Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session LZ: Instability: General III |
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Chair: Michael Bestehorn, Brandenburgische Technische Universitaet Cottbus Room: Hyatt Regency Long Beach Regency F |
Monday, November 22, 2010 3:35PM - 3:48PM |
LZ.00001: The Jeffery--Hamel similarity solution and its relation to symmetry breaking in two-dimensional, diverging-channel flow Philip Haines, Richard Hewitt, Andrew Hazel Jeffery--Hamel (JH) flows describe the steady two-dimensional flow of an incompressible viscous fluid between infinite plane walls separated by an angle $2\alpha$. They are are often used to approximate flows with a finite radial extent. However, whilst JH flow is characterised by a subcritical pitchfork bifurcation, studies in expanding channels of finite length typically find symmetry breaking via a supercritical bifurcation. Using the finite element method we calculate solutions for flow in a two-dimensional wedge of finite length bounded by arcs of constant radii, $R_1$ and $R_2$. We present a comprehensive picture of the bifurcation structure and nonlinear states for a net radial outflow of fluid. We find a series of nested neutral curves in the Reynolds number-$\alpha$ plane corresponding to pitchfork bifurcations that break the midplane symmetry of the flow. We show that these finite domain bifurcations remain distinct from the JH bifurcation even in the limit $R_2/R_1 \rightarrow \infty$. We also discuss a class of stable steady solutions apparently related to a steady, spatially periodic, wave first observed by Tutty (1996). [Preview Abstract] |
Monday, November 22, 2010 3:48PM - 4:01PM |
LZ.00002: Global Instability and Transient Growth in a Model Fusifom Aneurysm with Steady Inflow Gregory Sheard, Hugh Blackburn The stability of the flow through a model aneurysm is computed using a global linear stability analysis and a direct transient growth analysis. The geometry consists of sinusoidal expansion in a circular pipe. Dimensions are chosen to represent a human abdominal aortic aneurysm near to the critical bulge size requiring surgical intervention. The bulge length and maximum width are $2.9$ and $1.9$ times the pipe diameter, respectively. Subject to a steady inflow, the flow is found to be weakly unstable to quasi-periodic global eigenmodes with azimuthal wavenumbers of $4$ and $5$ at a Reynolds number (based on area-averaged velocity and pipe diameter) of $Re\approx 3900$. Perturbation structures in these eigenmodes are concentrated in the outer part of the bulge towards its downstream end. A transient growth analysis reveals that the flow is sensitive to transient disturbances beyond $Re=33$, well below the time-averaged Reynolds numbers of blood flow in the human abdominal aorta. [Preview Abstract] |
Monday, November 22, 2010 4:01PM - 4:14PM |
LZ.00003: A new analysis of the Rayleigh-B\`{e}nard instability Andrea Prosperetti An approach to the solution of the Rayleigh-B\`{e}nard stability problem different from the standard one produces a very simple approximate solution in closed form which differs by less than 1\% from the exact result. Using the same procedure, the effect of finite thermal conductivities of the top and bottom plates and of suspended, thermally active particles on the stability threshold is also investigated. [Preview Abstract] |
Monday, November 22, 2010 4:14PM - 4:27PM |
LZ.00004: Comparison of Linear Stability and 3-D Time Integration for Predicting Instabilities in a Thermocapillary Driven Liquid Bridge with Magnetic Stabilization Kenneth Davis, Yue Huang, Brent Houchens Flow in a cylindrical liquid bridge is driven by thermocapillary effects arising from a temperature gradient applied on the free surface. When the temperature difference is small and axisymmetric, the base flow will also be axisymmetric. However, as the temperature difference increases the flow becomes susceptible to three-dimensional instabilities, the first of which is either stationary or periodic depending on the Prandtl number of the liquid bridge. Instabilities predicted by linear stability theory are compared with those found using three-dimensional time integrations for low Prandtl number liquid bridges. Comparisons are drawn between spectral collocation and spectral element simulations, in terms of accuracy and computational efficiency. The impact of stabilizing the base state by applying a steady, axial magnetic field is also investigated. [Preview Abstract] |
Monday, November 22, 2010 4:27PM - 4:40PM |
LZ.00005: Convection onset in colloidal suspensions of particles Layachi Hadji A particulate medium model is used to investigate the onset of Rayleigh-B\'{e}nard convection in a colloidal suspension of inert solid particles. The model accounts for the effects of thermophoresis, sedimentation and Brownian diffusion. Depending on the size of the particles, the problem has up to four time scales. These are due to thermal diffusion, particle diffusion, particle migration due to thermophoresis, and sedimentation. The ratios of these time scales lead to the emergence of three parameters, one of which is the Lewis number $\tau$. The smallness of the latter makes the differential eigenvalue system governing convection onset singular. The other two are the density number $\Gamma$ and the dimensionless migration velocity $\beta$. For a given experimental set-up, $\beta$ can be viewed as a function of the particles' radius. A combination of asymptotics and numerical computations is used to capture the effect of the resulting thin particle concentration boundary layers on the leading order threshold values of the Rayleigh number $R_c$. Results, which are depicted as function of $\Gamma$ and $\beta$, reveal a non-monotonic dependence of $R_c$ on $\beta$. The curve $R_c(\beta)$ is bimodal and it exhibits a maximum ${R_c}^M$, the value of which increases very sharply with $\Gamma$ while the critical wavelength decreases, at $\beta$ values that correspond to nano sized particles. This implies that experimental parameters can be controlled so that the mixing of a small amount of nano size particles has a substantial stabilizing effect. [Preview Abstract] |
