Volume 22, Issue 2, February 2010

Decaying, quasitwodimensional turbulent flows in a rotating rectangular domain with a steplike topography are investigated by means of laboratory experiments and numerical simulations. The aim is to describe the role of a discontinuous topography on the evolution and organization of the vortices. Initially, vortex interactions lead to the selforganization of the flow, as in twodimensional turbulence. Afterwards, the interaction of vortices with the step leads to a flow along the topography that always maintains the shallow region on the right. The simulations have revealed the existence of a critical value determined by the strength of the flow and the step height, after which structures are not able to cross the topography. As a result, the flow evolves almost independently at the shallow and deep regions affecting the efficiency of the organization and therefore the final distribution of vorticity. The existence of a preferential distribution of vorticity due to the step for long times (several rotation periods) is discussed. Different distributions are found when using slightly different flow parameters, and therefore the existence of such a preferential final state is analyzed by using statistical methods.
 AWARD AND INVITED PAPERS


The art of mixing with an admixture of art: Fluids, solids, and visual imagination^{a)}
View Description Hide DescriptionAlthough creativity is often equated with art, it is just as present in science and technology. The Otto Laporte Lecture provides a forum to cover some of this ground—an opportunity to offer observations about scientific imagination, the role of collaborators and environment, creative processes in general, and even how science evolves. Very little has been written about these topics in the context of fluid dynamics, but I believe that such a viewpoint—understanding why and how scientific discoveries are made—provides significant insights which go far beyond my specific work.

Investigating slippage, droplet breakup, and synthesizing microcapsules in microfluidic systems^{a)}
View Description Hide DescriptionThe present paper reflects the presentation made in the 2008 APSDFD meeting; it is dedicated in discussing liquid slippage at solid walls, droplet breakup in microfluidic systems, and capsule generation in microfluidic devices. The analysis of the physical processes implied in these situations led to improve our knowledge on the importance of slippage phenomena in electroosmotic flows, the effect of the confinement in droplet breakup processes, and the effect of recirculating flows on the morphology of multiple droplets.

Designing largeeddy simulation of the turbulent boundary layer to capture lawofthewall scaling^{a)}
View Description Hide DescriptionLawofthewall (LOTW) scaling implies that at sufficiently high Reynolds numbers the mean velocity gradient in the turbulent boundary layer should scale on in the inertiadominated surface layer, where is the friction velocity and is the distance from the surface. In 1992, Mason and Thomson pointed out that largeeddy simulation(LES) of the atmospheric boundary layer (ABL) creates a systematic peak in in the surface layer. This “overshoot” is particularly evident when the first grid level is within the inertial surface layer and in hybrid LES/Reynoldsaveraged Navier–Stokes methods such as “detachededdy simulation,” where the overshoot is identified as a “logarithmic layer mismatch.” Negative consequences of the overshoot—spurious streamwise coherence, largeeddy structure, and vertical transport—are enhanced by buoyancy. Several studies have shown that adjustments to the modeling of the subfilter scale (SFS) stress tensor can alter the degree of the overshoot. A comparison among simulations indicates a lack of grid independence in the prediction of mean velocity that originates in surface layer deviations from LOTW. Here we analyze the broader framework of LES prediction of LOTW scaling—including, but extending beyond, “the overshoot.” Our theory includes a criterion that is necessary to remove the overshoot but is insufficient for LES to produce constant through the surface layer, and fully satisfy the LOTW. For mean shear to scale on in the surface layer, we show that two additional criteria must be satisfied. These criteria can be framed in terms of three nondimensional variables that define a parameter space in which systematic adjustments can be made to the simulation to achieve LOTW scaling. This occurs when the three parameters exceed critical values that we estimate from basic scaling arguments. The essential difficulty can be traced to a spurious numerical LESviscous length scale that interferes with the dimensional analysis underlying LOTW. When this spurious scale is suppressed sufficiently to retrieve LOTW scaling, the LES has been moved into the supercritical “high accuracy zone” (HAZ) of our parameter space. Using eddy viscosity closures for SFS stress, we show that to move the simulation into the HAZ, the model constant must be adjusted together with grid aspect ratio in coordinated fashion while guaranteeing that the surface layer is sufficiently well resolved in the vertical by the grid. We argue that, in principle, both the critical values that define the HAZ and the surface layer constant when LOTW scaling is achieved can depend on details of the SFS (and surface stress) models applied in the LES. We carried out over 110 simulations of the neutral roughsurface ABL to cover a wide portion of the parameter space using a low dissipation spectral code, the Smagorinsky SFS stress model and a standard model for fluctuatingsurface stress. The overshoot was found to systematically reduce and was found to systematically approach a constant value in the surface layer as the three parameters exceeded critical values and the LES moved into the HAZ, consistent with the theory. However, whereas constant was achieved over nearly the entire surface layer as the LES is moved into the HAZ, the model for surface shear stress continues to disrupt LOTW scaling at the first couple grid levels, and the predicted von Kármán constant is lower than traditional values. In a comprehensive discussion, we summarize the primary results of subsequent studies where we minimize the spurious influence of the surface stress model and show that the surface stress model and the SFS stress model constant influence the predicted value of the von Kármán constant for LES in the HAZ.
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 LETTERS


