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May 2010

Volume 22, Issue 5, Articles (05xxxx)

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Phys. Fluids 22, 051301 (2010); http://dx.doi.org/10.1063/1.3407662 (20 pages)

H. J. S. Fernando, D. Zajic, S. Di Sabatino, R. Dimitrova, B. Hedquist, and A. Dallman
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Flow, turbulence, and pollutant dispersion in urban atmospheres

H. J. S. Fernando, D. Zajic, S. Di Sabatino, R. Dimitrova, B. Hedquist, and A. Dallman

Phys. Fluids 22, 051301 (2010); http://dx.doi.org/10.1063/1.3407662 (20 pages) | Cited 8 times

Online Publication Date: 13 May 2010

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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 space-time 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 four-dimensional complexities of nature.
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92.60.Sz Air quality and air pollution
92.60.Fm Boundary layer structure and processes
47.27.-i Turbulent flows
89.60.-k Environmental studies
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Bubble entrapment through topological change

S. T. Thoroddsen, K. Takehara, and T. G. Etoh

Phys. Fluids 22, 051701 (2010); http://dx.doi.org/10.1063/1.3407654 (4 pages) | Cited 6 times

Online Publication Date: 3 May 2010

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When a viscous drop impacts onto a solid surface, it entraps a myriad of microbubbles at the interface between liquid and solid. We present direct high-speed video observations of this entrapment. For viscous drops, 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.
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47.55.D- Drops and bubbles
68.08.Bc Wetting

Locality properties of the energy flux in magnetohydrodynamic turbulence

J. Andrzej Domaradzki, Bogdan Teaca, and Daniele Carati

Phys. Fluids 22, 051702 (2010); http://dx.doi.org/10.1063/1.3431227 (4 pages) | Cited 3 times

Online Publication Date: 24 May 2010

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The scale locality functions, originally introduced by Kraichnan for hydrodynamic turbulence, are computed from results of direct numerical simulations of forced magnetohydrodynamic turbulence. It is found that asymptotically the dynamics is dominated by local interactions, but the locality is much weaker than in hydrodynamic turbulence, which is characterized by the scaling exponent of 4/3. Specifically, in magnetohydrodynamic turbulence, 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.
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.27.ek Direct numerical simulations
47.11.-j Computational methods in fluid dynamics
02.60.Cb Numerical simulation; solution of equations

The role of electric charge in microdroplets impacting on conducting surfaces

Weiwei Deng and Alessandro Gomez

Phys. Fluids 22, 051703 (2010); http://dx.doi.org/10.1063/1.3431739 (4 pages) | Cited 2 times

Online Publication Date: 24 May 2010

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A 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.
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47.55.dp Cavitation and boiling
47.65.-d Magnetohydrodynamics and electrohydrodynamics
68.03.Cd Surface tension and related phenomena
47.80.Jk Flow visualization and imaging

Quantifying the interaction between large and small scales in wall-bounded turbulent flows: A note of caution

Philipp Schlatter and Ramis Örlü

Phys. Fluids 22, 051704 (2010); http://dx.doi.org/10.1063/1.3432488 (4 pages) | Cited 7 times

Online Publication Date: 24 May 2010

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Turbulent 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. Fluids 21, 111703 (2009)] introduced and used a decoupling procedure based on the Hilbert transformation applied to the filtered small-scale 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 large-scale amplitude modulation of the small scales.
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47.27.nb Boundary layer turbulence

Anomalous memory effects on transport of inertial particles in turbulent jets

F. Picano, G. Sardina, P. Gualtieri, and C. M. Casciola

Phys. Fluids 22, 051705 (2010); http://dx.doi.org/10.1063/1.3432439 (4 pages) | Cited 4 times

Online Publication Date: 26 May 2010

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The letter focuses on a new phenomenology found in the far field of turbulent-free 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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47.55.Kf Particle-laden flows
47.27.wg Turbulent jets
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back to top Micro- and Nanofluid Mechanics

Oscillation of cylinders of rectangular cross section immersed in fluid

Douglas R. Brumley, Michelle Willcox, and John E. Sader

Phys. Fluids 22, 052001 (2010); http://dx.doi.org/10.1063/1.3397926 (15 pages) | Cited 6 times

