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Mar 2009

Volume 21, Issue 3, Articles (03xxxx)

Issue Cover Spotlight Figure

Phys. Fluids 21, 034106 (2009); http://dx.doi.org/10.1063/1.3093236 (11 pages)

Y. D. Cui, J. M. Lopez, T. T. Lim, and F. Marques
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Maximization of granular outflow by oblique exits and by obstacles

Björn Zelinski, Eric Goles, and Mario Markus

Phys. Fluids 21, 031701 (2009); http://dx.doi.org/10.1063/1.3103329 (3 pages)

Online Publication Date: 20 March 2009

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We investigate experimentally the intermittent discharge of a granular medium out of an exit at the bottom of a vertically shaken box. Changing the orientation of the bottom shows that there exists an angle (around 20°–25° with respect to the horizontal) at which the mean discharge rate increases up to a factor 1.9, as compared to the rate with horizontal bottom. Furthermore, adjusting the diameter and the distance of a cylindrical obstacle above the exit on the (horizontal) bottom, allows to optimize the mean rate of discharge up to 3.5 times the rate without obstacle.
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47.57.Gc Granular flow
47.60.-i Flow phenomena in quasi-one-dimensional systems
45.70.Mg Granular flow: mixing, segregation and stratification

Prolonged residence times for particles settling through stratified miscible fluids in the Stokes regime

Roberto Camassa, Claudia Falcon, Joyce Lin, Richard M. McLaughlin, and Richard Parker

Phys. Fluids 21, 031702 (2009); http://dx.doi.org/10.1063/1.3094922 (4 pages) | Cited 6 times

Online Publication Date: 25 March 2009

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The behavior of settling particles in stratified fluid is important in a variety of applications, from environmental to medical. We document a phenomenon in which a sphere, when crossing density transitions, slows down substantially in comparison to its settling speed in the bottom denser layer, due to entrainment of buoyant fluid. We present results from an experimental study of the effects of the fluid interface on flight times as well as a theoretical model derived from first principles in the low Reynolds number regimes for stratified miscible fluids. Our work provides a new predictive tool and gives insight into the role of strong stratification in particle settling.
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47.55.Kf Particle-laden flows
47.55.Hd Stratified flows
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back to top Interfacial Flows

Early post-impact time dynamics of viscous drops onto a solid dry surface

A. Mongruel, V. Daru, F. Feuillebois, and S. Tabakova

Phys. Fluids 21, 032101 (2009); http://dx.doi.org/10.1063/1.3079095 (13 pages) | Cited 5 times

Online Publication Date: 5 March 2009

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The spreading dynamics of liquid drops normally impacting a solid dry surface at high Reynolds and Weber numbers is experimentally and numerically studied at early post-impact times starting from 10−5 s after impact. The focus is on the emergence and growing of the axisymmetric liquid lamella underneath the drop, that is, on the time evolution of its thickness, radius, and velocity, as a function of impact velocity U and liquid viscosity ν. The Navier–Stokes equations for two-phase flows are solved numerically by an artificial compressibility method. A “shock-capturing” method is used for the tracking of the gas-liquid interface, neglecting surface tension effects. Experimental and numerical results are interpreted using a simple scaling analysis that reveals the characteristic lengths and velocities of the spreading dynamics. In particular, a finite characteristic time of appearance for the lamella is found, which is of the order of ν/U2. Rescaling of the data works satisfactorily in the considered range of parameters. Thus, the lamella ejection is limited by viscosity.
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47.55.D- Drops and bubbles
68.08.Bc Wetting
47.10.A- Mathematical formulations
47.55.Ca Gas/liquid flows

Three-dimensional thin film flow over and around an obstacle on an inclined plane

S. J. Baxter, H. Power, K. A. Cliffe, and S. Hibberd

Phys. Fluids 21, 032102 (2009); http://dx.doi.org/10.1063/1.3082218 (23 pages) | Cited 6 times

Online Publication Date: 10 March 2009

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Steady Stokes flow driven by gravity down an inclined plane over and around an attached obstacle is considered. The effects of the obstacle are examined for various flow configurations and results produced for flow over hemispherical obstacles. Comparison is made with previously published papers that assume that the obstacle is small and/or the free surface deflection and disturbance velocity are small. Values for the unit normal and curvature of the free surface are found using both finite difference approximations and Hermitian radial basis function interpolations, with the resulting solutions compared. Free surface profiles for thin film flows over hemispherical obstacles that approach the film surface are produced and the effects of near point singularities considered. All free surface profiles indicate an upstream peak, followed by a trough downstream of the obstacle with the peak decaying in a “horseshoe” shaped surface deformation. Flow profiles are governed by the plane inclination, the Bond number, and the obstacle geometry. An extension of this approach provides a new class of solutions where a thin film flows around a cylindrical obstacle. Notably, the static contact line angle between the free surface and the obstacle is introduced as an extra flow parameter and its effect investigated for a given set of flow parameters and fixed boundary conditions. Solutions are obtained where steady flow profiles can be found both over and around a cylindrical obstacle raising the awareness of possible multiple solutions.
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47.11.Bc Finite difference methods
02.70.Bf Finite-difference methods
02.60.Ed Interpolation; curve fitting

