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May 2013

Volume 25, Issue 5 (partial)

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Peregrine breather revisited

L. Shemer and L. Alperovich

Phys. Fluids 25, 051701 (2013); http://dx.doi.org/10.1063/1.4807055 (7 pages)

Online Publication Date: 20 May 2013

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Results of experiments on the evolution of the Peregrine breather (PB) in a wave tank are presented and compared with numerical simulations based on the Nonlinear Schrödinger (NLS) and the Dysthe equations. The experiments demonstrate notable deviation from the NLS solution due to significant asymmetric widening of the spectrum. Good agreement of measurements with the solutions of the Dysthe equation is obtained. Contrary to the PB NLS soliton, no return to the initial undisturbed wave train can be expected.
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47.35.Fg Solitary waves
92.10.Hm Ocean waves and oscillations
05.45.Yv Solitons
47.11.-j Computational methods in fluid dynamics
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Spatial ordering due to hydrodynamic interactions between a pair of colliding drops in a confined shear

Kausik Sarkar and Rajesh Kumar Singh

Phys. Fluids 25, 051702 (2013); http://dx.doi.org/10.1063/1.4805082 (7 pages)

Online Publication Date: 21 May 2013

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Pair-collision between viscous drops in a confined shear is simulated to show that the confinement alters the trajectories of the drops spatially ordering them at a finite separation in the center of the domain. In contrast to free shear where drops eventually adopt free streamlines with a finite cross-stream separation, here they move towards the centerline achieving zero cross-stream separation but a net stream-wise separation. The latter varies as inverse of capillary number and cube of the confinement (distance between the walls). The final stream-wise separation does not depend on the initial positions of the drops when the drops are in the same shear plane. The separation decreases approximately linearly with the initial separation in the vorticity direction. An analytical theory explaining the phenomenon is presented. Effects of the ratio of drop to matrix viscosity are briefly investigated.
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47.55.dr Interactions with surfaces
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.11.Bc Finite difference methods
47.32.Ff Separated flows
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Shear banding in polymer solutions

Michael Cromer, Michael C. Villet, Glenn H. Fredrickson, and L. Gary Leal

Phys. Fluids 25, 051703 (2013); http://dx.doi.org/10.1063/1.4805089 (7 pages)

Online Publication Date: 23 May 2013

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The current theoretical belief is that the steady-state shear banding in viscoelastic liquids requires a non-monotonic constitutive relationship between shear stress and shear rate. Although existing rheological studies conclude that the constitutive equation for entangled polymers is monotonic, recent experimental evidence suggests shear banding can nevertheless occur in polymer solutions. In this work, we predict, for the first time, steady state shear banding with a realistic monotonic constitutive theory for polymeric liquids. The key is that a proper account must be taken of the coupling of polymer stress to polymer concentration. We also predict multiple steady states at some shear rates as seen experimentally, with shear banding if the flow is ramped quickly enough from rest, but homogeneous linear shear flow otherwise.
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47.57.Ng Polymers and polymer solutions
47.50.Cd Modeling
47.57.Qk Rheological aspects
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Self-propelling uneven Leidenfrost solids

Guillaume Dupeux, Tobias Baier, Vincent Bacot, Steffen Hardt, Christophe Clanet, and David Quéré

Phys. Fluids 25, 051704 (2013); http://dx.doi.org/10.1063/1.4807007 (6 pages)

Online Publication Date: 23 May 2013

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Placed on a hot surface, a solid that sublimates at atmospheric pressure can levitate on a cushion of its own vapor. Discovered by Leidenfrost, this effect has mostly been studied with liquids. Whereas the shape of a droplet is determined by a competition between gravity, surface tension, and stress in the vapor layer, a solid does not deform. In this paper, we show experimentally and theoretically that asymmetric mass distributions in a Leidenfrost solid can lead to a non homogenous vapor layer in which the lubrication flow generates a lateral force able to propel the body.
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47.55.dr Interactions with surfaces
47.85.mf Lubrication flows
68.03.Cd Surface tension and related phenomena
64.70.Hz Solid-vapor transitions
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back to top Biofluid Mechanics

Force and torque on a cylinder rotating in a narrow gap at low Reynolds number: Scaling and lubrication analyses

J. Yang, C. W. Wolgemuth, and G. Huber

Phys. Fluids 25, 051901 (2013); http://dx.doi.org/10.1063/1.4803077 (20 pages)

