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BROWSE VOLUME

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BROWSE EARLY VOLUMES

March 2005

Volume 17, Issue 3,  Articles (03xxxx)

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SPECIAL TOPIC: BIOFLUID MECHANICS

Preface: Biofluid mechanics

James B. Grotberg

Phys. Fluids 17, 031401 (2005) (1 page)

Online Publication Date: 22 February 2005

Full Text: PDF (15 kB)

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 Abstract Unavailable
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01.30.-y, 87.19.Uv

Interactions between stably rolling leukocytes in vivo

Michael R. King, Aimee D. Ruscio, Michael B. Kim, and Ingrid H. Sarelius

Phys. Fluids 17, 031501 (2005) (3 pages)

Online Publication Date: 22 February 2005

Full Text: PDF (219 kB)

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We have characterized the two-dimensional spatial dependence of the hydrodynamic interactions between two adhesively rolling leukocytes in a live venule in the mouse cremaster muscle. Two rolling leukocytes were observed to slow each other down when rolling together in close proximity due to mutual sheltering from the external blood flow in the vessel lumen. A previous study of leukocyte rolling interactions using carbohydrate-coated beads in a parallel-plate flow chamber and a detailed computer model of adhesion in a multicellular environment is in qualitative agreement with the current in vivo results.
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87.19.Uv, 87.17.Jj, 47.55.Kf, 47.35.+i, 47.60.+i

An investigation of the influence of cell topography on epithelial mechanical stresses during pulmonary airway reopening

A. M. Jacob and D. P. Gaver, III

Phys. Fluids 17, 031502 (2005) (11 pages)

Online Publication Date: 23 February 2005

Full Text: PDF (580 kB)

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The goal of this study is to assess the local mechanical environment of the pulmonary epithelium in a computational model of airway reopening. To this end, the boundary element method (BEM) in conjunction with lubrication theory is implemented to assess the stationary-state behavior of a semi-infinite bubble traveling through a liquid-occluded parallel plate flow chamber lined with epithelial cells. The fluid occlusion is assumed to be Newtonian and inertia is neglected. The interactions between the microgeometry of the model airway's walls and the interfacial kinematics surrounding the bubble's tip result in a complex, spatially and temporally dependent stress distribution. The walls' nonplanar topography magnifies the normal and shear stresses and stress gradients. We find that decreasing the bubble's speed serves to increase the maximum normal stress and stress gradient but decrease the maximum shear stress and stress gradient. Our results give credence to the pressure-gradient-induced epithelial damage theory recently proposed by Bilek et al. [J. Appl. Physiol. 94, 770 (2003)] and Kay et al. [J. Appl. Physiol. 97, 269 (2004)]. We conclude that the amplified pressure gradients found in this study may be even more detrimental to the airway's cellular epithelium during airway reopening.
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87.19.Uv, 87.17.Aa, 47.55.Dz, 47.60.+i, 47.27.Lx, 47.35.+i, 47.10.+g

Axisymmetric motion of a file of red blood cells through capillaries

C. Pozrikidis

Phys. Fluids 17, 031503 (2005) (14 pages)

Online Publication Date: 23 February 2005

Full Text: PDF (744 kB)

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The axisymmetric, pressure-driven motion of red blood cells through cylindrical capillaries is investigated by numerical simulation. The mathematical formulation takes into consideration the nearly incompressible and elastic properties of the cell membrane with respect to shearing and bending deformation from the unstressed shape of the biconcave disk. In the theoretical model, the cells are arranged in a periodic file that is coaxial with the capillaries, and the evolution from the equilibrium to a highly deformed steady shape is computed using a boundary-integral method for axisymmetric Stokes flow. The results illustrate the significance of the capillary radius and cell spacing on the discharge hematocrit and apparent viscosity of the one-dimensional suspension, and validate the assumptions of approximate solutions based on the lubrication approximation for tightly fitting cells developed by previous authors.
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87.19.Uv, 47.60.+i, 47.55.Kf, 47.11.+j

The method of regularized Stokeslets in three dimensions: Analysis, validation, and application to helical swimming

Ricardo Cortez, Lisa Fauci, and Alexei Medovikov

Phys. Fluids 17, 031504 (2005) (14 pages)

Online Publication Date: 23 February 2005

Full Text: PDF (780 kB)

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The method of regularized Stokeslets is a Lagrangian method for computing Stokes flow driven by forces distributed at material points in a fluid. It is based on the superposition of exact solutions of the Stokes equations when forces are given by a cutoff function. We present this method in three dimensions, along with an analysis of its accuracy and performance on the model problems of flow past a sphere and the steady state rotation of rigid helical tubes. Predicted swimming speeds for various helical geometries are compared with experimental data for motile spirochetes. In addition, the regularized Stokeslet method is readily implemented in conjunction with an immersed boundary representation of an elastic helix that incorporates passive elastic properties as well as mechanisms of internal force generation.
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87.17.Jj, 47.32.-y, 47.60.+i, 47.50.+d, 47.10.+g

Three-dimensional numerical simulation of receptor-mediated leukocyte adhesion to surfaces: Effects of cell deformability and viscoelasticity

Damir B. Khismatullin and George A. Truskey

Phys. Fluids 17, 031505 (2005) (21 pages)

Online Publication Date: 24 February 2005

Full Text: PDF (956 kB)

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Computational fluid dynamics is used to investigate the effects of cell deformability and viscoelasticity on receptor-mediated leukocyte adhesion to endothelium or a ligand coated surface in a parallel-plate flow chamber. In the three-dimensional numerical code, a leukocyte is modeled as a compound viscoelastic drop (a nucleus covered by a thick layer of cytoplasm). The nucleus, cytoplasm, and extracellular fluid are considered as Newtonian or viscoelastic liquids of high viscosity. The receptor-ligand interaction is incorporated into the code by using the spring-peeling kinetic model under the assumption that leukocyte receptors are located on the tips of cylindrical microvilli distributed over the leukocyte membrane. The code is based on the volume-of-fluid method, and the Giesekus constitutive equation is implemented in the code to capture viscoelasticity of the cytoplasm and nucleus. Numerical simulations demonstrate the formation and breakup of membrane tethers observed in vitro and suggest that the elasticity of the cytoplasm is responsible for a teardrop shape of rolling leukocytes in vivo. When viewed from the top, as normally occurs during shear flow experiments in vitro, little or no deformation occurs, a side view shows significant deformation in the contact region. We show that the leukocyte membrane can be extended and disrupted under high shear if the receptor-ligand bonds live in a stressed state for a sufficiently long time. If the shear rate is low, the leukocyte rolls along the surface. The rolling velocity of the viscoelastic cell is smaller than that of the Newtonian cell. This is due to the increased deformability of the viscoelastic cell and, as a result, the decreased torque acting on this cell.
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87.19.Tt, 83.80.Lz, 87.19.Uv, 87.10.+e, 83.85.Pt, 83.50.Ax, 83.50.Lh, 87.15.La

