Volume 22, Issue 5, May 2010

The past half century has seen an unprecedented growth of the world’s urban population. While urban areas proffer the highest quality of life, they also inflict environmental degradation that pervades a multitude of spacetime scales. In the atmospheric context, stressors of human (anthropogenic) origin are mainly imparted on the lower urban atmosphere and communicated to regional, global, and smaller scales via transport and turbulence processes. Conversely, changes in all scales are transmitted to urban regions through the atmosphere. The fluid dynamics of the urban atmospheric boundary layer and its prediction is the theme of this overview paper, where it is advocated that decision and policymaking in urban atmospheric management must be based on integrated models that incorporate cumulative effects of anthropogenic forcing, atmospheric dynamics, and social implications (e.g., health outcomes). An integrated modeling system juxtaposes a suite of submodels, each covering a particular range of scales while communicating with models of neighboring scales. Unresolved scales of these models need to be parametrized based on flow physics, for which developments in fluid dynamics play an indispensible role. Illustrations of how controlled laboratory, outdoor (field), and numerical experiments can be used to understand and parametrize urban atmospheric processes are presented, and the utility of predictive models is exemplified. Field experiments in real urban areas are central to urban atmospheric research, as validation of predictive models requires data that encapsulate fourdimensional complexities of nature.
 AWARD AND INVITED PAPERS


Flow, turbulence, and pollutant dispersion in urban atmospheres^{a)}
View Description Hide DescriptionThe past half century has seen an unprecedented growth of the world’s urban population. While urban areas proffer the highest quality of life, they also inflict environmental degradation that pervades a multitude of spacetime scales. In the atmospheric context, stressors of human (anthropogenic) origin are mainly imparted on the lower urban atmosphere and communicated to regional, global, and smaller scales via transport and turbulence processes. Conversely, changes in all scales are transmitted to urban regions through the atmosphere. The fluid dynamics of the urban atmospheric boundary layer and its prediction is the theme of this overview paper, where it is advocated that decision and policymaking in urban atmospheric management must be based on integrated models that incorporate cumulative effects of anthropogenic forcing, atmospheric dynamics, and social implications (e.g., health outcomes). An integrated modeling system juxtaposes a suite of submodels, each covering a particular range of scales while communicating with models of neighboring scales. Unresolved scales of these models need to be parametrized based on flow physics, for which developments in fluid dynamics play an indispensible role. Illustrations of how controlled laboratory, outdoor (field), and numerical experiments can be used to understand and parametrize urban atmospheric processes are presented, and the utility of predictive models is exemplified. Field experiments in real urban areas are central to urban atmospheric research, as validation of predictive models requires data that encapsulate fourdimensional complexities of nature.
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 LETTERS


Bubble entrapment through topological change
View Description Hide DescriptionWhen a viscousdrop impacts onto a solid surface, it entraps a myriad of microbubbles at the interface between liquid and solid. We present direct highspeed video observations of this entrapment. For viscousdrops, the tip of the spreading lamella is separated from the surface and levitated on a cushion of air. We show that the primary mechanism for the bubble entrapment is contact between this precursor sheet of liquid with the solid and not air pulled directly through cusps in the contact line. The sheet makes contact with the solid surface,forming a wetted patch, which grows in size, but only entraps a bubble when it meets the advancing contact line. The leading front of this wet patch can also lead to the localized thinning and puncturing of the liquid film producing strong splashing of droplets.

Locality properties of the energy flux in magnetohydrodynamic turbulence
View Description Hide DescriptionThe scale locality functions, originally introduced by Kraichnan for hydrodynamicturbulence, are computed from results of direct numerical simulations of forced magnetohydrodynamicturbulence. It is found that asymptotically the dynamics is dominated by local interactions, but the locality is much weaker than in hydrodynamicturbulence, which is characterized by the scaling exponent of 4/3. Specifically, in magnetohydrodynamicturbulence, two distinct exponents are observed, 1/3 and 2/3. Despite that, direct numerical simulation results reported in this paper exhibit strong coupling between large scales from the forcing band and smallest resolved scales because the locality is too weak to achieve decoupling for the numerical resolution available.

