Volume 23, Issue 11, November 2011

Numerical analyses of the stability of a stratified twodimensional KelvinHelmholtz billow against three dimensional disturbances provide a theoretical means of identifying the primary mechanism(s) that induce transition to turbulence. We identify, through fully resolved threedimensional numerical simulations, secondary modes of instability which have been suggested by recent observations to be responsible for this transition. Our analyses lead us to two primary conclusions. First, as the Reynolds number is increased at a fixed stratification level, the vortex pairing process may be entirely suppressed by the rapid growth of threedimensional secondary instabilities. Second, the new transition mechanisms identified herein have significant implications for the efficiency of mixing in the turbulent flow that develops subsequent to saturation of the secondary instabilities.
 AWARD AND INVITED PAPERS


Dynamics of suspended colloidal particles near a wall: Implications for interfacial particle velocimetry^{a)}
View Description Hide DescriptionInterfacial transport due to surface forces is significant in many microfluidic devices with their relatively large surface areas and small volumes. Recently, velocimetry methods where evanescent waves illuminate fluorescent particles less than 1 μm in radius have been used to obtain fluid velocities within 500 nm or less of the wall. This review considers some of the phenomena affecting the dynamics of suspended colloidal particles near a wall. The measurement of interfacial flow velocities using such particles as tracers, illustrated by studies of Poiseuille and electrokinetically driven flows, is then discussed.
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 LETTERS


Threedimensionalization of the stratified mixing layer at high Reynolds number
View Description Hide DescriptionNumerical analyses of the stability of a stratified twodimensional KelvinHelmholtz billow against three dimensional disturbances provide a theoretical means of identifying the primary mechanism(s) that induce transition to turbulence. We identify, through fully resolved threedimensional numerical simulations, secondary modes of instability which have been suggested by recent observations to be responsible for this transition. Our analyses lead us to two primary conclusions. First, as the Reynolds number is increased at a fixed stratification level, the vortex pairing process may be entirely suppressed by the rapid growth of threedimensional secondary instabilities. Second, the new transition mechanisms identified herein have significant implications for the efficiency of mixing in the turbulent flow that develops subsequent to saturation of the secondary instabilities.

Orientational order in concentrated suspensions of spherical microswimmers
View Description Hide DescriptionWe use numerical simulations to probe the dynamics of concentrated suspensions of spherical microswimmers interacting hydrodynamically. Previous work in the dilute limit predicted orientational instabilities of aligned suspensions for both pusher and puller swimmers, which we confirm computationally. Unlike previous work, we show that isotropic suspensions of spherical swimmers are also always unstable. Both types of initial conditions develop longtime polar order of a nature which depends on the hydrodynamic signature of the swimmer but very weakly on the volume fraction up to very high volume fractions.

Stability of steady flow through an axially corrugated pipe
View Description Hide DescriptionThe linear stability of steady flow in pipes with circular crosssection and sinusoidal axial variation in diameter is studied by finding global eigenmodes with axial wavelength commensurate with that of the wall corrugation, chosen to be equal to one pipe mean radius. The maximum peaktopeak height of corrugation considered is approximately 8% of the mean diameter. At low corrugation amplitude and at low Reynolds numbers, the base flow remains attached to the wall, while at larger amplitudes and Reynolds numbers, an axisymmetric separation bubble forms within the corrugation. For all Reynolds numbers considered, flows remain stable to axisymmetric perturbations, but become unstable to standingwave modes of low azimuthal wavenumber, with critical Reynolds number first falling, then increasing with increasing corrugation height. Both attached and separated flows exhibit similar types of instability modes, which in the case of separated flow are most energetic near the reattachment line of the base flow. The leading instability modes consist of counterrotating vortices situated near the pipe wall.

