Volume 19, Issue 1, January 2007
 ANNOUNCEMENTS


Announcement: The 2006 François Naftali Frenkiel Award for Fluid Mechanics
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 LETTERS


Bimodal vortex shedding in a perturbed cylinder wake
View Description Hide DescriptionCylinder wakes display distinct modes of vortex shedding when perturbed by appropriate means. By investigating experimentally the wake of a circular cylinder perturbed by a periodic fluctuation imposed on the inflow velocity, it is shown that bimodal behavior is possible. During a given experiment, the wake switches back and forth between two different vortex shedding modes, more specifically, a 2S2P transition is observed. No discernible change in the timing of vortex formation is found to accompany the transition. Modal decomposition of the velocity field is employed to exemplify the interaction of the imposed symmetrical perturbation and the intrinsic antisymmetrical instability of the near wake.

Breakdown of ChapmanEnskog expansion and the anisotropic effect for latticeBoltzmann models of porous flow
View Description Hide DescriptionLatticeBoltzmann based models are frequently used to study fluid flow in porous media. The macroscopic governing equations as well as the viscosity and the permeability for such models are usually determined using a ChapmanEnskog expansion approach. However, this approach has been validated numerically only for a narrow range of the viscosity and the permeability. We have analytically derived the exact macroscopic governing equations of the latticeBoltzmann model for the case of simple shear flows in porous media. We find that the effective viscosity in the governing equations is different from the one obtained from the ChapmanEnskog expansion. These findings have been validated numerically. We also find that the effective viscosity is anisotropic. Implications for modeling flow in porous media are discussed.

Lagrangian velocity structure functions in Bolgiano turbulence
View Description Hide DescriptionSingleparticle Lagrangian velocity statistics in the Bolgiano–Obukhov regime of twodimensional turbulent convection is investigated. At variance with flows displaying the classical K41 phenomenology, here the leading contribution to the Lagrangian velocity fluctuations is given by the largest eddies. This implies a linear behavior in time for a typical velocity fluctuation in the time interval . The contribution to the Lagrangian velocity fluctuations of local eddies (i.e., with a characteristic time of order ), whose space/time scalings are ruled by the Bolgiano–Obukhov theory, is thus not detectable by standard Lagrangian statistical observables. To disentangle contributions arising from the large eddies from those of local eddies, a strategy based on exittime statistics has successfully been exploited. Lagrangian velocity increments in Bolgiano convection thus provide a physically relevant example of a signal with more than smooth fluctuations.
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 ARTICLES

 Interfacial Flows

An energy balance approach of the dynamics of drop impact on a solid surface
View Description Hide DescriptionThe description of physical mechanisms involved in the impact of a drop upon a dry, partially wettable substrate is still a matter of debate. One way to analyze the balance of these mechanisms is the development of an analytical onedimensional (1D) model based upon the energy equation. The assimilation of the drop to a cylinder allows a reduction of the energy equation to a secondorder differential equation. This paper proposes a semiempirical description of viscous dissipation taking into account the rolling motion near the contact line. The dissipation due to the rolling motion is added to the calculated dissipation in the core of the droplet. We compare our model to previous ones using a large set of literature data covering a wide range of viscosity, velocity impact, and equilibrium contact angle values. The new dissipation description proposed is shown to supersede those described in previous 1D models. Our model closely predicts the maximum spread factor and the time at which it is obtained on the whole range of Ohnesorge and Weber numbers considered. It also distinguishes between deposition with a steady variation in the wetted area from deposition with advancing and receding phases. The main limitations of the model lie in its inability to reproduce the spread factor at the very beginning of the impact and the rebounding observed after a receding phase for very high values of the equilibrium contact angle.

Stationary coaxial electrified jet of a dielectric liquid surrounded by a conductive liquid
View Description Hide DescriptionThe electrohydrodynamic problem describing the evolution of a coaxial jet of two immiscible Newtonian liquids injected through concentric orifices into a region of uniform electric field is formulated in the framework of the leaky dielectric model, and the dimensionless parameters governing the flow are identified. A simplified model is proposed combining a quasiunidirectional approximation for the flow and the transport of electric charge with a fully numerical evaluation of the electric field. Results of this model are compared with boundary element solutions of the full governing equations for viscositydominated flows. The current/flow rate characteristic of a coaxial viscositydominated jet is computed and the ranges of flow rates in which a stationary axisymmetric jet is realized are discussed in the case of an outer liquid of finite electrical conductivity surrounding a dielectric liquid, in which the electric shear that stretches the jet is concentrated at its outer surface. The dependence of the flow on the applied electric field and the flow rates of the liquids, as well as the effects of the viscosity and electrical conductivity of the inner liquid, and of the surface tension of the inner surface, are discussed.