Online Publication Date: 7 May 2013

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The hydrodynamic forces and torques on a rotating cylinder in a narrow channel are investigated in this paper using lubrication analysis and scaling analysis. To explore the effect of the shape of the gap, three different geometries are considered. The force and torque expressions from lubrication analysis agree well with numerical solutions when the gap between cylinder and wall is small. The solutions from scaling analysis can be applied over a broader range, but only if the scaling coefficients are properly deduced from numerical solution or lubrication analysis. Self-similarity in the solutions is discussed as well.
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47.32.Ef Rotating and swirling flows
47.53.+n Fractals in fluid dynamics
47.85.mf Lubrication flows
47.60.Dx Flows in ducts and channels
02.60.-x Numerical approximation and analysis

The near wake of a freely flying European starling

Adam J. Kirchhefer, Gregory A. Kopp, and Roi Gurka

Phys. Fluids 25, 051902 (2013); http://dx.doi.org/10.1063/1.4807064 (23 pages)

Online Publication Date: 21 May 2013

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The wake of a freely flying European starling (Sturnus vulgaris) has been measured using high speed, time-resolved, particle image velocimetry, simultaneously with high speed cameras which imaged the bird. These have been used to generate vector maps that can be associated with the bird's location and wing configuration in the wind tunnel. Time series of measurements have been expressed as composite wake plots which depict segments of the wing beat cycle for various spanwise locations in the wake. Measurements indicate that downwash is not produced during the upstroke, suggesting that the upstroke does not generate lift. As well, the wake velocities imply the presence of streamwise vortical structures, in addition to tip vortices. These two characteristics indicate similarities between the wake of a bird and the wake of a bat, which may be general features of the wakes of flapping wings.
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47.80.Jk Flow visualization and imaging
47.32.C- Vortex dynamics
back to top Micro- and Nanofluid Mechanics

Regularized 13 moment equations for hard sphere molecules: Linear bulk equations

Henning Struchtrup and Manuel Torrilhon

Phys. Fluids 25, 052001 (2013); http://dx.doi.org/10.1063/1.4802041 (29 pages)

Online Publication Date: 1 May 2013

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The regularized 13 moment equations of rarefied gas dynamics are derived for a monatomic hard sphere gas in the linear regime. The equations are based on an extended Grad-type moment system, which is systematically reduced by means of the Order of Magnitude Method [H. Struchtrup, “Stable transport equations for rarefied gases at high orders in the Knudsen number,” Phys. Fluids 16(11), 3921–3934 (2004)]10.1063/1.1782751. Chapman-Enskog expansion of the final equations yields the linear Burnett and super-Burnett equations. While the Burnett coefficients agree with literature values, this seems to be the first time that super-Burnett coefficients are computed for a hard sphere gas. As a first test of the equations the dispersion and damping of sound waves is considered.
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47.45.Ab Kinetic theory of gases
47.85.Gj Aerodynamics
02.60.Cb Numerical simulation; solution of equations
47.10.ad Navier-Stokes equations
47.11.-j Computational methods in fluid dynamics
47.35.Rs Sound waves

Shear-rate dependent effective thermal conductivity of H2O+SiO2 nanofluids

Chengzhen Sun (孙成珍), Bofeng Bai (白博峰), Wen-Qiang Lu (卢文强), and Jie Liu (刘捷)

Phys. Fluids 25, 052002 (2013); http://dx.doi.org/10.1063/1.4802049 (15 pages)

Online Publication Date: 1 May 2013

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Effective thermal conductivity (ETC) of water-based silicon dioxide nanofluids in shear flow fields (flow shear rate range was 0–820 1/s) was measured using a rotating Couette apparatus. The results show that the ETC of the nanofluids in shear flow fields is significantly higher than that in static states. For the flow shear rates lower than a critical value (infinite-shear rate), the ETC asymptotically increases with increasing the flow shear rate; for the flow shear rates higher than the critical value, the ETC displays a plateau value (infinite-shear thermal conductivity). The increase of the ETC with shear rate is more obvious as increase the nanoparticle diameter and the nanoparticle volume fraction. For 16 different measured nanofluids, the infinite-shear rates vary from 445.0 to 712.1 1/s, while the infinite-shear thermal conductivities increase by 9%–17% comparing with the zero-shear thermal conductivities. The conventional ETC prediction correlation proposed for the suspensions containing micro-sized particles is not suitable for the nanofluids qualitatively and quantitatively. Finally, an exponential correlation is proposed based on our measured data to predict the ETC of nanofluids considering the effects of flow shear rate, nanoparticle diameter, and nanoparticle volume fraction.
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47.55.Kf Particle-laden flows
47.57.E- Suspensions
47.80.Jk Flow visualization and imaging
82.70.Kj Emulsions and suspensions
66.25.+g Thermal conduction in nonmetallic liquids

