Volume 19, Issue 8, August 2007

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 simulatedparticle tracking computations is proposed, which is based on a variablevariance twodimensional Gaussianweighted 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 counterrotating vortex pair, which subsequently selfpropels 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 postarrest times.
 LETTERS


Effects of hydrophobic surfaces on the drag and lift of a circular cylinder
View Description Hide DescriptionEffects of hydrophobicsurfaces 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 noslip, a cylinder of which the entire surface is hydrophobic, and cylinders with alternating circumferential bands of slip and noslip conditions are considered. The width of the alternating bands ranges from to , where is a spanwise characteristic wavelength in the near wake. At Reynolds number 300, the hydrophobicsurface consisting of alternating slip and noslip bands of width is found to be most effective in enhancing wake instability, thereby decreasing the base suction, drag, and rms lift coefficients. At Reynolds number 3900, hydrophobicsurface treatments are found to delay flow separation, thereby decreasing the drag and rms lift.

Multiple modes of instability in a box heated from the side in lowPrandtlnumber fluids
View Description Hide DescriptionThe existence of multiple modes of instability in RayleighBénard or MarangoniBénard situations has been known for many years. This existence is shown for the first time for lowPrandtlnumber flows in threedimensional 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.

 ARTICLES

 Interfacial Flows

Suppression of the RayleighTaylor instability of thin liquid films by the Marangoni effect
View Description Hide DescriptionStabilization of the RayleighTaylor instability of a thin liquid film by the Marangoni effect arising from heating of the liquid at the gasliquid interface in a bilayer setting is investigated. Solution of timedependent NavierStokes and longwave 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.

Threedimensional capillarygravity waves generated by a moving disturbance
View Description Hide DescriptionSteady threedimensional capillarygravity 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.

Experimental investigation of steady buoyantthermocapillary convection near an evaporating meniscus
View Description Hide DescriptionMicroparticle image velocimetry measurements of the threedimensional (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 solidliquidvapor junction that creates a temperature gradient along the meniscus. This results in a surface tension gradient which, coupled with buoyancy effects, causes buoyantthermocapillary convection in the liquid film. The relative influence of buoyancy and thermocapillarity on the flow was investigated for tube diameters ranging from 75 to . A transition from a pure twodimensional thermocapillary flow to a 3D buoyantthermocapillary flow is observed with an increase in tube diameter. For the 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 smallerdiameter tubes drive stronger vortices. Particle streaks and microparticle image velocimetry images obtained in multiple horizontal and vertical planes provide an understanding of this threedimensional flow behavior. A scaling analysis shows the importance of thermocapillary convection in evaporating menisci.

Unsteady draining flows from a rectangular tank
View Description Hide DescriptionTwodimensional, unsteady flow of a twolayer 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.

Correction of Lamb’s dissipation calculation for the effects of viscosity on capillarygravity waves
View Description Hide DescriptionPurely irrotational theories of the flow of a viscous liquid are applied to model the effect of viscosity on the decay and oscillation of capillarygravity 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.

Nonlinear buoyantthermocapillary flows in a threelayer system with a temperature gradient along the interfaces
View Description Hide DescriptionThe nonlinear buoyantthermocapillary 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 heatinsulated lateral walls, are considered. The nonlinear simulations of the wavy convective regimes are performed by the finitedifference method.

Effects of gravity, inertia, and surfactant on steady plug propagation in a twodimensional channel
View Description Hide DescriptionLiquid 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 twodimensional liquidlined channel oriented at an angle with respect to gravity. We investigate the effects of gravity through the Bond number, Bo, and ; the plug propagation speed through the capillary number, Ca, or the Reynolds number, Re; the plug length , and the surfactant concentration . Without gravity, i.e., , 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 and , , 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 , however when the surfactant is present , 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 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 , Ca, Re, and , while it decreases with Bo. The total mass left behind in the trailing films increases with Bo for any at , Ca and for any value of .
 Viscous and NonNewtonian Flows

Polymer induced drag reduction in exact coherent structures of plane Poiseuille flow
View Description Hide DescriptionNonlinear traveling waves that are precursors to laminarturbulent transition and capture the main structures of the turbulentbuffer 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 FENEP constitutive model for polymer solutions. In experiments with a given fluid, Reynolds and Weissenberg numbers are linearly related (i.e., ). 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 (and ) 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 wallnormal 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 nearwall 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 (and ) 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, wallnormal 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 wallnormal extent of the ECS all increase monotonically with the increase of viscoelasticity, as is found in experiments.

