the internal layer. This work has been done in collaboration with Gelu Pasa. [Preview Abstract] |
Tuesday, March 11, 2008 8:36AM - 8:48AM |
H9.00004: Meandering instability of a rivulet on a partially wetting incline Adrian Daerr, Laurent Limat It is common to observe small rivulets in sinks or on window-panes which follow sinuous paths (stationary or not) instead of flowing down along the direction of steepest slope. A laboratory experiment shows that these meandering rivulets exist only for certain ranges of the control parameters (flow rate and substrate inclination). The geometrical properties of the resulting paths can be understood in terms of force balances between inertia, capillarity and contact line pinning. The nature of the instability, i.e. why the straight rivulet becomes unstable, however remains unclear. We study the rivulet near the onset for meandering to understand the role of noise and surface defects. [Preview Abstract] |
Tuesday, March 11, 2008 8:48AM - 9:00AM |
H9.00005: A quasi 2-D molecular dynamics study of the initiation and evolution of the Kelvin-Helmholtz instability Kyle Caspersen, Robert Rudd, David Richards, Jim Glosli, John Gunnels, Fredrick Streitz Typically hydrodynamic phenomena are modeled with continuum mechanics via integration of the Navier-Stokes (NS) equation or a closely related variant. However, as fluids are studied at smaller and smaller length scales atomistic effects can, and will, ultimately dominate; furthermore, even at micron scales it is not clear that the NS equation provides a complete description of the fluid, e.g. due to the initiation of instabilities at the molecular scale in initially quiescent fluids. To assess the effect of atomistic behavior on one particular hydrodynamic phenomenon--the Kelvin-Helmholtz instability--we have performed a very large molecular dynamics simulation of molten metals undergoing shear flow. Nine billion copper and aluminum atoms were sheared at a speed of 2000 m/sec for a total simulated time of more than a nanosecond. We present here results showing the initiation of the instabilities, the crossover to hydrodynamics, and the evolution and scaling behavior of the KH instability in a quasi 2-D geometry. Prepared by LLNL under Contract DE-AC52-07NA27344. [Preview Abstract] |
Tuesday, March 11, 2008 9:00AM - 9:12AM |
H9.00006: A fully 3-D molecular dynamics study of the initiation of the Kelvin-Helmholtz instability Robert E. Rudd, K.J. Caspersen, D.F. Richards, J.N. Glosli, J.A. Gunnels, F.H. Streitz The modeling of hydrodynamic phenomena has almost exclusively been the purview of continuum mechanics, specifically, through the use of the Navier-Stokes equation and closely related variants. Nevertheless, at the smallest length scales, where atomistic effects become important, it is not clear that this continuum approach provides a complete description of fluid behavior. To understand the effects of atomistics, we have performed a 62.5-billion-atom, fully 3-D molecular dynamics simulation of a cubic micron of molten copper and aluminum. The shear flow at 2 km/s exhibits complex phenomena associated with a Kelvin-Helmholtz (KH) instability. In this presentation we will discuss the initiation and early evolution of the KH instability, focusing specifically on the effects of full atomistic resolution. [Preview Abstract] |
Tuesday, March 11, 2008 9:12AM - 9:24AM |
H9.00007: Bubble Pinch-off at High Pressures J.C. Burton, P. Taborek Previously we have studied the pinch-off of conventional air bubbles in water [1]. For inviscid fluids, the shrinking of the neck radius of the bubble can be described by a power-law in time with an exponent close to 1/2. As the density of the interior gas is increased, instabilities are expected to occur in the liquid/gas interface [2]. We present high-speed videos and numerical simulations of the pinch-off of high-pressure gaseous bubbles in and exterior inviscid fluid. The density ratio between the exterior fluid and interior gas is D=$\rho_{ext}/\rho_{int}$. In the simple case of small D$\sim$0.001, the pinch-off is similar to that of a water drop pinching-off in air, while at large D$\sim$1000, the pinch-off is that of an air bubble in water. By using sulfur hexafluoride as a working gas, we are able to span a wide ranging of density ratios simply by increasing the pressure of the gas. A high-pressure ($\sim$30 atm) chamber with optical access through sapphire windows was constructed in order to view the pinch-off. The numerical simulations are performed assuming perfectly inviscid fluids using boundary-integral techniques. Instabilities in the interface are seen for intermediate density ratios. Comparisons between experimental and numerical results will be discussed. \newline [1] J.C. Burton, R. Waldrep, and P. Taborek. Phys. Rev. Lett. 94, 184502, (2005). \newline [2] D. Leppinen and J.R. Lister. Phys. Fluids 15, 568, (2003). [Preview Abstract] |