Effect of spanwise confinement on flag flutter: Experimental measurements
View Description Hide DescriptionThe effect of spanwise clearance on the critical velocity for fluttering of a cantilevered plate in a channel flow is addressed experimentally. It is found that the critical velocity is influenced by the presence of the walls when the ratio between the clearance and the length of the plate C/L is less than 0.1 and slowly converges to the critical velocity predicted by models considering infinite span plates. These results are in good agreement with the predictions of a potential flowmodel taking into account spanwise confinement.
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 ARTICLES

 Biofluid Mechanics

Dynamics of microcapsules in oscillating shear flow
View Description Hide DescriptionWe present a threedimensional numerical study on the dynamics of deformable capsules in sinusoidally oscillating shear flow. We consider capsules of spherical and oblate spheroid resting shapes. For spherical resting shapes, we find an identical deformation response during positive and negative vorticities. However, the deformation response becomes unequal and shows complex behavior for nonspherical resting shapes. The average elongation is higher in the retarding phase of the shear flow than in the accelerating phase. Primarily two types of dynamics are observed for nonspherical shapes: a clockwise/counterclockwise swinging motion in response to the altering flow direction that occurs at both high and low values of shear rate amplitudes, and a continuous/unidirectional tumbling motion that occurs at intermediate values. The unidirectional tumbling motion occurs despite the fact that the timeaverage vorticity is zero. Such a tumbling motion is accompanied by a continuous tanktreading motion of the membrane in the opposite direction. We obtain phase diagram that shows existence of two critical shear rates and two oscillation frequencies. The unidirectional tumbling motion occurs in the intermediate range, and the clockwise/counterclockwise swinging motion occurs otherwise. We also find that the dynamics is highly sensitive to the initial condition. A swinging is generally observed when the capsule is released aligned with the extensional or compressional axis of the shear flow, and a tumbling is observed otherwise. These results suggest the possibility of chaotic behavior of cells in timedependent flows. We provide explanations of such complex dynamics by analyzing the coupling between the shape and angular oscillation and the imposed flow oscillation.

Determination of the instantaneous forces on flapping wings from a localized fluid velocity field
View Description Hide DescriptionExpressions are derived to relate the instantaneous pressure force on a flapping wing to the velocity field on a plane at the trailing edge and on a highly localized region around and near the wing, valid when the vortexsheet is thin. In its more practical version, the formalism is applicable to wings with close to twodimensional geometry and has the advantage of not using spatial derivatives, but only a time derivative of a surface integral of the velocity. In the purely twodimensional case, the expression obtained is used to justify a much simpler one that only requires the evaluation of the time derivative of the wing circulation. A comparison with a numerical simulation in a twodimensional case shows a good representation of the forces, even with the most simplified expression, when the condition of a thin wake is met. Other examples are shown in which the wake is not thin in order to explore the limitations of the formalism. It is found in these cases that the thrust is sometimes not so well reproduced, with a tendency to be overestimated, while the lift is generally better reproduced. Remarkably, the simpler expression reproduces rather acceptably the phase and amplitude of both thrust and lift in all cases.

Coupling modes of three filaments in sidebyside arrangement
View Description Hide DescriptionA viscous flow past three filaments in sidebyside arrangement is studied by a numerical simulation and is accompanied by a previously established linear stability analysis. Other than the coupling modes reported previously, which include the inphase mode, symmetrical mode, and outofphase mode, three additional modes are identified in the nonlinear regime by systematically varying the separation distance between the filaments. These modes are the halffrequency mode, irrationalfrequency mode, and erratic flapping state. The dynamic characteristics of each mode at the saturated state is described, including the flapping amplitude, frequency, drag force, and mechanical energy of the filaments. Four typical vortex structures are observed in the wake of the filaments and are described as the coalesced vortices, symmetrical vortices, erratic vortices, and independent vortex streets. The vortex structures are closely related to the coupling modes and the dynamic characteristics of the filaments. As the Reynolds number is increased or as the bending rigidity is reduced, the filaments gain more energy and ordering of the coupling modes may change.
 Interfacial Flows

Shockwave solutions in twolayer channel flow. II. Linear and nonlinear stability
View Description Hide DescriptionWe investigate the flow of two immiscible fluids in an inclined channel, building on the work presented in Part I of this study. In this paper, we examine the stability of the flow to spanwise perturbations in both the linear and nonlinear regimes. The evolution equation governing the interfacial dynamics, derived using lubrication theory in Part I, is linearised to study the effect of system parameters on the linear stability of the interface. A transient growth analysis of the linearised equation is carried out with noflux conditions in the spanwise direction. The results of this analysis reveal that increasing the density and/or the viscosity of the upper layer, and/or increasing the countercurrent nature of the flow configuration exerts a stabilising influence. Inspection of the flow profiles indicates that single Laxshocks and the trailing Laxshocks in Laxundercompressive doubleshocks are unstable to finger formation; undercompressive shocks and rarefaction waves are stable. In unstably stratified cases, increasing the channel inclination away from verticality, such that a denser upper layer overhangs a less dense lower one, is found to be destabilising. These results are used to guide our transient numerical simulations aimed at studying the nonlinear development of fingering phenomena.