Three-dimensional instabilities of liquid-lined elastic tubes: A thin-film fluid-structure interaction model

Joseph P. White and Matthias Heil

Phys. Fluids 17, 031506 (2005) (17 pages)

Online Publication Date: 1 March 2005

Full Text: PDF (711 kB)

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We develop a theoretical model of surface-tension-driven, three-dimensional instabilities of liquid-lined elastic tubes—a model for pulmonary airway closure. The model is based on large-displacement shell theory, coupled to the equations of lubrication theory, modified to ensure the exact representation of the system's equilibrium configurations. The liquid film that lines the initially uniform, axisymmetric tube can become unstable to a surface-tension-driven instability. We show that, if the surface tension of the liquid lining is sufficiently large (relative to the tube's bending stiffness), the axisymmetric redistribution of fluid by this instability can increase the wall compression to such an extent that the system becomes unstable to a secondary, nonaxisymmetric instability which causes the tube wall to buckle. We establish the conditions for the occurrence of the nonaxisymmetric instability by a linear stability analysis and use finite element simulations to explore the system's subsequent evolution in the large-displacement regime. The simulations show that nonaxisymmetric instabilities allow the formation of occluding liquid bridges in situations in which the volume of fluid is insufficient to occlude the tube in its axisymmetric state. Finally, we discuss the implications of our results for the physiological problem of pulmonary airway closure.
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87.19.Uv, 47.11.+j, 47.60.+i, 47.20.Dr, 68.15.+e

The effect of gravity on liquid plug propagation in a two-dimensional channel

V. Suresh and J. B. Grotberg

Phys. Fluids 17, 031507 (2005) (15 pages)

Online Publication Date: 1 March 2005

Full Text: PDF (294 kB)

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The effect of plug propagation speed and gravity on the quasisteady motion of a liquid plug in a two-dimensional liquid-lined channel oriented at an angle alpha with respect to gravity is studied. The problem is motivated by the transport of liquid plugs instilled into pulmonary airways in medical treatments such as surfactant replacement therapy, drug delivery, and liquid ventilation. The capillary number Ca is assumed to be small, while the Bond number Bo is arbitrary. Using matched asymptotic expansions and lubrication theory, expressions are obtained for the thickness of the trailing films left behind by the plug and the pressure drop across it as functions of Ca, Bo, alpha and the thickness of the precursor films. When the Bond number is small it is found that the trailing film thickness and the flow contribution to the pressure drop scale as Ca2/3 at leading order with coefficients that depend on Bo and alpha. The first correction to the film thickness is found to occur at O(Ca) compared to O(Ca4/3) in the Bo = 0 case. Asymmetry in the liquid distribution is quantified by calculating the ratio of liquid volumes above and below the centerline of the channel, V<sub>R-dot</sub>. VR = 1 at Bo = 0, indicating a symmetric distribution, and decreases with Bo and Ca, but increases with the plug length Lp. The decrease of VR with Ca suggests that higher propagation speeds in small airways may result in less homogenous liquid distribution, which is in contrast to the expected effect in large airways. For given values of the other parameters, a maximum capillary number Cac is identified above which the plug will eventually rupture. When the Bond number becomes equal to an orientation-dependent critical value Boc, it is found that the scaling of the film thickness and pressure drop change to Ca1/2 and Ca1/6, respectively. It is shown that this scaling is valid for small increments of the Bond number over its critical value, Bo = Boc + BCa1/6, but for higher Bond numbers the asymptotic approach breaks down.
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47.10.+g, 47.60.+i, 47.55.Kf, 87.19.Uv

Transmission of steady and oscillatory fluid shear stress across epithelial and endothelial surface structures

Yuefeng Han, Peter Ganatos, and Sheldon Weinbaum

Phys. Fluids 17, 031508 (2005) (13 pages)

Online Publication Date: 1 March 2005

Full Text: PDF (341 kB)

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The glycocalyx on the apical surface of vascular endothelial cells and the microvilli and cilia on kidney epithelial cells have been modeled as surface layers with a hexagonal arrangement of structural elements. These elements have been proposed to serve a mechanosensory function in the initiation of intracellular signaling by fluid shear stress. In this paper we examine the response of these surface layers when steady or oscillating shear is applied at their outer edge. In the case of steady shear, our results show that the deflection of the structural elements is proportional to the product of the applied shear stress and their length L and inversely proportional to the natural damped vibration frequency of the structural element omegac. A fluid velocity boundary layer develops at the outer edge of the surface layers when the dimensionless Brinkman parameter alpha= L/sqrt(K[sub P]), where KP is the Darcy permeability, is asymptotically large. In the case of oscillating shear, we find that the motions of both the fluid and structural elements are in a quasisteady state at physiological conditions. No attenuation or phase shift of the torque is induced by the hydrodynamic drag when the applied frequency omega<omegac or omegar(= omega/omegac)<1. However, the velocity at the tips of the structural element is pi/2 out of phase with the applied shear in this frequency range, due to the elastic recoil of the element. Furthermore, the fluid velocity at the tips can also be out of phase with the applied shear at large alpha if the closely spaced structural elements of the glycocalyx on endothelial cells or microvilli on proximal tubule cells transport substantial fluid with them.
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87.17.Jj, 87.14.Ee, 87.17.Aa, 47.35.+i, 47.20.Ft, 47.27.Nz

