Volume 23, Issue 2, February 2011

We present results from an experimental study of the longwavelength “Crow” instability of a counterrotating vortex pair. Employing a vortex generator in a water tank, comprising rotating horizontal computercontrolled flaps, we follow the vortices, marked by laserinduced fluorescence, using dual simultaneous lightsheets to determine the growth rate of the Crow instability as a function of the perturbation wavelength. In order to make a meaningful comparison to theory [S. C. Crow, AIAA J.8, 2172 (1970); S. E. Widnall, Annu. Rev. Fluid Mech.4, 141 (1975)], one requires, as input to the theory, the distribution of circumferential velocity and thereby the “equivalent” core size of the vortices. These distributions are measured using particle image velocimetry. The resulting agreement of the growth rates, between theory and experiment, appears to be very good. Of relevance to this study, we compute a stability diagram using the exact expression for the selfinduced rotation speed of perturbation waves on the vortices.Measurement of the nondimensional reconnection time, when the vortex pair evolves into a series of rings at later times, is compared to existing numerical simulations, and we find evidence to suggest it varies with the inverse curvature of the vortices where they approach each other. The major axes of the resulting elliptical vortex rings switch with their minor axes, as the rings descend in the fluid, leading to a surprising phenomenon where the rings reconnect for the second time. By considering the conservation of impulse, and a linear relationship between the major axis length and the vortex spacing, we find that the relative descent speed of the rings increases with Reynolds number. It is coincidentally only at our chosen value that the descent speed of the subsequent rings appears to be close to the initial speed of the vortex pairs. Finally, the paper presents clear visualizations of the Crow instability phenomenon.
 AWARD AND INVITED PAPERS


Respiratory fluid mechanics
View Description Hide DescriptionThis article covers several aspects of respiratory fluid mechanics that have been actively investigated by our group over the years. For the most part, the topics involve twophase flows in the respiratory system with applications to normal and diseased lungs, as well as therapeutic interventions. Specifically, the topics include liquid plug flow in airways and at airway bifurcations as it relates to surfactant, drug, gene, or stem cell delivery into the lung;liquid plug rupture and its damaging effects on underlying airway epithelial cells as well as a source of crackling sounds in the lung; airway closure from “capillaryelastic instabilities,” as well as nonlinear stabilization from oscillatory core flow which we call the “oscillating butter knife;” liquid film, and surfactantdynamics in an oscillating alveolus and the steady streaming, and surfactant spreading on thin viscous films including our discovery of the Grotberg–Borgas–Gaver shock.
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 LETTERS


Mechanics of viscous vortex reconnection
View Description Hide DescriptionThis work is motivated by our longstanding claim that reconnection of coherent structures is the dominant mechanism of jet noise generation and plays a key role in both energy cascade and finescale mixing in fluid turbulence [F. Hussain, Phys. Fluids26, 2816 (1983); J. Fluid Mech.173, 303 (1986)]. To shed further light on the mechanism involved and quantify its features, the reconnection of two antiparallel vortex tubes is studied by direct numerical simulation of the incompressible Navier–Stokes equations over a wide range (250–9000) of the vortexReynolds number, Re at much higher resolutions than have been attempted. Unlike magnetic or superfluidreconnections,viscousreconnection is never complete, leaving behind a part of the initial tubes as threads, which then undergo successive reconnections (our cascade and mixing scenarios) as the newly formed bridges recoil from each other by selfadvection. We find that the time for orthogonal transfer of circulation scales as . The shortest distance between the tube centroids scales as before reconnection (collision) and as after reconnection (repulsion), where is the instant of smallest separation between vortex centroids. We find that is a constant, thus suggesting selfsimilarity, but is dependent on Re. Bridge repulsion is faster than collision and is more autonomous as local induction predominates, and, given the associated acceleration of vorticity, is potentially a source of intense sound generation. At the higher Re studied, the tails of the colliding threads are compressed into a planar jet with multiple vortex pairs. For , there is an avalanche of smaller scales during the reconnection, the rate of small scale generation and the spectral content (in vorticity, transfer function and dissipation spectra) being quite consistent with the structures visualized by the criterion. The maximum rate of vortex circulation transfer, enstrophy production, and dissipation scale as , , and , respectively. A more detailed study of subsequent reconnection of threads requires much higherresolution simulations that are currently not feasible.

