Volume 21, Issue 7, July 2009

We present the results of a combined experimental and numerical investigation of the coalescence of a drop with a liquid reservoir of a miscible but distinct fluid. Particular attention is given to elucidating the influence on the coalescence process of a surface tension difference between drop and reservoir. Drops are gently deposited on the surface of the reservoir, and so coalesce with negligible initial vertical velocity. Depending on the drop size and reservoir composition, partial or total coalescence may occur. Three distinct regimes, depending on the reservoir to dropsurface tension ratio, , are identified and delineated through both experiments and numerics. If , droplets are ejected from the top of the drop, while satellite droplets are left in its wake. For , only total coalescence is observed. When , partial coalescence is increasingly favored as the reservoir’s surface tension increases.
 LETTERS


The impact of a local perturbation on global properties of a turbulent wake
View Description Hide DescriptionStationary perturbation techniques are used to investigate the sensitivity of the global properties of the wake behind a bluff body at moderate Re. The entire recirculation bubble is found to be a sensitive region for the global frequency selection and the quality of the synchronization. A striking position is found at its center where synchronization is destroyed and the frequency is increased. High speed particle image velocimetry sheds some light into the underlying mechanisms, which are interpreted in terms of vorticity interaction, flow reattachment, and flow deviation. Strong mean flow modifications are observed to correspond to drastic changes in drag and its fluctuations.
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 ARTICLES

 Biofluid Mechanics

Simplified dragonfly airfoil aerodynamics at Reynolds numbers below 8000
View Description Hide DescriptionEffective aerodynamics at Reynolds numbers lower than 10 000 is of great technological interest and a fundamental scientific challenge. The current study covers a Reynolds number range of 2000–8000. At these Reynolds numbers, natural insect flight could provide inspiration for technology development. Insect wings are commonly characterized by corrugated airfoils. In particular, the airfoil of the dragonfly, which is able to glide, can be used for twodimensional aerodynamic study of fixed rigid wings. In this study, a simplified dragonfly airfoil is numerically analyzed in a steady freestream flow. The aerodynamic performance (such as mean and fluctuating lift and drag), are first compared to a “traditional” low Reynolds number airfoil: the EpplerE61. The numerical results demonstrate superior performances of the corrugated airfoil. A series of lowspeed wind and water tunnel experiments were performed on the corrugated airfoil, to validate the numerical results. The findings indicate quantitative agreement with the mean wake velocity profiles and shedding frequencies while validating the two dimensionality of the flow. A flow physics numerical study was performed in order to understand the underlying mechanism of corrugated airfoils at these Reynolds numbers. Airfoil shapes based on the flow field characteristics of the corrugated airfoil were built and analyzed. Their performances were compared to those of the corrugated airfoil, stressing the advantages of the latter. It was found that the flow which separates from the corrugations and forms spanwise vortices intermittently reattaches to the aftupper arc region of the airfoil. This mechanism is responsible for the relatively low intensity of the vortices in the airfoil wake, reducing the drag and increasing the flight performances of this kind of corrugated airfoil as compared to traditional low Reynolds number airfoils such as the Eppler E61.

Resonance and propulsion performance of a heaving flexible wing
View Description Hide DescriptionThe influence of the bending rigidity of a flexible heaving wing on its propulsive performance in a twodimensional imposed parallel flow is investigated in the inviscid limit. Potential flow theory is used to describe the flow over the flapping wing. The vortical wake of the wing is accounted for by the shedding of point vortices with unsteady intensity from the wing’s trailing edge. The trailingedge flapping amplitude is shown to be maximal for a discrete set of values of the rigidity, at which a resonance occurs between the forcing frequency and a natural frequency of the system. A quantitative comparison of the position of these resonances with linear stability analysis results is presented. Such resonances induce maximum values of the mean developed thrust and power input. The flapping efficiency is also shown to be greatly enhanced by flexibility.

