Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Session D9: Patterns, Nonlinear Dynamics followed by General Fluid Dynamics |
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Sponsoring Units: DFD Chair: Yuri Antipov, Louisiana State University, and Galen Gisler, University of Oslo Room: D220 |
Monday, March 21, 2011 2:30PM - 2:42PM |
D9.00001: Rayleigh B\'enard Convection-A Case Study on Pattern Formation Hira Siddiqui, Rudolf Friedrich Spiral turbulence in Rayleigh-Benard convection is studied numerically in the framework of generalized Swift Hohenberg equations. The model equation consist of an order parameter equation for the temperature field coupled to an equation for the mean flow field. In contrast to the earlier work, nonlinearities in the dynamics of the mean flow are retained leading to a two dimensional Navier-Stokes equation coupled to a Swift-Hohenberg equation. We present the numerical investigations of nonlinear effects due to the interaction of nonlinear two dimensional flows and the pattern forming process. [Preview Abstract] |
Monday, March 21, 2011 2:42PM - 2:54PM |
D9.00002: A simple approach to localized convection H. Pleiner, M.G. Clerc, J. Martinez-Mardones, L.M. Perez, D. Laroze Localized structures can be found in many different (dissipative) driven systems [1], an example being stationary and traveling convection structures in the thermal instability of binary fluids. Here, the special localized structure is a convective state between two quiescent, conductive ones, and can been interpreted as a pinning phenomenon close to a stationary sub-critical bifurcation. Generally, localized structures are described by using higher dimensional, complex amplitude or phenomenological prototype (e.g. Swift-Hohenberg) equations or by direct numerical integration of the hydrodynamic equations. Here we show, using the binary mixture convection in porous media as an example, that the analytically derived one-dimensional amplitude equation amended by non-adiabatic (non-resonant) terms important close to convection fronts, well describes localized convection states, in particular the slanted homoclinic bifurcation diagrams.\\[4pt] [1] O. Descalzi, M. Clerc, S. Residori, and G. Assanto (Eds.), Localized States in Physics: Solitons and Patterns, Springer, 2011. [Preview Abstract] |
Monday, March 21, 2011 2:54PM - 3:06PM |
D9.00003: The dynamics of cracks in torn thin sheets Yossi Cohen, Itamar Procaccia The stress field near the tip of a crack due to a mode III shear tearing of a thin plate of elastic material has a universal form but with a non-universal amplitude known as the Stress Intensity Factor. All the non-universal aspects of the stress distribution are collected in the Stress Intensity Factor which depends on everything, including the crack length, the boundary conditions and the history of the loads that drive the crack evolution. Although the equations of elasticity for thin plates are well known, there remains the question of selection of a path for a propagating crack. We invoke a generalization of the principle of local symmetry to provide a criterion for path selection and demonstrate the qualitative agreement of our results with the experimental findings. We also analyze the nature of the singularity at the crack tip with and without the nonlinear elastic contributions. Finally we present an exact analytic results for the stress intensity factor to the linear approximation for the crack developing in thin sheets. [Preview Abstract] |
Monday, March 21, 2011 3:06PM - 3:18PM |
D9.00004: Chaotic Plume-Like Bursts in Rimming Flows Gabriel Seiden, Victor Steinberg We report a detailed experimental investigation of chaotic, plume-like bursts observed in rimming flows of polymer solutions within a partially filled horizontal cylinder. In particular, we investigate the attractive interaction between adjacent plumes and the effect of rotation rate and polymer concentration on the statistics of these unique bursts. A comparison is also made between the Newtonian and non-Newtonian cases. [Preview Abstract] |
Monday, March 21, 2011 3:18PM - 3:30PM |
D9.00005: Cracks formation during blood drop evaporation Benjamin Sobac, David Brutin We firstly presented the pattern formation occurring when drops of whole blood desiccate in a recent publication [1]. The phenomena presented evidence to involve lots of physical field such as surface chemistry, haematolology, fluid mechanics, heat transfer, colloids science{\ldots} All these mechanisms are acting together and produce an axisymetric and reproducible pattern. Dried cellular components are segregated and deposited by a capillary flow. During the evaporation, the system is slowly drying and cracks when stresses are too important leading to the final pattern observed. In this presentation, we will present the mechanisms involved in the formation of crack patterns. The phenomenon presented here with red blood cells as the main colloids involved is very similar to the drying of drop of nanoparticules [2]. We will explain the common point and the differences encountered.\\[4pt] [1] D. Brutin, B. Sobac, B. Loquet and J. Sampol, Pattern formation in drying drops of blood, Journal of Fluid Mechanics, underpress, 2010.\\[0pt] [2] L. Pauchard, B. Abou, K. Sekimoto, Infuence of Mechanical Properties of Nanoparticles on Macrocrack Formation, Langmuir, 25(12), 6672-6677, 2009. [Preview Abstract] |