A method to estimate the planar, instantaneous body force distribution from velocity field measurements
View Description Hide DescriptionWe present a simple method to derive a planar, instantaneous body force distribution from a given twodimensional velocity field without knowledge of the pressure field, under the specific restriction that the body force is dominated by one component only. Spatial integration then completely recovers this component. Particle imagevelocimetry and direct numerical simulations of a wall jet induced by a known body force were conducted to validate the method, demonstrating a good agreement of the original and reconstructed force fields.

Interactions among baroclinicallygenerated vortex rings in building up an acting spike to a bow shock layer
View Description Hide DescriptionVortex rings with a constant circulation are repetitively generated by depositing laser pulse energies ahead of a bow shockwave over a 20mm diameter, flathead cylinder in Mach 1.94 flow. Each vortex ring is formed after baroclinic interaction between a laserheated gas and the bow shockwave. With increasing the pulse repetition frequency, , mutual interactions among the vortex rings become stronger; alternate pitching motions at and “slipthrough” motions at appear. Beyond that, a quasisteadystate acting spike which decreases the stagnation pressure is built up.

On the fluctuating wallshear stress in zero pressuregradient turbulent boundary layer flows
View Description Hide DescriptionRecent direct numerical simulation (DNS) results relating to the behavior of the fluctuating wallshear stress in turbulent boundary layerflows are discussed. This new compilation is motivated by a recent article [Wu and Moin, “Transitional and turbulent boundary layer with heat transfer,” Phys. Fluids22, 085105 (2010)], which indicates a need for clarification of the value of . It is, however, shown here, based on other recent DNS data, that most results, both in boundary layer and channel geometry, yield plus a small increase with Reynolds number coming from the growing influence of the outer spectral peak. The observed discrepancy in experimental data is mainly attributed to spatial resolution effects, as originally described by Alfredsson et al. [“The fluctuating wallshear stress and the velocity field in the viscous sublayer,” Phys. Fluids31, 1026 (1988)].
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 ARTICLES

 Biofluid Mechanics

Flow dynamics of a tethered elastic capsule
View Description Hide DescriptionA twodimensional model of a tethered capsule is used to elucidate the effects of capsule aspect ratio and capsule internal viscosity on capsule dynamics. Over the parameter space examined, the capsule initially elongates out into the flow and then slowly pivots toward the wall as the capsule relaxes to a steadystate shape. The region of the capsule membrane that would come into contact with the wall corresponds with a region of elevated tractionforce magnitude. The effect of viscosity is found to be negligible at low shear rates, but at high shear rates, an increase in internal viscosity leads to an increase in the maximum capsule deformation and maximum force on the tether. At low shear rates, capsules with higher aspect ratios experience less force and deformation. Conversely, at high shear rates, capsules with higher aspect ratios experience greater force and deformation.
 Micro and Nanofluid Mechanics

Origin of line tension for a LennardJones nanodroplet
View Description Hide DescriptionThe existence and origin of line tension has remained controversial in literature. To address this issue, we compute the shape of LennardJones nanodrops using molecular dynamics and compare them to density functional theory in the approximation of the sharp kink interface. We show that the deviation from Young’s law is very small and would correspond to a typical line tension length scale (defined as line tension divided by surface tension) similar to the molecular size and decreasing with Young’s angle. We propose an alternative interpretation based on the geometry of the interface at the molecular scale.

