Volume 21, Issue 5, May 2009

The interaction between planetary waves and an arbitrary zonal flow is studied from a phasespace viewpoint. Using the Wigner distribution, a planetary wave Vlasov equation is derived that includes the contribution of the mean flow to the zonal potential vorticity gradient. This equation is applied to the problem of planetary wave modulational instability, where it is used to predict a fastest growing mode of finite wavenumber. A wavemean flow numerical model is used to test the analytical predictions, and an intuitive explanation of modulational instability and jet asymmetry is given via the motion of planetary wavepackets in phase space.
 LETTERS


Flow behind a cylinder forced by a combination of oscillatory translational and rotational motions
View Description Hide DescriptionThe flow behind a cylinder undergoing forced combined oscillatory motion has been studied. The motion consists of two independent oscillations: crossstream translation and rotation. Previous studies have extensively investigated the effect of these motions individually on cylinder wakes; however, the investigation of their combined effect is new. The motivation lies in its application to vortexinduced vibration and its suppression and to biomimeticmotion. The focus is on the effect of the phase difference between the two motions. The results show that there is an unexpected loss of synchronization of the wake for a finite range of phase differences.

Turbulent boundary layers up to studied through simulation and experiment
View Description Hide DescriptionDirect numerical simulations (DNSs) and experiments of a spatially developing zeropressuregradient turbulent boundary layer are presented up to Reynolds number, based on momentum thickness and freestream velocity. For the first time direct comparisons of DNS and experiments of turbulent boundary layers at the same (computationally high and experimentally low) are given, showing excellent agreement in skin friction, mean velocity, and turbulent fluctuations. These results allow for a substantial reduction of the uncertainty of boundarylayer data, and cross validate the numerical setup and experimental technique. The additional insight into the flow provided by DNS clearly shows largescale turbulent structures, which scale in outer units growing with , spanning the whole boundarylayer height.

Experimental evidence of the kinematic Cosserat effect in dense granular flows
View Description Hide DescriptionTo capture shear localization in the flow of dense granular materials in a continuum description, it has earlier been proposed that granular materials be treated as Cosserat, or micropolar, continua. Here, we provide experimental verification of the kinematic Cosserat effect, or the deviation of the particle spin from the material spin induced by the velocity gradient. Contrary to earlier belief, we find this effect to be sizable even outside the shear layers. Remarkably, the particles and material elements spin in opposite directions in flow through a hopper.

 ARTICLES

 Biofluid Mechanics

Wave propagation and induced steady streaming in viscous fluid contained in a prestressed viscoelastic tube
View Description Hide DescriptionThe oscillatory and timemean motions induced by a propagating wave of small amplitude through a viscous incompressible fluid contained in a prestressed and viscoelastic (modeled as a Voigt material) tube are studied by a perturbation analysis based on equations of motion in the Lagrangian system. The classical problem of oscillatory viscousflow in a flexible tube is reexamined in the contexts of blood flow in arteries or pulmonary gas flow in airways. The wave kinematics and dynamics, including wavenumber, wave attenuation, velocity, and stress fields, are found as analytical functions of the wall and fluid properties, prestress, and the Womersley number for the cases of a free or tethered tube. On extending the analysis to the second order in terms of the small wave steepness, it is shown that the timemean motion of the viscoelastic tube with sufficient strength is short lived and dies out quickly as a limit of finite deformation is approached. Once the tube has attained its steady deformation, the steady streaming in the fluid can be solved analytically. Results are generated to illustrate the combined effects on the firstorder oscillatory flow and the secondorder steady streaming due to elasticity,viscosity, and initial stresses of the wall. The present model as applied to blood flow in arteries and gas flow in pulmonary airways during highfrequency ventilation is examined in detail through comparison with models in the literature.
 Micro and Nanofluid Mechanics

Time dependence of effective slip on textured hydrophobic surfaces
View Description Hide DescriptionIn this paper, we present results on waterflow past randomly textured hydrophobicsurfaces with relatively large surface features of the order of . Direct shear stress measurements are made on these surfaces in a channel configuration. The measurements indicate that the flow rates required to maintain a shear stress value vary substantially with water immersion time. At small times after filling the channel with water, the flow rates are up to 30% higher compared with the reference hydrophilicsurface. With time, the flow rate gradually decreases and in a few hours reaches a value that is nearly the same as the hydrophilic case. Calculations of the effective slip lengths indicate that it varies from about at small times to nearly zero or “no slip” after a few hours. Large effective slip lengths on such hydrophobicsurfaces are known to be caused by trapped air pockets in the crevices of the surface. In order to understand the time dependent effective slip length, direct visualization of trapped air pockets is made in stationary water using the principle of total internal reflection of light at the waterair interface of the air pockets. These visualizations indicate that the number of bright spots corresponding to the air pockets decreases with time. This type of gradual disappearance of the trapped air pockets is possibly the reason for the decrease in effective slip length with time in the flow experiments. From the practical point of usage of such surfaces to reduce pressure drop, say, in microchannels, this time scale of the order of 1 h for the reduction in slip length would be very crucial. It would ultimately decide the time over which the surface can usefully provide pressure drop reductions.