Online Publication Date: 4 May 2010

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The 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 thickness-to-width ratio. We also assess the validity and accuracy of the widely used infinitely-thin blade approximation. For thin rectangular cylinders of finite thickness, this approximation is found to be excellent for out-of-plane motion, whereas for in-plane oscillations it can exhibit significant error. A database of accurate numerical results for the hydrodynamic load as a function of the thickness-to-width ratio and normalized frequency is also presented, which is expected to be of value in practical application and numerical benchmarking.
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46.35.+z Viscoelasticity, plasticity, viscoplasticity
85.85.+j Micro- and nano-electromechanical systems (MEMS/NEMS) and devices
47.85.Dh Hydrodynamics, hydraulics, hydrostatics

Slip due to surface roughness for a Newtonian liquid in a viscous microscale disk pump

Phil Ligrani, Danny Blanchard, and Bruce Gale

Phys. Fluids 22, 052002 (2010); http://dx.doi.org/10.1063/1.3419081 (15 pages) | Cited 2 times

Online Publication Date: 5 May 2010

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In the present study, hydrophobic roughness is used to induce near-wall slip in a single rotating-disk 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 radial-line-averaged 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 near-wall microscale effects. The present slip-roughness effects are quantified experimentally over rotational speeds from 50 to 1200 rpm, pressure increases from 0 to 312 kPa, net flow rates of 0–100 μl/min, and fluid chamber heights from 6.85 to 29.2 μm. 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 radial-line-averaged 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 near-wall slip velocities, especially when the average roughness height amounts to 11% of the h = 6.86 μm passage height of the channel. Such scaling of the disk slip length bdisk with fluid chamber height h is consistent with d-type roughness scaling in macroscale flows.
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47.85.Np Fluidics
47.10.ad Navier-Stokes equations
47.15.-x Laminar flows
47.32.Ef Rotating and swirling flows
47.45.Gx Slip flows and accommodation
47.61.Fg Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)

The role of elastic flap deformation on fluid mixing in a microchannel

Ruth A. Lambert and Roger H. Rangel

Phys. Fluids 22, 052003 (2010); http://dx.doi.org/10.1063/1.3410268 (15 pages) | Cited 3 times

Online Publication Date: 7 May 2010

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We explore the capacity of a flexible flap to increase mixing in a microchannel for a flap Reynolds number Ref ranging from 0.3–80. The fictitious-domain (DLM) method is used to model the fluid and solid interactions. The momentum equations for the fluid and solid are solved individually using the finite-volume and finite-difference 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 transport equation for a solute with low molecular diffusivity and calculating a global mixing fraction M. 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.
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47.85.Np Fluidics
46.70.De Beams, plates, and shells
47.11.Bc Finite difference methods
47.11.Df Finite volume methods
47.51.+a Mixing
47.60.Dx Flows in ducts and channels

The geometry effect on steady electrokinetic flows in curved rectangular microchannels

Jang Ho Yun, Myung-Suk Chun, and Hyun Wook Jung

Phys. Fluids 22, 052004 (2010); http://dx.doi.org/10.1063/1.3427572 (10 pages) | Cited 1 time

Online Publication Date: 24 May 2010

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Microfluidic designs require the effort to understand the flow pattern depending on the channel geometry. An in-depth analysis based on the theoretical model is presented for the pressure-driven electrokinetic microflows in curved rectangular channels by applying the finite volume scheme with a SIMPLE (semi-implicit method for pressure-linked equations) algorithm. The external body force originated from between the nonlinear Poisson–Boltzmann field around the channel wall and the flow-induced 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 pressure-velocity 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., H/W = 0.2–5.0). 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.
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47.85.Np Fluidics
47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.60.Dx Flows in ducts and channels
47.10.ad Navier-Stokes equations

Nanoscale simulations of directional locking

Joel Koplik and German Drazer

Phys. Fluids 22, 052005 (2010); http://dx.doi.org/10.1063/1.3429297 (9 pages) | Cited 2 times

Online Publication Date: 27 May 2010

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When 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 nanometer-sized 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 higher-order 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.
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47.11.Mn Molecular dynamics methods
47.55.-t Multiphase and stratified flows
47.57.E- Suspensions

Electro-osmotic flows over highly polarizable dielectric surfaces

Ehud Yariv and Anthony M. J. Davis

Phys. Fluids 22, 052006 (2010); http://dx.doi.org/10.1063/1.3431695 (7 pages) | Cited 1 time