Tuesday, March 11, 2008 9:24AM - 9:36AM |
H9.00008: First order phase transition in the height of a meniscus in a tapered capillary Michael Pettersen, Etienne Rolley When a fluid rises in a capillary of non-uniform cross section, additional terms arise in the balance of capillary forces, compared to the case of a capillary of uniform cross section, due to the changing area of the meniscus. Recently, it has been pointed out that this can lead to a first order phase transition, resulting in a discontinuous jump in the equilibrium position of the meniscus. We present the results of an experiment using isopropanol and silicone oil in cones with apex upwards of different opening angles. The cone is slowly lowered into the liquid using a translation stage. We have measured the capillary rise in this geometry, and observed the predicted phase transition. [Preview Abstract] |
Tuesday, March 11, 2008 9:36AM - 9:48AM |
H9.00009: Luminescence from Laser-Induced Bubbles in Water-Glycerol Mixtures: Effect of Viscosity Erin Englert, Allison McCarn, Gary A. Williams We have studied the luminescence emitted from collapsing laser-induced bubbles in water-glycerol mixtures, as a function of the mixture concentration and applied hydrostatic pressure. The primary effect of increasing the glycerol concentration is to increase the viscoslty of the fluid. We find that the pulse duration of the luminescence increases by more than a factor of two as the concentration increases up to 33\% by volume, where the viscosity is nearly four time that of pure water. At higher concentrations the pulse duration remains nearly unchanged, until no luminescence can be observed at concentrations above 60\% (viscosity greater than 15 times that of water). The pulse duration further increases with applied pressures up to 8 bars, similar to that seen earlier in pure water. [Preview Abstract] |
Tuesday, March 11, 2008 9:48AM - 10:00AM |
H9.00010: Hysteretic and Chaotic Dynamics of Viscous Drops in Creeping Flows with Rotation Yuan-Nan Young, Jerzy Blawzdziewicz, Vittorio Cristini, Roy Goodman It has been shown in our previous publication (Blawzdziewicz et al 2003) that high-viscosity drops in two dimensional linear creeping flows with a nonzero vorticity component may have two stable stationary states. One state corresponds to a nearly spherical, compact drop stabilized primarily by rotation, and the other to an elongated drop stabilized primarily by capillary forces. Here we explore consequences of the drop bistability for the dynamics of highly viscous drops. Using both boundary-integral simulations and small-deformation theory we show that a quasi-static change of the flow vorticity gives rise to a hysteretic response of the drop shape, with rapid changes between the compact and elongated solutions at critical values of the vorticity. In flows with sinusoidal temporal variation of the vorticity we find chaotic drop dynamics in response to the periodic forcing. A cascade of period-doubling bifurcations is found to be directly responsible for the transition to chaos. In random flows we obtain a bimodal drop- length distribution. Some analogies with the dynamics of macromolecules and vesicles are pointed out. [Preview Abstract] |
Tuesday, March 11, 2008 10:00AM - 10:12AM |
H9.00011: A Temporal Period Doubling Route to Spatiotemporal Chaos in a System of Amplitude Equations for the Nematic Electroconvection Iuliana Oprea, Gerhard Dangelmayr We analyze the transition from periodic solutions to spatiotemporal chaos in a system of four globally coupled Ginzburg Landau equations describing the dynamics of instabilities in the electroconvection of nematic liquid crystals, in the weakly nonlinear regime. If spatial variations are ignored, these equations reduce to the normal form for a Hopf bifurcation with O(2) x O(2) symmetry. Coexistence of low dimensional and extensive spatiotemporal chaotic patterns, as well as a temporal period doubling route to spatiotemporal chaos, corresponding to a period doubling cascade towards a chaotic attractor in the normal form, are also identified and discussed, for values of the parameters including experimentally measured values of the nematic I52. [Preview Abstract] |