Flow and deformation of the capillary glycocalyx in the wake of a leukocyte

Edward R. Damiano and Thomas M. Stace

Phys. Fluids 17, 031509 (2005) (17 pages)

Online Publication Date: 1 March 2005

Full Text: PDF (305 kB)

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An analysis is presented of the axisymmetric axial and radial flow and deformation fields throughout the endothelial-cell glycocalyx surface layer in the wake region behind a leukocyte moving steadily through a capillary. The glycocalyx, modeled as a thin poroelastic surface layer lining the capillary wall, is assumed to consist of a binary mixture of a linearly viscous fluid constituent and an isotropic, highly compressible, linearly elastic solid constituent having a vanishingly small solid-volume fraction. Invoking the asymptotic approximations of lubrication theory in a frame of reference translating with the leukocyte, closed-form solutions are obtained to the leading-order boundary-value problems governing the axial and radial flow and deformation fields throughout the glycocalyx as well as the axial and radial flow fields throughout the free capillary lumen within the wake. A simple asymptotic expression is obtained for the length lchar of the wake region in terms of the translational speed U0 of the leukocyte, and the equilibrium thickness h0, permeability k0, and aggregate elastic modulus HA of the glycocalyx. The predicted wake length, as seen from an observer moving in a reference frame attached to the leukocyte, is consistent with the recovery time predicted from a one-dimensional analysis of glycocalyx deformation through a quiescent inviscid fluid. The two-dimensional fluid dynamical analysis presented here thus provides the appropriate relationships for extracting estimates of the mechanoelectrochemical properties of the glycocalyx from physiologically realistic constitutive models developed under simplified one-dimensional flow regimes. The directly measurable quantities lchar,  U0, and h0, which are obtainable from in vivo observations of the wake region behind a leukocyte moving steadily through a capillary, can therefore be connected, through the results of this analysis, to estimates of the mechanoelectrochemical properties of the glycocalyx on vascular endothelial cells.
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83.80.Lz, 83.85.Pt, 87.19.Rr, 83.50.-v, 87.17.Aa

A model of flow and surfactant transport in an oscillatory alveolus partially filled with liquid

Hsien-Hung Wei, Hideki Fujioka, Ronald B. Hirschl, and James B. Grotberg

Phys. Fluids 17, 031510 (2005) (16 pages)

Online Publication Date: 1 March 2005

Full Text: PDF (390 kB)

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The flow and transport in an alveolus are of fundamental importance to partial liquid ventilation, surfactant transport, pulmonary drug administration, cell-cell signaling pathways, and gene therapy. We model the system in which an alveolus is partially filled with liquid in the presence of surfactants. By assuming a circular interface due to sufficiently strong surface tension and small surfactant activity, we combine semianalytical and numerical techniques to solve the Stokes flow and the surfactant transport equations. In the absence of surfactants, there is no steady streaming because of reversibility of Stokes flow. The presence of surfactants, however, induces a nontrivial cycle-averaged surfactant concentration gradient along the interface that generates steady streaming. The steady streaming patterns (e.g., number of vortices) particularly depend on the ratio of inspiration to expiration periods (I:E ratio) and the sorption parameter K. For an insoluble surfactant, a single vortex is formed when the I:E ratio is either smaller or larger than 1:1, but the recirculations have opposite directions in the two cases. A soluble surfactant can lead to more complex flow patterns such as three vortices or saddle-point flow structures. The estimated unsteady velocity is 10–3  cm/s, and the corresponding Péclet number for transporting respiratory gas is O(1). For a cell-cell signaling molecule such as surfactant-associated protein-A for regulating surfactant secretion, the Péclet number could be O(10) or higher. Convection is either comparable to or more dominant than diffusion in these processes. The estimated steady velocity ranges from 10–6  to  10–4  cm/s, depending on I:E and K, and the corresponding steady Péclet number is between 10–8/Dm and 10–6/Dm (Dm is the molecular diffusivity with units of cm2/s). Therefore, for Dm<=10–8  cm2/s, the convective transport dominates.
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87.19.Uv, 47.32.Cc, 47.35.+i, 47.27.Te, 47.10.+g
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LETTERS

Predicting rogue waves in random oceanic sea states

A. L. Islas and C. M. Schober

Phys. Fluids 17, 031701 (2005) (4 pages)

Online Publication Date: 16 February 2005

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Using the inverse spectral theory of the nonlinear Schrödinger (NLS) equation we correlate the development of rogue waves in oceanic sea states characterized by the Joint North Sea Wave Project (JONSWAP) spectrum with the proximity to homoclinic solutions of the NLS equation. We find in numerical simulations of the NLS equation that rogue waves develop for JONSWAP initial data that are "near" NLS homoclinic data, while rogue waves do not occur for JONSWAP data that are "far" from NLS homoclinic data. We show the nonlinear spectral decomposition provides a simple criterium for predicting the occurrence and strength of rogue waves.
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92.10.Hm, 47.35.+i, 47.10.+g

Buoyancy driven miscible front dynamics in tilted tubes

T. Séon, J.-P. Hulin, D. Salin, B. Perrin, and E. J. Hinch

Phys. Fluids 17, 031702 (2005) (4 pages)

Online Publication Date: 22 February 2005

Full Text: PDF (238 kB)

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The velocity Vf of the fronts of light and heavy fluids in a tilted tube, interpenetrating many diameters, is studied as a function of the fluid viscosity µ, Atwood number At<<1 and tilt angle theta from vertical. Three flow regimes are observed: starting from vertical, Vf first increases with theta, reaches a plateau and then decreases again. In the first regime, Vf is controlled by segregation and mixing effects, respectively, increasing and decreasing with theta. On the plateau, Vf is independent of the fluid viscosity and proportional to (Atgd)1/2, indicating a balance between inertia and buoyancy. In the third regime close to horizontal, the fluids separate into two parallel countercurrents controlled by viscosity. The variations of Vf with theta, At, and µ in the second and third regimes and the crossover from one to the other are described by scaling laws based on characteristic viscous and inertial velocities.
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47.60.+i, 47.55.Kf

Computer simulations of the collapse of a granular column

Roberto Zenit

Phys. Fluids 17, 031703 (2005) (4 pages)