Optical interference effect on pattern formation in thin liquid films on solid substrates induced by irradiative heating
View Description Hide DescriptionThe pattern formation in thin liquid films on solid substrates induced by irradiative heating is investigated. A model to describe the evolution of both the filmsurface profile and temperature field in the system is developed, in which the energy absorption into the film and substrate, and the energy reflection to which optical absorption and interference contribute are taken into account. The model consists of a thin filmequation that describes the time evolution of the filmsurface profile and a heat equation for the substrate. The former is obtained within the framework of the longwave approximation, in which the fluid layer is assumed to be sufficiently thin compared to the lateral length scale, while the latter is unconstrained by the substrate thickness. In order to examine the interference effects on the pattern formation, focus is placed on a transparent film/absorbable substrate system irradiated by a monochromatic wave with laterally uniform intensity distribution. In such a case, the energy reflectance varies periodically with the film thickness due to optical interference. Numerical simulation results show that the stability of the film depends on the first derivative of the energy reflectance with respect to the film thickness at a reference point, and the resultant surfacepatterns, which include phase separation and periodic wavy patterns, differ depending on the reference thickness and initial perturbation. The stability revealed by the numerical results is confirmed by linear stability analysis of a simplified model.

Maximum speed of dewetting on a fiber
View Description Hide DescriptionA solid object can be coated by a nonwetting liquid since a receding contact line cannot exceed a critical speed. We theoretically investigate this forced wetting transition for axisymmetric menisci on fibers of varying radii. First, we use a matched asymptotic expansion and derive the maximum speed of dewetting. For all radii, we find the maximum speed occurs at vanishing apparent contact angle. To further investigate the transition, we numerically determine the bifurcation diagram for steady menisci. It is found that the meniscus profiles on thick fibers are smooth, even when there is a filmdeposited between the bath and the contact line, while profiles on thin fibers exhibit strong oscillations. We discuss how this could lead to different experimental scenarios of film deposition.

Molecular dynamics study of the processes in the vicinity of the ndodecane vapour/liquid interface
View Description Hide DescriptionMolecular dynamics (MD) simulation is used to study the evaporation and condensation of ndodecane (C_{12}H_{26}), the closest approximation to Diesel fuel. The interactions in chainlike molecular structures are modelled using an optimised potential for liquid simulation (OPLS). The thickness of the transition layer between the liquid and vapour phases at equilibrium is estimated. It is shown that molecules at the liquid surface need to obtain relatively large translational energy to evaporate. The vapour molecules with large translational energy can easily penetrate deeply into the transition layer and condense in the liquid phase. The evaporation/condensation coefficient is estimated and the results are shown to be compatible with the previous estimates based on the MD analysis and the estimate based on the transition state theory. The velocity distribution functions of molecules at the liquidvapour equilibrium state are found in the liquid phase, interface, and the vapour phase. These functions in the liquid phase and at the interface are shown to be close to isotropic Maxwellian for all velocity components. The velocity distribution function in the vapour phase is shown to be close to biMaxwellian with the temperature for the distribution normal to the interface being larger than the one for the distribution parallel to the interface.
 Viscous and NonNewtonian Flows

Secondary breakup of coal water slurry drops
View Description Hide DescriptionTo investigate secondary atomization of coal water slurry (CWS), deformation and breakup of eight kinds of CWS drops are presented using high speed digital camera. Based on morphology, deformation and breakup regimes of CWS drops can be termed some different modes: deformation, multimode breakup (including two submodes: hole breakup and tensile breakup), and shear breakup. Correlations on the ranges of breakup modes are also obtained. The conventional Weber number and Ohnesorge number are found to be insufficient to classify all breakup modes of CWS drops, so two other nondimensional numbers based on rheology of CWS are suggested to use in the deformation and breakup regime map. Finally, total breakup time is studied and correlated, which increases with Ohnesorge number.
 Particulate, Multiphase, and Granular Flows