Role of geometry and fluid properties in droplet and thread formation processes in planar flow focusing

Wingki Lee, Lynn M. Walker, and Shelley L. Anna

Phys. Fluids 21, 032103 (2009); http://dx.doi.org/10.1063/1.3081407 (14 pages) | Cited 28 times

Online Publication Date: 13 March 2009

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Droplet formation processes in microfluidic flow focusing devices have been examined previously and some of the key physical mechanisms for droplet formation revealed. However, the underlying physical behavior is still too poorly understood to utilize it for generating droplets of precise size. In this work, we formulate scaling arguments to define dimensionless variables which capture all the parameters that control the droplet breakup process, including the flow rates and the viscosities of the two immiscible fluids, the interfacial tension between the fluids and the numerous dimensions in the flow focusing device. To test these arguments, we perform flow focusing experiments and systematically vary the dimensional parameters. Through these experiments, we confirm the validity of the scaling arguments and find a power law relationship between the normalized droplet size and the capillary number. We demonstrate that droplet formation can be separated into an upstream process for primary droplet formation and a downstream process for thread formation. These results are key to the ability to tune the flow focusing process for specific applications that require monodisperse micron and submicron droplets and particles.
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47.85.Np Fluidics
68.03.Cd Surface tension and related phenomena
47.55.df Breakup and coalescence

Charge separation in the conical meniscus of an electrospray of a very polar liquid: Its effect on the minimum flow rate

F. J. Higuera

Phys. Fluids 21, 032104 (2009); http://dx.doi.org/10.1063/1.3088491 (11 pages) | Cited 2 times

Online Publication Date: 17 March 2009

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An analysis is presented of the flow and the distribution of charge in the meniscus of an electrospray of a very polar liquid which is fed with a low flow rate. The shape of the meniscus is taken to be a Taylor cone. The characteristic value of the flow rate at which the liquid ceases to be quasineutral in a certain relaxation region of the conical meniscus under the action of the applied field is estimated, and the current/flow rate characteristic of the electrospray is numerically computed in these conditions. A state of complete charge separation, in which the ions that are pushed by the electric field away from the tip of the meniscus cease to reach the jet of the electrospray, is found for a finite value of the flow rate, and no stationary solution exists below this flow rate. For very polar liquids of small viscosity, this minimum flow rate is of the order of the experimental minimum for the cone-jet regime when the flux of the electric field in the jet is taken into account. The flow induced in the meniscus by the Coulomb force in the bulk of the liquid and the electric shear stress at its surface is computed and its effect on the distribution of charge and the minimum flow rate is analyzed. Estimates of the flow and the electric current in the jet are worked out for a range of flow rates above the minimum.
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.60.Kz Flows and jets through nozzles
47.55.np Contact lines
47.11.-j Computational methods in fluid dynamics

Marangoni-driven spreading along liquid-liquid interfaces

S. Berg

Phys. Fluids 21, 032105 (2009); http://dx.doi.org/10.1063/1.3086039 (12 pages) | Cited 6 times

Online Publication Date: 18 March 2009

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Marangoni-driven spreading at gas-liquid interfaces has been studied extensively over the past years but so far the spreading kinetics along the interface between immiscible liquids has not been investigated systematically. In this study, the spreading kinetics of aqueous solutions of sodium dodecyl sulfate and dodecyl trimethyl ammonium bromide along the interface between thick layers of water and decane has been investigated by means of two different optical visualization techniques (dye tracer and laser shadowgraphy). The spreading kinetics follows a power law where the radius r as function of time t scales as r(t)∝t3/4 indicating large similarities with Marangoni-driven spreading at air-liquid interfaces. The existing scaling law for spreading at air-liquid interfaces is based on the balance between an interfacial tension gradient and the viscous stress in the fluid layers beneath the interface. When the viscous dissipation in the two boundary layers below and above the interface is factored into the scaling law, quantitative agreement with experimental data is obtained. Marangoni-driven spreading along an interface is a fast transport mechanism. The velocity of the leading edge lies within the range of group velocities of capillary waves.
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68.03.Cd Surface tension and related phenomena
47.80.Jk Flow visualization and imaging
47.27.N- Wall-bounded shear flow turbulence

