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Aug 2007

Volume 19, Issue 8, Articles (08xxxx)

Issue Cover Spotlight Figure

Phys. Fluids 19, 083601 (2007); http://dx.doi.org/10.1063/1.2754346 (14 pages)

G. J. Sheard, T. Leweke, M. C. Thompson, and K. Hourigan
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Effects of hydrophobic surfaces on the drag and lift of a circular cylinder

Donghyun You and Parviz Moin

Phys. Fluids 19, 081701 (2007); http://dx.doi.org/10.1063/1.2756578 (4 pages) | Cited 8 times

Online Publication Date: 8 August 2007

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Effects of hydrophobic surfaces on the drag and lift of a circular cylinder at Reynolds numbers of 300 and 3900 are investigated using numerical simulations. A cylinder of which the entire surface is no-slip, a cylinder of which the entire surface is hydrophobic, and cylinders with alternating circumferential bands of slip and no-slip conditions are considered. The width of the alternating bands ranges from 0.5λz to 2λz, where λz is a spanwise characteristic wavelength in the near wake. At Reynolds number 300, the hydrophobic surface consisting of alternating slip and no-slip bands of width λz is found to be most effective in enhancing wake instability, thereby decreasing the base suction, drag, and rms lift coefficients. At Reynolds number 3900, hydrophobic surface treatments are found to delay flow separation, thereby decreasing the drag and rms lift.
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47.60.-i Flow phenomena in quasi-one-dimensional systems
47.85.Np Fluidics
47.11.-j Computational methods in fluid dynamics
47.15.-x Laminar flows
47.27.wb Turbulent wakes
47.20.-k Flow instabilities

Multiple modes of instability in a box heated from the side in low-Prandtl-number fluids

D. Henry and H. BenHadid

Phys. Fluids 19, 081702 (2007); http://dx.doi.org/10.1063/1.2770514 (4 pages) | Cited 2 times

Online Publication Date: 28 August 2007

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The existence of multiple modes of instability in Rayleigh-Bénard or Marangoni-Bénard situations has been known for many years. This existence is shown for the first time for low-Prandtl-number flows in three-dimensional cavities heated from the side. For such a situation, the study of the flow transitions has long remained a challenge, as these transitions occur in already very intense flows. The study is possible here thanks to performing numerical methods, and the ten first instability modes are determined for a wide range of aspect ratios and Prandtl number values. The most striking feature of our results is the very frequent change of leading mode when aspect ratios or Prandtl number are changed, which indicates different flow structures triggered at the transitions, either steady or oscillatory and breaking some of the symmetries of the problem.
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47.20.-k Flow instabilities
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.11.-j Computational methods in fluid dynamics
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back to top Interfacial Flows

Suppression of the Rayleigh-Taylor instability of thin liquid films by the Marangoni effect

Alexander Alexeev and Alexander Oron

Phys. Fluids 19, 082101 (2007); http://dx.doi.org/10.1063/1.2750307 (9 pages) | Cited 4 times

Online Publication Date: 9 August 2007

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Stabilization of the Rayleigh-Taylor instability of a thin liquid film by the Marangoni effect arising from heating of the liquid at the gas-liquid interface in a bilayer setting is investigated. Solution of time-dependent Navier-Stokes and long-wave evolution equations in both two and three dimensions shows the emergence of nontrivial nonruptured steady states in the system when the applied temperature gradient exceeds a certain critical value.
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47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
68.15.+e Liquid thin films
68.03.Cd Surface tension and related phenomena
47.55.Hd Stratified flows
47.10.ad Navier-Stokes equations

Three-dimensional capillary-gravity waves generated by a moving disturbance

E. I. Părău, J.-M. Vanden-Broeck, and M. J. Cooker

Phys. Fluids 19, 082102 (2007); http://dx.doi.org/10.1063/1.2750293 (6 pages) | Cited 3 times

Online Publication Date: 16 August 2007

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Steady three-dimensional capillary-gravity waves generated by a moving pressure distribution are considered. Solutions of the full Euler equations are computed by using a boundary integral equation method. The radiation condition is imposed by introducing a small Rayleigh viscosity in the dynamic boundary condition. The results generalize previous linear findings.
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47.35.Pq Capillary waves
47.35.Bb Gravity waves

Experimental investigation of steady buoyant-thermocapillary convection near an evaporating meniscus

Hemanth K. Dhavaleswarapu, Pramod Chamarthy, Suresh V. Garimella, and Jayathi Y. Murthy

Phys. Fluids 19, 082103 (2007); http://dx.doi.org/10.1063/1.2752477 (11 pages) | Cited 14 times