Online Publication Date: 23 February 2005

Full Text: PDF (235 kB)

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Recently, two independent groups reported experimental results on the process of collapse of a cylindrical granular column. It was found that the shape of the final deposit depended mostly on column aspect ratio; surprisingly, the frictional properties of the material appeared not to influence the results significantly. In this investigation, making use of discrete element code, simulations of an equivalent two-dimensional system were carried out. The numerical results qualitatively reproduce the behavior observed in experiments. Performing an energy balance of the system, the different deposit regimes can be discerned.
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47.55.Kf, 47.60.+i, 47.11.+j

A vortex model for Richtmyer–Meshkov instability accounting for finite Atwood number

Oleg A. Likhachev and Jeffrey W. Jacobs

Phys. Fluids 17, 031704 (2005) (3 pages)

Online Publication Date: 23 February 2005

Full Text: PDF (49 kB)

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The vortex model developed by Jacobs and Sheeley ["Experimental study of incompressible Richtmyer–Meshkov instability," Phys. Fluids 8, 405 (1996)] is essentially a solution to the governing equations for the case of a uniform density fluid. Thus, this model strictly speaking only applies to the case of vanishing small Atwood number. A modification to this model for small to finite Atwood number is proposed in which the vortex row utilized is perturbed such that the vortex spacing is smaller across the spikes and larger across the bubbles, a fact readily observed in experimental images. It is shown that this modification more effectively captures the behavior of experimental amplitude measurements, especially when compared with separate bubble and spike data. In addition, it is shown that this modification will cause the amplitude to deviate from the logarithmic result given by the heuristic models at late time.
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47.32.Cc, 47.55.Dz, 47.10.+g, 47.20.Ma, 47.55.Kf, 47.35.+i

Spiral shear layers: Roll-up and incipient instability

Christophe Lepage, Thomas Leweke, and Alberto Verga

Phys. Fluids 17, 031705 (2005) (4 pages)

Online Publication Date: 1 March 2005

Full Text: PDF (396 kB)

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The structure and roll-up of thin shear layers generated by the impulsive motion of a plate is investigated through experiments and numerical computations. At large Reynolds numbers, the shear layer rolls up into a self-similar spiral, compatible with a power-law geometry, to which an oscillation is superimposed. This modulation is also manifest in the distributions of the circulation density and the strain rate, which are found to be nonmonotonic along the layer. A sequence of stretching and compression regions is observed, critical for the stability of the sheet.
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47.32.Cc, 47.11.+j, 47.20.Ft, 47.27.Lx, 47.53.+n

The existence of vortices in the wakes of simulated raindrops

J. R. Saylor and B. K. Jones

Phys. Fluids 17, 031706 (2005) (4 pages)

Online Publication Date: 1 March 2005

Full Text: PDF (145 kB)

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Flow visualizations are presented of the wakes behind water droplets traveling at terminal velocity in a vertically directed airflow. These images, obtained by levitating water drops in a vertical wind tunnel, reveal vortices in the wake behind the drop. It has long been postulated that such wakes trigger transverse oscillations in raindrops. Although such transverse oscillations were not observed here, the images do show a canting of the oblate drop which appears to be connected to the vortex shedding process. These are the first images of simulated raindrops that visualize both the shape of the drop and the vortices in the wake immediately behind the drop.
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47.10.+g, 47.32.Cc, 47.27.Vf, 47.55.Dz, 47.60.+i, 47.35.+i

Turbulence in dilute polymer solutions

A. Liberzon, M. Guala, B. Lüthi, W. Kinzelbach, and A. Tsinober

Phys. Fluids 17, 031707 (2005) (4 pages)

Online Publication Date: 1 March 2005

Full Text: PDF (492 kB)

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The work reported below is a comparative study of the properties of turbulence with weak mean flow in a Newtonian fluid and in a dilute polymer solution with an emphasis on the small scale phenomena. The main tool used is a three-dimensional particle tracking system allowing to measure and follow in a Lagrangian manner the field of velocities, as well as velocity derivatives, and thus vorticity, strain, and a variety of related and dynamically significant quantities. The comparison of data from the two flows allows to directly observe the influence of polymers on these quantities as well as the evolution of material elements in the presence of polymers.
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47.27.Gs, 47.50.+d, 47.32.Cc, 47.55.Kf
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ARTICLES

Interfacial Flows

Spraying modes in coaxial jet electrospray with outer driving liquid

Xiaopeng Chen, Laibing Jia, Xiezhen Yin, Jiusheng Cheng, and Jian Lu

Phys. Fluids 17, 032101 (2005) (7 pages)

Online Publication Date: 4 February 2005

Full Text: PDF (486 kB)

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Coaxial jet electrospray is a technique to generate microencapsules, which uses electric forces to create a coaxial microjet from two immiscible liquids. Compound droplets with narrow size distribution are produced after the jet breaks up. In this paper, the spraying modes are investigated experimentally with proper flow rates of the inner and outer liquids. Ethanol/glycerol/tween mixture (outer liquid) and cooking oil (inner liquid) are fed into the gap between outer and inner capillaries and the inner capillary, respectively. The spraying modes presented in our experiments are "dripping mode," "dripping mode in spindle," "cone-jet mode," "pulse mode in cone," and "multijets mode" sequentially, as the applied voltage increases. The region of stable cone-jet mode extends with decrease of the outer liquid flow rate and increase of the inner one. It is found that the spray phenomena are mainly determined by properties of the outer liquid, which is viscous and electric conductive enough. A rudimentary physical model is developed, in which both the viscosity and liquid interface tension are taken into account.
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47.27.Wg, 47.55.Kf, 47.55.Dz, 47.65.+a, 47.20.Dr, 47.20.Ma, 47.20.Gv, 47.10.+g

The stability of an encapsulated cylindrical liquid bridge subject to off-centering

A. Kerem Uguz and R. Narayanan

Phys. Fluids 17, 032102 (2005) (7 pages)

Online Publication Date: 8 February 2005

Full Text: PDF (118 kB)