Effects of curvature on rarefied gas flows between rotating concentric cylinders

Nishanth Dongari, Craig White, Thomas J. Scanlon, Yonghao Zhang, and Jason M. Reese

Phys. Fluids 25, 052003 (2013); http://dx.doi.org/10.1063/1.4807072 (17 pages)

Online Publication Date: 23 May 2013

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The gas flow between two concentric rotating cylinders is considered in order to investigate non-equilibrium effects associated with the Knudsen layers over curved surfaces. We investigate the nonlinear flow physics in the near-wall regions using a new power-law (PL) wall-scaling approach. This PL model incorporates Knudsen layer effects in near-wall regions by taking into account the boundary limiting effects on the molecular free paths. We also report new direct simulation Monte Carlo results covering a wide range of Knudsen numbers and accommodation coefficients, and for various outer-to-inner cylinder radius ratios. Our simulation data are compared with both the classical slip flow theory and the PL model, and we find that non-equilibrium effects are not only dependent on Knudsen number and accommodation coefficient but are also significantly affected by the surface curvature. The relative merits and limitations of both theoretical models are explored with respect to rarefaction and curvature effects. The PL model is able to capture some of the nonlinear trends associated with Knudsen layers up to the early transition flow regime. The present study also illuminates the limitations of classical slip flow theory even in the early slip flow regime for higher curvature test cases, although the model does exhibit good agreement throughout the slip flow regime for lower curvature cases. Torque and velocity profile comparisons also convey that a good prediction of integral flow properties does not necessarily guarantee the accuracy of the theoretical model used, and it is important to demonstrate that field variables are also predicted satisfactorily.
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47.45.Dt Free molecular flows
47.45.Gx Slip flows and accommodation
47.32.Ef Rotating and swirling flows
47.11.-j Computational methods in fluid dynamics
02.70.Uu Applications of Monte Carlo methods

Weakly nonlinear electrophoresis of a highly charged colloidal particle

Ory Schnitzer, Roman Zeyde, Irad Yavneh, and Ehud Yariv

Phys. Fluids 25, 052004 (2013); http://dx.doi.org/10.1063/1.4804672 (19 pages)

Online Publication Date: 24 May 2013

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At large zeta potentials, surface conduction becomes appreciable in thin-double-layer electrokinetic transport. In the linear weak-field regime, where this effect is quantified by the Dukhin number, it is manifested in non-Smoluchowski electrophoretic mobilities. In this paper we go beyond linear response, employing the recently derived macroscale model of Schnitzer and Yariv [“Macroscale description of electrokinetic flows at large zeta potentials: Nonlinear surface conduction,” Phys. Rev. E 86, 021503 (2012)10.1103/PhysRevE.86.021503] as the infrastructure for a weakly nonlinear analysis of spherical-particle electrophoresis. A straightforward perturbation in the field strength is frustrated by the failure to satisfy the far-field conditions, representing a non-uniformity of the weak-field approximation at large distances away from the particle, where salt advection becomes comparable to diffusion. This is remedied using inner-outer asymptotic expansions in the spirit of Acrivos and Taylor [“Heat and mass transfer from single spheres in Stokes flow,” Phys. Fluids 5, 387 (1962)10.1063/1.1706630], with the inner region representing the particle neighborhood and the outer region corresponding to distances scaling inversely with the field magnitude. This singular scheme furnishes an asymptotic correction to the electrophoretic velocity, proportional to the applied field cubed, which embodies a host of nonlinear mechanisms unfamiliar from linear electrokinetic theories. These include the effect of induced zeta-potential inhomogeneity, animated by concentration polarization, on electro-osmosis and diffuso-osmosis; bulk advection of salt; nonuniform bulk conductivity; Coulomb body forces acting on bulk volumetric charge; and the nonzero electrostatic force exerted upon the otherwise screened particle-layer system. A numerical solution of the macroscale model validates our weakly nonlinear analysis.
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47.57.jd Electrokinetic effects
47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.55.Kf Particle-laden flows
73.25.+i Surface conductivity and carrier phenomena
82.45.-h Electrochemistry and electrophoresis
back to top Interfacial Flows