Online Publication Date: 17 August 2007

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Micro-particle image velocimetry measurements of the three-dimensional (3D) convection patterns generated near an evaporating meniscus in horizontally oriented capillary tubes are presented. Analysis of the vapor diffusion away from the meniscus reveals a zone of intense heat flux near the solid-liquid-vapor junction that creates a temperature gradient along the meniscus. This results in a surface tension gradient which, coupled with buoyancy effects, causes buoyant-thermocapillary convection in the liquid film. The relative influence of buoyancy and thermocapillarity on the flow was investigated for tube diameters ranging from 75 to 1575 μm. A transition from a pure two-dimensional thermocapillary flow to a 3D buoyant-thermocapillary flow is observed with an increase in tube diameter. For the 75 μm tube, a symmetrical toroidal vortex is observed near the meniscus. For larger tubes, buoyancy effects become apparent as they dominate the flow field. The high mass fluxes in smaller-diameter tubes drive stronger vortices. Particle streaks and micro-particle image velocimetry images obtained in multiple horizontal and vertical planes provide an understanding of this three-dimensional flow behavior. A scaling analysis shows the importance of thermocapillary convection in evaporating menisci.
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47.55.nb Capillary and thermocapillary flows
47.32.C- Vortex dynamics
47.60.-i Flow phenomena in quasi-one-dimensional systems
68.03.Cd Surface tension and related phenomena
47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.20.Dr Surface-tension-driven instability

Unsteady draining flows from a rectangular tank

Lawrence K. Forbes and Graeme C. Hocking

Phys. Fluids 19, 082104 (2007); http://dx.doi.org/10.1063/1.2759891 (14 pages) | Cited 2 times

Online Publication Date: 17 August 2007

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Two-dimensional, unsteady flow of a two-layer fluid in a tank is considered. Each fluid is inviscid and flows irrotationally. The lower, denser fluid flows with constant speed out through a drain hole of finite width in the bottom of the tank. The upper, lighter fluid is recharged at the top of the tank, with an input volume flux that matches the outward flux through the drain. As a result, the interface between the two fluids moves uniformly downwards, and is eventually withdrawn through the drain hole. However, waves are present at the interface, and they have a strong effect on the time at which the interface is first drawn into the drain. A linearized theory valid for small extraction rates is presented. Fully nonlinear, unsteady solutions are computed by means of a novel numerical technique based on Fourier series. For impulsive start of the drain, the nonlinear results are found to agree with the linearized theory initially, but the two theories differ markedly as the interface approaches the drain and nonlinear effects dominate. For wide drains, curvature singularities appear to form at the interface within finite time.
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47.60.-i Flow phenomena in quasi-one-dimensional systems
47.20.-k Flow instabilities

Correction of Lamb’s dissipation calculation for the effects of viscosity on capillary-gravity waves

J. C. Padrino and D. D. Joseph

Phys. Fluids 19, 082105 (2007); http://dx.doi.org/10.1063/1.2760244 (6 pages) | Cited 1 time

Online Publication Date: 21 August 2007

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Purely irrotational theories of the flow of a viscous liquid are applied to model the effect of viscosity on the decay and oscillation of capillary-gravity waves. In particular, the dissipation approximation used in this analysis gives rise to a viscous correction of the frequency of the oscillations which was not obtained by Lamb’s [ H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge, UK, 1932) (reprinted in 1993) ] dissipation calculation. Moreover, our dissipation method goes beyond Lamb’s in the sense that it yields an eigenvalue relation valid for the entire continuous spectrum of wave numbers. Comparisons are presented between the purely irrotational theories and Lamb’s exact solution, showing good to reasonable agreement for long, progressive waves and for short, standing waves, even for very viscous liquids. The performance of the irrotational approximations deteriorates within an interval of wave numbers containing the cutoff where traveling waves become standing ones.
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47.35.Pq Capillary waves

Nonlinear buoyant-thermocapillary flows in a three-layer system with a temperature gradient along the interfaces

Ilya B. Simanovskii

Phys. Fluids 19, 082106 (2007); http://dx.doi.org/10.1063/1.2766959 (9 pages) | Cited 2 times

Online Publication Date: 24 August 2007

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The nonlinear buoyant-thermocapillary flows in three superposed liquid layers bounded by two solid planes and subjected to a temperature gradient directed along the interfaces, are investigated. Two types of boundary conditions, periodic boundary conditions and heat-insulated lateral walls, are considered. The nonlinear simulations of the wavy convective regimes are performed by the finite-difference method.
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47.55.Hd Stratified flows
47.11.Bc Finite difference methods
47.27.te Turbulent convective heat transfer
44.25.+f Natural convection

Effects of gravity, inertia, and surfactant on steady plug propagation in a two-dimensional channel

Y. Zheng, H. Fujioka, and J. B. Grotberg

Phys. Fluids 19, 082107 (2007); http://dx.doi.org/10.1063/1.2762256 (16 pages) | Cited 11 times