Liquid plug propagation in flexible microchannels: A small airway model
View Description Hide DescriptionIn the present study, we investigate the effect of wall flexibility on the plug propagation and the resulting wall stresses in small airway models with experimental measurements and numerical simulations. Experimentally, a flexible microchannel was fabricated to mimic the flexible small airways using soft lithography. Liquid plugs were generated and propagated through the microchannels. The local wall deformation is observed instantaneously during plug propagation with the maximum increasing with plug speed. The pressure drop across the plug is measured and observed to increase with plug speed, and is slightly smaller in a flexible channel compared to that in a rigid channel. A computational model is then presented to model the steady plug propagation through a flexible channel corresponding to the middle plane in the experimental device. The results show qualitative agreements with experiments on wall shapes and pressure drops and the discrepancies bring up interesting questions on current field of modeling. The flexible wall deforms inward near the plug core region, the deformation and pressure drop across the plug increase with the plug speed. The wall deformation and resulting stresses vary with different longitudinal tensions, i.e., for large wall longitudinal tension, the wall deforms slightly, which causes decreased fluid stress and stress gradients on the flexible wall comparing to that on rigid walls; however, the wall stress gradients are found to be much larger on highly deformable walls with small longitudinal tensions. Therefore, in diseases such as emphysema, with more deformable airways, there is a high possibility of induced injuries on lining cells along the airways because of larger wall stresses and stress gradients.
 Micro and Nanofluid Mechanics

Droplet breakup in microfluidic Tjunctions at small capillary numbers
View Description Hide DescriptionWe perform experimental studies of droplet breakup in microfluidic Tjunctions in a range of capillary numbers lying between and and for two viscosity ratios of the fluids forming the dispersed and continuous phases. The present paper extends the range of capillary numbers explored by previous investigators by two orders of magnitude. We single out two different regimes of breakup. In a first regime, a gap exists between the droplet and the wall before breakup occurs. In this case, the breakup process agrees well with the analytical theory of Leshansky and Pismen [Phys. Fluids21, 023303 (Year: 2009)]. In a second regime, droplets keep obstructing the Tjunction before breakup. Using physical arguments, we introduce a critical droplet extension for describing the breakup process in this case.

Nonlinear alternating electric field dipolophoresis of spherical nanoparticles
View Description Hide DescriptionWe consider the nonlinear electrokinetic problem of a freely suspended conducting (infinitely polarized) spherical micro or nanosize particle surrounded by an unbounded electrolyte solution. The uncharged particle is exposed to an alternating (ac),nonuniform, and axisymmetric ambient electric field. As a result, the particle acquires a dipolophoretic (DIP) mobility of magnitude, which is quadratic in the amplitude of the applied electric field. The resulting phoretic velocity is driven by two independent nonlinear mechanisms. One is the common dielectrophoretic effect, whereby the nonuniform field exerts an electrostatic force on the image multipole singularity system within the particle. The other is the socalled “inducedcharge electrophoresis” resulting from the action of the electric field on the excess charge around the particle induced in the diffused layer by the field itself. Both effects are quadratic in the amplitudes of the electric field and depend on the forcing frequency and on the dimensionless Debye screening length scale. It is demonstrated in the sequel that the two generally act in opposite directions which may result in mutual cancellation. Under the assumptions of a “weak” electric field and the neglect of surfaceconductance, we present a concise analysis of the resulting nonlinear streaming (dc) velocity (averaged over a period) for a spherical metalic particle that is exposed to a timeharmonic oscillating (ac)electric field. The analysis of this fundamental nonlinear DIP problem is provided for arbitrary forcing frequencies and for any Debye thickness. Numerical simulations are given for the case of a “twomode” interaction consisting of a uniformgradient electric field combined with a uniform field, where the two modes are either “in” or “out” of phase.
 Interfacial Flows