Monday, March 21, 2011 3:30PM - 3:42PM |
D9.00006: ABSTRACT WITHDRAWN |
Monday, March 21, 2011 3:42PM - 3:54PM |
D9.00007: Pattern formation and coarsening in crystalline membranes Daniel A. Vega, Aldo D. Pezzutti We study through a Brazovskii-Helfrich Hamiltonian the process of defect formation, annealing and coarsening of two dimensional crystalline membranes. In good agreement with the cosmological model of Kibble and Zurek, proposed to determine the density of topological defects at the onset of a symmetry breaking phase transition, we found that the collision of orientationally uncorrelated domains produces a structure of grains with an average density of topological defects controlled by the temperature of the quench. The strain field of the dislocations and disclinations generated during the phase separation process can induce the buckling of the membrane, slowing down the Lifshitz-Safran mechanism of coarsening observed in flat systems. [Preview Abstract] |
Monday, March 21, 2011 3:54PM - 4:06PM |
D9.00008: Pattern formation in ternary lipid membranes with composition-deformation coupling Matthew Demers, Francisco Solis, Monica Olvera de la Cruz We study patterns formed in three-component lipid membranes, where composition is coupled to shape via differences in spontaneous curvature. The system is examined in the strong segregation regime. System morphology is determined by the competition of bending energy, surface tension, and line tension. We will present the phase behavior as determined by numerical minimization, as well as analytic solutions for select cases. [Preview Abstract] |
Monday, March 21, 2011 4:06PM - 4:18PM |
D9.00009: Supercavitating flow past an elastic curvilinear hydrofoil Yuri Antipov A nonlinear inverse fluid-structure interaction problem is considered. The obstacle is a curvilinear elastic hydrofoil, and the cavity formed behind is modeled according to the single-spiral-vortex model by Tulin. First, the model for a rigid polygonal supercavitating hydrofoil is solved by the method of conformal mappings. The mapping function is expressed through the solutions of two Riemann-Hilbert problems. To identify the vertices of the polygon where the jets break away from the foil, the Brillouin-Villat separation condition is applied. The unknown parameters of the conformal mapping are computed on solving a system of transcendental equations. Next, by increasing the number of vertices of a regular $N$-polygon, the cavitation problem for a circular arc is solved, pressure on the foil is defined, and a boundary- value problem for a thin shell subject to normal loading is stated. The elastic problem is solved exactly for an arc with clamped ends, and the new hydrofoil profile is determined. Finally, a new cavitation problem for the deformed foil is stated and solved. Numerical experiments reveals the presence of two thin partial cavities near the foil ends. [Preview Abstract] |
Monday, March 21, 2011 4:18PM - 4:30PM |
D9.00010: Drag calculations using the inviscid Euler equations alone Galen Gisler Recently Hoffman and Johnson$^{1}$ have proposed a new resolution of d'Alembert's Paradox, the problem that inviscid potential flow predicts zero drag on a body, in contrast to observations. They reject the commonly accepted resolution, that drag results from the very thin viscous boundary layer between the no-slip condition on the surface of the body and the free-flowing fluid. Instead they argue that drag results from turbulence in the body's wake, even if free-slip is assumed. They used a finite-volume code to verify their conclusions. While their calculations look promising, and offer prospects for calculation of rather more complex flows at modest resolution, it is desirable to perform independent verification. I will present independent tests of the Hoffman-Johnson resolution using a finite-volume Euler-equation code, studying the dependence of the inferred drag on meshing style and resolution. \\[4pt] [1] Johan Hoffman and Claes Johnson, J. Math. Fl. Dyn. 12, 321-334 (2010). [Preview Abstract] |
Monday, March 21, 2011 4:30PM - 4:42PM |