Online Publication Date: 29 August 2007

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Liquid plugs may form in pulmonary airways during the process of liquid instillation or removal in many clinical treatments. Studies have shown that the effectiveness of these treatments may depend on how liquids distribute in the lung. Better understanding of the fundamental fluid mechanics of liquid plug transport will facilitate treatment strategies. In this paper, we develop a numerical model of steady plug propagation driven by gravity and pressure in a two-dimensional liquid-lined channel oriented at an angle α with respect to gravity. We investigate the effects of gravity through the Bond number, Bo, and α; the plug propagation speed through the capillary number, Ca, or the Reynolds number, Re; the plug length LP, and the surfactant concentration C0. Without gravity, i.e., Bo = 0, the plug is symmetric, and there are two regimes for the flow: two wall layers and two trapped vortices in the core. There is no flow interaction between the upper and lower half plug domains. When Bo ≠ 0 and α ≠ 0, π, fluid is found to flow from the upper precursor film, through the core and into the lower trailing film. Then the number of vortices can be zero, one, or two, depending on the flow parameters. The vortices have stagnation points on the interface when C0 = 0, however when the surfactant is present (C0>0), the vortices detach from the interface and create saddle points inside the core. The front meniscus develops a capillary surface wave extending into the precursor film. This is where the film is thinnest and thus the wall shear stress is highest, as high as ∼ 100 dyn/cm2 in adult airways, which indicates a significant risk of pulmonary airway epithelial cell damage. Adding surfactant can decrease the peak magnitude of the shear stress, thus reducing the risk of cell damage. The prebifurcation asymmetry of the plug is quantified by the volume ratio, Vr, defined as the ratio of the liquid above to that below the center line of the channel. Vr is found to increase with LP, Ca, Re, and C0, while it decreases with Bo. The total mass left behind in the trailing films increases with Bo for any α at α>2π/5, Ca and α for any value of Bo>0.
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47.63.Ec Pulmonary fluid mechanics
back to top Viscous and Non-Newtonian Flows

Polymer induced drag reduction in exact coherent structures of plane Poiseuille flow

Wei Li and Michael D. Graham

Phys. Fluids 19, 083101 (2007); http://dx.doi.org/10.1063/1.2748443 (15 pages) | Cited 5 times

Online Publication Date: 15 August 2007

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Nonlinear traveling waves that are precursors to laminar-turbulent transition and capture the main structures of the turbulent buffer layer have recently been found to exist in all the canonical parallel flow geometries. The present work examines the effect of polymer additives on these “exact coherent states” (ECS) in the plane Poiseuille geometry, using the FENE-P constitutive model for polymer solutions. In experiments with a given fluid, Reynolds and Weissenberg numbers are linearly related (i.e., Wi/Re = const). In this situation, we study the effects of viscoelasticity on velocity field and polymer stress field along some experimental paths, which represent different flow behaviors as Re (and Wi) increases. The changes to the velocity field for the viscoelastic nonlinear traveling waves qualitatively capture many of those experimentally observed in fully turbulent flows of polymer solutions at low to moderate levels of drag reduction: drag is reduced, streamwise velocity fluctuations increase, and wall-normal and spanwise velocity fluctuations decrease. The mechanism underlying these observations is the suppression of streamwise vortices by the polymer forces exerted on the fluid. Specifically, at sufficiently high wall shear rates, viscoelasticity completely suppresses these streamwise vortices in the near-wall region, as is found in experiments in the maximum drag reduction regime. The mean shear stress balance for the nonlinear traveling waves shows that Reynolds shear stress decreases and polymer stress increases monotonically with the increase of viscoelasticity, as is found in full turbulence. The study of the influence of the viscoelasticity on the turbulent kinetic energy and Reynolds stress budgets shows that as Re (and Wi) increases, there is a consistent decrease in the production, diffusion, and dissipation of turbulent kinetic energy. The decrease in the velocity pressure gradient term leads to a redistribution of the turbulent kinetic energy among the streamwise, wall-normal and spanwise directions. The influence of the rheological parameters on the viscoelastic ECS is analyzed. It is found that the degree of drag reduction is determined primarily by the extensional viscosity and Weissenberg number. The optimum wavelength conditions under which the viscoelastic ECS first come into existence are also investigated. The wavelengths in streamwise and spanwise directions and the wall-normal extent of the ECS all increase monotonically with the increase of viscoelasticity, as is found in experiments.
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47.50.Cd Modeling
47.27.Cn Transition to turbulence
47.15.Fe Stability of laminar flows
47.27.nb Boundary layer turbulence
47.57.Qk Rheological aspects
47.35.-i Hydrodynamic waves

A novel low inertia shear flow instability triggered by a chemical reaction

Teodor Burghelea, Kerstin Wielage-Burchard, Ian Frigaard, D. Mark Martinez, and James J. Feng

Phys. Fluids 19, 083102 (2007); http://dx.doi.org/10.1063/1.2759190 (13 pages) | Cited 3 times