The role of electric charge in microdroplets impacting on conducting surfaces
View Description Hide DescriptionA rich phenomenology is revealed by temporally resolved image sequences of electrically charged ethanol microdroplets impacting on a conductive surface at temperatures bracketing the liquid boiling point. Notable phenomena include the flattening of the sessile droplets with reduced contact angle, increased evaporation rates for substrate temperatures below the fluid boiling point, and the hindrance of droplet rebound at the Leidenfrost temperature. Scaling considerations are presented to rationalize the observed behavior and to generalize conclusions to a broader droplet size range.

Quantifying the interaction between large and small scales in wallbounded turbulent flows: A note of caution
View Description Hide DescriptionTurbulent flow close to solid walls is dominated by an ensemble of fluctuations of large and small spatial scales. Recent work by Mathis et al. [J. Fluid Mech.628, 311 (2009); Phys. Fluids21, 111703 (2009)] introduced and used a decoupling procedure based on the Hilbert transformation applied to the filtered smallscale component of the fluctuating streamwise velocity. This method is employed as a robust tool to quantify a dominant amplitude modulation of the small scales by the large scales found in the outer part of the boundary layer. In the present study, however, we demonstrate by means of experimental and synthetic signals that the correlation coefficient used to quantify the amplitude modulation is related to the skewness of the original signal, and hence, for the Reynolds numbers considered here, may not be an independent tool to unambiguously detect or quantify the effect of largescale amplitude modulation of the small scales.

Anomalous memory effects on transport of inertial particles in turbulent jets
View Description Hide DescriptionThe letter focuses on a new phenomenology found in the far field of turbulentfree jets, where small inertial particles exhibit a local concentration peak on the axis. This finding contrasts with the prediction of classical models based on turbulent kinetic energy gradient transport assumptions, whereby particles should move away from the local kinetic energy maxima. This behavior is universal, i.e., it occurs no matter the details of the specific jet, and takes place irrespective of the inertia of the particles. As anomalous signature of the near field dynamics, it cannot be predicted on purely dimensional grounds. A new form of similarity allows to collapse the local particle flux profile on a universal curve.
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 ARTICLES

 Micro and Nanofluid Mechanics

Oscillation of cylinders of rectangular cross section immersed in fluid
View Description Hide DescriptionThe ability to calculate flows generated by oscillating cylinders immersed in fluid is a cornerstone in micro and nanodevice development. In this article, we present a detailed theoretical analysis of the hydrodynamic load experienced by an oscillating rigid cylinder, of arbitrary rectangular cross section, that is immersed in an unbounded viscous fluid. We also consider the formal limit of inviscid flow for which exact analytical and asymptotic solutions are derived. Due to its practical importance in application to the atomic force microscope and nanoelectromechanical systems, we conduct a detailed assessment of the dependence of this load on the cylinder thicknesstowidth ratio. We also assess the validity and accuracy of the widely used infinitelythin blade approximation. For thin rectangular cylinders of finite thickness, this approximation is found to be excellent for outofplane motion, whereas for inplane oscillations it can exhibit significant error. A database of accurate numerical results for the hydrodynamic load as a function of the thicknesstowidth ratio and normalized frequency is also presented, which is expected to be of value in practical application and numerical benchmarking.

Slip due to surface roughness for a Newtonian liquid in a viscous microscale disk pump
View Description Hide DescriptionIn the present study, hydrophobic roughness is used to induce nearwall slip in a single rotatingdisk micropump operating with Newtonian water. The amount of induced slip is altered by employing different sizes of surface roughness on the rotating disk. The magnitudes of slip length and slip velocities increase as the average size of the surface roughness becomes larger. In the present study, increased slip magnitudes from roughness are then associated with reduced pressure rise through the pump and lower radiallineaveraged shear stress magnitudes (determined within slip planes). Such shear stress and pressure rise variations are similar to those which would be present if the slip is induced by the intermolecular interactions which are associated with nearwall microscale effects. The present sliproughness effects are quantified experimentally over rotational speeds from 50 to 1200 rpm, pressure increases from 0 to 312 kPa, net flow rates of , and fluid chamber heights from 6.85 to . Verification is provided by comparisons with analytic results determined from the rotating Couette flow forms of the Navier–Stokes equations, with different disk rotational speeds, disk roughness levels, and fluid chamber heights. These data show that slip length magnitudes show significant dependence on radiallineaveraged shear stress for average disk roughness heights of 404 and 770 nm. These slip length data additionally show a high degree of organization when normalized using by either the average roughness height or the fluid chamber height. For the latter case, such behavior provides evidence that the flow over a significant portion of the passage height is affected by the roughness, and nearwall slip velocities, especially when the average roughness height amounts to 11% of the passage height of the channel. Such scaling of the disk slip length with fluid chamber height is consistent with dtype roughness scaling in macroscale flows.