Dynamic wetting of shear thinning fluids
View Description Hide DescriptionThe impact of nonNewtonian behavior on dynamic wetting is critical since many fluids exhibit such behavior somewhere in the highshear environment inherent in the wedge flow near a moving contact line. This impact will be different for two broad categories of nonNewtonian behavior, shear thinning, and elasticity. In this paper, we discuss the steadystate wetting of a fluid, aqueous solutions of xanthan gum, dominated by shear thinning but with negligible elasticity. In the shear thinning fluid, viscous bending near the contact line is greatly reduced compared to a Newtonian fluid having the same zeroshear viscosity. Concomitant with this reduction in viscous bending, the effective dynamic contact angle has a much weaker dependence on capillary number, Ca, than is observed in, or predicted for, Newtonian fluids. A simple lubrication model using a constitutive relation with powerlaw shear thinning at high shear rates and a Newtonian plateau at low shear rates mimics the trends seen in our data and elucidates the origins of the reduced viscous bending.

Mechanisms of freesurface breakup in vibrationinduced liquid atomization
View Description Hide DescriptionThe mechanisms of dropletformation that take place during vibrationinduced drop atomization are investigated experimentally. Droplet ejection results from the breakup of transient liquid spikes that form following the localized collapse of freesurface waves. Breakup typically begins with capillary pinchoff of a droplet from the tip of the spike and can be followed by additional pinchoffs of satellite droplets if the corresponding capillary number is sufficiently small (e.g., in lowviscosity liquids). If the capillary number is increased (e.g., in viscousliquids), breakup first occurs near the base of the spike, with or without subsequent breakup of the detached, threadlike spike. The formation of these detached threads is governed by a breakup mechanism that is separated from the tipdominated capillary pinchoff mechanism by an order of magnitude in terms of dimensionless driving frequency . The dependence of breakup time and unbroken spike length on fluid and driving parameters is established over a broad range of dimensionless driving frequencies . It is also shown that the dropletejection acceleration threshold of lowviscosity liquids depends on the dimensionless drop diameter . Moreover, in the limit , the dropletejection threshold becomes independent of . This limit state is described by a scaling equivalent to that of Goodridge, Shi, and Lathrop [Phys. Rev. Lett.76, 1824 (1996)] derived for the onset of droplet ejection from Faraday waves. It is shown in the present study that the acceleration threshold in this limit scales like .

Deformations of thin liquid spherical shells in liquidliquidgas systems
View Description Hide DescriptionDeformation characteristics of a millimetersized thin liquid spherical shell moving at intermediate Reynolds numbers in immiscible liquid are investigated both numerically and experimentally. Experiments are made using the novel principle of sequential production of the shell developed by the authors. Numerical results of the flow pattern around the liquid shell, deformation ratio, and the drag coefficient are compared to experimental results for wide flow conditions. They are in reasonable agreement from the viewpoint of practical engineering. Furthermore, effects of shell deformation on heat transfercharacteristics are also investigated numerically. The present research provides the fluid dynamical knowledge for various applications of liquid spherical shells.

Direct simulation of film boiling including electrohydrodynamic forces
View Description Hide DescriptionThis paper presents simulations of film boiling including electrohydrodynamic forces. The coupled levelset and volumeoffluid interface tracking method is augmented with a mass transfer model, a model for surface tension, and electrohydrodynamic force terms. The bulk fluids are perfect dielectrics—viscous, heat conducting, and incompressible. We explore film boiling on a horizontal surface and we consider the effect of an applied electric potential. The electrodynamic equation for the evolving electric field is solved in both phases during saturated horizontal film boiling, and the effects are described.
 Viscous and NonNewtonian Flows