Online Publication Date: 17 August 2007

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We present an experimental investigation of a novel low Reynolds number shear flow instability triggered by a chemical reaction. An acid-base reaction taking place at the interface between a Newtonian fluid and carbopol-940 solution leads to a strong viscosity stratification, which locally destabilizes the flow. Our experimental observations are made in the context of a miscible displacement flow, for which the flow instability promotes local mixing and subsequently improves the displacement efficiency. The experimental study is complemented by a simplified normal mode analysis to shed light on the origin of the instability.
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47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.70.Fw Chemically reactive flows
47.50.Gj Instabilities
47.55.Hd Stratified flows
47.51.+a Mixing
47.85.Dh Hydrodynamics, hydraulics, hydrostatics

Velocity measurements in confined swirling flow of polymer solutions with vortex shedding

Shinji Tamano, Motoyuki Itoh, Yuichiro Ide, and Kazuhiko Yokota

Phys. Fluids 19, 083103 (2007); http://dx.doi.org/10.1063/1.2754246 (8 pages)

Online Publication Date: 20 August 2007

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A particle image velocimetry system is used to examine the velocity field in the unsteady swirling flow of polyacrylamide (PAA) solutions (PAA 0.5 wt. % and 1.0 wt. %) with the vortex shedding due to a rotating disk in a cylindrical casing. In our earlier work [ Tamano et al., Phys. Fluids 19, 023103 (2007) ], the vortex shedding is investigated by the flow visualization technique. In this work, we investigate the velocity field for better understanding of the vortex shedding mechanism and the nonaxisymmetric ring vortex which was observed for the higher Reynolds number compared to that of the axisymmetric ring vortex. It was found that the fluid within the ring vortex formed near the rotating disk rotates with semirigid rotation, where the angular velocity of the ring vortex was about 0.9 times that of the rotating disk. A high shear layer existed at the boundary between the ring vortex and the outer large-scale secondary flow. When the ring vortex was shed, the surrounding large-scale secondary flow rushed into near the rotating axis, so that strong axial flow was observed near the rotating axis. For the nonaxisymmetric ring vortex, azimuthal and radial velocities oscillate periodically with considerably large amplitude. In addition, the joint probability density function showed that the correlation between azimuthal and radial velocity fluctuations varied with the radial locations.
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47.32.Ef Rotating and swirling flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.80.Cb Velocity measurements
47.57.Ng Polymers and polymer solutions
47.32.cf Vortex reconnection and rings
47.32.cd Vortex stability and breakdown

Propulsion in a viscoelastic fluid

Eric Lauga

Phys. Fluids 19, 083104 (2007); http://dx.doi.org/10.1063/1.2751388 (13 pages) | Cited 42 times

Online Publication Date: 24 August 2007

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Flagella beating in complex fluids are significantly influenced by viscoelastic stresses. Relevant examples include the ciliary transport of respiratory airway mucus and the motion of spermatozoa in the mucus-filled female reproductive tract. We consider the simplest model of such propulsion and transport in a complex fluid, a waving sheet of small amplitude free to move in a polymeric fluid with a single relaxation time. We show that, compared to self-propulsion in a Newtonian fluid occurring at a velocity UN, the sheet swims (or transports fluid) with velocity U/UN = (1+De2ηs/η)/(1+De2), where ηs is the viscosity of the Newtonian solvent, η is the zero-shear-rate viscosity of the polymeric fluid, and De is the Deborah number for the wave motion, product of the wave frequency by the fluid relaxation time. Similar expressions are derived for the rate of work of the sheet and the mechanical efficiency of the motion. These results are shown to be independent of the particular nonlinear constitutive equations chosen for the fluid, and are valid for both waves of tangential and normal motion. The generalization to more than one relaxation time is also provided. In stark contrast with the Newtonian case, these calculations suggest that transport and locomotion in a non-Newtonian fluid can be conveniently tuned without having to modify the waving gait of the sheet but instead by passively modulating the material properties of the liquid.
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47.63.-b Biological fluid dynamics

Measurement of temperature profiles in turbulent pipe flow of polymer and surfactant drag-reducing solutions

K. Gasljevic, G. Aguilar, and E. F. Matthys

Phys. Fluids 19, 083105 (2007); http://dx.doi.org/10.1063/1.2770257 (18 pages) | Cited 4 times

Online Publication Date: 29 August 2007

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A device was built to measure temperature profiles of turbulent pipe flows of various drag-reducing fluids. It is easy to use and reliable. We measured temperature profiles over a range of conditions leading to accurate measurements down to y+ ≈ 10, for tests carried over Reynolds numbers (Re) between 10 000 and 90 000. The effects of high heat fluxes and buoyancy, in particular, were quantified to ascertain the parameter range for accurate measurements. Temperature profiles measured for type-A polymer solution and for cationic surfactant solutions allowed us to see strong similarity between velocity and temperature profiles for drag-reducing surfactant solutions. A comparison between the slopes of the thermal and velocity buffer layers resulted in calculated turbulent Prandtl numbers between 6 and 9 for those drag-reducing solutions. We also used this tool to investigate drag reduction for a nonionic surfactant solution, which showed a significantly different fan-type profile, and also for a type-B drag-reducing polymer solution (Xanthan gum).
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47.60.-i Flow phenomena in quasi-one-dimensional systems
47.27.nf Flows in pipes and nozzles
back to top Particulate, Multiphase, and Granular Flows