The role of elastic flap deformation on fluid mixing in a microchannel
View Description Hide DescriptionWe explore the capacity of a flexible flap to increase mixing in a microchannel for a flap Reynolds number ranging from 0.3–80. The fictitiousdomain (DLM) method is used to model the fluid and solid interactions. The momentum equations for the fluid and solid are solved individually using the finitevolume and finitedifference methods. The equations are coupled using distributed Lagrange multipliers. The stress in the solid is derived from the nonlinear beam equations.Fluid mixing is quantified by solving the mass transportequation for a solute with low molecular diffusivity and calculating a global mixing fraction . The flap is actuated using a distributed follower force along the length of the flap. The results show that mixing is enhanced for larger flap displacements and for dimensionless frequencies Sl between 1 and 2. Optimal mixing occurs when the flap length is 2/3 the microchannel height. The influence of the hydrodynamic force on the beam bending motion enhances the mixing process. Under optimal conditions the flap behaves as a rapid mixing device where 80% of the long time mixing fraction is reached during an initial time interval of 3.8 s.

The geometry effect on steady electrokinetic flows in curved rectangular microchannels
View Description Hide DescriptionMicrofluidic designs require the effort to understand the flow pattern depending on the channel geometry. An indepth analysis based on the theoretical model is presented for the pressuredriven electrokineticmicroflows in curved rectangular channels by applying the finite volume scheme with a SIMPLE (semiimplicit method for pressurelinked equations) algorithm. The external body force originated from between the nonlinear Poisson–Boltzmann field around the channel wall and the flowinduced electric field is employed in the Navier–Stokes equation, and the Nernst–Planck equation is taken into further consideration. Unknown pressure terms of the momentum equation are solved by using the continuity equation as the pressurevelocity coupling achieves convergence. Attention is focused on the geometry effect on the fluid velocity profile at the turn of charged rectangular channels with ranging complementary channel aspect ratios (i.e., ). Simulation results exhibit that the streamwise axial velocity at the turn skews the profile to the inner region of the microchannel. This is due to the stronger effect of spanwise pressure gradient arising from a sufficiently low Dean number. The skewed pattern in the velocity profile becomes greater with decreasing channel aspect ratio as well as degree of the channel curvature. Quantitative predictions for the decreasing velocity due to the electrokinetic interaction were also provided in both cases of shallow and deep microchannels.

Nanoscale simulations of directional locking
View Description Hide DescriptionWhen particles suspended in a fluid are driven through a regular lattice of cylindrical obstacles, their average motion is usually not in the direction of the force, and in the high Péclet number limit, particles tend to lock into periodic trajectories along certain lattice directions. By means of molecular dynamics simulations we show that this effect persists for nanometersized particles and in the presence of molecular diffusion, provided the Péclet number is not very small. The main effect of diffusion is to smooth the sharp transitions between locking directions found in the convective limit and to suppress the higherorder locking directions. We show that trajectory locking is independent of the driving mechanism and qualitatively insensitive to the particle and obstacle size and spacing. The absolute roughness of the solid surfaces is found to be the relevant quantity in locking. We observe trajectory locking in all cases, and in particular in semidilute suspensions of particles of different sizes. The degree of locking varies with particle size, and therefore these flows can have application as a nanoparticle separation technique.

Electroosmotic flows over highly polarizable dielectric surfaces
View Description Hide DescriptionA thinDebyelayer macroscale model is developed and analyzed for electrokineticflows about dielectric surfaces, wherein solid polarization modifies the zetapotential distribution. The harmonic electric potential within the solid is governed by a nonlinear boundary condition, which constitutes a generalization of the linear Robintype condition of Yossifon et al. [Phys. Fluids19, 068105 (2007)] to voltages comparable with the thermal scale. The resulting polarization model is demonstrated in the classical context of sphericalparticle electrophoresis, where the electrophoreticmobility—now a function of appliedfield magnitude and solid permittivity—is evaluated using both eigenfunction series expansions and asymptotic approximations. For strong polarization, the mobility saturates at a fielddependent value which is lower than the comparable Smoluchowski slope. At strongly applied fields, the mobility diminishes at a rate that corresponds to a logarithmic increase of particle velocity with appliedfield magnitude.
 Interfacial Flows