Huge reduction in pressure drop of water, glycerol/water mixture, and aqueous solution of polyethylene oxide in high speed flows through microorifices
View Description Hide DescriptionMicrofluid mechanics is one of the most exciting research areas in modern fluid mechanics and fluid engineering because of its many potential industrial and biological applications. In the present study, pressure drops (PDs) were measured for water, a 50/50 glycerol/water mixture, and a 0.1% aqueous solution of polyethylene oxide (PEO) 8000 flowing at high velocities through various sizes of microorifice. It was found that the measured PD of water and the glycerol/water mixture agrees with the prediction of the Navier–Stokes equation for orifices 100 and in diameter, but it is lower for orifices less than in diameter. In particular, the measured maximum PD was almost two orders of magnitude lower than the prediction for the 10 and diameter orifices. The glycerol/water mixture, possessing a viscosity ten times higher than water, provided nearly the same PDs as water when the reduction was generated. The solution of PEO produced a lower PD than water and the glycerol/water mixture except for the diameter orifice. Several factors, including orifice shape, deformation of orifice foil, wall slip, transition,cavitation, and elasticity were considered but the evidence suggests that the reduction in PD may be caused by wall slip or the elasticity induced in a flow of high elongational rate.

Gravitydriven slug motion in capillary tubes
View Description Hide DescriptionThe velocity of a liquid slug falling in a capillary tube is lower than predicted for Poiseuille flow due to presence of menisci, whose shapes are determined by the complex interplay of capillary, viscous, and gravitational forces. Due to the presence of menisci, a capillary pressure proportional to surface curvature acts on the slug and streamlines are bent close to the interface, resulting in enhanced viscous dissipation at the wedges. To determine the origin of dragforce increase relative to Poiseuille flow, we compute the force resultant acting on the slug by integrating Navier–Stokes equations over the liquid volume. Invoking relationships from differential geometry we demonstrate that the additional drag is due to viscous forces only and that no capillary drag of hydrodynamic origin exists (i.e., due to hydrodynamic deformation of the interface). Requiring that the force resultant is zero, we derive scaling laws for the steady velocity in the limit of small capillary numbers by estimating the leading order viscous dissipation in the different regions of the slug (i.e., the unperturbed Poiseuillelike bulk, the static menisci close to the tube axis and the dynamic regions close to the contact lines). Considering both partial and complete wetting, we find that the relationship between dimensionless velocity and weight is, in general, nonlinear. Whereas the relationship obtained for completewetting conditions is found in agreement with the experimental data of Bico and Quéré [J. Bico and D. Quéré, J. Colloid Interface Sci.243, 262 (2001)], the scaling law under partialwetting conditions is validated by numerical simulations performed with the Volume of Fluid method. The simulated steady velocities agree with the behavior predicted by the theoretical scaling laws in presence and in absence of static contact angle hysteresis. The numerical simulations suggest that wedgeflow dissipation alone cannot account for the entire additional drag and that the nonPoiseuille dissipation in the static menisci (not considered in previous studies) has to be considered for large contact angles.

Chaotic mixing in electroosmotic flows driven by spatiotemporal surface charge modulation
View Description Hide DescriptionThis paper presents an investigation into chaotic mixing in an electroosmotic flow through a microchannel. In the mixing system, the continuous throughput flow has the form of a pluglike electroosmotic flow induced by a permanent surface charge on the wall surface, while electroosmotic flows contributed by spatiotemporal surface charge variations act as a perturbed flow. The spatiotemporal surface charge variations are achieved using the fieldeffect control method. The analyses consider two different spatiotemporal surface charge modulation schemes, designated as “MS I” and “MS II,” respectively. It is shown that both modulation schemes prompt the crossing of the flow streamlines at different instances in time and produce a chaotic mixing effect. Utilizing the thin double layer assumption, the study commences by solving the biharmonic equation for the electroosmotic flow fields analytically. The mixing phenomena induced by the two modulation schemes are then analyzed using the Lagrangian particle tracing method. Finally, the mixing performances of the two schemes are evaluated analytically using the Poincaré section method, the finitetime Lyapunov exponent (FTLE) technique, and a stretching value distribution analysis method, respectively. It is found that the mean FTLE combined with the coefficient of variance of the FTLE distribution provides the most suitable criterion for obtaining quantitative estimates of the mixing performance and therefore provides a feasible means of estimating the amplitude and timeswitching period of the perturbed flows which optimize the mixing performance. The validity of the analytical results is confirmed via a comparison with the results obtained from the backtrace imaging method and direct numerical simulations based on a species convectiondiffusion equation, respectively. In addition, the direct numerical simulation results show that the dimensionless mixing length and dimensionless mixing time required to achieve a 90% mixing both vary as a logarithmic function of the Péclet number when the mixing system is in a nearly fully chaotic state.