Numerical investigation of elongated drops in a microfluidic Tjunction
View Description Hide DescriptionWe present a combined numerical and asymptotic approach for modeling droplets in microchannels. The magnitude of viscous forces relative to the surface tension force is characterized by a capillary number, Ca, which is assumed to be small. The numerical results successfully capture existing asymptotic solutions for the motion of drops in unconfined and confined flows; examples include the analytic Stokes flow solution for a twodimensional inviscid bubble placed in an unbounded parabolic flow field and asymptotic formulas for slender bubbles and drops in confined flows. An extensive investigation of the accuracy of the computations is presented to probe the efficacy of the methodology and algorithms. Thereafter, numerical simulations are presented for droplet breakup in a symmetric microfluidic Tjunction. The results are shown to support a proposed mechanism for breakup, driven by a pressure drop in a narrow gap between the droplet and the outer channel wall, which was formally derived in the limit [A. M. Leshansky and L. M. Pismen, “Breakup of drops in a microfluidic T junction,” Phys. Fluids21, 023303 (2009)].

Streaming potential generated by a pressuredriven flow over superhydrophobic stripes
View Description Hide DescriptionThe streaming potential generated by a pressuredriven flow over a weakly charged slipstick surface [the zeta potential of the surface is smaller than the thermal potential (25 mV)] with an arbitrary double layer thickness is theoretically studied by solving the Debye–Huckel equation and Stokes equation. A series solution of the streaming potential is derived. Approximate expressions for the streaming potential in the limits of thin double layers and thick double layers are also given in excellent agreement with the full solution. To understand the impact of the slip, the streaming potential is compared against that over a homogeneously charged smooth surface. Our results indicate that the streaming potential over a superhydrophobicsurface can only be enhanced under certain conditions. Moreover, as the double layer thickness increases, the advantage of the superhydrophobicsurface diminishes. In addition, the Onsager relation which directly relates the magnitude of electroosmotic effect to that of the streaming current effect has been explicitly proved to be valid for thin and thick double layers and homogeneously charged superhydrophobicsurfaces. Comparisons between the streaming current and electroosmoticmobility for an arbitrary electric double layer thickness under various conditions indicate that the Onsager relation seems applicable for arbitrary weakly charged superhydrophobicsurfaces although there is no general proof. Knowledge of the streaming potential over a slipstick surface can provide guidance for designing novel and efficient microfluidic energyconversion devices using superhydrophobicsurfaces.

The effect of confinementinduced shear on drop deformation and breakup in microfluidic extensional flows
View Description Hide DescriptionDroplets of deionized water and four aqueous surfactant solutions were generated in oil using a microfluidic flowfocusing device. The morphological developments of the drops in extensional flow and confinementinduced shear flow at various extension rates were studied using a hyperbolic contraction. This novel approach to dropletdeformation within a microfluidic device allowed the probing of droplets within a nearly uniform extensional flow. The focus of this work was to study the effect of confinementinduced shear on dropletdeformation and breakup in extensional flows.Dropletdeformation was found to increase with both increasing capillary number and increasing confinement, for a fixed viscosity ratio of , with the effect of the shear induced by confinement being quite dramatic. The addition of surfactant to the droplets resulted in the production of tails, which streamed from the rear of the droplets and produced daughter droplets much smaller than the parent droplet. In the partially confined limit, where the flow was purely extensional, a single tail was formed at the center of the droplets trailing edge. With enhanced confinement, shear effects from the wall became important, the droplets were observed to take on a bulletlike shape, and two tails formed at the trailing edge of the droplet. The critical value of the capillary number and confinement needed for the formation of tails varied with the surfactant used.

An experimental investigation of turbulent thermal convection in waterbased alumina nanofluid
View Description Hide DescriptionWe report heat transfer and flow dynamics measurements of alumina nanofluid in turbulent convective flow. Under the condition of fixed temperature at the top plate and fixed input heat flux at the bottom plate, it has been found that the convective heat transfer coefficient, , Nusselt number, , and Rayleigh number, , all decrease with the increasing volume fraction of the nanoparticle. In contrast, the velocity of the convective flow showed no significant change within experimental uncertainty and over the range of nanoparticle concentration of the measurement (from 0% to 1.08%). Under the condition of constant nanoparticle concentration , a second set of measurements of the heat transport and flowproperties have been made over a broad range of (from to ). For heat transport, a transition near has been found. For , the measured of the nanofluid is roughly the same as that of water in terms of both its magnitude and its scaling relation with , which suggests that the nanofluid can be treated as a single phase fluid in this parameter range. For , becomes smaller than that of the water and the deviation becomes larger with decreasing . In the parameter range of , the measured instantaneous shows strong and quasiperiodic fluctuations, which is absent when . This suggests that the significant decrease of the nanofluid comparing to that of water may be caused by the mass diffusion of nanoparticles. Furthermore, measurements of the flow velocity of the bulk nanofluid showed no significant difference from that of water for either above or below . From estimated thermal boundary layer thickness, we found that the deviations of the nanofluid from that of water for corresponds to the thickening of the thermal boundary layer at both the top and bottom plates. This thickening of the boundary layer at low input heat flux (or low driving strength of the convective flow) cannot be attributed to possible sedimentation of the nanoparticles.