Experimental investigation of the propagation of a planar shock wave through a twophase gasliquid medium
View Description Hide DescriptionWe conducted a series of shock tube experiments to study the influence of a cloud of water droplets on the propagation of a planar shock wave. In a vertically oriented shock tube, the cloud of droplets was released downwards into the air at atmospheric pressure while the shock wave propagated upwards. Two shock waveMach numbers, 1.3 and 1.5, and three different heights of clouds, 150 mm, 400 mm, and 700 mm, were tested with an airwater volume fraction and a droplet diameter fixed at 1.2% and 500 μm, respectively. From highspeed visualization and pressure measurements, we analyzed the effect of water clouds on the propagation of the shock wave. It was shown that the pressure histories recorded in the twophase gasliquid mixture are different from those previously obtained in the gassolid case. This different behavior is attributed to the process of atomization of the droplets, which is absent in the gassolid medium. Finally, it was observed that the shock waveattenuation was dependent on the exchange surface crossed by the shock combined with the breakup criterion.

Rheology of binary granular mixtures in the dense flow regime
View Description Hide DescriptionWe study the rheology of granular mixtures in a steady, fully developed, gravitydriven flow on an inclined plane, by means of discrete element method (DEM) simulations. Results are presented for a single component system and binary mixtures with particles of different size and density. Inclination angles, composition, size ratios and density ratios are varied to obtain different segregated configurations at equilibrium. Steady state profiles of the mean velocity, volume fractions, shear stress, shear rate, inertial number and apparent viscosity across the depth of the flowing layer are reported for the different cases. The viscosity varies with height and is found to depend on the local bulk density and composition, which, in turn, depend on the size ratio, the mass ratio and the degree of segregation. For a single component system, a viscoplastic rheological model [P. Jop et al., Nature 441, 727 (2006)] describes the data quite well. We propose a modification of the model for the case of mixtures. The mixture model predicts the viscosity for both wellmixed and segregated granular mixtures differing in size, density or both, using the same model parameters as obtained for the single component system. The predictions of a model for the volume fraction of the mixtures also agree well with simulation results.

Simulations of granular bed erosion due to laminar shear flow near the critical Shields number
View Description Hide DescriptionDirect numerical simulations of granular beds consisting of uniformly sized spherical particles being eroded by a shear flow of Newtonian liquid have been performed. The latticeBoltzmann method has been used for resolving the flow of the interstitial liquid. Fluid and solid dynamics are fully coupled with the particles having finite size and undergoing hardsphere collisions. Only laminar flow has been considered with particlebased Reynolds numbers in the range 0.02 to 0.6. The parameter range of the simulations covers the transition between static and mobilized beds. The transition occurs for with the Shields number. The transition is insensitive of the Reynolds number and the solidoverliquid density ratio. Incipient bed motion has been interpreted in terms of the probability density functions of the hydrodynamic forces acting on the spheres in the upper layer of the bed.

Acceleration statistics of solid particles in turbulent channel flow
View Description Hide DescriptionDirect numerical simulations (DNS) are used here to study inertial particle acceleration statistics in the nearwall region of a turbulent channel flow. The study is motivated by observations in homogeneous isotropic turbulence (HIT) suggesting that when particle inertia increases, particle acceleration variance decreases due to both particle preferential accumulation and the filtering effect of inertia. In accordance with these studies, the present DNS shows that for increasing inertia, solid particle accelerationprobability density functions(PDFs), scaled by the acceleration rootmeansquare (RMS), depart from that of the fluid. The tails of these PDFs become narrower. However, in turbulent channel flow, as the Stokes number increases up to 5, the streamwise acceleration RMS in the nearwall region increases, while further increase of the Stokes number is characterized by the streamwise acceleration RMS decrease. In parallel, contrary to calculations in homogeneous isotropic turbulence, the conditional acceleration statistics of the fluid seen by the solid particle show that while the vertical and transverse acceleration RMS components remain close to the unconditional fluid acceleration, the longitudinal RMS component is remarkably higher in the near wall region. This feature is more pronounced as the Stokes number is increased. Additionally, the conditional accelerationPDFs overlap almost perfectly with the unconditional fluid PDFs, normalized by the acceleration RMS. The enhanced longitudinal acceleration variance of the fluid seen by the particles may be due to the spanwise alternation of highandlow speed streaks. Depending on inertia, particles may respond to those fluid solicitations (experiencing an increase of the longitudinal acceleration RMS) or ignore the wall turbulent structures (presenting in that case a more homogeneous concentration).
 Laminar Flows