Monday, November 22, 2010 4:40PM - 4:53PM |
LZ.00006: Magnetic Fields Applied to Paramagnetic Suspensions: The Hump-Jet Transition Scott S.H. Tsai, Zhenzhen Li, Pilnam Kim, Howard A. Stone When a suspension of paramagnetic beads is in a sufficiently strong magnetic field gradient, a jet forms. Based on this approach, we report a technique for depositing an aggregate of paramagnetic beads on a substrate. Our setup is similar to the classical electrohydrodynamic jet setup originally used by Zeleny (1917), Wilson and Taylor (1925), who investigated the case of a single-phase liquid. In contrast, our system consists of a dilute suspension of micron-size paramagnetic beads suspended in the fluid. In response to a weak magnetic field, all of the beads collect at the almost planar interface, which then deforms modestly as the field strength is increased to form a hump. Above a critical field strength, the hump where the beads have collected goes unstable to form a jet. We use high-speed videos to study the system's hump-jet transition. We also propose an analytical scaling model that predicts the critical conditions for the transition by the balance of magnetic and capillary forces acting on the aggregate of beads. [Preview Abstract] |
Monday, November 22, 2010 4:53PM - 5:06PM |
LZ.00007: Linear stability analysis of capillary instabilities for concentric cylindrical shells Xiangdong Liang, Daosheng Deng, Jean-Christophe Nave, Steven G. Johnson We present a linear stability analysis of capillary instabilities in concentric cylindrical flows of $N$ fluids with arbitrary viscosities, thicknesses, and surface tensions. This generalizes previous work by Tomotika ($N=2$) and Stone \& Brenner ($N=3$, equal viscosities). We briefly explain the derivation, consider interesting limiting cases for $N=3$ and $N \to \infty$, and predict a phenomenon of competing breakup lengthscales in a 3-fluid system that we demonstrate with full 3d calculations. [Preview Abstract] |
Monday, November 22, 2010 5:06PM - 5:19PM |
LZ.00008: Generalized Rayleigh-Taylor and Richtmyer-Meshkov instabilities in particle-seeded flow Peter Vorobieff, Joseph Conroy, Michael Anderson, Ross White, C. Randall Truman, Sanjay Kumar We describe a hydrodynamic instability analogous to Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities in gravity-driven or impulsively-accelerated two-phase flows where the seeding density of the second phase (and the resulting average density) is initially non-uniform. The forcing causes the second phase (in our experiments, submicron-sized droplets in gas) to move with respect to the embedding medium. With sufficient seeding concentration, this leads to entrainment of the embedding phase. The resulting movement is similar to the movement that would evolve in a mixing flow with no second phase seeding, but with non-uniform density (e.g., a mixture of lighter and heavier gases), where RT and RM instabilities develop in the case of gravity-induced and impulsive acceleration respectively. [Preview Abstract] |
Monday, November 22, 2010 5:19PM - 5:32PM |
LZ.00009: Mixing two miscible liquids with Faraday instabilty Farzam Zoueshtiagh, Sakir Amiroudine, Ranga Narayanan The generation of waves near the interface of one or two liquid layers that is subjected to vertical vibrations is known as the Faraday instability. This instability occurs on account of a resonance that is set up when there is a tuning of the imposed frequency with the natural frequency of the free surface which possesses surface potential energy. Now if the free surface was removed by completely confining the container then no such instability could occur unless potential energy was introduced in some other way, say via density gradients. In this regard, we have recently shown experimentally and numerically that Faraday type of instability can also occur between two miscible liquids with different densities [1]. Here, we report on experimental and numerical study of Faraday instability used as a mixing tool. In particular, we characterize the mixing efficiency by the instability by measuring the size of the volume where the two liquids were fully mixed under different external vibration parameters. \\[4pt] [1] Zoueshtiagh, F.,Amiroudine, S., Narayanan, R., J.Fluid Mech., 628, pp.43-55, 2009. [Preview Abstract] |
Monday, November 22, 2010 5:32PM - 5:45PM |
LZ.00010: Buoyancy-driven instabilities of miscible two-layer stratifications P.M.J. Trevelyan, C. Almarcha, A. De Wit Buoyancy-driven instabilities of a horizontal interface between two miscible solutions in the gravity field are studied for porous media by a theoretical approach. Beyond the classical Rayleigh-Taylor and double-diffusive instabilities that can affect such a two-layer stratification right at the initial time of contact, diffusive-layer convection as well as delayed-double diffusive instabilities can set in at later time when differential diffusion effects act upon the evolving density profile starting from a step-function initial condition between the two miscible solutions. The conditions for these instabilities to occur can therefore not be obtained using linear base state profiles but can be computed only by considering time evolving base state profiles. To do so, we perform a linear stability analysis based on a quasi steady state approximation as well as nonlinear simulations of a diffusion-convection model. We classify and analyze all possible buoyancy-driven instabilities of a stratification of a solution of A on top of a miscible one of B as a function of a buoyancy number $R$ quantifying the ratio of the relative contribution of B and A to the density and of $\delta$ the ratio of diffusion coefficients of these two species. [Preview Abstract] |
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