Semianalytical study of hemispherical meniscus oscillation with an anchored edge on a conductive flat plate under an ac electric field
View Description Hide DescriptionThis paper presents an experimental observation and a semianalytical simulation of the oscillations of an anchored hemispherical liquidmeniscus on a conductive flat plate under an acelectric field. For the simulation, the liquid is assumed to be an incompressible, inviscid, and perfectly conductive fluid in a zerogravity environment. The mutual interaction between the electric field and the hydrodynamics is iteratively solved. As a result, the simulation can follow the oscillating meniscus shapes and contours of the electric field outside the meniscus according to the applied frequency. The velocity profile of the liquid inside the meniscus is also presented. The present theory can be used to predict the oscillation shape of a liquiddroplet on a plate with a certain applied frequency. The simulated oscillation shape is in agreement with the experimental result. The effects of the liquid density, the liquid surface tension, and the radius of the hemispherical meniscus on the oscillation are investigated. Then the oscillation of the drop on hydrophobic and hydrophilic substrates is also experimentally studied. Furthermore, we investigated the effects of the applied electric field on the coffee stain effect while the droplet is drying.
 Interfacial Flows

Confined thermocapillary motion of a threedimensional deformable drop
View Description Hide DescriptionIn this paper, simulations are performed of the thermocapillary motion of threedimensional and axisymmetric drops in a confined apparatus. The refined levelset grid method is used to track the interface and resolve very small deformations. We compare our results to theoretically predicted thermocapillary migration velocities of drops and to experimentally measured migration velocities in microgravity experiments. The motivation of the present work is to address four important questions surrounding thermocapillary migration. These are as follows. (1) What is the impact of initial conditions on both the initial transient and steady state drop behavior? (2) What is the impact of the domain geometry on drop behavior? (3) Do drops deform for intermediate Marangoni numbers and are those deformations axisymmetric? (4) Can the assumption of constant temperature fluid properties be used when simulating physical experiments? To answer the first question, we explore the parameter space of initial drop temperature distribution and drop holding time. We find that in lower Marangoni number regimes, the drop rapidly settles to a quasisteady state. For larger Marangoni numbers, the initial conditions dominate the drop behavior. To address the second and third questions, we look at the spatial distribution of tangential temperature gradients on the surface of the drop as well as drop deformations and migration velocities. The domain geometry induces nonaxisymmetric deformations and temperature distributions. The results of several axisymmetric runs with realistic physical properties are examined to answer the fourth question. It is found that the variation of material properties influences the drop migration behavior in a nontrivial way.

Thin film flow on the inside surface of a horizontally rotating cylinder: Steady state solutions and their stability
View Description Hide DescriptionWe present an approximate evolution equation for the film thickness on the inner surface of a horizontally rotating cylinder and solve it numerically by a collocation method. The influences of gravity, inertia, viscous and surface tension forces, and liquid volume fraction are included in the model. We investigate steady twodimensional solutions and their linear stability to both axially uniform and twodimensional perturbations and map stable and unstable regions depending on the relevant dimensionless numbers. It is shown that while an increase of the liquid volume fraction or surface tension always has a destabilizing effect on the solution, inertia may stabilize or destabilize the flow depending on the values of other parameters. At the same time, the inertial influence on the solution itself is relatively small. To obtain more insights into the flow after the loss of stability, we examine the growth rate of disturbances and demonstrate that it varies significantly through the considered parameter range. In addition, we obtain the most unstable wave numbers. This provides a means to distinguish between capillary and inertial instabilities. Finally, we present some steady threedimensional solutions to illustrate possible film shapes that can be obtained after the loss of stability.