Viscous coalescence of droplets: A lattice Boltzmann study

M. Gross, I. Steinbach, D. Raabe, and F. Varnik

Phys. Fluids 25, 052101 (2013); http://dx.doi.org/10.1063/1.4803178 (14 pages)

Online Publication Date: 2 May 2013

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The coalescence of two resting liquid droplets in a saturated vapor phase is investigated by Lattice Boltzmann simulations in two and three dimensions. We find that, in the viscous regime, the bridge radius obeys a t1/2-scaling law in time with the characteristic time scale given by the viscous time. Our results differ significantly from the predictions of existing analytical theories of viscous coalescence as well as from experimental observations. While the underlying reason for these deviations is presently unknown, a simple scaling argument is given that describes our results well.
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47.55.df Breakup and coalescence
66.20.-d Viscosity of liquids; diffusive momentum transport
66.20.Cy Theory and modeling of viscosity and rheological properties, including computer simulation
47.11.Qr Lattice gas

A mapping method for distributive mixing with diffusion: Interplay between chaos and diffusion in time-periodic sine flow

Conor P. Schlick, Ivan C. Christov, Paul B. Umbanhowar, Julio M. Ottino, and Richard M. Lueptow

Phys. Fluids 25, 052102 (2013); http://dx.doi.org/10.1063/1.4803897 (22 pages)

Online Publication Date: 14 May 2013

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We present an accurate and efficient computational method for solving the advection-diffusion equation in time-periodic chaotic flows. The method uses operator splitting, which allows the advection and diffusion steps to be treated independently. Taking advantage of flow periodicity, the advection step is solved using a mapping method, and diffusion is “added” discretely after each iteration of the advection map. This approach results in the construction of a composite mapping matrix over an entire period of the chaotic advection-diffusion process and provides a natural framework for the analysis of mixing. To test the approach, we consider two-dimensional time-periodic sine flow. By comparing the numerical solutions obtained by our method to reference solutions, we find qualitative agreement for large time steps (structure of concentration profile) and quantitative agreement for small time steps (low error). Further, we study the interplay between mixing through chaotic advection and mixing through diffusion leading to an analytical model for the evolution of the intensity of segregation with time. Additionally, we demonstrate that our operator splitting mapping approach can be readily extended to three dimensions.
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47.52.+j Chaos in fluid dynamics
47.51.+a Mixing
47.57.eb Diffusion and aggregation
47.60.-i Flow phenomena in quasi-one-dimensional systems
02.60.-x Numerical approximation and analysis

Travelling-wave similarity solutions for a steadily translating slender dry patch in a thin fluid film

Y. M. Yatim, B. R. Duffy, and S. K. Wilson

Phys. Fluids 25, 052103 (2013); http://dx.doi.org/10.1063/1.4803906 (27 pages)

Online Publication Date: 21 May 2013

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A novel family of three-dimensional travelling-wave similarity solutions describing a steadily translating slender dry patch in an infinitely wide thin fluid film on an inclined planar substrate when surface-tension effects are negligible is obtained, the flow being driven by gravity and/or a prescribed constant shear stress on the free surface of the film. For both driving mechanisms, the dry patch has a parabolic shape (which may be concave up or concave down the substrate), and the film thickness increases monotonically away from the contact lines to its uniform far-field value. The two most practically important cases of purely gravity-driven flow and of purely surface-shear-stress-driven flow are analysed separately.
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47.35.-i Hydrodynamic waves
47.20.-k Flow instabilities
47.10.-g General theory in fluid dynamics
68.15.+e Liquid thin films

Spontaneous penetration of a non-wetting drop into an exposed pore

Pengtao Yue and Yuriko Renardy

Phys. Fluids 25, 052104 (2013); http://dx.doi.org/10.1063/1.4804957 (19 pages)