Mechanism study of deformation and mass transfer for binary droplet collisions with particle method

Zhongguo Sun, Guang Xi, and Xi Chen

Phys. Fluids 21, 032106 (2009); http://dx.doi.org/10.1063/1.3089587 (13 pages) | Cited 6 times

Online Publication Date: 19 March 2009

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The binary collision of two identical liquid droplets is simulated using the moving particle semi-implicit method. We focus on various coalescence and separation mechanisms and the accompanying mass transfer characteristics. A modified surface-tension model is implemented in three-dimensional numerical simulations to study the large deformation processes. Both head-on collision and eccentric impact are investigated, and a mechanism map is established to qualitatively distinguish different regimes of impact. Mass transfer properties are obtained by tracking the movement of particles, which are useful for identifying the mixing rate of the droplets after coalescence or separation as well as the source of the newly formed satellite droplets. A mixing map (in terms of impact speed and impact number) is also established to provide guidelines of pursuing higher efficiency of mixing two liquids using collision. The results qualitatively agree with previous experiments and the versatile numerical protocol may also find applications in studying the free surface flows and interface deformation.
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47.55.D- Drops and bubbles
68.03.Cd Surface tension and related phenomena

Influence of electric field on saturated film boiling

G. Tomar, G. Biswas, A. Sharma, and S. W. J. Welch

Phys. Fluids 21, 032107 (2009); http://dx.doi.org/10.1063/1.3095917 (8 pages) | Cited 1 time

Online Publication Date: 20 March 2009

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Electrohydrodynamic (EHD) forces enhance heat and mass transfer in fluid flows. In two-phase flows under the influence of an electric field, an EHD force acts on the interface resulting in an enhanced interfacial motion. We perform a numerical study of the effect of the application of an electric field on bubble density and heat transfer characteristics during saturated film boiling. Application of electric field results in shorter bubble separation distances, faster growth of the instability, and higher bubble release frequency. Increasing the electric-field intensity shows an increase in the space averaged Nusselt number, thus indicating the role of electric field in the enhancement of heat transfer. We perform full nonlinear simulations of saturated film boiling coupled with electrohydrodynamics using a coupled level set and volume of fluid algorithm. Simulations have been performed for water and refrigerant R123a at near critical pressures.
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.20.-k Flow instabilities
47.55.D- Drops and bubbles
FREE

Capillary oscillations of a constrained liquid drop

J. B. Bostwick and P. H. Steen

Phys. Fluids 21, 032108 (2009); http://dx.doi.org/10.1063/1.3103344 (10 pages) | Cited 23 times

Online Publication Date: 27 March 2009

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An inviscid spherical liquid drop held by surface tension exhibits linear oscillations of a characteristic frequency and mode shape (Rayleigh oscillations). If the drop is pinned on a circle of contact the mode shapes change and the frequencies are shifted. The linear problem of inviscid, axisymmetric, volume-preserving oscillations of a liquid drop constrained by pinning along a latitude is solved here. The formulation gives rise to an integrodifferential boundary value problem, similar to that for Rayleigh oscillations, and for oscillations of a drop in contact with a spherical bowl [ M. Strani and F. Sabetta, J. Fluid Mech. 141, 233 (1984) ], only more constrained. A spectral method delivers a truncated solution to the eigenvalue problem. A numerical routine has been used to generate the eigenfrequencies/eigenmodes as a function of the location of the pinned circle of constraint. The effect of pinning the drop is to introduce a new low-frequency eigenmode. The center-of-mass motion, important in application, is partitioned among all the eigenmodes but the low-frequency mode is its principal carrier.
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47.55.D- Drops and bubbles
68.03.Cd Surface tension and related phenomena
02.60.Nm Integral and integrodifferential equations
02.60.Lj Ordinary and partial differential equations; boundary value problems
02.10.Ud Linear algebra

Dynamics of liquid jets and threads under the action of radial electric fields: Microthread formation and touchdown singularities

Qiming Wang, S. Mählmann, and D. T. Papageorgiou

Phys. Fluids 21, 032109 (2009); http://dx.doi.org/10.1063/1.3097888 (19 pages) | Cited 3 times