Threedimensional stability of a thin film between two approaching drops
View Description Hide DescriptionIn most simulations of the coalescence process, the rupture of the thin film between two drops is assumed to be axisymmetric. In this paper, we examine the possibility of a nonaxisymmetric rupture by carrying out a threedimensional linear stability analysis of an axisymmetric thin film region. First, the effect of tangential interfacial velocity on the stability of a flat film is analyzed and a scaling analysis is provided to predict the dependence of the critical film thickness on the dimensionless parameters of the problem: the capillary number Ca, the dimensionless Hamaker constant , and the viscosity ratio . Multigrid integration and implicit eigensystem solution techniques are used to simultaneously solve the boundary integral and film evolution equations for the disturbance shape and growth rate. The calculations show that a fixedend disturbance, which decays to zero at the edge of the film, exhibits maximum instability in the axisymmetric mode. On the other hand, the first nonaxisymmetric mode is the most unstable for the class of freeend disturbances that approach the edge of the film with zero slope. Next, the stability calculation is interfaced with the full axisymmetric simulation of two drops approaching in a biaxial extensional flow in order to obtain the correct basestate film shape at each time interval. In this case, the thin film first becomes unstable to a nonaxisymmetric disturbance for both kinds of boundary conditions. The critical thickness from the stability calculation is compared with the critical film thickness obtained earlier from numerical calculations of the collision and interaction of a pair of fully axisymmetric drops and the effect of basestate curvature on film stability is investigated.

Numerical studies of the influence of the dynamic contact angle on a droplet impacting on a dry surface
View Description Hide DescriptionWe numerically investigated liquiddroplet impact behavior onto a dry and flat surface. The numerical method consists of a coupled level set and volumeoffluid framework, volume/surface integrated average based multimoment method, and a continuum surface force model. The numerical simulation reproduces the experimentally observed droplet behavior quantitatively, in both the spreading and receding phases, only when we use a dynamic contact angle model based on experimental observations. If we use a sensible simplified dynamic contact angle model, the predicted time dependence of droplet behavior is poorly reproduced. The result shows that precise dynamic contact angle modeling plays an important role in the modeling of droplet impact behavior.

The effect of liquid viscosity on bubble pinchoff
View Description Hide DescriptionThe collapse stage of an air bubble immersed in a stagnant viscousliquid is experimentally and theoretically investigated, focusing on the effect of liquidviscosity on the final instants previous to pinchoff. Our experiments are consistent with recent investigations, and at the same time highlight several important limitations of previous works. In particular, it is shown that the use of a power law to describe the collapse dynamics of the bubble is not appropriate in an intermediate range of liquidviscosities, for which a transition from an inviscid to a fully viscous pinchoff takes place. Under these conditions, the instantaneous exponent varies during a single pinchoff event from the typical values of inviscid collapse, , to the value corresponding to a fully viscousdynamics,. Consequently, the effective exponent of the power law is not correctly defined in these cases. However, as in the work of BolañosJiménez et al. [Phys. Fluids20, 112104 (2008)], we show that the pinchoff process can be accurately described by the use of a pair of Rayleighlike differential equations for the time evolution of the minimum radius, , and half the axial curvature evaluated at the minimum radius, . In particular, the theoretical model is able to describe the smooth transition which takes place from inviscid to viscousdominated pinchoff in liquids of intermediate viscosity,, and accounts for the fact that the axial curvature remains constant when the local Reynolds number becomes small enough, in close agreement with our experimental measurements.

Stickslip dynamics of an oscillated sessile drop
View Description Hide DescriptionWe consider theoretically the dynamics of an oscillated sessile drop of incompressible liquid and focus on the contact line hysteresis. We address the situation of the smallamplitude and highfrequency oscillations imposed normally to the substrate surface. We deal with the drop whose equilibrium surface is hemispherical and the equilibrium contact angle equals . We apply the dynamicboundary condition that involves an ambiguous dependence of the contact angle on the contact line velocity: The contact line starts to slide only when the deviation of the contact angle exceeds a certain critical value. As a result, the stickslip dynamics can be observed. The frequency response of surface oscillations on the substrate and at the pole of the drop are analyzed. It is shown that novel features such as the emergence of antiresonant frequency bands and nontrivial competition of different resonances are caused by contact line hysteresis.