Rarefied gas flow in microtubes at different inletoutlet pressure ratios
View Description Hide DescriptionA model is developed for rarefied gasflow in long microtubes with different inletoutlet pressure ratios at low Mach numbers. The model accounts for significant changes in Knudsen number along the length of the tube and is therefore applicable to gas flow in long tubes encountering different flow regimes along the flow length. Predictions from the model show good agreement with experimental measurements of mass flow rate, pressure drop, and inferred streamwise pressure distribution obtained under different flow conditions and offer a better match with experiments than do those from a conventional slip flowmodel.
 Interfacial Flows

Evaporation of a thin droplet on a thin substrate with a high thermal resistance
View Description Hide DescriptionA mathematical model for the quasisteady evaporation of a thin liquid droplet on a thin substrate that incorporates the dependence of the saturation concentration of vapor at the free surface of the droplet on temperature is used to examine an atypical situation in which the substrate has a high thermal resistance relative to the droplet (i.e., it is highly insulating and/or is thick relative to the droplet). In this situation diffusion of heat through the substrate is the ratelimiting evaporative process and at leading order the local mass flux is spatially uniform, the total evaporation rate is proportional to the surface area of the droplet, and the droplet is uniformly cooled. In particular, the qualitative differences between the predictions of the present model in this situation and those of the widely used “basic” model in which the saturation concentration is independent of temperature are highlighted.

Sloshing of a layered fluid with a free surface as a Hamiltonian system
View Description Hide DescriptionThe aim of this paper is the investigation of a layered sloshing fluid system using both a new Hamiltonian mathematical model and new laboratory experiments. The mathematical model is defined for a cylindrical tank with an arbitrary shape and subjected to an arbitrary rigid motion. The model consists of a pure evolution system of partial differential first order equations in the canonical four unknowns: water elevation at the upper free surface and at the separation surface and the gap in momentum potential density computed at each fluid surface. The system of equations is obtained by avoiding the construction of the Hamiltonian and its variational derivatives. An important advantage of this formulation, with respect to the Lagrangian formulation, is that the nonevolution constraint, which imposes for each fluid the same velocity component along the normal direction of the separation surface, is fulfilled by the model itself. The model implementation needs to define the socalled Neumann–Dirichlet operators, which are computed by an efficient algorithm, for any instantaneous configuration of the two fluid domains. A numerical integration of the model is performed by a suitable Galerkin projection of the evolution equations. New laboratory experiments, simulating the sloshing of a layered fluid system, inside a tank with a squared cross section, were performed. The experiments, with a twodimensional sloshing, were carried out by varying the forcing frequency, the oscillation amplitude and the ratio of the two fluids’ depths. In some experiments, a traveling wave, with a shape similar to a moving hydraulic jump, was observed at the separation surface. Measurements of the spacetime evolution of both the free and the separation surfaces were performed and compared with the model’s predictions. A good agreement between the model predictions and laboratory measurements is found, even for strong nonlinear cases such as the traveling wave.

Inertia dominated drop collisions. I. On the universal flow in the lamella
View Description Hide DescriptionThis study is devoted to the analysis of inertia dominated axisymmetric drop collisions with a dry substrate or with another liquid drop. All the previous theoretical and semiempirical models of drop collisions are based on the assumption that the flow in the lamella and its thickness are determined by the impact conditions, mainly by the Reynolds and Weber numbers. In this study the existing experimental data are compared to existing and new numerical simulations for the shape of the lamella generated at the early times of drop impact for various impact conditions. The results show that if the Reynolds and Weber numbers are high enough, the evolution of the lamella thickness almost does not depend on the viscosity and surface tension. Therefore these results completely change our understanding of the flow generated by drop collisions. Moreover, we demonstrate that the theoreticalmodels based on the approximation of the shape of the deforming drop by a disk and the models based on the energy balance approach are not correct. Finally, universal dimensionless distributions for the lamella thickness, velocity, and pressure are obtained from the numerical simulations of drop impact onto a symmetry plane (associated with the binary drop collisions). These universal distributions are valid for high impact Weber and Reynolds numbers.