Online Publication Date: 27 March 2009

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We study theoretically the axisymmetric nonlinear dynamics of viscous conducting liquid jets or threads under the action of a radial electric field. The field is generated by a potential difference between the jet surface and a concentrically placed electrode of given radius. We develop a long wave nonlinear model that is used to predict the dynamics of the system and, in particular, to address the effect of the radial electric field on jet breakup. Two canonical regimes are identified that depend on the size of the gap between the outer electrode and the unperturbed jet surface. For relatively large gap sizes, long waves are stabilized for sufficiently strong electric fields but remain unstable as in the nonelectrified case for electric field strengths below a critical value. For relatively small gaps, an electric field of any strength enhances the instability of long waves as compared to the nonelectrified case. We carry out numerical simulations based on our nonlinear models to describe the nonlinear evolution and terminal states in these two regimes. We find that jet pinching does not occur irrespective of the parameters. We identify regimes where capillary instability leads to the formation of stable quasistatic microthreads (connected to large main drops) whose radius decreases with the strength of the electric field. The generic ultimate singular event described by our models is the attraction of the jet surface toward the enclosing electrode and its contact with the electrode in finite time. A self-similar closed form solution is found that describes this event with the interface near touchdown having locally a cusp geometry. The theory is compared to the time-dependent simulations with excellent agreement.
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.54.Bd Theoretical aspects
47.35.-i Hydrodynamic waves
47.55.nb Capillary and thermocapillary flows
47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.53.+n Fractals in fluid dynamics
back to top Viscous and Non-Newtonian Flows

Oxygen and carbon dioxide transport in time-dependent blood flow past fiber rectangular arrays

Jennifer R. Zierenberg, Hideki Fujioka, Ronald B. Hirschl, Robert H. Bartlett, and James B. Grotberg

Phys. Fluids 21, 033101 (2009); http://dx.doi.org/10.1063/1.3056413 (29 pages) | Cited 2 times

Online Publication Date: 5 March 2009

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The influence of time-dependent flows on oxygen and carbon dioxide transport for blood flow past fiber arrays arranged in in-line and staggered configurations was computationally investigated as a model for an artificial lung. Both a pulsatile flow, which mimics the flow leaving the right heart and passing through a compliance chamber before entering the artificial lung, and a right ventricular flow, which mimics flow leaving the right heart and directly entering the artificial lung, were considered in addition to a steady flow. The pulsatile flow was modeled as a sinusoidal perturbation superimposed on a steady flow while the right ventricular flow was modeled to accurately depict the period of flow acceleration (increasing flow) and deceleration (decreasing flow) during systole followed by zero flow during diastole. It was observed that the pulsatile flow yielded similar gas transport as compared to the steady flow, while the right ventricular flow resulted in smaller gas transport, with the decrease increasing with Re. The pressure drop across the fiber array (a measure of the resistance), work (an indicator of the work required of the right heart), and shear stress (a measure of potential blood cell activation and damage) are lowest for steady flow, followed by pulsatile flow, and then right ventricular flow. The pressure drop, work, shear stress, and Sherwood numbers (a measure of the gas transport efficiency) decrease with increasing porosity and are smaller for AR<1 as compared to AR>1 (AR is the distance between fibers in the flow direction/distance between fibers in direction perpendicular to flow), although for small porosities the Sherwood numbers are of similar magnitude. In general, for any fiber array geometry, high pressure drop, work, and shear stresses correlate with high Sherwood numbers, and low pressure drop, work, and shear stresses correlate with low Sherwood numbers creating a need for a compromise between pressure drop/work/shear stresses and gas transport.
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87.19.U- Hemodynamics
47.63.Cb Blood flow in cardiovascular system
47.63.-b Biological fluid dynamics
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.56.+r Flows through porous media

Swimming speeds of filaments in nonlinearly viscoelastic fluids

Henry C. Fu, Charles W. Wolgemuth, and Thomas R. Powers

Phys. Fluids 21, 033102 (2009); http://dx.doi.org/10.1063/1.3086320 (10 pages) | Cited 17 times

Online Publication Date: 11 March 2009

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Many micro-organisms swim through gels and non-Newtonian fluids in their natural environments. In this paper, we focus on micro-organisms which use flagella for propulsion. We address how swimming velocities are affected in nonlinearly viscoelastic fluids by examining the problem of an infinitely long cylinder with arbitrary beating motion in the Oldroyd-B fluid. We solve for the swimming velocity in the limit in which deflections of the cylinder from its straight configuration are small relative to the radius of the cylinder and the wavelength of the deflections; furthermore, the radius of the cylinder is small compared to the wavelength of deflections. We find that swimming velocities are diminished by nonlinear viscoelastic effects. We apply these results to examine what types of swimming motions can produce net translation in a nonlinear fluid, comparing to the Newtonian case, for which Purcell’s “scallop” theorem describes how time-reversibility constrains which swimming motions are effective. We find that a leading order violation of the scallop theorem occurs for reciprocal motions in which the backward and forward strokes occur at different rates.
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47.63.Gd Swimming microorganisms

An efficient direct simulation Monte Carlo method for low Mach number noncontinuum gas flows based on the Bhatnagar–Gross–Krook model