Influence of surfactant solubility on the deformation and breakup of a bubble or capillary jet in a viscous fluid
View Description Hide DescriptionIn a previous study [M. Hameed et al., J. Fluid Mech.594, 307 (2008)] the authors investigated the influence of insoluble surfactant on the evolution of a stretched, inviscid bubble surrounded by a viscous fluid via direct numerical simulation of the Navier–Stokes equations, and showed that the presence of surfactant can cause the bubble to contract and form a quasisteady slender thread connecting parent bubbles, instead of proceeding directly toward pinchoff as occurs for a surfactantfree bubble. Insoluble surfactant significantly retards pinchoff and the thread is stabilized by a balance between internal pressure and reduced capillary pressure due to a high concentration of surfactant that develops during the initial stage of contraction. In the present study we investigate the influence of surfactantsolubility on thread formation. The adsorptiondesorption kinetics for solubility is in the diffusion controlled regime. A longwave model for the evolution of a capillary jet is also studied in the Stokes flow limit, and shows dynamics that are similar to those of the evolving bubble. With solublesurfactant, depending on parameter values, a slender thread forms but can pinchoff later due to exchange of surfactant between the interface and exterior bulk flow.

A comparison of viscoelastic stress wakes for twodimensional and threedimensional Newtonian drop deformations in a viscoelastic matrix under shear
View Description Hide DescriptionA recent experimental study of a Newtonian drop suspended in a viscoelastic matrix undergoing simple shear displays a transient overshoot in dropdeformation which is qualitatively similar to twodimensional (2D) numerical simulation results. Despite the similarity, an interpretation in light of the 2D result is misleading because the overshoot is absent in the fully threedimensional (3D) simulation. This motivates a study of regimes where qualitatively different and interesting features such as overshoots in deformation occur for a 2D drop but not for a 3D drop. The influence of viscoelastic “wakes” that emanate from the drop tips is reported. The viscoelastic wakes are larger and of higher magnitude in 3D than in 2D, and lead to more deformation in 3D. During drop evolution, the less deformeddrop is found to be aligned more with the flow direction. As the droptomatrix viscosity ratio increases from 1 to past 3, drop rotation is promoted, with accompanying retraction when the capillary number is sufficiently high. Thus, a 3D overshoot in deformation is promoted with increasing viscosity ratio.

The influence of surface tension gradients on drop coalescence
View Description Hide DescriptionWe present the results of a combined experimental and numerical investigation of the coalescence of a drop with a liquid reservoir of a miscible but distinct fluid. Particular attention is given to elucidating the influence on the coalescence process of a surface tension difference between drop and reservoir. Drops are gently deposited on the surface of the reservoir, and so coalesce with negligible initial vertical velocity. Depending on the drop size and reservoir composition, partial or total coalescence may occur. Three distinct regimes, depending on the reservoir to dropsurface tension ratio, , are identified and delineated through both experiments and numerics. If , droplets are ejected from the top of the drop, while satellite droplets are left in its wake. For , only total coalescence is observed. When , partial coalescence is increasingly favored as the reservoir’s surface tension increases.
 Viscous and NonNewtonian Flows

Analysis of accommodation coefficients of noble gases on aluminum surface with an experimental/computational method
View Description Hide DescriptionA method that connects measurements of radiometric forces on a heated vane in the transitional flow regime with the kinetic modeling of the flow, and derives the accommodation coefficients through the successive analysis of measured and computed results, is proposed. The method utilizes the fact that radiometric forces exerted on heated objects immersed in rarefied gases are governed by the interaction of gas molecules with the surface. Experimental results on radiometric forces on a 0.11 m diameter circular vane are obtained on a nanoNewton thrust stand in a 3 m long vacuum chamber for pressures ranging from approximately 0.01 to 1 Pa. The vane was heated to 419 K on the hot side and 396 K on the cold side. The numerical modeling is conducted using a combined ellipsoidal statistical Bhatnagar–Gross–Krook/direct simulation Monte Carlo approach that allows accurate and time efficient analysis of radiometric forces on a vane in large vacuum chambers filled with rarefied gas. Accommodation coefficients for the Maxwellmodel are estimated for argon, xenon, and helium on a machined aluminumsurface, and found to be 0.81, 0.86, and 0.53, respectively.