Breakup of an electrified viscous thread with charged surfactants
View Description Hide DescriptionThe dynamics and breakup of electrified viscous jets in the presence of ionic surfactants at the interface are investigated theoretically. Axisymmetric configurations are considered and the jet is surrounded by a concentrically placed cylindrical electrode, which is held at a constant voltage potential. The annular region between the jet and the electrode is taken to be a hydrodynamically passive dielectric medium and an electric field is set up there and drives the flow, along with other physical mechanisms including capillary instability and viscous effects. The jet fluid is taken to be a symmetric electrolyte and proper modeling of the cationic and anionic species is used by considering the Nernst–Planck equations in order to find the volume charge density that influences the electric field in the jet. A positively charged insoluble surfactant is present at the interface, and its evolution, as well as the resulting value of the local surface tension coefficient, is coupled with the voltage potential at the interface. The resulting coupled nonlinear systems are derived and analytical progress is made by carrying out a nonlinear slender jet approximation. The reduced model is described by a number of hydrodynamic, electrical, and electrokinetic parameters, and an extensive computational study is undertaken to elucidate the dynamics along with allied linear properties. It is established that the jet ruptures in finite time provided the outer electrode is sufficiently far away, and numerous examples are given where the dimensionless parameters can be used to control the size of the satellite drops that form beyond the topological transition, as well as the time to break up. It is also shown that pinching solutions follow the selfsimilar dynamics of clean viscous jets at times close to the breakup time. Finally, a further asymptotic theory is developed for large Debye layers to produce an additional model that incorporates the effects of surface charge diffusion. Numerical solutions establish that the presence of electrostatic and electrokineticeffects increases the sizes of satellites but have a rather weak influence on the time to rupture.

Drop fragmentation due to hole formation during Leidenfrost impact
View Description Hide DescriptionDrop impacts on a smooth plate heated above the Leidenfrost temperature are investigated in the range of large Weber number. Liquid fragmentation due to the rupture of the expanding lamella during the impact—by hole nucleation and subsequent growth—is studied. Control of this rupturing process is achieved experimentally through the use of single modeldefects attached to the substrate which act as an initiating spots for the hole formation, whereas the liquid does not contact the substrate. Overall, the lamella rupture is shown to take place above a critical impact velocity, the value of which decreases with increasing defect size. Comparing this rupture mechanism to classical splash, it is shown to be the relevant fragmentation phenomenon below a critical ratio between drop and defect sizes of .

Insights on the impact of a plane drop on a thin liquid film
View Description Hide DescriptionNumerical simulations of early and intermediate instants of a plane twodimensional dropimpact on a preexisting thin film of the same liquid are performed. The evolution of the phenomenon is analyzed by solving the freesurface Navier–Stokes equations by means of a volume of fluid (VOF) method. Viscous, inertial and surface tension forces are taken into account; gravity is neglected. The socalled splashing regime is emphasized, where the emergence of an initial horizontal ejecta sheet is followed by the formation of an almost vertical lamella sheet, which is the planar counterpart of the well known splashingcrown of spherical geometry. Overall velocity and pressure fields as well as detailed interface shapes are presented, and several insights on the relevant scaling laws are furnished. In the ejecta sheet (jet) regime a major result is the finding of a deviation from the standard square root behavior for the dependence on time of the contact length of sheet first emergence, which is proved to be crucial in the subsequent original application of the potential theory of Howison et al. [J. Fluid Mech.542, 1 (2005)]. In the lamella sheet regime, the outwards expansion of its base is discussed in connection with the theory of the formation of a kinematic discontinuity within the underneath film of Yarin and Weiss [J. Fluid Mech.283, 141 (1995)]. Analogies between planar and axysymmetric configurations are discussed.
 Viscous and NonNewtonian Flows