Control of vortical structures on a flapping wing via a sinusoidal leadingedge
View Description Hide DescriptionThe flow structure generated by a flapping wing in the form of a plate is fundamentally altered if the leadingedge has a sinusoidal shape. It is possible to attenuate both the positive and negative spanwise flows along the plate surface, as well as the onset and development of largescale concentrations of positive and negative streamwise vorticities at inboard locations. These alterations of the inboard flow structure have an insignificant influence on the structure of the tip vortex.

Multiple localized states in centrifugally stable rotating flow
View Description Hide DescriptionWe report experimental and numerical results from investigations into the onset of novel localized cellular states in the centrifugally stable regime of Taylor–Couette flow at sufficiently high rates of counterrotation of the outer cylinder. Quantitative comparison is made between experimental results and those obtained from numerical bifurcation studies of the steady axisymmetric Navier–Stokes equations. The onset of the vortices is smooth but they appear over a narrow range of Reynolds number. This enables the use of a suitable measure to produce excellent quantitative agreement between calculation and experiment. The numerical methods are also used to uncover evidence for a homoclinic snake which indicates rich multiplicity in the steady solution set.
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 ARTICLES

 Micro and Nanofluid Mechanics

Ensembleaveraged particle orientation and shear viscosity of singlewallcarbonnanotube suspensions under shear and electric fields
View Description Hide DescriptionThe ensembleaveraged particleorientation angles and apparent shear viscosities of dilute suspensions of singlewall carbon nanotubes(SWNTs) in a liquid solvent, terpineol, were experimentally studied under combined shear flow and electric fields. An optical polarizationmodulation method was used to measure the orientation angles of individual and small bundles of SWNTs, while a modified concentriccylinder viscometer was used to make simultaneous electrorheological measurements of the apparent viscosity. The particleorientation response occurs on time scales one to two orders of magnitude faster than the macroscopic electrorheological response, and does not appear to directly affect the apparent viscosity at these low concentrations. Particleorientation angles for various shear rates and electric fields are found to collapse when plotted against the parameter, , as predicted by the theory developed by Mason and coworkers for the equilibrium orientation angle of ellipsoids under electric fields and shear flow. However, comparison between measured and predicted particleorientation angles shows poor agreement at intermediate values of . Electrostatic interactions between largeaspectratio particles are shown to be significant, and may account for the discrepancy between the measurements and classical theory for even dilute suspensions of nanotubes under both shear and electric fields.

Thermal capillary waves relaxing on atomically thin liquid films
View Description Hide DescriptionAtomistic simulations are used to investigate the relaxation dynamics of thermal capillary waves on thin flat liquid films. Short LennardJones polymers (, 4, and 8) model the liquid in films of thickness to , where is the LennardJones atomic lengthscale parameter. Assuming noslip boundary conditions on the solid wall and constant surface tension and viscosity, the standard continuum model predicts that capillary waves decay with rates that scale with wavenumber as for long wavelengths and for short wavelengths. The atomistic simulations do indeed show these scalings for ranges of , and, of course, this model must fail for large as wavelengths approach atomic scales. However, before a complete breakdown of the continuum description, an unexpected intermediate regime is found. Here the decay rates follow an apparent power law. The behavior in this range collapses for all the cases simulated when is scaled with the radius of gyration of the polymers, indicating that a molecularscale effect underlies the relaxation mechanics of these short waves.
 Interfacial Flows