Displacement flows in horizontal, narrow, eccentric annuli with a moving inner cylinder
View Description Hide DescriptionWe analyze the effects of rotation and axial motion of the inner cylinder of an eccentric annular duct during the displacement flow between two Newtonian fluids of differing density and viscosity. The annulus is assumed narrow and is oriented near the horizontal. The main application is the primary cementing of horizontal oil and gas wells, in which casing rotation and reciprocation is becoming common. In this application it is usual for the displacing fluid to have a larger viscosity than the displaced fluid. We show that steady traveling wave displacements may occur, as for the situation with stationary walls. For small buoyancy numbers and when the annulus is near to concentric, the interface is nearly flat and a perturbation solution can be found analytically. This solution shows that rotation reduces the extension of the interface in the axial direction and also results in an azimuthal phase shift of the steady shape away from a symmetrical profile. Numerical solution is used for larger buoyancy numbers. We see that the phase shift results in the positioning of heavy fluid over light fluid along segments of the interface. When the axial extension of the interface is sufficiently large, this leads to a local buoyancydriven fingering instability, for which a simple predictive theory is advanced. Over longer times, the local fingering is replaced by steady propagation of a diffuse interfacial region that spreads slowly due to dispersion. Slow axial motion of the annulus walls on its own is apparently less interesting. There is no breaking of the symmetry of the interface and hence no instability. However, axial wall motion does generate secondary flows which may combine with those from cylinder rotation resulting in enhanced dispersive effects.
 Particulate, Multiphase, and Granular Flows

Particle deposition onto a microsieve
View Description Hide DescriptionThe objective of the present work is to investigate experimentally the deposition of micronsized particles onto the surface of a microsievemembrane, which consists in a thin screen with patterned circular holes. A dilute suspension of spherical, monodisperse, polystyrene particles flows at an imposed flow rate through the membrane, in a frontal filtration mode (i.e., the flow direction is perpendicular to the membrane). The particletopore diameter ratio is inferior to one. The particle and flow Reynolds numbers are both smaller than 0.1 for the flow regimes investigated in the present study. The particles are nonBrownian, inertialess, and their buoyancy is negligible. Direct visualizations of the membrane are made using video microscopy. A statistical analysis of the particle deposition locations, based on an automatic processing of video images of the membranesurface recorded during the experiment, is made possible by the periodicity of the pore distribution. Experiments show the existence of two preferential locations for particle deposition, for the whole range of flow rates investigated in the present study and the three microsieve patterns used. This puzzling result is discussed in the light of earlier theoretical and numerical simulations works, dealing with the low Reynolds number motion of a single particle in the vicinity of a pore, in the presence of physicochemical interactions between the particle and the membranesurface.

Particle clusters settling under gravity in a viscous fluid
View Description Hide DescriptionClusters made of a small number of close solid spherical particles at a random configuration, sedimenting through a viscous fluid at small Reynolds number, were experimentally investigated at a shorttime scale. The cluster settling velocities were measured and shown to be well approximated by the ensembleaveraged formula derived earlier for the uniform distribution of the point particles inside a spherical volume. It was emphasized that the “effective radius” of this volume in general should be smaller than the actual radius of a cluster made of the spheres, and the relation between both radii was determined. The formula was also shown to account well for the gravitational settling of rigid conglomerates, measured and computed elsewhere.