Twodimensional and threedimensional direct numerical simulation of corotating vortices
View Description Hide DescriptionTwodimensional (2D) and threedimensional (3D) simulations are presented for corotating vortices with distributed vorticity at different values of the separation distance . The ratio between the vortices’ radius and is smaller than the critical value for merging in inviscid conditions of blobs of constant vorticity. The dependence of merging on Reynolds number and on has been investigated in 2D simulations. In 2D the resolution can be increased to perform simulations at when very long filaments are generated. These simulations confirm the findings of Brandt and Nomura [L. K. Brandt and K. K. Nomura, Phys. Fluids18, 51701 (2006)] that the filaments play a minor role in merging. It has been found that a large increase of ( is the pressure) indicates merging. Time evolving 3D simulations at , are similar to the laboratory experiments by Meunier and Leweke [P. Meunier and T. Leweke, J. Fluid Mech.533, 125 (2005)]. At the same values of as used in 2D, 3D simulations demonstrate that the merging is more complex than in 2D, and that it largely depends on the kind of axial disturbances imposed, at , on the two vortices. 3D simulations of vortices evolving in space and time, without disturbances at , have shown that at the results, in a convective frame, do not differ from those in 2D simulations. This assumption, attempting to reproduce the evolution of the vortices behind aircrafts, demonstrates that, with the present computational resources, DNS at practical Reynolds numbers are not feasible.

Threedimensional chaotic mixing inside drops driven by a transient electric field
View Description Hide DescriptionWe numerically study the threedimensional (3D) chaotic trajectories inside a neutrally buoyant drop driven by periodically switching a uniform electric field through an angle . Periodically switching the field is equivalent to periodically alternating the direction of the interfacial electric force; thus, symmetries of the steady Taylor circulation are broken and 3D chaotic advection is generated inside the drop. The extent of the chaotic mixing is related to two parameters: the switching angle and modulation period . The parametric dependence of mixing is investigated by tracing trajectories of Lagrangian particles. Analysis shows that depending on the range of there are either four or eight center fixed points (CFPs), around which invariant surfaces exist and chaotic mixing is suppressed. Our calculations of the mixed volume fraction and Lyapunov exponents suggest an optimal range of for best mixing. For a given , by varying modulation period , we find that a resonant phenomena may occur, and global uniform mixing is possible. Therefore, the numerical results suggest optimum operation conditions for our future experiments.
 Particulate, Multiphase, and Granular Flows

Simulation of slowly dragging a cylinder through a confined pressurized bed of granular materials using the discrete element method
View Description Hide DescriptionA nonlinear spring dash pot model to describe the interaction forces between confined granules under high pressures based on Hertz contact theory is proposed. The discrete element method (DEM) is used to simulate the movement and calculate the normal and tangential contact forces among the granules when a cylinder is dragged through a granular bed at low velocities. The timedependent, total drag force required to pull the circular cylinder is also calculated and used to compare the effect of material and boundary conditions on flow behavior. Simulation results show that drag force increases with cylinder diameter, granular volume fraction, granular size, and the friction coefficient between granules. Drag force was found to be independent of the velocity of the cylinder at low speed, the friction coefficient between the granules and the cylinder, and the friction coefficient between the granules and the container walls.
 Laminar Flows

Flow and species transport control in grooved microchannels using local electrokinetic forces
View Description Hide DescriptionWe present numerical simulation results for flow and species transport control in grooved microchannels using locally applied electric fields, and zeta potential patterned groove surfaces. The resulting mixed electroosmotic/pressuredriven flow enables entrapment and release of prescribed amounts of scalar species in the grooves. The groove size and shape determine the volume of the entrapped species. Depending on the local electric field and zeta potential, each groove can simultaneously contain up to two species. This framework allows control over the interspecies diffusion and mixing using simple flow kinematics, and it is easily applicable for electrically neutral species. We envision utilization of this technique for combinatorial chemistry experiments in a microchannel with multiple grooves, where each groove can be addressed (filled, emptied, or mixed) independently. Alternatively, the technique can be used for electronic cooling, where the grooves increase heat transfer surface area without the adverse effects of recirculating flowpattern.