Shriram Ramanathan and Donald L. Koch

Phys. Fluids 21, 033103 (2009); http://dx.doi.org/10.1063/1.3081562 (11 pages) | Cited 4 times

Online Publication Date: 18 March 2009

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The direct simulation Monte Carlo (DSMC) method is the preferred approach for simulating rarefied gas flows in complex geometries. However, the standard DSMC method becomes inefficient in the limit M = math/〈c〉→0 when the thermal velocity fluctuations which scale with the speed of sound 〈c〉 are much larger than characteristic ensemble-averaged flow speed math. In this paper, we propose a modified DSMC algorithm which simulates the linearized Bhatnagar–Gross–Krook (BGK) approximation to the Boltzmann equation. The particles in this method are uniformly distributed in space and have a rest-state, equilibrium Maxwellian velocity distribution. The deviations from the equilibrium state are captured by weightings, indicating that each particle represents a noninteger expectation for finding gas molecules with the simulation particle’s velocity in the spatial cell where it is found. The BGK approximation makes the implementation of such a method simple and efficient because the BGK collision rule can be implemented by adjusting particle weightings without the need to create new particles during the simulation. The method can be incorporated into existing DSMC simulation programs with minimal changes. We apply the new algorithm to two test problems—pressure-driven flow through a nanochannel and flow around an isolated sphere. Results obtained with the new method are in excellent agreement with previous theories and simulations.
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47.61.Cb Non-continuum effects
47.11.-j Computational methods in fluid dynamics
47.60.Dx Flows in ducts and channels

On the flow of associative polymers past a sphere: Evaluation of negative wake criteria

A. J. Mendoza-Fuentes, R. Montiel, R. Zenit, and O. Manero

Phys. Fluids 21, 033104 (2009); http://dx.doi.org/10.1063/1.3090180 (13 pages) | Cited 2 times

Online Publication Date: 18 March 2009

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A study on falling spheres descending in associative polymers with sphere-container ratios of 0.05–0.15 for various polymer concentrations and Weissenberg numbers is presented. The fluid exhibits constant viscosity over a wide range of small to moderate shear rates, and shear thinning for large shear rates. The simple shear rheology and linear viscoelasticity of these polymers are modeled with the BMP equation of state [ F. Bautista, J. M. de Santos, J. E. Puig, and O. Manero, J. Non-Newtonian Fluid Mech. 80, 93 (1999) ; O. Manero, F. Bautista, J. F. A. Soltero, and J. E. Puig, J. Non-Newtonian Fluid Mech. 106, 1 (2002) ], which enables the prediction of the extensional viscosity as a function of the strain rate. The particle image velocimetry technique allows the measurement of the velocity field in the rear of the sphere. The container wall affects the formation of the negative wake at a critical Weissenberg number, which closely corresponds to the region around the peak of extension thickening of the Trouton ratio in the solution. A characteristic strain rate is estimated from the distance of the sphere surface to the stagnant point where the velocity changes direction. Using these data, various criteria for the appearance of the negative wake are discussed. Conclusions reached by Dou and Phan-Thien [ Rheol. Acta 43, 203 (2004) ] on the physical mechanisms for negative wake generation, are in agreement with the results exposed in this work.
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47.50.-d Non-Newtonian fluid flows
47.15.Tr Laminar wakes
47.57.Qk Rheological aspects
47.57.Ng Polymers and polymer solutions

Volume viscosity in fluids with multiple dissipative processes

Allan J. Zuckerwar and Robert L. Ash

Phys. Fluids 21, 033105 (2009); http://dx.doi.org/10.1063/1.3085814 (12 pages) | Cited 2 times

Online Publication Date: 20 March 2009

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The variational principle of Hamilton is applied to derive the volume viscosity coefficients of a reacting fluid with multiple dissipative processes. The procedure, as in the case of a single dissipative process, yields two dissipative terms in the Navier–Stokes equation: The first is the traditional volume viscosity term, proportional to the dilatational component of the velocity; the second term is proportional to the material time derivative of the pressure gradient. Each dissipative process is assumed to be independent of the others. In a fluid comprising a single constituent with multiple relaxation processes, the relaxation times of the multiple processes are additive in the respective volume viscosity terms. If the fluid comprises several relaxing constituents (each with a single relaxation process), the relaxation times are again additive but weighted by the mole fractions of the fluid constituents. A generalized equation of state is derived, for which two special cases are considered: The case of “low-entropy production,” where entropy variation is neglected, and that of “high entropy production,” where the progress variables of the internal molecular processes are neglected. Applications include acoustical wave propagation, Stokes flow around a sphere, and the structure and thickness of a normal shock. Finally, it is shown that the analysis presented here resolves several misconceptions concerning the volume viscosity of fluids.
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47.40.Nm Shock wave interactions and shock effects
47.10.A- Mathematical formulations