Role of solid surface structure on evaporative phase change from a completely wetting corner meniscus
View Description Hide DescriptionThe transport processes that occur at small length scales are greatly influenced by interfacial and intermolecular forces. Surface roughness at the nanoscale generates additional intermolecular interactions that arise due to the increased surface area. In this work, we have experimentally studied how the magnitude as well as the shape of surface roughness influences the microscale transport processes that occur in the contact line region of a liquid corner meniscus. The surface roughness contribution to the interaction potential was calculated and a direct relationship between the wetting properties of the liquid and the underlying surface properties was obtained. Since the underlying roughness alters the surface potential, the shape of the meniscus and in turn, the resulting capillary and disjoining pressure forces also changed. Atomic force microscopy was utilized to obtain a detailed characterization of the shape of the prepared surfaces.Surface morphology features were obtained from a heightheight correlation function. These features were related to the wetting and transport properties of the meniscus at the contact line. Finally, the modified capillary and disjoining pressure forces on the structured surfaces were observed to influence the evaporative heat transfer from the corner meniscus.

Convective dominated flows in open capillary channels
View Description Hide DescriptionThis paper is concerned with convective dominated liquid flows in open capillary channels. The channels consist of two parallel plates bounded by free liquid surfaces along the open sides. In the case of steady flow the capillary pressure of the free surface balances the differential pressure between the liquid and the surrounding constant pressure gas phase. A maximum flow rate is achieved when the adjusted volumetric flow rate exceeds a certain limit leading to a collapse of the free surfaces. The convective dominated flow regime is a special case of open capillary flow, since the viscous forces are negligibly small compared with the convective forces. Flows of this type are of peculiar interest since the free surfaces possess a quasisymmetry in the flow direction. This quasisymmetry enables the application of a new effective method for evaluation of the flow limit. The flow limit is caused by a choking effect. This effect is indicated by the speed index, S, which is defined by the ratio of the flow velocity and the longitudinal capillary wave speed. The speed index is defined analogously to Mach number and tends toward unity in the case of flow limitation, i.e., when the maximum flow rate is reached. Utilizing the quasisymmetry, a new approach for a very precise determination of the speed index is presented. This approach uses a new approximation for the curvature of the surfaces by means of the empirical surface profiles. On the basis of empirical and theoretical data, the paper discusses the typical features of the stable flow. The experiments were performed under microgravity aboard the sounding rockets TEXUS 41 and TEXUS 42. The experiment setup enables the approach to the flow limit through either increase in flow rate or channel length. The theoretical data have been gained from numerical solutions of a onedimensional flow model. The empirical and theoretical results are in good agreement and both confirm the choking effect as cause of the flow limitation. A general relation for the speed index as function of the flow rate and the channel length has been found which clarifies the fundamental behavior of the choking effect.

Linear and nonlinear instability waves in spatially developing twophase mixing layers
View Description Hide DescriptionTwophase laminar mixing layers are susceptible to shearflow and interfacialinstabilities, which originate from infinitesimal disturbances. Linear stability theory has successfully described the early stages of instability. In particular, parallelflow linear analyses have demonstrated the presence of mode competition, where the dominant unstable mode can vary between internal and interfacial modes, depending on the flow parameters. However, the dynamics of twophase mixing layers can be sensitive to additional factors, such as the spreading of the mean flow. In addition, beyond the early linear stage, the amplitude of the instability waves becomes finite and nonlinear effects become appreciable. As a result, an accurate description of the evolution of the mixing layer must account for nonlinear interactions including the generation of higher harmonics of the instability waves and the modification of the mean flow. These effects are investigated herein using the framework of the nonlinear parabolized stability equations. The formulation includes nonparallel effects, nonlinear modal interactions, a coupled mean flow correction, and finite amplitude deformation of the interface. Mode competition between liquid and interfacial modes is investigated. We demonstrate that nonparallelism and streamwise evolution of the flow can significantly alter the predictions of locally parallel, linear stability analyses. This is followed by a discussion on nonlinear interactions of two and threedimensional instability waves. It is shown that nonlinear effects can serve dual purposes. On one hand, they can be a limiting mechanism for the growth of instability waves. On the other hand, they can destabilize high frequency, linearly stable modes, and thus lead to the generation of smaller scale features in the flow.