Inertia dominated drop collisions. II. An analytical solution of the Navier–Stokes equations for a spreading viscous film
View Description Hide DescriptionThis study is devoted to a theoretical description of an unsteady laminar viscousflow in a spreading film of a Newtonian fluid. Such flow is generated by normal drop impact onto a dry substrate with high Weber and Reynolds numbers. An analytical selfsimilar solution for the viscousflow in the spreading drop is obtained which satisfies the full Navier–Stokes equations. The characteristic thickness of a boundary layer developed near the wall uniformly increases as a square root of time. An expression for the thickness of the boundary layer is used for the estimation of the residual film thickness formed by normal drop impact and the maximum spreading diameter. The theoretical predictions agree well with the existing experimental data. A possible explanation of the mechanism of formation of an uprising liquid sheet leading to splash is also proposed.

The effective slip length and vortex formation in laminar flow over a rough surface
View Description Hide DescriptionThe flow of viscous incompressible fluid over a periodically corrugated surface is investigated numerically by solving the Navier–Stokes equation with the local slip and noslip boundary conditions. We consider the effective slip length which is defined with respect to the level of the mean height of the surface roughness. With increasing corrugation amplitude the effective noslip boundary plane is shifted toward the bulk of the fluid, which implies a negative effective slip length. The analysis of the wall shear stress indicates that a flow circulation is developed in the grooves of the rough surface provided that the local boundary condition is noslip. By applying a local slip boundary condition, the center of the vortex is displaced toward the bottom of the grooves and the effective slip length increases. When the intrinsic slip length is larger than the corrugation amplitude, the flow streamlines near the surface are deformed to follow the boundary curvature, the vortex vanishes, and the effective slip length saturates to a constant value. Inertial effects promote vortexflow formation in the grooves and reduce the effective slip length.

Nonlinear regimes of anticonvection, thermocapillarity, and Rayleigh–Benard convection in twolayer systems
View Description Hide DescriptionThe nonlinear regimes of anticonvection and Rayleigh–Benard convection in a twolayer system with periodic boundary conditions on lateral walls in the presence of the interfacial heat release are studied. The region where anticonvective and the Rayleigh–Benard instability mechanisms act simultaneously is considered. The influence of the thermocapillary effect on anticonvective and Rayleigh–Benard flows, is investigated. New types of nonlinear traveling waves and modulated traveling waves are found.

Characterization of string cavitation in largescale Diesel nozzles with tapered holes
View Description Hide DescriptionThe cavitation structures formed inside enlarged transparent replicas of tapered Diesel valve covered orifice nozzles have been characterized using high speed imaging visualization. Cavitation images obtained at fixed needle lift and flow rate conditions have revealed that although the conical shape of the converging tapered holes suppresses the formation of geometric cavitation, forming at the entry to the cylindrical injection hole, string cavitation has been found to prevail, particularly at low needle lifts. Computational fluid dynamics simulations have shown that cavitation strings appear in areas where largescale vortices develop. The vortical structures are mainly formed upstream of the injection holes due to the nonuniform flow distribution and persist also inside them. Cavitation strings have been frequently observed to link adjacent holes while inspection of identical realsize injectors has revealed cavitation erosion sites in the area of string cavitation development. Image postprocessing has allowed estimation of their frequency of appearance, lifetime, and size along the injection hole length, as function of cavitation and Reynolds numbers and needle lift.
 Viscous and NonNewtonian Flows

Abrupt contraction flow of magnetorheological fluids
View Description Hide DescriptionContraction and expansion flows of magnetorheological fluids occur in a variety of smart devices. It is important therefore to learn how these flows can be controlled by means of applied magnetic fields. This paper presents a first investigation into the axisymmetric flow of a magnetorheological fluid through an orifice (socalled abrupt contraction flow). The effect of an external magnetic field, longitudinal or transverse to the flow, is examined. In experiments, the pressureflow rate curves were measured, and the excess pressure drop (associated with entrance and exit losses) was derived from experimental data through the Bagley correction procedure. The effect of the longitudinal magnetic field is manifested through a significant increase in the slope of the pressureflow rate curves, while no discernible yield stress occurs. This behavior, observed at shear Mason numbers , is interpreted in terms of an enhanced extensional response of magnetorheological fluids accompanied by shrinkage of the entrance flow into a conical funnel. At the same range of Mason numbers, the transverse magnetic field appears not to influence the pressure drop. This can be explained by a total destruction of magnetic particle aggregates by large hydrodynamic forces acting on them when they are perpendicular to the flow. To support these findings, we have developed a theoretical model connecting the microstructure of the magnetorheological fluid to its extensional rheological properties and predicting the pressureflow rate relations through the solution of the flow equations. In the case of the longitudinal magnetic field, our model describes the experimental results reasonably well.