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Liquid bridges are usually encapsulated with another liquid in float-zone crystal growth processes to ensure the containment of volatile components. This paper is concerned with the stability of an inviscid liquid bridge that is off-centered with respect to its encapsulant. Perturbation theory is used to study the stability of such a bridge subject to inertial disturbances. It is concluded that while the off-centered nature does not change the neutral point it does affect the rate of growth and decay of the disturbances causing the unstable regions to become less unstable and stable regions to become less stable. Limiting conditions are considered in order to provide a better understanding of the physics of off-centering.
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47.10.+g, 47.20.Cq, 47.55.Kf, 81.10.Fq

Breakup and capture of two sedimenting drops in a vertical temperature gradient

Michael A. Rother and Robert H. Davis

Phys. Fluids 17, 032103 (2005) (12 pages)

Online Publication Date: 9 February 2005

Full Text: PDF (345 kB)

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A curvatureless three-dimensional boundary-integral algorithm has been developed for tangential Marangoni stresses and used to study breakup and capture of two deformable drops for arbitrary drop-to-medium viscosity and thermal conductivity ratios in parallel and antiparallel arrangements of gravity and an applied vertical temperature gradient. When the driving forces are opposed, the previously observed inhibition of breakup by a weak thermocapillary effect for drops with equal viscosity and thermal conductivity ratios is shown to be almost exclusively the result of changing interfacial tension, with Marangoni stresses having virtually no influence. Alignment of gravity and the temperature gradient in the same direction enhances breakup more than opposing driving forces reduce it, with the limitation that the drops are moving toward a region of zero interfacial tension. The thermal conductivity ratio has negligible impact on these interactions. For bubbles, the effect of a temperature gradient on gravitational results is much less pronounced than for drops. Under certain conditions, parallel orientation of the driving forces weakly inhibits the capture interaction for bubbles, while antiparallel orientation enhances the phenomenon.
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47.55.Dz, 02.30.Rz

Electrically induced pattern formation in thin leaky dielectric films

R. V. Craster and O. K. Matar

Phys. Fluids 17, 032104 (2005) (17 pages)

Online Publication Date: 9 February 2005

Full Text: PDF (439 kB)

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The stability of the interface between two thin leaky dielectric liquid layers bounded between two flat electrodes is considered. A coupled system of evolution equations is derived for the interfacial location and charge density using lubrication theory. This system is parametrized by the dielectric constants of the two fluids in addition to ratios of their conductivities, viscosities, and thicknesses. A linear stability analysis is conducted and the behavior of the system in the nonlinear regime is also examined. The system is destabilized by electrical stresses that are resisted by capillarity and modified by viscous dissipation. Our results suggest that decreasing the thickness ratio is destabilizing, giving rise to periodic structures of decreasing wavelength. Decreasing the viscosity ratio was also found to lead to the formation of sharp-edged structures whose vertical extent is virtually equal to the gap width between the electrodes. Similar structures were also determined upon increasing the ratio of the dielectric constants and electric conductivities.
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47.54.+r, 47.10.+g, 77.84.Nh, 77.55.+f, 68.15.+e, 47.20.Ma, 47.20.Gv

Enhanced damping of capillary bridge oscillations using velocity feedback

Wei Wei, David B. Thiessen, and Philip L. Marston

Phys. Fluids 17, 032105 (2005) (11 pages)

Online Publication Date: 16 February 2005

Full Text: PDF (243 kB)

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In reduced gravity, the stability of cylindrical liquid bridges and other systems having free surfaces is affected by ambient vibrations of the spacecraft. Such vibrations are expected to excite capillary modes. The lowest-order unstable mode of a liquid bridge is particularly susceptible to vibration as the length of the bridge approaches the stability limit. This mode is known as the (2,0) mode and is an axisymmetric varicose mode of one wavelength in the axial direction. In this work, an optical system is used to detect the (2,0)-mode amplitude. The derivative of the error signal produced by this detector is used to produce the appropriate voltages on a pair of annular disk electrodes which are concentric with the bridge. A mode-coupled Maxwell stress profile is thus generated in proportion to the modal velocity. Depending on the sign of the gain, the damping of the capillary oscillation can be either increased or decreased. This effect has been demonstrated in Plateau-tank experiments. Increasing the damping of the capillary modes on free liquid surfaces in space could be beneficial for containerless processing and other technologies.
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47.35.+i

Viscous versus inviscid instability of two-phase mixing layers with continuous velocity profile

Thomas Boeck and Stéphane Zaleski

Phys. Fluids 17, 032106 (2005) (11 pages)

Online Publication Date: 24 February 2005

Full Text: PDF (227 kB)

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We consider the temporal instability of parallel two-phase mixing layers. The viscous case is examined using a composite error-function velocity profile. The inviscid case is considered for the broken-line velocity profile, where the thickness of the boundary layer in each fluid next to the interface is chosen to match the viscous error-function profile at the interface and far away from it. Viscosity modifies the inviscid stability properties quantitatively, but we can also discern an additional unstable mode exclusively related to viscous shear. In the absence of interfacial tension, this mode dominates at large wavenumbers when the Reynolds number is sufficiently high. The various viscous modes cannot generally be attributed to either one of the phases due to mode mixing or exchange. For parameters resembling those of atomization experiments and applications, the most unstable wavelength and growthrate in the viscous case can exceed the inviscid values significantly. The viscous stability analysis also provides better agreement with recent experimental results for air and water than inviscid stability calculations.
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47.55.Kf, 47.27.Nz, 47.20.Gv, 47.20.Cq, 47.35.+i

On-shell description of stationary flames

Kirill A. Kazakov

Phys. Fluids 17, 032107 (2005) (15 pages)

Online Publication Date: 1 March 2005

Full Text: PDF (186 kB)