Online Publication Date: 28 May 2010

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A thin-Debye-layer macroscale model is developed and analyzed for electrokinetic flows about dielectric surfaces, wherein solid polarization modifies the zeta-potential distribution. The harmonic electric potential within the solid is governed by a nonlinear boundary condition, which constitutes a generalization of the linear Robin-type condition of Yossifon et al. [Phys. Fluids 19, 068105 (2007)] to voltages comparable with the thermal scale. The resulting polarization model is demonstrated in the classical context of spherical-particle electrophoresis, where the electrophoretic mobility—now a function of applied-field magnitude and solid permittivity—is evaluated using both eigenfunction series expansions and asymptotic approximations. For strong polarization, the mobility saturates at a field-dependent 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 applied-field magnitude.
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
82.45.Un Dielectric materials in electrochemistry
77.22.Ej Polarization and depolarization
47.55.-t Multiphase and stratified flows
77.22.Ch Permittivity (dielectric function)
back to top Interfacial Flows

Role of solid surface structure on evaporative phase change from a completely wetting corner meniscus

Manas Ojha, Arya Chatterjee, George Dalakos, Peter C. Wayner, and Joel L. Plawsky

Phys. Fluids 22, 052101 (2010); http://dx.doi.org/10.1063/1.3392771 (15 pages) | Cited 4 times

Online Publication Date: 4 May 2010

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The 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 height-height 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.
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68.03.Fg Evaporation and condensation of liquids
68.08.Bc Wetting
47.55.nb Capillary and thermocapillary flows
68.03.Cd Surface tension and related phenomena
47.80.Jk Flow visualization and imaging

Convective dominated flows in open capillary channels

Uwe Rosendahl, Aleksander Grah, and Michael E. Dreyer

Phys. Fluids 22, 052102 (2010); http://dx.doi.org/10.1063/1.3379847 (13 pages)

Online Publication Date: 21 May 2010

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This 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 one-dimensional 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.
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47.55.pb Thermal convection
47.55.nb Capillary and thermocapillary flows
47.35.Pq Capillary waves
47.60.Dx Flows in ducts and channels
47.11.-j Computational methods in fluid dynamics
02.60.Cb Numerical simulation; solution of equations

Linear and nonlinear instability waves in spatially developing two-phase mixing layers

Lawrence C. Cheung and Tamer A. Zaki

Phys. Fluids 22, 052103 (2010); http://dx.doi.org/10.1063/1.3425788 (21 pages) | Cited 2 times

Online Publication Date: 21 May 2010

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Two-phase laminar mixing layers are susceptible to shear-flow and interfacial instabilities, which originate from infinitesimal disturbances. Linear stability theory has successfully described the early stages of instability. In particular, parallel-flow 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 two-phase 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 three-dimensional 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.
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47.15.Fe Stability of laminar flows
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.51.+a Mixing
47.55.nd Spreading films
47.10.A- Mathematical formulations

The impulsive motion of a small cylinder at an interface

Dominic Vella and Jie Li

Phys. Fluids 22, 052104 (2010); http://dx.doi.org/10.1063/1.3427241 (12 pages) | Cited 1 time

Online Publication Date: 21 May 2010

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We study the unsteady motion caused by an impulse acting at time t = 0 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 r and impact speeds U 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 moving-boundary 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 r/t2/3. 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. Fluids 19, 072108 (2007)] . This comparison suggests that the influence of contact line effects, neglected here, may be important in the transition from floating to sinking.
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68.03.Cd Surface tension and related phenomena
47.11.Df Finite volume methods

Thin films flowing down inverted substrates: Two dimensional flow

Te-Sheng Lin and Lou Kondic

Phys. Fluids 22, 052105 (2010); http://dx.doi.org/10.1063/1.3428753 (10 pages) | Cited 1 time

Online Publication Date: 24 May 2010

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We 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 D = (3 Ca)1/3cot α, where Ca is the capillary number and α 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 D 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.
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47.20.Dr Surface-tension-driven instability
68.03.Cd Surface tension and related phenomena
47.85.mf Lubrication flows
47.35.Fg Solitary waves

Stationary spiral waves in film flow over a spinning disk

G. M. Sisoev, D. B. Goldgof, and V. N. Korzhova

Phys. Fluids 22, 052106 (2010); http://dx.doi.org/10.1063/1.3429601 (6 pages)

Online Publication Date: 27 May 2010

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Stationary 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 film flow on a rotating disk,” Exp. Fluids 26, 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.
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68.15.+e Liquid thin films
47.32.Ef Rotating and swirling flows
47.15.gm Thin film flows
47.35.-i Hydrodynamic waves