Dissipation in quasitwodimensional flowing foams
View Description Hide DescriptionThe dissipation between twodimensional (2D) monolayers of bubbles, the socalled quasi2D foams, and a wall is investigated in two setups: a “liquid pool” system, where the foam is confined between a soap solution and a glass coverslip, and a HeleShaw cell, where the foam occupies the narrow gap between two plates. This experimental study reports dissipation measurements for mobile gas/liquid interfaces (free shear boundary condition) over a large range of parameters: in the liquid pool system, velocity and bubble area; in the HeleShaw cell, velocity and liquid fraction. The effect of the latter quantity is measured for the first time over more than three orders of magnitude. A full comparison between our results and other experimental studies is proposed and enables to rescale all measurements on a single master curve. It shows that for mobile gas/liquid interfaces, the existing models systematically underestimate the dissipation in flowing foams. This is quantified by a discrepancy factor , ratio of the experimental dissipation measurements to the theoretical predictions, which scales as with the Plateau border radius and the bubble area, showing that the discrepancy is higher for dry foams.
 Particulate, Multiphase, and Granular Flows

Peristaltic particle transport using the lattice Boltzmann method
View Description Hide DescriptionPeristaltic transport refers to a class of internal fluid flows where the periodic deformation of flexible containing walls elicits a nonnegligible fluid motion. It is a mechanism used to transport fluid and immersed solid particles in a tube or channel when it is ineffective or impossible to impose a favorable pressure gradient or desirous to avoid contact between the transported mixture and mechanical moving parts. Peristaltic transport occurs in many physiological situations and has myriad industrial applications. We focus our study on the peristaltic transport of a macroscopic particle in a twodimensional channel using the lattice Boltzmann method. We systematically investigate the effect of variation of the relevant dimensionless parameters of the system on the particle transport. We find, among other results, a case where an increase in Reynolds number can actually lead to a slight increase in particle transport, and a case where, as the wall deformation increases, the motion of the particle becomes nonnegative only. We examine the particle behavior when the system exhibits the peculiar phenomenon of fluid trapping. Under these circumstances, the particle may itself become trapped where it is subsequently transported at the wave speed, which is the maximum possible transport in the absence of a favorable pressure gradient. Finally, we analyze how the particle presence affects stress, pressure, and dissipation in the fluid in hopes of determining preferred working conditions for peristaltic transport of shearsensitive particles. We find that the levels of shear stress are most hazardous near the throat of the channel. We advise that shearsensitive particles should be transported under conditions where trapping occurs as the particle is typically situated in a region of innocuous shear stress levels.

Particle migration and suspension structure in steady and oscillatory plane Poiseuille flow
View Description Hide DescriptionA structuretensorbased model is used to compute the microstructure and velocity field of concentrated suspensions of hard spheres in a fully developed, pressuredriven channel flow. The model is comprised of equations governing conservation of mass and momentum in the bulk suspension,conservation of particles, and conservation of momentum in the particle phase. The equations governing the relation between structure and stress in hardsphere suspensions were developed previously and were shown to reproduce quantitatively results obtained by Stokesian dynamics simulations of linear shear flows. In nonhomogeneous, pressuredriven flows, the divergence of the particle contribution to the stress is nonzero and acts as a body force that causes particles to migrate across streamlines. Under steady conditions, the model predicts that the resulting migration causes particles to move to the center of the channel, where the concentration approaches the maximum packing for hardsphere suspensions. In oscillatory flow, the behavior depends strongly on the amplitude of the strain. For oscillations with large strains, the particles migrate to the channel center. However, when the strain is small, the maximum concentration is located either at a position between the channel center and walls or, in the limit of very small strains, at the wall. The migration to the wall induced by smallstrain oscillation occurs in conjunction with the suspension microstructure becoming ordered. This behavior agrees qualitatively with experimental observations reported in the literature. However, the predicted rate of migration toward the wall in the simulations is significantly slower than what is observed experimentally.