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The problem of nonperturbative description of stationary flames with arbitrary gas expansion is considered. On the basis of the Thomson circulation theorem an implicit integral of the flow equations is constructed. With the help of this integral, a simple explicit expression for the vortex mode of the burnt gas flow near the flame front is obtained. Furthermore, a dispersion relation for the potential mode at the flame front is written down, thus reducing the initial system of bulk equations and jump conditions for the flow variables to a set of integrodifferential equations for the flame front position and the flow velocity at the front. The developed approach is applied to the case of thin flames. Finally, an asymptotic expansion of the derived equations is carried out in the case theta-->1 where theta is the gas expansion coefficient, and a single equation for the front position is obtained in the second post-Sivashinsky approximation. It is demonstrated, in particular, how the well-known problem of correct normalization of the front velocity is resolved in our approach. It is verified also that in the first post-Sivashinsky approximation, the equation reduces to the Sivashinsky–Clavin equation corrected according to Cambray and Joulin. Analytical solutions of the derived equations are found, and compared with the results of numerical simulations.
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47.70.Fw, 47.32.Cc, 47.10.+g

Viscous and Non-Newtonian Flows

Aging and free surface flow of a thixotropic fluid

H. T. Huynh, N. Roussel, and P. Coussot

Phys. Fluids 17, 033101 (2005) (9 pages)

Online Publication Date: 2 February 2005

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Free surface flows of thixotropic fluids such as paints, self-compacting concrete, or natural mudflows are of noticeable practical interest. Here we study the basic characteristics of the uniform flow of a layer of thixotropic fluid under gravity. A theoretical approach relying on a simple thixotropy constitutive equation shows that after some time at rest over a small slope angle the fluid layer should start to flow rather abruptly beyond a new, larger, critical slope angle. The theory also predicts that the critical time at which the layer velocity should significantly increase is proportional to the duration of the preliminary rest and tends to infinity when the new slope approaches the critical slope. Experiments carried out with different suspensions show that the qualitative trends of the flows are in very good agreement with the theoretical predictions, except that the critical time for flow start appears to be proportional to a power 0.6 of the time of rest whereas the theory predicts a linear dependence. We show that this indicates a restructuration process at rest differing from the restructuration process under flow.
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81.05.Zx, 47.60.+i

Collapse and merging of cavity regions in a granular material due to viscous flow

Yoshifumi Kaneko and Osamu Sano

Phys. Fluids 17, 033102 (2005) (8 pages)

Online Publication Date: 4 February 2005

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Experimental studies are made on the collapse of macroscopic cavity regions placed in an otherwise homogeneous granular material due to viscous flow. First, an initially circular two-dimensional hole is exposed to a uniform flow at infinity and the process of boundary shape deformation due to locally enhanced stress components is clarified. Above a certain critical velocity, particles on the upstream-side boundary lose contact with neighboring ones, and are carried to the other side of the boundary. At the same time the fluidized region develops towards upstream direction in the granular material. A simple scaling law on the reduction of the void area is obtained. Second, attention is paid to the interaction of two circular cavities of equal radii, whose center-to-center distance and angle of attack are varied. In some configuration of cavities, lowering of the critical velocity of collapse is recognized. Successive processes on the collapse of upstream-side and downstream-side cavities are classified depending on the magnitude of velocity and the configuration of cavities. A possible scenario on the growth of global scale patterns in granular material such as water vein formation and landslides is suggested.
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47.55.Mh, 47.55.Kf

Distributed forcing of flow over a circular cylinder

Jinsung Kim and Haecheon Choi

Phys. Fluids 17, 033103 (2005) (16 pages)

Online Publication Date: 4 February 2005

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In the present study, we apply a distributed (i.e., spatially varying) forcing to flow over a circular cylinder for drag reduction. The distributed forcing is realized by a blowing and suction from the slots located at upper and lower surfaces of the cylinder. The forcing profile from each slot is sinusoidal in the spanwise direction but is steady in time. We consider two different phase differences between the upper and lower blowing/suction profiles: zero (in-phase forcing) and pi (out-of-phase forcing). The Reynolds numbers considered are from 40 to 3900 covering various regimes of flow over a circular cylinder. For all the Reynolds numbers larger than 47, the present in-phase distributed forcing attenuates or annihilates the Kármán vortex shedding and thus significantly reduces the mean drag and the drag and lift fluctuations. The optimal wavelength and amplitude of the in-phase forcing for maximum drag reduction are also obtained for the Reynolds number of 100. It is shown that the in-phase forcing produces the phase mismatch along the spanwise direction in the vortex shedding, weakens the strength of vortical structures in the wake, and thus reduces the drag. Unlike the in-phase forcing, the out-of-phase distributed forcing does not reduce the drag at low Reynolds numbers, but it reduces the mean drag and the drag and lift fluctuations at a high Reynolds number of 3900 by affecting the evolution of the separating shear layer, although the amount of drag reduction is smaller than that by the in-phase forcing.
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47.50.+d, 47.32.Cc, 47.15.Ki, 47.27.Vf, 47.27.Nz, 47.11.+j, 47.55.Kf, 47.20.Ft

The effect of added polymers on the formation of drops ejected from a nozzle

Heather J. Shore and Graham M. Harrison

Phys. Fluids 17, 033104 (2005) (7 pages)

Online Publication Date: 4 February 2005

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The presence of small amounts of polymer in Newtonian solvents can have a significant impact on the flow behavior of these fluids in extension-dominated flows. This study investigates the effect of elasticity on the on-demand drop formation through the use of low viscosity elastic liquids. A high-speed camera is employed to observe drops ejected from a nozzle. The drops are created using a piezoelectric sleeve that contracts around a nozzle forcing fluid out. We observe that the satellite drops commonly produced with Newtonian fluids of identical shear viscosity in the same geometry can be suppressed when polymers with sufficient molecular weight are added. For our nozzle, the minimum required molecular weight is 300k PEO at a concentration of 25 ppm. However, the resultant increased elasticity in the solution requires a greater pulse strength to eject the drop. In addition, the fluids containing polymers have a longer thread, a longer time to separation, and a lower velocity than the Newtonian fluids with similar shear viscosity.
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47.50.+d, 47.55.Dz, 47.60.+i

Ferrofluid pipe flow in an oscillating magnetic field

Alexei P. Krekhov, Mark I. Shliomis, and Shinichi Kamiyama

Phys. Fluids 17, 033105 (2005) (8 pages)

Online Publication Date: 1 March 2005

Full Text: PDF (124 kB)