A study of similarity solutions for laminar swirling axisymmetric flows with both buoyancy and initial momentum flux
View Description Hide DescriptionUsing an asymptotic approach, the established similarity solution for a plume is extended to the case of a plume with a small amount of angular momentum flux. Numerical simulations of laminar flows are performed in order to verify the similarity solution and to further examine the behavior of plumes with and without swirl and to compare with those of jets and swirling jets. Vortex breakdown of jets and plumes is explored, and an analytical estimate for the critical swirl in plumes is obtained, which compares well with the simulation results. A comparison is made between vortex breakdown in jets, where vortex breakdown destroys the jetlike behavior, and plumes, where vortex breakdown has a weak effect and the flow continues to have plumelike behavior. Simulation results of buoyant jets and injected plumes are presented, and the behavior of vortex breakdown of these hybrid flows is discussed in reference to the pure cases.

Asymptotic properties of wallinduced chaotic mixing in point vortex pairs
View Description Hide DescriptionThe purpose of this work is to analyze the flow due to a potential point vortex pair in the vicinity of a symmetry line (or “wall”), in order to understand why the presence of the wall, even far from the vortices, accelerates fluid mixing around the vortex pair. An asymptotic analysis, in the limit of large distances to the wall, allows to approximate the wall effect as a constant translation of the vortex pair parallel to the wall, plus a straining flow which induces a natural blinking vortex mechanism with period half the rotation period. A Melnikov analysis of lagrangian particles, in the frame translating and rotating with the vortices, shows that a homoclinic bifurcation indeed occurs, so that the various separatrices located near the vortex pair (and rotating with it) do not survive when a wall is present. The thickness of the resulting inner stochastic layer is estimated by using the separatrix map method and is shown to scale like the inverse of the squared distance to the wall. This estimation provides a lowerbound to the numerical thickness measured from either Poincaré sections or simulations of lagrangian particles transported by the exact potential velocity field in the laboratory frame. In addition, it is shown that the outer homoclinic cycle, separating the vortices from the external (open) flow, is also perturbed from inside by the rotation of the vortex pair. As a consequence, a stochastic layer is shown to exist also in the vicinity of this cycle, allowing fluid exchange between the vortices and the outer flow. However, the thickness of this outer stochastic zone is observed to be much smaller than the one of the inner stochastic zone near vortices, as soon as the distance to the wall is large enough.
 Instability and Transition

Resonant three–wave interaction of Holmboe waves in a sharply stratified shear flow with an inflection–free velocity profile
View Description Hide DescriptionWithin the context of the wellknown interpretation in terms of the wave interaction [P. G. Baines and H. Mitsudera, J. Fluid Mech. 276, 327 (1994); J. R. Carpenter et al., Phys. Fluids 22, 054104 (2010)], instability of sharply stratified (so that the vertical scale ℓ of density variation is much smaller than the scale Λ of velocity shear) flows with inflectionfree velocity profiles should be treated as Holmboe’s instability. In such flows with a relatively weak stratification (when the bulk Richardson number J < (ℓ/Λ)^{3/2}), eigenoscillations (i.e., Holmboe waves) have much the same phase velocities in a broad spectral range. This creates favorable conditions for a wide variety of threewave interactions, in contrast to the homogeneous boundary layers where subharmonic resonance is the only effective threewave process. In the paper, evolution equations are derived which describe threewave interactions of Holmboe waves and have the form of nonlinear integral equations. Analytical and numerical methods are both used to find their solutions in different cases, and it is shown that at the nonlinear stage disturbances increase, as a rule, explosively. Some possible relations of the results obtained with those of numerical simulations and laboratory experiments are briefly discussed.