Dynamics of free jets submitted to upstream acoustic modulations
View Description Hide DescriptionThe response of low Reynolds number air jets to acoustic modulations is investigated with systematic experiments. Flow transfer functions, power spectral densities of the perturbations plotted in the form of spacefrequency maps, instantaneous jet images recorded using laser tomography, and phaseconditioned velocity fields serve to identify the different regimes of motion. Results indicate that five regions can be distinguished in a diagram where the jet Strouhal number serves as a horizontal coordinate while the shear layer Strouhal number constitutes the vertical coordinate. Boundaries of the different regions are defined by the characteristic values of these two dimensionless groups at preferred mode and neutral wave conditions, corresponding, respectively, to a maximum of amplification and a vanishing rate of growth. The forcing frequencies imparted to the flow can be ordered with respect to these characteristic parameters. The flow transfer functions at the excitation frequency indicate that perturbations have a different nature depending on the value of the jet Strouhal number based on the exhaust diameter . Convective, mixed type, and acoustic ranges are identified. Detailed measurements of the spatial evolution of the forced components and corresponding harmonics provide information on the nonlinear power transfer between the different modes for modulation amplitudes reaching 10% of the mean flowvelocity. The mapping is used to categorize the various modes of interaction observed in the experiments.

Induction and measurement of minute flow rates through nanopipes
View Description Hide DescriptionA simple technique to simultaneously induce fluid flow through an individual nanopipe and measure the flow rate and the pressure difference across the pipe is described. Two liquiddrops of different sizes are positioned at the two ends of the nanopipe. Due to the higher capillary pressure of the smaller drop,flow is driven from the smaller drop to the bigger drop. The instantaneous pressures of the two drops are estimated from the drops’ shapes and sizes. The flow rate is estimated by monitoring the sizes of the drops as functions of time with a microscope and a video camera. A theory that correlates the drops’ sizes and the flow rate is derived. Measurements are carried out with an ionic salt and glycerin to estimate the effective tube radius of the nanopipes with diameters ranging from 200 to . The tubes’ diameters are independently measured with a scanning electron microscope. The method is also verified by tracking the motion of fluorescent particles through the nanopipe. The paper provides a simple technique for studying extremely low flow rates in nanofluidic systems. When working with lowevaporation fluids such as ionic salts, the measurements can be carried out with an electron microscope.
 Instability and Transition

Direct numerical simulation and the theory of receptivity in a hypersonic boundary layer
View Description Hide DescriptionDirect numerical simulation of receptivity in a boundary layer over a sharp wedge of halfangle is carried out with twodimensional perturbations introduced into the flow by periodicintime blowingsuction through a slot. The freestream Mach number is equal to 8. The perturbationflow field downstream from the slot is decomposed into normal modes with the help of the biorthogonal eigenfunction system. Filteredout amplitudes of two discrete normal modes and of the fast acoustic modes are compared with the linear receptivity problem solution. The examples illustrate how the multimode decomposition technique may serve as a tool for gaining insight into computational results.

Suppression of global modes in lowdensity axisymmetric jets using coflow
View Description Hide DescriptionExperiments conducted in helium axisymmetric jets with an annular coflowing air stream yield critical values of the velocity ratio needed to suppress global instability inherent in these lowdensity flows. Global mode suppression was achieved for coflowing velocities less than approximately 20% of the jet centerline velocity, though the critical velocity ratio displayed a nonmonotonic relationship with the initial shear layer momentum thickness. The experiments are supported by spatiotemporal inviscid stability theory, where the convectiveabsolute transition was tracked in an operating domain including and . For initially thick shear layers, the experimental observations are in good agreement with linear theory, but deviate considerably as the separating shear layer thickness is reduced.

Optimal and robust control of small disturbances in a channel flow with a normal magnetic field
View Description Hide DescriptionActive closedloop control of subcritical and supercritical instabilities amplified in a channel flow submitted to a constant normal magnetic field is investigated. Control is carried out at both the upper and lower walls by blowing and suction (velocity control) or by a perturbation of the normal magnetic field (magnetic control). Even if a velocity control is more efficient than a magnetic one, we found that magnetic control succeeds in stabilizing supercritical instabilities. Development of new actuators using magnetic field for flow control may thus be promising. Closedloop control modifies the optimal perturbation but does not destruct the liftup effect.

Convection in a supercritical fluid: A reduced model for geophysical flows
View Description Hide DescriptionConvection in a fluid, slightly above its gasliquid critical point, is numerically investigated in two configurations where the strong stratification of the fluid—induced by its high compressibility—controls the development and/or the onset of convection: (i) the evolution of a thermal plume in a stable environment where the penetrative convection is found to be blocked by the fluid stratification, and (ii) the convection onset and outset in a supercritical fluid layer according to the Schwarzschild criterion, which usually occurs in the atmosphere when the local temperature gradient exceeds the adiabatic temperature one. Hence, two situations, commonly encountered in largescale geophysical flows, are reproduced in a centimetric cell containing a supercritical fluid.