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Ferrofluid pipe flow in an oscillating magnetic field along the pipe axis is studied theoretically in a wide range of the flow rate. The field-dependent part of viscosity (it can be positive or negative) reveals significant dependence on the flow vorticity, i.e., ferrofluids exhibit non-Newtonian behavior. This is manifested in an alteration of the velocity profile—it ceases to be parabolic—and deviation of the flow rate from the value prescribed by Poiseuille's formula. The presented model based on the conventional ferrohydrodynamic equations and an assumption of the ferrofluid structure fits well experimental data recently obtained by Schumacher, Sellien, Konke, Cader, and Finlayson ["Experiment and simulation of laminar and turbulent ferrofluid pipe flow in an oscillating magnetic field," Phys. Rev. E 67, 026308 (2003)].
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47.65.+a, 47.60.+i, 47.32.Cc, 47.10.+g, 47.35.+i, 47.50.+d, 47.55.Kf

Particulate, Multiphase, and Granular Flows

A smooth particle-mesh Ewald algorithm for Stokes suspension simulations: The sedimentation of fibers

David Saintillan, Eric Darve, and Eric S. G. Shaqfeh

Phys. Fluids 17, 033301 (2005) (21 pages)

Online Publication Date: 1 March 2005

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Large-scale simulations of non-Brownian rigid fibers sedimenting under gravity at zero Reynolds number have been performed using a fast algorithm. The mathematical formulation follows the previous simulations by Butler and Shaqfeh ["Dynamic simulations of the inhomogeneous sedimentation of rigid fibres," J. Fluid Mech. 468, 205 (2002)]. The motion of the fibers is described using slender-body theory, and the line distribution of point forces along their lengths is approximated by a Legendre polynomial in which only the total force, torque, and particle stresslet are retained. Periodic boundary conditions are used to simulate an infinite suspension, and both far-field hydrodynamic interactions and short-range lubrication forces are considered in all simulations. The calculation of the hydrodynamic interactions, which is typically the bottleneck for large systems with periodic boundary conditions, is accelerated using a smooth particle-mesh Ewald (SPME) algorithm previously used in molecular dynamics simulations. In SPME the slowly decaying Green's function is split into two fast-converging sums: the first involves the distribution of point forces and accounts for the singular short-range part of the interactions, while the second is expressed in terms of the Fourier transform of the force distribution and accounts for the smooth and long-range part. Because of its smoothness, the second sum can be computed efficiently on an underlying grid using the fast Fourier transform algorithm, resulting in a significant speed-up of the calculations. Systems of up to 512 fibers were simulated on a single-processor workstation, providing a different insight into the formation, structure, and dynamics of the inhomogeneities that occur in sedimenting fiber suspensions.
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47.11.+j, 47.55.Kf

Laminar Flows

Chaotic mixing in thermocapillary-driven microdroplets

Roman O. Grigoriev

Phys. Fluids 17, 033601 (2005) (8 pages)

Online Publication Date: 4 February 2005

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Liquid microdroplets represent a convenient system for studies of mixing by chaotic advection in discrete microscopic volumes. The mixing properties of the flows in microdroplets are governed by their symmetries, which give rise to invariant surfaces serving as barriers to transport. Thorough mixing via chaotic advection requires destruction of all such invariant surfaces. To illustrate this idea, we demonstrate that quick and thorough mixing inside a spherical microdroplet suspended in a layer of substrate fluid can be obtained by moving the droplet along a two-dimensional path using temperature-induced surface tension gradients. The use of flow invariants also provides a convenient way to analyze the mixing properties of flows in many other experimental implementations.
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47.55.Dz, 47.27.Te, 47.52.+j, 47.55.Kf, 68.03.Cd

Sharp scalar and tensor bounds on the hydrodynamic friction and mobility of arbitrarily shaped bodies in Stokes flow

J. Blawzdziewicz, E. Wajnryb, J. A. Given, and J. B. Hubbard

Phys. Fluids 17, 033602 (2005) (9 pages)

Online Publication Date: 8 February 2005

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We prove rigorous inequalities for the hydrodynamic translational friction and mobility matrices zeta and µO of an arbitrarily shaped rigid particle in terms of the electrostatic capacitance C of a conducting particle of identical shape. Specifically, we derive the scalar and matrix inequalities (1/3)tr   zeta   –1<=(1/3)tr  µO<=C  –1 and (2/3) zeta   –1<=C  –1  I, where all quantities are normalized by the corresponding values for a sphere, and the mobility matrix is evaluated in the center-of-mobility reference frame. These bounds are obtained using a variational approach with the energy dissipation functional expressed in terms of the induced force distribution on the surface of the particle. To relate the hydrodynamic problem to the solution of the corresponding electrostatic problem, the trial force field is expressed in terms of the charge distribution on the equipotential particle surface. This procedure yields the first rigorous bounds on hydrodynamic friction that apply to bodies with translation-rotation coupling. We demonstrate that the error of the Hubbard–Douglas approximation (1/3)tr   zeta   –1[approximate]C  –1, corresponding to our scalar bound, is quadratic in the deviation of the trial induced-force field from the exact form—which explains why this relation is highly accurate for many particle shapes. Our numerical results confirm that the Hubbard–Douglas approximation is accurate for a variety of objects, including helices with translational–rotational coupling. In addition, we establish a rigorous, sharp bound on the effective (scalar) Brownian diffusion coefficient of an arbitrarily shaped particle.
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47.10.+g, 47.65.+a, 47.55.Kf

Instability and Transition

Richtmyer–Meshkov instability of arbitrary shapes

Karnig O. Mikaelian

Phys. Fluids 17, 034101 (2005) (13 pages)

Online Publication Date: 28 January 2005

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We consider the effect of a shock passing through an arbitrarily shaped interface y(x,0) between two fluids. The evolution of the interface into a new shape, written formally as y(x,t) = y(x,0) + tF(x), is found by applying the linear, classical Richtmyer–Meshkov instability result to each mode in the Fourier expansion of the original interface. We provide several examples where the new shape F(x) can be found analytically. For any interface y(x,0) we define an associated dual interface ydual(x,0) and show that F(x) = dydual(x,0)/dx. Representing a shock by a new mathematical operator we find how y(x,0),  ydual(x,0), and F(x) transform under the effect of a shock. Kink-singularities are found in F(x) when and where y(x,0) has a discontinuous change in its first derivative. These are the locations where jetting occurs. We briefly discuss the effects of nonlinearity, compressibility, viscosity, etc., all of which suppress kink-singularities, and present hydrocode simulations of shock tube and high-explosive-driven experiments to highlight the influence of compressibility, nonlinearity, and material strength.
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47.20.Ky, 47.20.Ma, 47.11.+j, 47.40.Nm, 47.55.Kf, 47.20.Dr