Online Publication Date: 21 May 2013

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We consider the penetration process of a liquid drop approaching an exposed pore along the axis of symmetry, which is intended to model the penetration of non-wetting drops into a porous medium. Inertia and gravity are neglected at the current stage. In addition to the penetration into a capillary tube in the literature, the drop may spread on the outer surface of the porous medium. Based on the mechanical equilibrium states, we find the critical drop radius, below which the drop penetration is spontaneous. We further identify five penetration regimes based on the drop radius and the static contact angle, all of which are exemplified by phase-field simulations. The free energy as a function of penetration depth reveals only two stable equilibrium states: the drop either enters the pore completely (maximum penetration) or stays at the pore inlet (zero penetration). For a non-penetrating drop radius, the free energy has a local maximum which constitutes an energy barrier that prevents spontaneous penetration. Finally, we modify the Lucas-Washburn equation to describe the dynamic process of penetration. Due to the neglect of dissipation from moving contact lines and entry flow, the modified Lucas-Washburn equation greatly overestimates the penetration rate, especially at the initial stage.
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47.55.D- Drops and bubbles
47.55.np Contact lines
47.56.+r Flows through porous media
68.03.Cd Surface tension and related phenomena
47.55.dm Thermocapillary effects
47.55.dr Interactions with surfaces

The fastest drop climbing on a wet conical fibre

Er Qiang Li and Sigurdur T. Thoroddsen

Phys. Fluids 25, 052105 (2013); http://dx.doi.org/10.1063/1.4805068 (13 pages)

Online Publication Date: 21 May 2013

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We use high-speed video imaging to study the capillary-driven motion of a micro-droplet along the outside of a pre-wetted conical fiber. The cones are fabricated on a glass-puller with tip diameters as small as 1 μm, an order of magnitude smaller than in previous studies. The liquid is fed through the hollow fiber accumulating at the fiber tip to form droplets. The droplets are initially attached to the opening as they grow in size before detaching and traveling up the cone. This detachment can produce a transient oscillation of high frequency. The spatial variation of the capillary pressure drives the droplets towards the wider side of the cone. Various liquids were used to change the surface tension by a factor of 3.5 and viscosity by a factor of 1500. Within each droplet size and viscous-dissipation regime, the data for climbing speeds collapse on a single curve. Droplets traveling with and against gravity allow us to pinpoint the absolute strength of the driving capillary pressure and viscous stresses and thereby determine the prefactors in the dimensionless relationships. The motions are consistent with earlier results obtained from much larger cones. Translation velocities up to 270 mm/s were observed and overall the velocities follow capillary-viscous scaling, whereas the speed of the fastest droplets is limited by inertia following their emergence at the cone tip.
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47.55.dm Thermocapillary effects
47.55.dr Interactions with surfaces
47.55.nb Capillary and thermocapillary flows
47.80.Jk Flow visualization and imaging
68.03.Cd Surface tension and related phenomena
66.20.Ej Studies of viscosity and rheological properties of specific liquids

Rim instability of bursting thin smectic films

Torsten Trittel, Thomas John, Kinko Tsuji, and Ralf Stannarius

Phys. Fluids 25, 052106 (2013); http://dx.doi.org/10.1063/1.4807377 (10 pages)

Online Publication Date: 24 May 2013

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The rupture of thin smectic bubbles is studied by means of high speed video imaging. Bubbles of centimeter diameter and film thicknesses in the nanometer range are pierced, and the instabilities of the moving rim around the opening hole are described. Scaling laws describe the relation between film thickness and features of the filamentation process of the rim. A flapping motion of the retracting smectic film is assumed as the origin of the observed filamentation instability. A comparison with similar phenomena in soap bubbles is made. The present experiments extend studies on soap films [H. Lhuissier and E. Villermaux, Phys. Rev. Lett. 103, 054501 (2009)10.1103/PhysRevLett.103.054501] to much thinner, uniform films of thermotropic liquid crystals.
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47.20.-k Flow instabilities
47.55.dd Bubble dynamics
47.80.Jk Flow visualization and imaging
61.30.-v Liquid crystals
68.15.+e Liquid thin films
back to top Viscous and Non-Newtonian Flows

Non-equilibrium pressure control of the height of a large-scale, ground-coupled, rotating fluid column

R. L. Ash and I. R. Zardadkhan

Phys. Fluids 25, 053101 (2013); http://dx.doi.org/10.1063/1.4807068 (19 pages)