Effective viscosity of a dilute suspension of membrane-bound inclusions

Mark L. Henle and Alex J. Levine

Phys. Fluids 21, 033106 (2009); http://dx.doi.org/10.1063/1.3086831 (14 pages) | Cited 3 times

Online Publication Date: 31 March 2009

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When particulate suspensions are sheared, perturbations in the shear flows around the rigid particles increase the local energy dissipation so that the viscosity of the suspension is effectively higher than that of the solvent. For bulk (three-dimensional) fluids, understanding this viscosity enhancement is a classic problem in hydrodynamics that originated over a century ago with Einstein’s study of a dilute suspension of spherical particles [ A. Einstein, Ann. Phys. 19, 289 (1906) ]. In this paper, we investigate the analogous problem of the effective viscosity of a suspension of disks embedded in a two-dimensional membrane or interface. Unlike the hydrodynamics of bulk fluids, low-Reynolds number membrane hydrodynamics is characterized by an inherent length scale generated by the coupling of the membrane to the bulk fluids that surround it. As a result, we find that the size of the particles in the suspension relative to this hydrodynamic length scale has a dramatic effect on the effective viscosity of the suspension. Our study also helps elucidate the mathematical tools needed to solve the mixed boundary value problems that generically arise when considering the motion of rigid inclusions in fluid membranes.
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47.57.E- Suspensions
47.55.Kf Particle-laden flows
82.70.Kj Emulsions and suspensions
66.20.-d Viscosity of liquids; diffusive momentum transport
47.10.A- Mathematical formulations
02.60.Lj Ordinary and partial differential equations; boundary value problems
back to top Particulate, Multiphase, and Granular Flows

Effects of particle properties on segregation-band drift in particle-laden rimming flow

E. Guyez and P. J. Thomas

Phys. Fluids 21, 033301 (2009); http://dx.doi.org/10.1063/1.3081046 (10 pages) | Cited 1 time

Online Publication Date: 17 March 2009

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We experimentally study rimming flow of a particle-laden fluid. We begin to investigate the details of the spatiotemporal segregation-band dynamics that were first documented by us elsewhere [ E. Guyez and P. J. Thomas, Phys. Rev. Lett. 100, 074501 (2008) ]. There exist eight relevant nondimensional parameters that must be expected to affect the drift dynamics of segregation bands in particle-laden rimming flow. Here we summarize results from experiments investigating the effects of three of these parameters that involve the particle size and the particle density. It is shown that two of the parameters are crucial to the initiation of the band drift and that bands become stationary whenever either one of the two parameters adopts values below an associated critical threshold. Based on the physical relevance of the two parameters it is concluded that the initiation of band drift is strongly affected by a competition between capillary forces and gravitational forces. The third nondimensional parameter studied here characterizes the bulk particle concentration and it is found that it controls the band-drift speed in the parameter regime where band drift exists.
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47.55.-t Multiphase and stratified flows
45.70.Mg Granular flow: mixing, segregation and stratification

Forces on a finite-sized particle located close to a wall in a linear shear flow

Lanying Zeng, Fady Najjar, S. Balachandar, and Paul Fischer

Phys. Fluids 21, 033302 (2009); http://dx.doi.org/10.1063/1.3082232 (18 pages) | Cited 13 times

Online Publication Date: 18 March 2009

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To understand and better model the hydrodynamic force acting on a finite-sized particle moving in a wall-bounded linear shear flow, here we consider the two limiting cases of (a) a rigid stationary spherical particle in a linear wall-bounded shear flow and (b) a rigid spherical particle in rectilinear motion parallel to a wall in a quiescent ambient flow. In the present computations, the particle Reynolds number ranges from 2 to 250 at separation distances to the wall from nearly sitting on the wall to far away from the wall. First we characterize the structure of the wake for a stationary particle in a linear shear flow and compare with those for a particle moving parallel to a wall in a quiescent ambient [see L. Zeng, S. Balachandar, and P. Fischer, J. Fluid Mech. 536, 1 (2005) ]. For both these cases we present drag and lift results and obtain composite drag and lift correlations that are valid for a wide range of Re and distance from the wall. These correlations have been developed to be consistent with all available low Reynolds number theories and approach the appropriate uniform flow results at large distance from the wall. Particular attention is paid to the case of particle in contact with the wall and the computational results are compared with those from experiments.
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47.27.N- Wall-bounded shear flow turbulence
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.11.-j Computational methods in fluid dynamics
47.55.-t Multiphase and stratified flows

Hydrodynamic diffusion and mass transfer across a sheared suspension of neutrally buoyant spheres