Capillary-gravity waves generated by a sudden object motion

F. Closa, A. D. Chepelianskii, and E. Raphaël

Phys. Fluids 22, 052107 (2010); http://dx.doi.org/10.1063/1.3430004 (6 pages) | Cited 2 times

Online Publication Date: 27 May 2010

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We study theoretically the capillary-gravity waves created at the water-air interface by a small object during a sudden accelerated or decelerated rectilinear motion. We analyze the wave resistance corresponding to the transient wave pattern 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 cmin = 23 cm s−1. These results might be important for a better understanding of the propulsion of water-walking insects where accelerated and decelerated motions frequently occur.
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47.35.Pq Capillary waves
47.35.Bb Gravity waves
back to top Viscous and Non-Newtonian Flows

Merging of shielded Gaussian vortices and formation of a tripole at low Reynolds numbers

Gábor Tóth and Gábor Házi

Phys. Fluids 22, 053101 (2010); http://dx.doi.org/10.1063/1.3428539 (7 pages) | Cited 1 time

Online Publication Date: 27 May 2010

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The interaction between two corotating shielded Gaussian vortices is studied by two-dimensional 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.
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47.11.-j Computational methods in fluid dynamics
47.15.-x Laminar flows
47.15.ki Inviscid flows with vorticity
47.32.-y Vortex dynamics; rotating fluids
back to top Particulate, Multiphase, and Granular Flows

Shear migration and chaotic mixing of particle suspensions in a time-periodic lid-driven cavity

B. Xu and J. F. Gilchrist

Phys. Fluids 22, 053301 (2010); http://dx.doi.org/10.1063/1.3394981 (7 pages)

Online Publication Date: 5 May 2010

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This work simulates segregation of noncolloidal particle suspensions in a two dimensional time-periodic flow. Two different mixing protocols having alternating moving boundaries in a cavity known to generate chaotic advection while maintaining a constant energy input rate are applied to each suspension. A diffusive flux model is used to capture the essence of shear-induced migration. In this system, fluid deformation drives both mixing and segregation where the local rheology is a function of particle volume fraction. The impact of migration strength, altered by varying the particle size and bulk volume fraction, and topology, altered by breaking symmetry in the flow when varying the period length, are investigated. As a result of the complex interplay between the flow topology and shear migration, the concentration profile ranges from that representing the underlying topology to that of steady flow in a lid-driven cavity and depends on the parameters mentioned above and the structure produced by the two mixing protocols. In this system, increasing the size of chaotic regions does not result in enhancing mixing. These results challenge conventional wisdom in designing small scale flows for mixing and separations in microscale applications.
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47.57.ef Sedimentation and migration
47.61.Jd Multiphase flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.52.+j Chaos in fluid dynamics
47.51.+a Mixing
47.57.eb Diffusion and aggregation
back to top Laminar Flows

Homotopy based solutions of the Navier–Stokes equations for a porous channel with orthogonally moving walls

Hang Xu, Zhi-Liang Lin, Shi-Jun Liao, Jie-Zhi Wu, and Joseph Majdalani

Phys. Fluids 22, 053601 (2010); http://dx.doi.org/10.1063/1.3392770 (18 pages) | Cited 14 times

Online Publication Date: 4 May 2010

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This paper focuses on the theoretical treatment of the laminar, incompressible, and time-dependent flow of a viscous fluid in a porous channel with orthogonally moving walls. Assuming uniform injection or suction at the porous walls, two cases are considered for which the opposing walls undergo either uniform or nonuniform motions. For the first case, we follow Dauenhauer and Majdalani [Phys. Fluids 15, 1485 (2003)] by taking the wall expansion ratio α to be time invariant and then proceed to reduce the Navier–Stokes equations into a fourth order ordinary differential equation with four boundary conditions. Using the homotopy analysis method (HAM), an optimized analytical procedure is developed that enables us to obtain highly accurate series approximations for each of the multiple solutions associated with this problem. By exploring wide ranges of the control parameters, our procedure allows us to identify dual or triple solutions that correspond to those reported by Zaturska et al. [Fluid Dyn. Res. 4, 151 (1988)] . Specifically, two new profiles are captured that are complementary to the type I solutions explored by Dauenhauer and Majdalani. In comparison to the type I motion, the so-called types II and III profiles involve steeper flow turning streamline curvatures and internal flow recirculation. The second and more general case that we consider allows the wall expansion ratio to vary with time. Under this assumption, the Navier–Stokes equations are transformed into an exact nonlinear partial differential equation that is solved analytically using the HAM procedure. In the process, both algebraic and exponential models are considered to describe the evolution of α(t) from an initial α0 to a final state α1. In either case, we find the time-dependent solutions to decay very rapidly to the extent of recovering the steady state behavior associated with the use of a constant wall expansion ratio. We then conclude that the time-dependent variation of the wall expansion ratio plays a secondary role that may be justifiably ignored.
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47.56.+r Flows through porous media
47.10.ad Navier-Stokes equations
47.60.Dx Flows in ducts and channels
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
02.30.Hq Ordinary differential equations
47.15.Cb Laminar boundary layers