Evaluation of master equations for the droplet size distribution in condensing flow
View Description Hide DescriptionThe kinetic equation (KE) and its first and secondorder approximations, the general dynamic equation (GDE), and the Fokker–Planck equation (FPE), respectively, have been evaluated based on (a) their equilibrium distributions, (b) a nucleation pulse experiment, and (c) an expanding nozzle flow. Large differences are observed between the equilibrium distributions of the FPE and KE, whereas the GDE does not have an equilibrium distribution at all. For the nucleation pulse experiment, good agreement is found between the KE, FPE, and GDE due to quasisteady nucleation. For the condensing nozzle flow, the difference between the GDE and the KE distributions is large, although the relevant flow variables show fair agreement. A sensitivity study of the KE solution with respect to uncertainties in (a) the surface tension model, (b) the sticking probability, and (c) the equilibrium distribution revealed that both the sticking probability and the equilibrium distribution have a significant influence on the predicted condensation onset. Furthermore, it is found that the proposed Wölk and Streycorrected Courtney equilibrium distribution yields the best agreement with the reported measurements.
 Laminar Flows

Mixing induced by a transversely oscillating circular cylinder in a straight channel
View Description Hide DescriptionFlow past a transversely oscillating circular cylinder in a channel can be used as an active mesoscale mixer, kinematics of which was investigated by Celik et al. [“Flow past an oscillating circular cylinder in a channel with an upstream splitter plate,” Phys. Fluids20, 103603 (2008)] at . This study presents numerical simulations of species transport in the mixer, obtained for various cylinder excitation frequencies and the species inlet configurations for a wide range of Peclet numbers. Mixing indices are calculated on the vortex spacing based mixing blocks, which is a newly introduced concept that utilizes periodicity of the vorticity field. Mixing index comparisons show that mixing efficiency is strongly dependent on the identity of the species within wall shear layers and vortex cores. For the cylinder excitation frequency of 25% higher than the natural vortex shedding frequency, 60% and 46% mixing enhancements relative to the straight channel and the stationary cylinder cases are observed at , respectively.

Eddy genesis and manipulation in plane laminar shear flow
View Description Hide DescriptionEddy formation and presence in a plane laminar shear flow configuration consisting of two infinitely long plates orientated parallel to each other is investigated theoretically. The upper plate, which is planar, drives the flow; the lower one has a sinusoidal profile and is fixed. The governing equations are solved via a full finite element formulation for the general case and semianalytically at the Stokes flow limit. The effects of varying geometry (involving changes in the mean plate separation or the amplitude and wavelength of the lower plate) and inertia are explored separately. For Stokes flow and varying geometry, excellent agreement between the two methods of solution is found. Of particular interest with regard to the flow structure is the importance of the clearance that exists between the upper plate and the tops of the corrugations forming the lower one. When the clearance is large, an eddy is only present at sufficiently large amplitudes or small wavelengths. However, as the plate clearance is reduced, a critical value is found, which triggers the formation of an eddy in an otherwise fully attached flow for any finite amplitude and arbitrarily large wavelength. This is a precursor to the primary eddy to be expected in the liddriven cavity flow, which is formed in the limit of zero clearance between the plates. The influence of the flow driving mechanism is assessed by comparison with corresponding solutions for the case of gravitydriven fluid films flowing over an undulating substrate. When inertia is present, the flow generally becomes asymmetrical. However, it is found that for large mean plate separations the flow local to the lower plate becomes effectively decoupled from the inertia dominated overlying flow if the wavelength of the lower plate is sufficiently small. In such cases the local flow retains its symmetry. A local Reynolds number based on the wavelength is shown to be useful in characterizing these largegap flows. As the mean plate separation is reduced, the form of the asymmetry caused by inertia changes and becomes strongly dependent on the plate separation. For lower plate wavelengths which do not exhibit a kinematically induced secondary eddy, an inertially induced secondary eddy can be created if the mean plate separation is sufficiently small and the global Reynolds number is sufficiently large.