Online Publication Date: 23 May 2013

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When a ground-coupled, rotating fluid column is modeled incorporating non-equilibrium pressure forces in the Navier-Stokes equations, a new exact solution results. The solution has been obtained in a similar manner to the classical equilibrium solution. Unlike the infinite-height, classical solution, the non-equilibrium pressure solution yields a ground-coupled rotating fluid column of finite height. A viscous, non-equilibrium Rankine vortex velocity distribution, developed previously, was used to demonstrate how the viscous and non-equilibrium pressure gradient forces, arising in the vicinity of the velocity gradient discontinuity that is present in the classical Rankine vortex model, effectively isolate the rotating central fluid column from the outer potential vortex region. Thus, the non-equilibrium region acts to confine and shield the central, rigid-body-like, rotating fluid core, justifying this examination of how such a rotating fluid column can interact with the ground. The resulting non-equilibrium ground-coupled, rotating fluid column solution was employed to estimate the central column heights of three well-documented dust devils, and the central column height predictions were consistent with published dust devil height statistics.
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47.32.cb Vortex interactions
47.10.ad Navier-Stokes equations
47.32.Ef Rotating and swirling flows
back to top Particulate, Multiphase, and Granular Flows

Magnetic resonance imaging study on near miscible supercritical CO2 flooding in porous media

Yongchen Song, Ningjun Zhu, Yuechao Zhao, Yu Liu, Lanlan Jiang, and Tonglei Wang

Phys. Fluids 25, 053301 (2013); http://dx.doi.org/10.1063/1.4803663 (14 pages)

Online Publication Date: 7 May 2013

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CO2 flooding is one of the most popular secondary or tertiary recoveries for oil production. It is also significant for studying the mechanisms of the two-phase and multiphase flow in porous media. In this study, an experimental study was carried out by using magnetic resonance imaging technique to examine the detailed effects of pressure and rates on CO2/decane flow in a bead-pack porous media. The displacing processes were conducted under various pressures in a region near the minimum miscibility pressure (the system tuned from immiscible to miscible as pressure is increasing in this region) and the temperature of 37.8 °C at several CO2 injection volumetric rates of 0.05, 0.10, and 0.15 ml/min (or linear rates of 3.77, 7.54, and 11.3 ft/day). The evolution of the distribution of decane and the characteristics of the two phase flow were investigated and analyzed by considering the pressure and rate. The area and velocity of the transition zone between the two phases were calculated and analyzed to quantify mixing. The area of transition zone decreased with pressure at near miscible region and a certain injection rate and the velocity of the transition zone was always less than the “volumetric velocity” due to mutual solution and diffusion of the two phases. Therefore, these experimental results give the fundamental understanding of tertiary recovery processes at near miscible condition.
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47.56.+r Flows through porous media
47.55.Ca Gas/liquid flows
47.80.Jk Flow visualization and imaging
88.10.gf Imaging fluid flow
93.85.Tf Oil prospecting, pipelines, and conduits
47.85.Np Fluidics

Analytical solution of the problem of the rise of a Taylor bubble

Yuri B. Zudin

Phys. Fluids 25, 053302 (2013); http://dx.doi.org/10.1063/1.4803878 (16 pages)

Online Publication Date: 13 May 2013

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In the classical works of Prandtl and Taylor devoted to the analysis of the problem of the rise of a Taylor bubble in a round tube, a solution of the Laplace equation is used, which contains divergent infinite series. The present paper outlines a method for the correct analysis of the mentioned problem. Using the method of superposition of “elementary flows,” a solution was obtained for flow of an ideal fluid over a body of revolution in a pipe. Satisfying the free surface condition in the vicinity of the stagnation point and using the limiting transition with respect to the main parameter lead to the relation for the rise velocity of a Taylor bubble expressed in terms of the Froude number. In order to validate the method of superposition, it was applied to the problem of the rise of a plane Taylor bubble in a flat gap, which also has an exact analytical solution obtained with the help of the complex variable theory.
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47.55.dd Bubble dynamics
47.20.-k Flow instabilities
47.10.-g General theory in fluid dynamics
02.30.-f Function theory, analysis

Dynamics and rheology of concentrated, finite-Reynolds-number suspensions in a homogeneous shear flow

Kyongmin Yeo and Martin R. Maxey

Phys. Fluids 25, 053303 (2013); http://dx.doi.org/10.1063/1.4802844 (24 pages)