Stability of planar buoyant jets in stratified fluids

Samuel P. Schofield and Juan M. Restrepo

Phys. Fluids 22, 053602 (2010); http://dx.doi.org/10.1063/1.3415493 (12 pages) | Cited 1 time

Online Publication Date: 7 May 2010

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We consider the flow structure and stability of a planar saline jet descending into a stable, density-stratified fluid. The jet exhibits a rapid acceleration on release, then deceleration, as it encounters the more dense surrounding fluid, yet retains its slender shape due to the low salt diffusion. As the jet descends it entrains fresher water which as it encounters the increasingly dense ambient fluid returns toward the nozzle forming a recirculation zone. Our numerical simulations agree qualitatively with previous experiments and thus serve as a tool to explain the basic kinematics of the jet. We also use numerical means to capture the three instability modes: an antisymmetric instability in the jet core, a symmetric instability in the jet core, and a symmetric instability in the entrained conduit of less saline water. For the dominant antisymmetric instability we determine the range of parameters that demarcate stable and unstable regions.
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47.15.Uv Laminar jets
47.60.Kz Flows and jets through nozzles
47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.55.Hd Stratified flows
47.11.-j Computational methods in fluid dynamics

Frequency-dependent viscous flow in channels with fractal rough surfaces

Andrea Cortis and James G. Berryman

Phys. Fluids 22, 053603 (2010); http://dx.doi.org/10.1063/1.3407659 (11 pages) | Cited 2 times

Online Publication Date: 11 May 2010

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The viscous dynamic permeability of some fractal-like channels is studied. For our particular class of geometries, the ratio of the pore surface area-to-volume tends to ∞ (but has a finite cutoff), and the universal scaling of the dynamic permeability, k(ω), needs modification. We performed accurate numerical computations of k(ω) for channels characterized by deterministic fractal wall surfaces, for a broad range of fractal dimensions. The pertinent scaling model for k(ω) introduces explicitly the fractal dimension of the wall surface for a range of frequencies across the transition between viscous and inertia dominated regimes. The new model provides excellent agreement with our numerical simulations.
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47.60.Dx Flows in ducts and channels
47.11.-j Computational methods in fluid dynamics
47.15.Cb Laminar boundary layers
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.53.+n Fractals in fluid dynamics
47.56.+r Flows through porous media

Particle image velocimetry measurements of vortex rings head-on collision with a heated vertical plate

G. Arévalo, R. H. Hernández, C. Nicot, and F. Plaza

Phys. Fluids 22, 053604 (2010); http://dx.doi.org/10.1063/1.3410800 (8 pages)

Online Publication Date: 20 May 2010

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We report particle image velocimetry measurements of the collision of a vortex ring with a heated wall kept at constant temperature. We consider the case when both the vortex ring and the thermal boundary layer generated by the vertical heated wall are stable and laminar prior to any interaction. The impingement process can be divided into two parts. (i) A ring-driven stage, where the vortex ring grows in diameter while approaching the wall and therefore it sweeps progressively an increased surface on the wall. (ii) A boundary layer-driven stage, where the vortex ring moves upward due to the thermal convective motion generated by the heated wall. In some cases, the head-on collision triggers the ring’s azimuthal instability as revealed by the formation of vortical structures arranged on a wavy starlike pattern and confirmed by flow visualizations. A single collision generates important velocity gradients and shear stresses along the wall accompanied with the creation of local vorticity normal to the vertical heated wall. Peak wall shear stresses occur near the point of impact of the vortex ring core.
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47.80.Jk Flow visualization and imaging
47.15.Cb Laminar boundary layers
47.15.ki Inviscid flows with vorticity
47.32.-y Vortex dynamics; rotating fluids
47.55.P- Buoyancy-driven flows; convection
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