Instability of a moving liquid sheet in the presence of acoustic forcing
View Description Hide DescriptionThe excitation of thin planar liquid sheets formed by impinging two collinear water jets to acoustic waves was studied at varying frequencies and sound pressure levels (SPLs). Experiments were conducted over a range of liquid velocities that encompassed the stable and flapping regimes of the sheet. For a given frequency, there was a threshold value of SPL below which the sheet was unaffected. The threshold SPL increased with frequency. Further, the sheet was observed to respond to a set of specific frequencies lying in the range of 100–300 Hz, the frequency set varying with the Weber number of the liquid sheet. The magnitude of the response for a fixed pressure level, characterized by the reduction in the extent of the sheet, was larger at lower frequencies. The droplet sizes formed by the disintegration of the sheet reduced with an increase in the measured response and the dropshedding frequency was near the imposed frequency. Model equations for inviscid flow and accounting for the varying pressure field across the moving liquid sheet of constant thickness was solved to determine the linear stability of the system. Numerical solution shows that the most unstable wavelengths in the presence of the forcing to be smaller than in the absence, which is in line with observations. Both the dilatational and sinuous modes are coupled at the lowest order and become significant for the range of acoustic forcing studied. The model calculation suggests that the parametric resonance involving the dilatational mode may be responsible for the observed instability although the model was unable to predict the observed variation of threshold SPL with frequency.

A mechanism of Marangoni instability in evaporating thin liquid films due to soluble surfactant
View Description Hide DescriptionIn film coating and other applications involving thin liquid films,surfactants are typically employed to suppress the usually undesirable instabilities driven by surface phenomena. Yet, in the present study a mechanism of Marangoni instability in evaporating thin films is presented and analyzed, which has its origin on the effects of a solublesurfactant. As the film thins due to evaporation, thickness perturbations lead to surfactant concentration perturbations, which in turn drive film motion and tend to enhance uneven drying. A thinfilm analysis is applied and evolution equations for the film thickness and the surfactant concentration are derived and analyzed by the techniques of linear stability and numerical simulation. In the linear analysis a nonautonomous system is obtained for the film thickness and surfactant concentration perturbations, which shows that the instability will manifest itself provided that an appropriate Marangoni number is relatively large and the surfactantsolubility in the bulk is large as well. On the other hand, low solubility in the bulk, diffusion, and the effect of surfactant on interfacial mobility through the surfaceviscosity are found to suppress disturbance growth. Direct numerical simulations of the full nonlinear evolution equations confirm those results and add to the picture obtained for the physical system behavior. Estimates of the relevant dimensionless parameters suggest that the conditions for instability may be met in relatively thick films, on the order of tens of microns, for which the effects of molecular forces and disjoining pressure are not dominant. Moreover, the stabilizing effects of diffusion and interfacial mobility are not likely to become significant unless the films are much thinner, i.e., on the order of or below.

Effect of normal and parallel magnetic fields on the stability of interfacial flows of magnetic fluids in channels
View Description Hide DescriptionThe effect of an imposed magnetic field on the linear stability of immiscible twofluid Poiseuille flow in a channel is examined for low Reynolds numbers. Surface tension acts on the interface, the fluids have different densities and viscosities, and one fluid is magnetic (ferrofluid). A Langevin function is used to model the fluid magnetization, resulting in a nonlinear permeability; the stability properties depend on this permeability relation both directly and indirectly, through the base state solution. Uniform magnetic fields applied normal or parallel to the interface both lead to an interfacial instability. Normal fields excite longer wavelength modes, generally having higher growth rates, but parallel fields can excite faster growing modes in high permeability fluids at large applied field strength. Whether or not the field stabilizes or destabilizes the flow depends on the viscosity and layer thickness ratios in a simple way, while the placement of the magnetic fluid layer does not play a major role. Growth rates predicted for realistic microchannel conditions are shown to be large enough to make ferrofluid manipulation a practical method of control.

Thickness of the rim of an expanding lamella near the splash threshold
View Description Hide DescriptionThe evolution of the ejected liquid sheet, or lamella, created after impact of a liquiddrop onto a solid surface is studied using highspeed video in order to observe the detailed time evolution of the thickness of the rim of the lamella. Since it has been suggested that splashing behavior is set at very early times after impact, we study early times up to , where and are the diameter and speed of the impacting drop, respectively, for different liquidviscosities and impact speeds below the splashing threshold. Within the regime of our experiments, our results are not consistent with the idea that the lamella rim grows similar to the boundary layer thickness. Rather, we find that the rim thickness is always much larger than the boundary layer thickness, and that the rim thickness decreases with increasing impact speed. For lower impact speeds, the increase in the rim thickness is consistent with a response over the limited time range available, but the dependence is not simply proportional to , where is the kinematicviscosity, and there is a strong dependence of the rim thickness on the impact speed . Scaling of the rim height using a balance of inertial and surface tension forces provides some collapse of the data at lower impact speeds. We also observe an unusual plateau behavior in thickness versus time at higher impact speeds as we approach the splash threshold.
 Viscous and NonNewtonian Flows