The impulsive motion of a small cylinder at an interface
View Description Hide DescriptionWe study the unsteady motion caused by an impulse acting at time on a small cylinder floating horizontally at a liquid–gas interface. This is a model for the impact of a cylinder onto a liquid surface after the initial splash. Following the impulse, the motion of the cylinder is determined by its weight per unit length (pulling it into the bulk liquid) and resistance from the liquid, which acts to keep the cylinder at the interface. The range of cylinder radii and impact speeds considered is such that the resistance from the liquid comes from both the interfacial tension and hydrodynamic pressures. We use two theoretical approaches to investigate this problem. In the first, we apply the arbitrary Lagrangian Eulerian (ALE) method developed by Li et al. [“An arbitrary Lagrangian Eulerian method for movingboundary problems and its application to jumping over water,” J. Comput. Phys.208, 289 (2005)] to compute the fluid flow caused by the impulse and the (coupled) motion of the cylinder. We show that at early times the interfacial deformation is given by a family of shapes parametrized by . We also find that for a given density and radius there is a critical impulse speed below which the cylinder is captured by the interface and floats but above which it pierces the interface and sinks. Our second theoretical approach is a simplified one in which we assume that the interface is in equilibrium and derive an ordinary differential equation for the motion of the cylinder. Solving this we again find the existence of a critical impulse speed for sinking giving us some quantitative understanding of the results from the ALE simulations. Finally, we compare our theoretical predictions with the results of experiments for cylinder impacts by Vella and Metcalfe [“Surface tension dominated impact,” Phys. Fluids19, 072108 (2007)]. This comparison suggests that the influence of contact line effects, neglected here, may be important in the transition from floating to sinking.

Thin films flowing down inverted substrates: Two dimensional flow
View Description Hide DescriptionWe consider free surface instabilities of films flowing on inverted substrates within the framework of lubrication approximation. We allow for the presence of fronts and related contact lines and explore the role which they play in instability development. It is found that a contact line, modeled by a commonly used precursor film model, leads to free surface instabilities without any additional natural or excited perturbations. A single parameter , where Ca is the capillary number and is the inclination angle, is identified as a governing parameter in the problem. This parameter may be interpreted to reflect the combined effect of inclination angle, film thickness, Reynolds number, and fluid flux. Variation of leads to change in the wavelike properties of the instabilities, allowing us to observe traveling wave behavior, mixed waves, and the waves resembling solitary ones.

Stationary spiral waves in film flow over a spinning disk
View Description Hide DescriptionStationary spiral waves in liquid film flowing over a spinning disk have been observed in earlier experiments [H. Espig and R. Hoyle, “Waves in a thin liquid layer on a rotating disk,” J. Fluid Mech.22, 671 (1965); A. F. Charwat et al., “The flow and stability of thin liquid films on a rotating disk,” J. Fluid Mech.53, 227 (1972); G. Leneweit et al., “Surface instabilities of thin liquid filmflow on a rotating disk,” Exp. Fluids26, 75 (1999)]. In the framework of a mathematical model derived by the integral method, it is shown that the waves develop due to nonaxisymmetric liquid feeding onto the spinning disk, and the wave shapes are approximated by the Archimedean spirals, whose coefficients depend on the Eckman number. The dependence has been confirmed by experimental data from recorded videos.

Capillarygravity waves generated by a sudden object motion
View Description Hide DescriptionWe study theoretically the capillarygravity waves created at the waterair interface by a small object during a sudden accelerated or decelerated rectilinear motion. We analyze the wave resistance corresponding to the transient wavepattern and show that it is nonzero even if the involved velocity (the final one in the accelerated case, the initial one in the decelerated case) is smaller than the minimum phase velocity . These results might be important for a better understanding of the propulsion of waterwalking insects where accelerated and decelerated motions frequently occur.
 Viscous and NonNewtonian Flows

Merging of shielded Gaussian vortices and formation of a tripole at low Reynolds numbers
View Description Hide DescriptionThe interaction between two corotating shielded Gaussian vortices is studied by twodimensional numerical simulations at low Reynolds numbers. It is shown that the outcome of the interactions can be a shielded monopole, a tripole, or dipolar breaking depending on the initial separation distance and Reynolds number. A flow regime map is given in the parameter space of initial separation distance and Reynolds number. Using formal decomposition for vorticity, we show that the tripole formation is due the same physical mechanism than merging of unshielded vortices, while in dipolar breaking both the symmetric and antisymmetric vorticity contributions play important role.