Preferential accumulation of bubbles in Couette-Taylor flow patterns

Eric Climent, Marie Simonnet, and Jacques Magnaudet

Phys. Fluids 19, 083301 (2007); http://dx.doi.org/10.1063/1.2752839 (12 pages) | Cited 4 times

Online Publication Date: 17 August 2007

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We investigate the migration of bubbles in several flow patterns occurring within the gap between a rotating inner cylinder and a concentric fixed outer cylinder. The time-dependent evolution of the two-phase flow is predicted through three-dimensional Euler-Lagrange simulations. Lagrangian tracking of spherical bubbles is coupled with direct numerical simulation of the Navier-Stokes equations. We assume that bubbles do not influence the background flow (one-way coupling simulations). The force balance on each bubble takes into account buoyancy, added-mass, viscous drag, and shear-induced lift forces. For increasing velocities of the rotating inner cylinder, the flow in the fluid gap evolves from the purely azimuthal steady Couette flow to Taylor toroidal vortices and eventually a wavy vortex flow. The migration of bubbles is highly dependent on the balance between buoyancy and centripetal forces (mostly due to the centripetal pressure gradient) directed toward the inner cylinder and the vortex cores. Depending on the rotation rate of the inner cylinder, bubbles tend to accumulate alternatively along the inner wall, inside the core of Taylor vortices or at particular locations within the wavy vortices. A stability analysis of the fixed points associated with bubble trajectories provides a clear understanding of their migration and preferential accumulation. The location of the accumulation points is parameterized by two dimensionless parameters expressing the balance of buoyancy, centripetal attraction toward the inner rotating cylinder, and entrapment in Taylor vortices. A complete phase diagram summarizing the various regimes of bubble migration is built. Several experimental conditions considered by Djéridi, Gabillet, and Billard [Phys. Fluids 16, 128 (2004)] are reproduced; the numerical results reveal a very good agreement with the experiments. When the rotation rate is increased further, the numerical results indicate the formation of oscillating bubble strings, as observed experimentally by Djéridi et al. [Exp. Fluids 26, 233 (1999)] . After a transient state, bubbles collect at the crests or troughs of the wavy vortices. An analysis of the flow characteristics clearly indicates that bubbles accumulate in the low-pressure regions of the flow field.
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47.55.D- Drops and bubbles
47.15.-x Laminar flows
47.11.-j Computational methods in fluid dynamics
47.10.ad Navier-Stokes equations
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.32.C- Vortex dynamics
back to top Laminar Flows

Flow around an impulsively arrested circular cylinder

G. J. Sheard, T. Leweke, M. C. Thompson, and K. Hourigan

Phys. Fluids 19, 083601 (2007); http://dx.doi.org/10.1063/1.2754346 (14 pages) | Cited 11 times

Online Publication Date: 8 August 2007

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The vortex dynamics of the flow around a suddenly arrested translating circular cylinder is investigated by direct numerical simulation and water tank experiments. In the numerical study, a method of visualization of streaklines in simulated-particle tracking computations is proposed, which is based on a variable-variance two-dimensional Gaussian-weighted summation of particles in the vicinity of each interpolation point, and for which a close similarity with physical dye visualizations is found. This technique is used to identify the trajectory of both the wake vortices, as well as the secondary vortices induced as the original wake convects over the arrested cylinder. Observations show that, in a fashion similar to the flow past an arresting sphere, each wake vortex induces a counter-rotating vortex pair, which subsequently self-propels over a range of sometimes surprising trajectories as the Reynolds number and cylinder translation distance are varied. At low Reynolds numbers and short translation distances, the wake vortices propel past the cylinder, continuing in the direction of the original cylinder motion. At higher Reynolds numbers, the vortices deviate outwards in circular arcs of increasing curvature, even to the extent that the vortex pairs collide behind the cylinder. These trajectory curvatures are analyzed with respect to the circulation of the vortex pairs. At sufficiently long translation distances, a wake instability destroys the reflective symmetry about the wake centerline. This regime is investigated by both comparison with experiment and analysis of the discrepancy between the vorticity and particle fields at large post-arrest times.
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47.32.Ef Rotating and swirling flows
47.32.cd Vortex stability and breakdown
47.80.Jk Flow visualization and imaging
47.11.-j Computational methods in fluid dynamics