Deformation of a partially engulfed compound drop slowly moving in an immiscible viscous fluid
View Description Hide DescriptionCompound drops are comprised of two or more immiscible phases, one of which entirely or partially engulfs the others. In this work, we consider a partially engulfed compound drop comprised of two immiscible incompressible fluids, dispersed in an isothermal liquid, and that moved under the action of gravity and buoyancy. The contact angles between the three phases are determined by three interfacial tensions associated with the different fluids comprising the compound drop. The surfacesdeform as the drop moves through the ambient fluid. If the capillary number is small , corrections to the shapes of the undeformable case are constructed, making use of a perturbation technique. We report on stationary drops’ deformation for a variety of the physical parameters involved, such as volume ratio and surface tension of each interface, which determine the unperturbed configuration and the distribution of density between the two phases of the drop. Several examples of various transient behaviors of highly deformable compound drops are computed using FLUENT software and are presented as well.
 Particulate, Multiphase, and Granular Flows

Modeling and simulation of multiple bubble entrainment and interactions with two dimensional vortical flows
View Description Hide DescriptionSimulations of bubble entrainment and interactions with two dimensional vortical flows are preformed using a discrete element model. In this EulerianLagrangian approach, solution to the carrier phase is obtained using direct numerical simulation whereas motion of subgrid bubbles is modeled using Lagrangian tracking. The volumetric displacement of the fluid by the finite size of the bubbles is modeled along with interphase momentumexchange for a realistic coupling of the bubbles to the carrier phase. In order to assess the importance of this volumetric coupling effect, even at low overall volume loading, simulations of a small number of microbubbles entrained in a traveling vortex tube are studied in detail. The test case resembles the experiments conducted by Sridhar and Katz [JFM, 1999] on bubble entrainment in vortex rings. It is shown that under some conditions, the entrainment of eight small bubbles, or less in diameter, result in significant levels of vortex distortion when modeled using the volumetric coupling effect. Neglecting these effects, however, does not result in any vortex distortion due to entrained bubbles. The nondimensionalized vortex strength versus bubble settling locations are compared with experimental data to show collapse of the data along the trends observed in experiments only when the volumetric effects are modeled. Qualitative and quantitative assessments of this distortion observed with volumetric coupling are made using three methods; bubble induced vortex asymmetry, relative change in the decay of angular momentum, and relative change in the peak vorticity. It is found that in all cases the volumetric effects result in a relative increase of the vortex decay rate. The concept of a relative reaction force, defined as the ratio of net bubble to fluid reaction to the local driving force of the vortex, is introduced to analyze this effect. It is shown that the global increases in vortex decay rate are directly proportional to the magnitude of this highly local relative reaction force.
 Laminar Flows

Exact averaging of laminar dispersion
View Description Hide DescriptionWe use the Liapunov–Schmidt (LS) technique of bifurcation theory to derive a lowdimensional model for laminar dispersion of a nonreactive solute in a tube. The LS formalism leads to an exact averaged model, consisting of the governing equation for the crosssection averaged concentration, along with the initial and inlet conditions, to all orders in the transverse diffusion time. We use the averaged model to analyze the temporal evolution of the spatial moments of the solute and show that they do not have the centroid displacement or variance deficit predicted by the coarsegrained models derived by other methods. We also present a detailed analysis of the first three spatial moments for short and long times as a function of the radial Peclet number and identify three clearly defined time intervals for the evolution of the solute concentration profile. By examining the skewness in some detail, we show that the skewness increases initially, attains a maximum for time scales of the order of transverse diffusion time, and the solute concentration profile never attains the Gaussian shape at any finite time. Finally, we reason that there is a fundamental physical inconsistency in representing laminar (Taylor) dispersion phenomena using truncated averaged models in terms of a single crosssection averaged concentration and its large scale gradient. Our approach evaluates the dispersion flux using a local gradient between the dominant diffusive and convective modes. We present and analyze a truncated regularized hyperbolic model in terms of the cupmixing concentration for the classical Taylor–Aris dispersion that has a larger domain of validity compared to the traditional parabolic model. By analyzing the temporal moments, we show that the hyperbolic model has no physical inconsistencies that are associated with the parabolic model and can describe the dispersion process to first order accuracy in the transverse diffusion time.