Transient growth without inertia
View Description Hide DescriptionWe study transient growth in inertialess plane Couette and Poiseuille flows of viscoelastic fluids. For streamwiseconstant threedimensional fluctuations, we demonstrate analytically the existence of initial conditions that lead to quadratic scaling of both the kinetic energy density and the elastic energy with the Weissenberg number, We. This shows that in strongly elastic channel flows of viscoelastic fluids, both velocity and polymer stress fluctuations can exhibit significant transient growth even in the absence of inertia. Our analysis identifies the spatial structure of the initial conditions (i.e., components of the polymer stress tensor at ) responsible for this large transient growth. Furthermore, we show that the fluctuations in streamwise velocity and the streamwise component of the polymer stress tensor achieve and growth, respectively, over a time scale before eventual asymptotic decay. We also demonstrate that the large transient responses originate from the stretching of polymer stress fluctuations by a background shear and draw parallels between streamwiseconstant inertial flows of Newtonian fluids and streamwiseconstant creeping flows of viscoelastic fluids. One of the main messages of this paper is that at the level of velocity fluctuation dynamics,polymer stretching and the Weissenberg number in elasticitydominated flows of viscoelastic fluids effectively assume the role of vortex tilting and the Reynolds number in inertiadominated flows of Newtonian fluids.
 Particulate, Multiphase, and Granular Flows

Selfexcited oscillations in buoyant confined bubbly mixing layers
View Description Hide DescriptionIn this experimental investigation we analyze the nature of the primary instability of a bubbly mixing layer. We consider upward flows that develop in a vertical channel of finite dimensions, with bubbles injected on one side of the mixing layer at the inlet. The induced buoyancy effect generates longitudinal accelerations, which are at the origin of selfexcited largescale oscillations under certain conditions. We provide experimental evidence that these oscillations are global modes, and we develop a simple model able to predict the conditions of appearance of these global modes. The model includes as essential mechanisms the buoyancy and a transverse mass transfer due to liquid miscibility in the mixing layer.
 Laminar Flows

Dynamics and shape instability of thin viscous sheets
View Description Hide DescriptionAn asymptotic theory for predicting the thickness distribution and geometry of the boundaries of a thin nearly planar fluid sheet and analyzing the stability of its shape is developed starting from the balance law for mass and momentum for a continuous medium. The resulting equations comprise a transient twodimensional model where the sheet thickness and out of plane displacement are additional distributed parameters along with the continuum velocities. The analysis of the sheet motion in the transverse direction showed that the existence of compressive stresses inevitably leads to viscoussheet shape instability, while the equations describing the out of plane sheet displacement become of mixed type. As examples, two practical problems involving nonisoviscous sheets have been considered: a twodimensional viscoussheet, which shape is unstable in the case when the compressive stress is applied at the exit end, and a threedimensional problem of viscoussheet redraw (constant stretching), where the existence of the compressive stresses leads to the development of hyperbolic zones in the sheet, resulting in the sheet shape instability.

Steady flow through a curved tube with wavy walls
View Description Hide DescriptionThe problem of fully developed steady flow of an incompressible Newtonian fluid through a mildly curved tube with wavy walls of small amplitudetowavelength ratio around the tube circumference is solved via a perturbationsolution. Dean’s original solution for tubes with circular crosssection is used as the foundation to solve the current regular perturbation problem. In general, the wavy walls are found to mitigate the effect of a given term in Dean’s expansion. For instance, the first order effect of the wavy walls is to reduce the strength of the secondary flowvortices and minimize the reduction of the volumetric flow rate caused by the curvature. A related effect is a general reduction in the average axial and circumferential wall shear stresses. The local wall shear stress, however, increases at the points of maximum incursion of the protrusions into the flow and decreases in the valleys between the protuberances. The general form of the solution for an arbitrary number of protuberances is presented to first order in the geometric perturbation and to fourth order in the Dean number.
 Instability and Transition

Miscible viscous fingering involving viscosity changes of the displacing fluid by chemical reactions
View Description Hide DescriptionIn our previous study, we experimentally studied the effects of changes in the viscosity of the displaced moreviscous liquid by instantaneous reactions on miscibleviscous fingering pattern [Y. Nagatsu, K. Matsuda, Y. Kato, and Y. Tada, “Experimental study on miscibleviscous fingering involving viscosity changes induced by variations in chemical species concentrations due to chemical reactions,” J. Fluid Mech.571, 475 (2007)]. In the present study, experiments have been performed on the miscibleviscous fingering involving changes in the viscosity of the displacing lessviscous liquid by instantaneous reactions in a radial HeleShaw cell. We have found that the shielding effect is suppressed and the fingers are widened when the viscosity is increased. As a result, the reaction makes the fingering pattern denser. In contrast, the shielding effect is enhanced, and the fingers are narrowed when the viscosity is decreased. As a result, the reaction makes the fingering pattern less dense. These results are essentially same as those obtained by the abovementioned previous study. This shows that the effects of changes in the viscosity due to the instantaneous reactions are independent of whether the changes occur in the displaced liquid or in the displacing liquid. A mechanism for the independence is discussed.