D9.00011: Dynamics of induced dipole ER fluid: a continuous energetic approach Jianwei Zhang, Wenfeng Li, Jiaxi Li We studied dynamics of Electrorheological (ER) fluid by continuum induced dipole fluid method [1]. We found that the velocity profile of ER fluid increases in high shear-rate region and solid particles are separated from colloid in high electric field. These findings demonstrated the breakdown of Bingham fluid model under high shear-rate and high electric field. Our continuum approach describes ER fluid's behaviors under most conditions. We also found that the shift of maximum shear stress under different electric field follows the same trend as that of the maximum static stress. This indicates that the static and dynamic stresses are both dominated by the same energetic process. A connection between micro-particles' structures and macro-dynamic properties under varying conditions is established by our continuum method. Our studies probe the physics of induced dipole ER fluid. \\[4pt] [1] Jianwei Zhang, Xiuqing Gong, Chun Liu, Weijia Wen, and Ping Sheng, Physical Review Letters 101, 194503, 2008. [Preview Abstract] |
Monday, March 21, 2011 4:42PM - 4:54PM |
D9.00012: Velocity fluctuations in steadily sedimenting suspensions K. Vijay Kumar, Sriram Ramaswamy The simplest model of a homogeneous suspension steadily sedimenting under gravity at low Reynolds number indicates that the velocity fluctuations should diverge with the system size. This is, however, not seen in experiments. We improve on a previously described coarse-grained model proposed for this problem by identifying certain crucial missing terms in the equations of motion. These terms are allowed by symmetry considerations and can be generated by a mechanism which is natural in the dynamics of low Reynolds number sedimentation. A dynamical renormalization group calculation of our model leads to the conclusion that these extra terms are always relevant. If these terms are stabilizing, this suggests a natural mechanism for suppressing fluctuations in sedimenting suspensions. We analyze the properties of the critical point where these extra terms vanish. [Preview Abstract] |
Monday, March 21, 2011 4:54PM - 5:06PM |
D9.00013: Stabilization of toroidal droplets using viscoelastic media Ekapop Pairam, Alberto Fernandez- Nieves We inject a viscous liquid through a needle into another rotating viscous liquid to generate toroidal droplets. These droplets are unstable and undergo a transformation into spherical droplets driven by surface tension: They either break ala Rayleigh-Plateau or grow fatter to become a single spherical droplet depending on the aspect ratio of the torus. By replacing the outer phase with a viscoelastic fluid with a non-zero yield stress we can stabilize these and other non-zero genus droplets. We will examine this stabilization mechanism and present criteria to effectively prevent the break-up of these droplets. [Preview Abstract] |
Monday, March 21, 2011 5:06PM - 5:18PM |
D9.00014: Iron chemistry at aqueoues interfaces by near edge X-ray spectroscopy David Vaknin, Wenjie Wang, Alex Travesset, Ivan Kuzmenko Employing synchrotron X-ray absorption near-edge spectroscopy (XANES) combined with X-ray fluorescence (XF) and reflectivity (XR) techniques, we monitor the state of ferrous and ferric iron as it binds to charged carboxylic and phosphate groups. By subphase pH manipulation, arachidic acid and dihexadcyl phosphate monolayers can provide a range of surface charge density from nearly charge-neutral to a fully charged monolayer to which iron ions are attracted from solutions. Analysis of our results from fluorescence show that the driving forces attracting Fe$^{3+}$ and Fe$^{2+}$ to the interface originate from chemical interactions and electrostatic, respectively. XANES shows that the electronic and geometric structure of iron complexes at interface are different from those in the bulk. Moreover, the XANES results demonstrate that valence state and bonding of the interfacially bound Fe$^{3+}$ and Fe$^{2+}$ are practically indistinguishable. This, we argue, is due to the versatility of iron ions in behaving as electron acceptors (Fe$^{3+}$) or as donors (Fe$^{2+}$). [Preview Abstract] |
Monday, March 21, 2011 5:18PM - 5:30PM |
D9.00015: Interfacial microrheology in viscoelastic membranes Gopal Subedi, Kenneth W. Desmond, Eric R. Weeks Prior studies on interfaces using microrheology have typically been applied to interfaces with only a surface viscosity component and not an elastic one. We are extending the application of interfacial microrheology to viscoelastic lipid monolayers. We use a DPPC and cholesterol lipid monolayer in a Langmuir trough as a model system. The Langmuir trough gives us the flexibility to control the concentration and thus the phase of the monolayer. The microrheology technique allows us to measure the rheology at specific concentrations or in situations as the concentration is changed. The microrheology technique employs video microscopy to record the diffusive motion of micron size spheres placed at the interface. Since the diffusive motion of the microspheres is dominated by the interfacial rheology of the monolayer, the recorded motions of the microspheres are used to infer the rheological properties of the interface. We hope to extend our understanding of viscoelastic interfaces with the study. [Preview Abstract] |
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