Luying Wang, Donald L. Koch, Xiaolong Yin, and Claude Cohen

Phys. Fluids 21, 033303 (2009); http://dx.doi.org/10.1063/1.3098446 (15 pages) | Cited 5 times

Online Publication Date: 27 March 2009

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We present experimental, theoretical, and numerical simulation studies of the transport of fluid-phase tracer molecules from one wall to the opposite wall bounding a sheared suspension of neutrally buoyant solid particles. The experiments use a standard electrochemical method in which the mass transfer rate is determined from the current resulting from a dilute concentration of ions undergoing redox reactions at the walls in a solution of excess nonreacting ions that screen the electric field in the suspension. The simulations use a lattice-Boltzmann method to determine the fluid velocity and solid particle motion and a Brownian tracer algorithm to determine the chemical tracer mass transfer. The mass transport across the bulk of the suspension is driven by hydrodynamic diffusion, an apparent diffusive motion of tracers caused by the chaotic fluid velocity disturbances induced by suspended particles. As a result the dimensionless rate of mass transfer (or Sherwood number) is a nearly linear function of the dimensionless shear rate (Peclet number) at moderate values of the Peclet number. At higher Peclet numbers, the Sherwood number grows more slowly due to the mass transport resistance caused by a molecular-diffusion boundary layer near the solid walls. Fluid inertia enhances the rate of mass transfer in suspensions with particle Reynolds numbers in the range of 0.5–7.
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47.57.E- Suspensions
82.70.Kj Emulsions and suspensions
47.11.Qr Lattice gas
47.52.+j Chaos in fluid dynamics
82.30.-b Specific chemical reactions; reaction mechanisms

Dispersion of heavy particles in stably stratified turbulence

M. van Aartrijk and H. J. H. Clercx

Phys. Fluids 21, 033304 (2009); http://dx.doi.org/10.1063/1.3099333 (14 pages) | Cited 4 times

Online Publication Date: 31 March 2009

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The dispersion of heavy inertial particles in statistically stationary stably stratified turbulence is studied by means of direct numerical simulations. The following issues have been addressed: What distinguishes dispersion in such stratified flows from dispersion processes in statistically stationary homogeneous isotropic turbulence? How is the dispersion process affected by the Stokes number of the inertial particles (0.1≲St = τp/τK≲10, with τp the particle response time and τK the Kolmogorov time)? What is the interplay between buoyancy and the Stokes number? And what is the effect, if any, of particle settling, nonlinear drag, and lift forces (particularly relevant for stratified turbulence with its vertical shear layers) on particle dispersion? The long-time dispersion in isotropic turbulence is found to be maximum around St = 1, in agreement with the observation of preferential concentration for St ≈ 1. In stably stratified turbulence such a maximum in the dispersion is only found for the horizontal direction. The horizontal and vertical dispersions in stably stratified turbulence show different behaviors due to the anisotropy of the flow, and in particular, vertical dispersion is strongly affected by the inertia of the particles. With increasing St the classical plateau found for vertical fluid particle dispersion becomes less pronounced and it even vanishes for Stokes numbers of O(10) and higher. Furthermore, the long-time vertical dispersion increases with increasing St. The effects of gravity, nonlinear drag, and lift forces have been considered in more detail. It turned out that the settling enhancement of inertial particles, as observed in isotropic turbulence, is suppressed by stratification and by nonlinear drag effects. Moreover, nonlinear drag only affects the dispersion in the vertical direction in stably stratified turbulence. Finally, it is found that lift forces can safely be neglected for dispersion studies under the current parameter settings.
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47.27.ek Direct numerical simulations
47.55.Hd Stratified flows
back to top Laminar Flows

Mode coupling and flow energy harvesting by a flapping foil

Qiang Zhu and Zhangli Peng

Phys. Fluids 21, 033601 (2009); http://dx.doi.org/10.1063/1.3092484 (10 pages) | Cited 11 times

Online Publication Date: 13 March 2009

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As demonstrated in recent studies, the bioinspired flapping foils are capable of harvesting kinetic energy from incoming wind or current. A practical measure to achieve this is via the coupling between different modes in a system with multiple degrees of freedom. A typical scenario includes external activation of one motion mode and extracting the mechanical energy from other modes that follow. In this study we create a numerical model based upon the Navier–Stokes equations to investigate the performance of such a system in low Reynolds numbers. The effects of both the mechanical design and the operational parameters are examined. Specifically, we concentrate on the vorticity control mechanisms involved in the process, and demonstrate that through vortex-body interactions energy of the leading-edge vortices can be partially recovered to enhance the energy harvesting capacity.
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47.10.A- Mathematical formulations
47.32.-y Vortex dynamics; rotating fluids
back to top Instability and Transition