Stokes flow in a rectangular cavity by rotlet forcing

D. van der Woude, H. J. H. Clercx, G. J. F. van Heijst, and V. V. Meleshko

Phys. Fluids 19, 083602 (2007); http://dx.doi.org/10.1063/1.2742679 (19 pages) | Cited 1 time

Online Publication Date: 14 August 2007

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The Stokes flow inside a two-dimensional rectangular cavity ∣x∣ ⩽ a, ∣y∣ ⩽ b is analyzed for a highly viscous, incompressible fluid flow, driven by a single rotlet placed at position (0,c). Specifically, a rigorous solution of the governing two-dimensional biharmonic equation for the stream function is constructed analytically by means of the superposition principle. With this solution, multicellular flow patterns can be described for narrow cavities, in which the number of flow cells is directly related to the value of the aspect ratio A = b/a. The solution also shows that for a certain rotlet position (0,c0), which depends on a and b, the flow has a stagnation point (0,−c0) symmetrically placed inside the rectangle. As the flow would not be affected by placing a second (inactive) rotlet in this stagnation point, this allows us to construct a blinking rotlet model for the rectangular cavity, with the inactive rotlet in the stagnation point of the flow induced by the active rotlet. For rectangular cavities, it holds that more than one of these special rotlet positions can be found for cavities that are elongated to sufficiently large aspect ratios. The blinking rotlet model is applied to illustrate several aspects of stirring in a Stokes flow in a rectangular domain.
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47.60.-i Flow phenomena in quasi-one-dimensional systems
47.32.Ef Rotating and swirling flows

Vortex ring head-on collision with a heated vertical plate

G. Arévalo, R. H. Hernández, C. Nicot, and F. Plaza

Phys. Fluids 19, 083603 (2007); http://dx.doi.org/10.1063/1.2759880 (9 pages) | Cited 3 times

Online Publication Date: 21 August 2007

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We report experimental results of the normal impact of a vortex ring in air on a vertical heated plate at constant temperature. We address the case in which the natural convection boundary layer is laminar and the vortex ring is stable. Vortex rings are created by pushing air through a circular exit orifice of a cavity, using a piston-cylinder system. The impinging vortex ring perturbs both the thermal and dynamical boundary layers where we measure the total heat flux exchanged by the heated plate and visualize the vortex motion during the impact. This unsteady impingement process is investigated for different vortex sizes and self-induced velocities, characterized by the Reynolds number of the ring. As a result, a localized heat transfer enhancement is originated by the ring impingement, which increases with the Reynolds number.
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47.15.Cb Laminar boundary layers
44.20.+b Boundary layer heat flow

Modeling RedOx-based magnetohydrodynamics in three-dimensional microfluidic channels

Hussameddine Kabbani, Aihua Wang, Xiaobing Luo, and Shizhi Qian

Phys. Fluids 19, 083604 (2007); http://dx.doi.org/10.1063/1.2759532 (12 pages) | Cited 4 times

Online Publication Date: 30 August 2007

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RedOx-based magnetohydrodynamic (MHD) flows in three-dimensional microfluidic channels are investigated theoretically with a coupled mathematical model consisting of the Nernst-Planck equations for the concentrations of ionic species, the local electroneutrality condition for the electric potential, and the Navier-Stokes equations for the flow field. A potential difference is externally applied across two planar electrodes positioned along the opposing walls of a microchannel that is filled with a dilute RedOx electrolyte solution, and a Faradaic current transmitted through the solution results. The entire device is positioned under a magnetic field which can be provided by either a permanent magnet or an electromagnet. The interaction between the current density and the magnetic field induces Lorentz forces, which can be used to pump and/or stir fluids for microfluidic applications. The induced currents and flow rates in three-dimensional (3D) planar channels obtained from the full 3D model are compared with the experimental data obtained from the literature and those obtained from our previous two-dimensional mathematical model. A closed form approximation for the average velocity (flow rate) in 3D planar microchannels is derived and validated by comparing its predictions with the results obtained from the full 3D model and the experimental data obtained from the literature. The closed form approximation can be used to optimize the dimensions of the channel and to determine the magnitudes and polarities of the prescribed currents in MHD networks so as to achieve the desired flow patterns and flow rates.
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47.60.-i Flow phenomena in quasi-one-dimensional systems
47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.10.ad Navier-Stokes equations
82.30.-b Specific chemical reactions; reaction mechanisms

Active micromixer based on artificial cilia

Vinayak V. Khatavkar, Patrick D. Anderson, Jaap M. J. den Toonder, and Han E. H. Meijer

Phys. Fluids 19, 083605 (2007); http://dx.doi.org/10.1063/1.2762206 (13 pages) | Cited 27 times