A novel low inertia shear flow instability triggered by a chemical reaction
View Description Hide DescriptionWe present an experimental investigation of a novel low Reynolds number shear flow instability triggered by a chemical reaction. An acidbase reaction taking place at the interface between a Newtonian fluid and carbopol940 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.

Velocity measurements in confined swirling flow of polymer solutions with vortex shedding
View Description Hide DescriptionA particle imagevelocimetry system is used to examine the velocity field in the unsteady swirling flow of polyacrylamide (PAA) solutions (PAA and ) with the vortex shedding due to a rotating disk in a cylindrical casing. In our earlier work [Tamano et al., Phys. Fluids19, 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 largescale secondary flow. When the ring vortex was shed, the surrounding largescale 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.

Propulsion in a viscoelastic fluid
View Description Hide DescriptionFlagella 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 mucusfilled 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 polymericfluid with a single relaxation time. We show that, compared to selfpropulsion in a Newtonian fluid occurring at a velocity , the sheet swims (or transports fluid) with velocity , where is the viscosity of the Newtonian solvent, is the zeroshearrate viscosity of the polymericfluid, and is the Deborah number for the wave motion, product of the wave frequency by the fluidrelaxation 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 nonNewtonian 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.

Measurement of temperature profiles in turbulent pipe flow of polymer and surfactant dragreducing solutions
View Description Hide DescriptionA device was built to measuretemperature profiles of turbulent pipe flows of various dragreducing fluids. It is easy to use and reliable. We measuredtemperature profiles over a range of conditions leading to accurate measurements down to , for tests carried over Reynolds numbers () 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 typeA polymer solution and for cationic surfactantsolutions allowed us to see strong similarity between velocity and temperature profiles for dragreducingsurfactantsolutions. A comparison between the slopes of the thermal and velocity buffer layers resulted in calculated turbulent Prandtl numbers between 6 and 9 for those dragreducingsolutions. We also used this tool to investigate drag reduction for a nonionic surfactantsolution, which showed a significantly different fantype profile, and also for a typeB dragreducingpolymer solution (Xanthan gum).
 Particulate, Multiphase, and Granular Flows

Preferential accumulation of bubbles in CouetteTaylor flow patterns
View Description Hide DescriptionWe 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 timedependent evolution of the twophase flow is predicted through threedimensional EulerLagrange simulations. Lagrangian tracking of spherical bubbles is coupled with direct numerical simulation of the NavierStokes equations. We assume that bubbles do not influence the background flow (oneway coupling simulations). The force balance on each bubble takes into account buoyancy, addedmass, viscous drag, and shearinduced 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. Fluids16, 128 (Year: 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. Fluids26, 233 (Year: 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 lowpressure regions of the flow field.
 Laminar Flows

Flow around an impulsively arrested circular cylinder
View Description Hide DescriptionThe 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 simulatedparticle tracking computations is proposed, which is based on a variablevariance twodimensional Gaussianweighted 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 counterrotating vortex pair, which subsequently selfpropels 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 postarrest times.

Stokes flow in a rectangular cavity by rotlet forcing
View Description Hide DescriptionThe Stokes flow inside a twodimensional rectangular cavity , is analyzed for a highly viscous, incompressible fluid flow, driven by a single rotlet placed at position . Specifically, a rigorous solution of the governing twodimensional 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 . The solution also shows that for a certain rotlet position , which depends on and , the flow has a stagnation point 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.

Vortex ring headon collision with a heated vertical plate
View Description Hide DescriptionWe 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 convectionboundary 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 pistoncylinder 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 selfinduced 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.

Modeling RedOxbased magnetohydrodynamics in threedimensional microfluidic channels
View Description Hide DescriptionRedOxbased magnetohydrodynamic (MHD)flows in threedimensional microfluidic channels are investigated theoretically with a coupled mathematical model consisting of the NernstPlanck equations for the concentrations of ionic species, the local electroneutrality condition for the electric potential, and the NavierStokes 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 RedOxelectrolytesolution, 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 threedimensional (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 twodimensional 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.

Active micromixer based on artificial cilia
View Description Hide DescriptionWe propose a design for an active micromixer that is inspired by the motion of ciliated microorganisms 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 fluidstructure model. This model is based on a fictitious domain method that couples the microactuator motion to the concomitant fluid flow, fully capturing the mutual fluidstructure 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 timeperiodic 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 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.