Online Publication Date: 14 May 2013

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We present the lubrication-corrected force-coupling method for the simulation of concentrated suspensions under finite inertia. Suspension dynamics are investigated as a function of the particle-scale Reynolds number Rmath and the bulk volume fraction ϕ in a homogeneous linear shear flow, in which Rmath is defined from the density ρf and dynamic viscosity μ of the fluid, particle radius a, and the shear rate math as Rmath = ρfmatha2/μ. It is shown that the velocity fluctuations in the velocity-gradient and vorticity directions decrease at larger Rmath. However, the particle self-diffusivity is found to be an increasing function of Rmath as the motion of the suspended particles develops a longer auto-correlation under finite fluid inertia. It is shown that finite-inertia suspension flows are shear-thickening and the particle stresses become highly intermittent as Rmath increases. To study the detailed changes in the suspension microstructure and rheology, we introduce a particle-stress-weighted pair-distribution function. The stress-weighted pair-distribution function clearly shows that the increase of the effective viscosity at high Rmath is mostly related to the strong normal lubrication interaction in the compressive principal axis of the shear flow.
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82.70.Kj Emulsions and suspensions
47.57.Qk Rheological aspects
47.85.mf Lubrication flows

Momentum transfer in a turbulent, particle-laden Couette flow

David H. Richter and Peter P. Sullivan

Phys. Fluids 25, 053304 (2013); http://dx.doi.org/10.1063/1.4804391 (20 pages)

Online Publication Date: 14 May 2013

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A point-force model is used to study turbulent momentum transfer in the presence of moderate mass loadings of small (relative to Kolmogorov scales), dense (relative to the carrier phase density) particles. Turbulent Couette flow is simulated via direct numerical simulation, while individual particles are tracked as Lagrangian elements interacting with the carrier phase through a momentum coupling force. This force is computed based on the bulk drag of each particle, computed from its local slip velocity. By inspecting a parameter space consisting of particle Stokes number and mass loading, a general picture of how and under what conditions particles can alter near-wall turbulent flow is developed. In general, it is found that particles which adhere to the requirements for the point-particle approximation attenuate small-scale turbulence levels, as measured by wall-normal and spanwise velocity fluctuations, and decrease turbulent fluxes. Particles tend to weaken near-wall vortical activity, which in turn, through changes in burst/sweep intensities, weakens the ability of the turbulent carrier-phase motion to transfer momentum in the wall-normal direction. Compensating this effect is the often-ignored capacity of the dispersed phase to carry stress, resulting in a total momentum transfer which remains nearly unchanged. The results of this study can be used to interpret physical processes above the ocean surface, where sea spray potentially plays an important role in vertical momentum transfer.
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47.55.Kf Particle-laden flows
47.27.nb Boundary layer turbulence
47.15.Cb Laminar boundary layers
47.11.-j Computational methods in fluid dynamics
47.45.Gx Slip flows and accommodation
47.27.ek Direct numerical simulations
back to top Laminar Flows

Active control of a cylinder wake flow by using a streamwise oscillating foil

Y. Bao and J. Tao

Phys. Fluids 25, 053601 (2013); http://dx.doi.org/10.1063/1.4802042 (17 pages)

Online Publication Date: 1 May 2013

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In this study, numerical experiments are carried out to control the vortex shedding of a circular cylinder by utilizing an oscillating foil. The thin foil of elliptic shape undergoes prescribed harmonic oscillations in the streamwise direction in the near wake region. This simplified model is intended to study how wake dynamics are modified via localized wake disturbance, and then to stabilize the global wake instability. The results show that, at proper gap spacing, the oscillating foil can completely suppress the wake unsteadiness and recover the recirculating bubble type flow. The global instability suppression is then established on the imposition of local symmetry into the reversed flow behind the cylinder. It is revealed that the dynamic interaction between the main shears layer and oscillatory boundary layers is responsible for the wake stabilization mechanism. In addition, the kinematic/dynamic parameters related to foil motions and flow properties are widely discussed to reveal their effects on the performance of wake stabilization and drag reduction.
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47.15.Tr Laminar wakes
47.32.Ef Rotating and swirling flows
47.85.lb Drag reduction
47.85.ld Boundary layer control
47.15.Cb Laminar boundary layers
47.15.Fe Stability of laminar flows