Online Publication Date: 30 August 2007

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We propose a design for an active micromixer that is inspired by the motion of ciliated micro-organisms occurring in nature. The conceptual design consists of an array of individually addressable artificial cilia in the form of microactuators covering the channel wall. The microactuators can be set into motion by an external stimulus such as an electric or a magnetic field, inducing either a primary or secondary motion in the surrounding fluid. To validate the concept and to help to design the precise mixer configuration, we developed a computational fluid-structure model. This model is based on a fictitious domain method that couples the microactuator motion to the concomitant fluid flow, fully capturing the mutual fluid-structure interactions. The simulated flow patterns resulting from the motion of single and multiple actuated elements (in a microchannel filled with a Newtonian fluid) under the action of a time-periodic forcing function are analyzed using dynamical systems theory to quantify the mixing efficiency. The results show that with a proper actuation scheme, two microactuators placed on the same wall of a microchannel can indeed induce effective mixing by chaotic advection; their distance should be small, but collisions should be avoided, and they can be actuated in a rather broad regime around 90° out of phase. Placing actuators on opposite walls also induces exponential stretching in the fluid, but if their length is relatively small, of the order of 20% of the channel height, mixing effectiveness is higher when they are arranged on the same wall.
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47.85.Np Fluidics
47.61.Ne Micromixing
47.61.Fg Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.52.+j Chaos in fluid dynamics
47.10.Fg Dynamical systems methods
back to top Instability and Transition

Experimental studies of labyrinthine instabilities of miscible ferrofluids in a Hele-Shaw cell

C.-Y. Wen, Ching-Yao Chen, and D.-C. Kuan

Phys. Fluids 19, 084101 (2007); http://dx.doi.org/10.1063/1.2756083 (8 pages) | Cited 5 times

Online Publication Date: 3 August 2007

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The first systematic experimental studies on the labyrinthine instabilities of miscible ferrofluids in a Hele-Shaw cell are presented. Two distinct features of instabilities are observed: (i) the miscible labyrinthine fingers caused by the magnetic dipolar forces; (ii) the secondary waves dominated by the third-dimensional effects. Prominence of the labyrinthine fingers is confirmed to be affected significantly by both the magnetic field strength and the cell gap width. On the other hand, wave selection of the secondary wave numbers is mainly dominated by the gap width. The characteristic wavelength λ of the secondary waves follows a nearly linear correlation with the gap width h, which is consistent with earlier findings on the viscous fingering instability. The wavelength can be approximated as λ ≈ (7±1)h.
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47.20.-k Flow instabilities
47.35.Tv Magnetohydrodynamic waves
47.65.Cb Magnetic fluids and ferrofluids
75.50.Mm Magnetic liquids

On the transitional wake behind a heated circular cylinder

Ming-Hsun Wu and An-Bang Wang

Phys. Fluids 19, 084102 (2007); http://dx.doi.org/10.1063/1.2756582 (9 pages) | Cited 7 times

Online Publication Date: 8 August 2007

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Wake characteristics of flow over a heated circular cylinder in the three-dimensional transitional wake regimes are studied using smoke wire flow visualizations and hot-wire anemometry techniques. The onset of wake from laminar vortex shedding to transition is found to be delayed by heating of the cylinder and the transitional wakes still developed at higher Reynolds numbers. As the cylinder is heated, vortex shedding frequencies are reduced throughout the Reynolds number range and discontinuities in St-Re relationships are typical in all temperature ratios studied. Critical Reynolds numbers for all transitional wake regimes increase linearly with increasing temperature ratios. Criteria for measuring the onset of transition for flow around a heated cylinder are proposed. Excellent agreement in Strouhal-effective Reynolds number relationships for the heated and unheated cylinders validates the applicability of the effective Reynolds number concept in both laminar and transitional wake regimes (47<Re<400).
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47.27.wb Turbulent wakes
47.80.Jk Flow visualization and imaging
47.27.Cn Transition to turbulence
47.15.Fe Stability of laminar flows
47.32.-y Vortex dynamics; rotating fluids

The onset of Soret-driven convection in a binary mixture heated from above

Min Chan Kim, Chang Kyun Choi, and Jong-Kee Yeo

Phys. Fluids 19, 084103 (2007); http://dx.doi.org/10.1063/1.2756824 (8 pages) | Cited 5 times

Online Publication Date: 8 August 2007

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The onset of buoyancy-driven convection in an initially quiescent, horizontal fluid layer heated from above is analyzed theoretically. The present system of binary mixtures is a thermally stable one but the Soret diffusion can induce buoyancy-driven motion. With highly unstable density gradients the convective motion sets in during the transient diffusion stage. Here the onset time of convective motion is analyzed by employing the propagation theory. The dimensionless critical time τc and the critical wavenumber ac to mark the onset of convective motion is presented as a function of the Rayleigh number Ra, the Lewis number Le, and the separation ratio ψ. The results show that the onset time decreases with increasing buoyancy force Ra(Le/ψ)−1 and the predicted ac-values agree well with available experimental data. For the ethanol-water system the predicted critical reduced Rayleigh number rc( = Rac/1708) = −0.0464 agrees reasonably with existing experimental results of r = −0.1. It is found that the visible motion can be detected from a certain time τ ≅ 43/4τc.
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47.55.P- Buoyancy-driven flows; convection
47.27.te Turbulent convective heat transfer