Tuesday, March 11, 2008 10:12AM - 10:24AM |
H9.00012: Angular momentum transport in complex fluids Xiaoyu Zheng, Peter Palffy-Muhoray, Michael Shelley When dyes are dissolved in nematic liquid crystals, the light intensity required for the optical Freedericksz transition can be dramatically decreased. This is due to the torque exerted by the dye on the liquid crystal. The dye molecules absorb light energy and rotate; torque balance is mediated by angular momentum transport from the cell walls via shear flow generated by the rotation [1]. We present a model which accounts for the transport of angular momentum caused by singular vortices present in these complex fluids. The singular vortices generate flow, and are transported by the flow which they generate. For simple fluids, the distribution of vorticity satisfies the biharmonic equation in the Stokes limit, which can be solved analytically. In the case of the non-Newtonian fluids, such as liquid crystals, Leslie-Ericksen continuum theory is used to describe the interactions between the rod-like molecules. [1] P. Palffy-Muhoray, T. Kosa and Weinan E, ``Brownian Motors in the Photoalignment of Liquid Crystals'', \textit{Appl. Phys. A} \textbf{75}, 293-300 (2002). [Preview Abstract] |
Tuesday, March 11, 2008 10:24AM - 10:36AM |
H9.00013: Particle Dynamics in Bi-Disperse Liquid Fluidized Beds Phil Segre, Gary L. Hunter, James Davidheiser, Elizabeth Baker We study particle velocities and concentration profiles of mixtures of $2$ different sized particles in concentrated liquid fluidized beds. For binary systems of particles of the same density, we find that there is always a complete phase separation in the bed. The larger particles occupy a zone in the lower part of the bed, and the smaller ones a zone in the upper part. For binary systems of particles of {\it different} density materials, conditions are found where the binary particles are either fully separated, partially mixed together, and at a single point called the inversion point, fully mixed into a one phase state. Results will be presented on the phase diagrams of several binary suspensions as well as the properties of the velocity fluctuation magnitudes and spatial correlation lengths. [Preview Abstract] |
Tuesday, March 11, 2008 10:36AM - 10:48AM |
H9.00014: Polygonal hydraulic jump on microtextured surfaces Emilie Dressaire, Laurent Courbin, Jerome Crest, Howard A. Stone Fluid motion can be drastically influenced by the nature of boundaries. For instance, we have shown recently \footnote{L. Courbin, E. Denieul, E. Dressaire, M. Roper, A. Ajdari and H.A. Stone, Nature~Mater. \textbf{6}, 661 (2007)} that a substrate with a regular array of micron-size posts can cause partially wetting fluids to take on polygonal shapes. Here, we report on the hydraulic jump that occurs when a water jet impinges a topographically patterned surface, i.e. an array of micron-size posts arranged on square or hexagonal lattice. By varying the topographic features (shape and height of the posts, lattice distance) and the jet properties (size of the nozzle, flow rate), we obtain a variety of stable shapes including hexagons, eight corner stars and circles. We rationalize our results by taking into account a fluid velocity that depends on the orientation of the lattice. [Preview Abstract] |
Tuesday, March 11, 2008 10:48AM - 11:00AM |
H9.00015: Enstrophy-constrained stability analysis of beta-plane Kolmogorov flow with drag Yue-Kin Tsang, William Young For forced two-dimensional flows, energy injected at a certain wavenumber is redistributed to both larger and smaller wavenumbers. This results in a constraint on the time evolution of the difference between the energy and enstrophy. By incorporating this constraint in an energy stability analysis of Kolmogorov flow on a beta-plane with drag, we establish an extended region in the parameter space of beta and the drag coefficient where the flow is stable to arbitrary perturbations. Complementary to this nonlinear stability result, linear instability theory is used to determine the part of the parameter space where the flow is unstable to infinitesimal perturbations. We also find that the most unstable mode in the linear stability analysis has a discontinuous change in structure as beta decreases below a certain value. Results from numerical simulations spanning the parameter space support the theoretical predictions. [Preview Abstract] |
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