An analytical solution for Dean flow in curved ducts with rectangular cross section

M. Norouzi and N. Biglari

Phys. Fluids 25, 053602 (2013); http://dx.doi.org/10.1063/1.4803556 (15 pages)

Online Publication Date: 7 May 2013

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In this paper, a full analytical solution for incompressible flow inside the curved ducts with rectangular cross-section is presented for the first time. The perturbation method is applied to solve the governing equations and curvature ratio is considered as the perturbation parameter. The previous perturbation solutions are usually restricted to the flow in curved circular or annular pipes related to the overly complex form of solutions or singularity situation for flow in curved ducts with non-circular shapes of cross section. This issue specifies the importance of analytical studies in the field of Dean flow inside the non-circular ducts. In this study, the main flow velocity, stream function of lateral velocities (secondary flows), and flow resistance ratio in rectangular curved ducts are obtained analytically. The effect of duct curvature and aspect ratio on flow field is investigated as well. Moreover, it is important to mention that the current analytical solution is able to simulate the Taylor-Görtler and Dean vortices (vortices in stable and unstable situations) in curved channels.
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47.60.Dx Flows in ducts and channels
02.30.Sa Functional analysis
47.10.A- Mathematical formulations
47.32.-y Vortex dynamics; rotating fluids

Vortex-shedding suppression in two-dimensional mixed convective flows past circular and square cylinders

Nadeem Hasan and Rashid Ali

Phys. Fluids 25, 053603 (2013); http://dx.doi.org/10.1063/1.4804387 (27 pages)

Online Publication Date: 21 May 2013

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Vortex-shedding suppression in two-dimensional mixed convective flows past circular and square cylinders is investigated numerically at two supercritical Reynolds numbers, Re = 60 and 100, at a fixed Prandtl (Pr) number of 0.71. The Richardson number (Ri) and free-stream orientation (α) are varied in the range [0, 1.6] and [0, π/2], respectively. The investigations involve the numerical solutions of mass, momentum, and energy equations subject to Boussinesq approximation in generalized curvilinear body-fitted coordinates. The critical Richardson numbers corresponding to the onset of suppression of vortex-shedding are determined for different free-stream orientations using the numerical data and the Stuart-Landau theory. For the case of circular cylinder, the critical Richardson number exhibits a “cosine-law” with respect to the free-stream orientation, while a non-monotonic trend is observed for the case of the square cylinder. By examining the near critical steady flow field data, two distinct components of the baroclinic vorticity generation rate are identified that appear to control the shedding suppression laws (relationships between the critical Richardson number and free-stream orientation) in theRi-α parametric space for the circular and the square cylinders. Supported by numerical experiments, the plausible roles of these baroclinic vorticity generation rate components are identified and utilized to theoretically deduce the functional forms of the shedding suppression laws that agree with the laws observed in the numerical experiments.
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47.32.-y Vortex dynamics; rotating fluids
47.15.-x Laminar flows
02.60.Gf Algorithms for functional approximation
47.85.L- Flow control

Reaction of initially distant scalars in a cylinder wake

John P. Crimaldi and Tanaya R. Kawakami

Phys. Fluids 25, 053604 (2013); http://dx.doi.org/10.1063/1.4807062 (16 pages)

Online Publication Date: 23 May 2013

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We used analytical and numerical techniques to investigate the effect of a quasi-steady-state laminar wake behind a circular cylinder on the second-order reaction between two initially distant scalars. The scalars are released continuously from locations upstream of the cylinder, and are separated from each other by a lateral distance that initially impedes the reaction. By comparing the laterally integrated reaction evolution for cases with and without the cylinder wake, the direct effect of the wake on reaction enhancement is determined. We compute the reaction for a range of reaction speeds, scalar diffusivities, and scalar release geometries. The presence of the cylinder wake generates significant reaction enhancement for all cases; the ratio of the reaction with and without the cylinder increases with the initial scalar separation distance. We identify the mechanism for the reaction enhancement, and demonstrate that the reaction rate in the cylinder wake can be predicted by a simple analytical model of a stretched scalar interface.
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47.70.Fw Chemically reactive flows
47.15.Tr Laminar wakes
47.11.-j Computational methods in fluid dynamics
02.60.Cb Numerical simulation; solution of equations
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