Effects of noncircular collars on an axisymmetric jet

T. H. New, K. S. Tan, and H. M. Tsai

Phys. Fluids 19, 084104 (2007); http://dx.doi.org/10.1063/1.2754349 (14 pages) | Cited 3 times

Online Publication Date: 9 August 2007

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An experimental investigation was carried out to study the effects of noncircular collars on an axisymmetric jet using surface flow visualization and hot-wire anemometry. Circular, square, and triangular collars with expansion ratios of 1.20, 1.35, and 1.54, respectively, with collar lengths of up to two jet diameters were used. Flow visualization shows that circular collars led to equidistant flow reattachments along the collar wall, while square and triangular collars resulted in the formation of a pair of counter-rotating vortex-pairs on each side of the collar wall. These vortex-pairs are caused by the presence of the three-dimensional velocity gradients between locations of minimum and maximum step-heights, which drove fluid from the collar wall centerlines towards the corners. Time-averaged velocity measurements show that the circular collar required the shortest collar length to achieve maximum centerline velocity decay, followed by square and triangular collars. Centerline turbulence intensity and velocity spectra results reveal that all three collars were able to suppress vortex-pairing events when they were sufficiently long with the triangular collar being the most effective. Furthermore, the triangular collar also produces the widest overall jet-spread, ahead of square and circular collars, respectively, even though it demonstrates significantly different jet-spreads along planes of minimum and maximum step-height. Self-excitation frequencies from all three collars could be distinguished into distinct frequency bands with changes in the collar lengths. Within each band, the circular collar results in the largest variation of excitation frequency over the square and triangular collars, respectively. Lastly, square and triangular collars require wider ranges of collar lengths for each of the frequency bands, as compared to the circular collar.
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47.15.Uv Laminar jets
47.80.Jk Flow visualization and imaging
47.32.-y Vortex dynamics; rotating fluids

Three-dimensional evolution of vortical structures and associated flow bifurcations in the wake of two side-by-side square cylinders

Amalendu Sau, Tai-Wen Hsu, and Shan-Hwei Ou

Phys. Fluids 19, 084105 (2007); http://dx.doi.org/10.1063/1.2757712 (17 pages) | Cited 1 time

Online Publication Date: 13 August 2007

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In this paper, we focus on the three-dimensional growth of the vortical structures behind two square cylinders when placed in a side-by-side arrangement and examine different possible modes of flow bifurcation along their spanwise extended corelines. For this, unsteady three-dimensional flow simulations are conducted with five different values of gap/diameter ratios (g*), namely, 2.1, 1.7, 0.7, 0.5, and 0.2, that cover important known phases, i.e., coshedding (g* = 2.1 and 1.7), asymmetric (g* = 0.7 and 0.5), and single-body type (g* = 0.2) of wake evolution. In order to exploit flow physics within the transition range, the Reynolds number of the flow is taken as 100. Notably, for all the investigated cases, parallel vortex shedding has been observed behind the two cylinders. However, with the decrease of gap ratio g*, the downstream flow gradually lost stability and the corelines of the shedded vortices appeared in a wavy fashion. While for g* = 2.1 and 1.7, the simulated streamwise flows exhibit antiphase and in-phase synchronization of the wake, respectively, there is also observed a notable difference in the structural growth of corresponding spanwise flows. For the antiphase flow (at g* = 2.1) the downstream wake evolved through a symmetry-breaking mode-I Hopf bifurcation along various spanwise extended vortex corelines. However, the presence of an additional mode-II Hopf bifurcation was detected in the wake of an in-phase flow (at g* = 1.7). The development of a number of local pressure maxima over different spanwise extended vortex corelines, and the gradual decrease of pressure along their left and right, respectively, are noted to be responsible for initiating such flow bifurcations. In the biased (asymmetric) regime, with g* = 0.7 and 0.5, the flow behind the cylinders showed visible signs of growing instability and there occurred significant spanwise pressure fluctuations, which in turn inflicted large three dimensionality into the downstream wake and local velocity irregularities. The corresponding wake evolution patterns are thereby noted to exhibit predominantly unsteady and transitional features. In this biased flow regime, the gap flow flip-flopped randomly and became deflected alternately towards the top and bottom cylinders. On the one hand, clear dominance of both mode-I and mode-II flow bifurcations was observed with both of these initially locked biased flows. However, due to increased flow asymmetry the spanwise length scales of such bifurcations changed significantly. On the other hand, for the single-body regime flow with g* = 0.2, the occurrence of only mode-I bifurcation was detected in the wake of the cylinders.
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47.32.C- Vortex dynamics
47.11.-j Computational methods in fluid dynamics
47.52.+j Chaos in fluid dynamics
47.27.wb Turbulent wakes
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