Onset of oscillatory convection in two liquid layers with phase change

G. B. McFadden and S. R. Coriell

Phys. Fluids 21, 034101 (2009); http://dx.doi.org/10.1063/1.3083345 (8 pages) | Cited 3 times

Online Publication Date: 6 March 2009

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We perform linear stability calculations for horizontal fluid bilayers that can undergo a phase transformation in the presence of a vertical temperature gradient. We reconsider the oscillatory instability calculated by Huang and Joseph [J. Fluid Mech. 242, 235 (1992) ] for the water-steam system cooled from below at temperatures near 100 °C, where there is a large difference in the densities of the two fluids. We find that buoyancy and surface tension gradients are unimportant for this instability. Numerical solutions demonstrate that the properties of the vapor and liquid systems at these temperatures are sufficiently different that an approximate treatment is possible in which the equations for the vapor phase can be eliminated from the overall governing equations. Further analytical approximations suggested by the numerical solution are also presented, and the results are in good agreement with the numerical solution for the full set of governing equations. A simple model of the oscillatory instability is developed which gives insight into its origins.
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47.55.P- Buoyancy-driven flows; convection
47.20.-k Flow instabilities
68.03.Cd Surface tension and related phenomena
64.70.F- Liquid-vapor transitions
47.55.Ca Gas/liquid flows
47.55.Hd Stratified flows

Stability of layered channel flow of magnetic fluids

Philip Yecko

Phys. Fluids 21, 034102 (2009); http://dx.doi.org/10.1063/1.3083220 (13 pages) | Cited 2 times

Online Publication Date: 10 March 2009

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The stability of a sheared interface separating a viscous magnetic fluid (ferrofluid) and an ordinary viscous fluid is examined for arbitrary wavelength disturbances using three dimensional linear perturbation theory. The unperturbed state corresponds to a two-layer Poiseuille profile in which a uniform magnetic field of arbitrary orientation is imposed. Coupling between the field and fluid occurs via the magnetic Maxwell stress tensor, formulated here for nonlinear magnetic material, expanding the scope of previous studies of linear media. Neutral curves and stability characteristics at low Reynolds number are presented and analyzed, and are found to depend sensitively on the linear and nonlinear magnetic properties of the material. The stability properties of the flow are shaped by a small set of the least stable modes of the spectrum, a result that evades single mode or potential flow analyses. The gravest modes can be of different character, resembling either interfacial or shear modes, modified by magnetic effects. The commonly cited ferrofluid interface properties of “stabilization by a tangential field” and “destabilization by a normal field” are shown to be invalid here, although the origins of these features can be identified within this problem.
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47.65.Cb Magnetic fluids and ferrofluids
47.60.Dx Flows in ducts and channels
47.20.-k Flow instabilities
47.55.Hd Stratified flows

Experimental study of Rayleigh–Taylor instability with a complex initial perturbation

D. H. Olson and J. W. Jacobs

Phys. Fluids 21, 034103 (2009); http://dx.doi.org/10.1063/1.3085811 (13 pages) | Cited 4 times

Online Publication Date: 13 March 2009

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Experiments have been performed investigating the Rayleigh–Taylor instability initialized with a complex initial perturbation. The experiments utilize a miscible fluid combination with Atwood number A ≈ 0.2. The initially stably stratified fluids are contained within a Plexiglas tank mounted to a linear rail system. The tank was then oscillated vertically to impose nearly sinusoidal three-dimensional internal waves of varying wavelength and complexity at the fluid interface. After imposing this perturbation, the tank is accelerated down the rails at a rate greater than Earth’s gravity (g0) resulting in a body force of approximately 0.8g0. The flow is visualized with either backlit photography or planar laser induced fluorescence. Image sequences from the experiments show bubble and spike merging, leading to a growth of length scale with time. Averaged vertical concentration distributions show self-similarity after ∼ 233 ms with a total experiment time of ∼ 300 ms. In addition, after this time, the square root of the mixing zone width appears to grow linearly with (Ag)1/2t. Values for the self-similar growth parameter, α, obtained by curve fitting to the linear portion of these curves yield values that are lower than those obtained in other experiments but are in good agreement with values found in computational studies initiated with perturbations similar to those used here. The measured α values do not show a dependence on the initial perturbation amplitude. The method for the determination of α using the expression α = math2/4Agh proposed by Cabot and Cook [Nat. Phys. 2, 562 (2006) ] yields a value in agreement with that measured by curve fitting the h1/2 versus matht curves, and which is also in better agreement with computational studies.
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47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.35.-i Hydrodynamic waves
47.55.D- Drops and bubbles
47.55.Hd Stratified flows
47.80.Jk Flow visualization and imaging
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