Effect of rotation on the electrohydrodynamic instability of a fluid layer with an electrical conductivity gradient
View Description Hide DescriptionThe electrohydrodynamicinstability of a horizontal rotating fluid layer with a vertical electrical conductivity gradient is considered. An external electric field is applied across the fluid layer to induce an unstably stratified electrical body force. A linear stability analysis has been performed to study the effect of rotation on the onset of electrohydrodynamicinstability in the fluid layer. Results show that the instability behaviors depend heavily on the boundary condition of bottom surface. In the case of stressfree condition, rotation enhances the stability and the onset of instability will be dominated by the oscillatory mode once the speed of rotation (or Taylor number) exceeds a critical value. In contrast, in the case of rigid bottom surface, rotation also tends to stabilize the fluid layer and the stationary mode will prevail eventually with increasing Taylor number. However rotation becomes destabilizing as the critical mode shifts from oscillatory to stationary. Moreover, under the same electrical conductivity gradient, the case with stressfree bottom surface is always more unstable than that with rigid bottom surface in the small Taylor number domain. However this situation is reversed at high Taylor number region since the stability of the stressfree case will be enhanced more rapidly than the rigid case.

Viscous linear stability of axisymmetric lowdensity jets: Parameters influencing absolute instability
View Description Hide DescriptionViscous linear stability calculations are presented for model lowdensity axisymmetric jet flows. Absolute growth transitions for the jet column mode are mapped out in a parametric space including velocity ratio, density ratio, Reynolds number, momentum thickness, and subtle differences between velocity and density profiles. Strictly speaking, the profiles used in most jet stability studies to date are only applicable to unity Prandtl numbers and zero pressure gradient flows—the present work relaxes this requirement. Results reveal how subtle differences between the velocity and density profiles generally used in jet stability theory can dramatically alter the absolute growth rate of the jet column mode in these lowdensity flows. The results suggest heating/cooling or mass diffusion at the outer nozzle surface can suppress absolute instability and potentially global instability in lowdensity jets.

Dynamics of an open elastic rod with intrinsic curvature and twist in a viscous fluid
View Description Hide DescriptionA twisted elastic rod with intrinsic curvature is considered. We investigate the dynamics of the rod in a viscous incompressible fluid. This fluid is governed by the Navier–Stokes equations and the fluidrod interaction problem is solved by the generalized immersed boundary method combined with the Kirchhoff rod theory. We classify the equilibrium configurations of an open elastic rod as they depend on the rod’s intrinsic characteristics and fluid properties. We assume that the intrinsic curvature and twist are distributed uniformly along the rod. In the case of zero intrinsic curvature (i.e., the stressfree state of the rod is straight), we find a critical value of twist, below which the straight state of the rod is stable. When the twist is above this critical value, however, the rod buckles locally and produces a loop or a plectoneme or a combination of both. When the constant intrinsic curvature is nonzero, we also find a critical value of twist that distinguishes a buckled rod from a stable helix. We also find that fluid viscosity plays an important role in determining equilibrium configuration in this paper.
 Turbulent Flows

Experiments and simulations on selforganization of confined quasitwodimensional turbulent flows with discontinuous topography
View Description Hide DescriptionDecaying, quasitwodimensional turbulent flows in a rotating rectangular domain with a steplike topography are investigated by means of laboratory experiments and numerical simulations. The aim is to describe the role of a discontinuous topography on the evolution and organization of the vortices. Initially, vortex interactions lead to the selforganization of the flow, as in twodimensional turbulence. Afterwards, the interaction of vortices with the step leads to a flow along the topography that always maintains the shallow region on the right. The simulations have revealed the existence of a critical value determined by the strength of the flow and the step height, after which structures are not able to cross the topography. As a result, the flow evolves almost independently at the shallow and deep regions affecting the efficiency of the organization and therefore the final distribution of vorticity. The existence of a preferential distribution of vorticity due to the step for long times (several rotation periods) is discussed. Different distributions are found when using slightly different flow parameters, and therefore the existence of such a preferential final state is analyzed by using statistical methods.