Instability of isolated compressible entropy-stratified vortices

Igor Men'shov and Yoshiaki Nakamura

Phys. Fluids 17, 034102 (2005) (15 pages)

Online Publication Date: 28 January 2005

Full Text: PDF (2004 kB)

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The normal mode linear analysis is applied to investigate the stability of a circular isolated compressible vortex with the emphasis on studying the effect of entropy stratification of the basic flow on stability properties. We study a family of vortices that have zero total circulation, with the swirl velocity being presented by a Taylor-type distribution in the radial direction. The stratification of entropy is modeled by a Gaussian two-parametric profile whose parameters control the maximal deviation from the homentropic distribution and the extent of the entropic zone. Results presented concern the effect of these parameters and the vortex intensity on instability characteristics. In particular, in the case of homentropic flow, vortices considered are found to be stable only for sufficiently high intensities and cease to be stable as the intensity weakens. As an example of the situation where unstable normal modes can be excited, the scattering of sound waves by the vortex flow is considered. By simulating this process numerically, we show that the scattered field becomes unstable in the course of time and acquires a typical periodical pattern in polar angle. The characteristics of this instability (viz., the growth rate and the azimuthal phase frequency) coincide with those of the linear analysis very closely. This fact shows conclusively that the instability is caused by the induction of unstable normal modes in the vortex by means of sound irradiation.
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47.32.Cc, 47.55.Hd, 47.40.-x, 47.20.-k, 47.11.+j

Characteristic modes and evolution processes of shear-layer vortices in an elevated transverse jet

Rong F. Huang and Jen Lan

Phys. Fluids 17, 034103 (2005) (13 pages)

Online Publication Date: 2 February 2005

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Characteristics and evolution processes of the traveling coherent flow structure in the shear layer of an elevated round jet in crossflow are studied experimentally in an open-loop wind tunnel. Streak pictures of the smoke flow patterns illuminated by the laser-light sheet in the median and horizontal planes are recorded with a high speed digital camera. Time histories of the instantaneous velocity of the vortical flows in the shear layer are digitized by a hot-wire anemometer through a high-speed data acquisition system. By analyzing the streak pictures of the smoke flow visualization, five characteristic flow structures, mixing-layer type vortices, backward-rolling vortices, forward-rolling vortices, swing-induced mushroom vortices, and jet-type vortices, are identified in the shear layer evolving from the up-wind edge of the jet exit. The behaviors and mechanisms of the vortical flow structure in the bent shear layer are prominently distinct in different flow regimes. The frequency characteristics, Strouhal number, power-spectrum density functions, autocorrelation coefficient, as well as the time and length scales of the coherent structure and the Lagrangian integral scales are obtained by processing the measured instantaneous velocity data. The Strouhal number is found to decay exponentially with the increase of the jet-to-crossflow momentum flux ratio. The autocorrelation coefficients provide the information for calculating the statistical time scales of the coherent structure and the integral time scales of turbulence fluctuations. The corresponding length scales of the vortical structure and the integral length scales of turbulence in the shear layer are therefore obtained and discussed.
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47.32.Cc, 47.27.Wg, 47.27.Nz, 47.20.Ft

Precession driven dynamos

A. Tilgner

Phys. Fluids 17, 034104 (2005) (6 pages)

Online Publication Date: 8 February 2005

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The dynamo effect is demonstrated numerically in precession driven flow in a spherical container. Both laminar as well as unstable flows act as dynamos. At low Ekman numbers in unstable flows, the dynamo mechanism relies predominantly on the components of the flow excited by instabilities. All calculations are performed in a frame of reference attached to the boundaries. In this frame, the rotation axis of the fluid executes a periodic motion with a period equal to the rotation period of the boundaries, whereas the magnetic dipole moment undergoes slower variations interrupted by reversals.
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47.85.Dh, 47.65.+a, 47.11.+j, 47.60.+i, 47.15.-x, 47.20.Gv

Experiments on the late-time development of single-mode Richtmyer–Meshkov instability

J. W. Jacobs and V. V. Krivets

Phys. Fluids 17, 034105 (2005) (10 pages)

Online Publication Date: 10 February 2005

Full Text: PDF (899 kB)

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The late-time development of Richtmyer–Meshkov instability is studied in shock tube experiments. This investigation makes use of the experimental apparatus and visualization methods utilized in the earlier study of Collins and Jacobs [J. Fluid Mech. 464, 113 (2002)] but employs stronger shocks and initial perturbations with shorter wavelengths to obtain much later-time (in the dimensionless sense) images of the single-mode instability. These modifications produce a very detailed look at the evolution of the late-time single-mode instability, revealing the transition and development of turbulence in the vortex cores that eventually results in the disintegration of the laminar vortex structures into small scale features. Amplitude measurements taken from these images are shown to be effectively collapsed when plotted in dimensionless variables defined using the wave number and the initial growth rate. The amplitude measurements are compared with several late-time nonlinear models and solutions. The best agreement is obtained with the model of Sadot et al. [Phys. Rev. Lett. 80, 1654 (1998)] which can be slightly improved by modifying the expression for the late-time asymptotic growth rate.
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47.15.Fe, 47.27.Cn, 47.40.Nm, 47.15.Ki

Linear stability analysis of axisymmetric perturbations in imperfectly conducting liquid jets

J. M. López-Herrera, P. Riesco-Chueca, and A. M. Gañán-Calvo

Phys. Fluids 17, 034106 (2005) (22 pages)

Online Publication Date: 1 March 2005

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A discussion is presented on the role of limited conductivity and permittivity on the behavior of electrified jets. Under certain conditions, significant departures with respect to the perfect-conductor limit are to be expected. In addition, an exploration is undertaken concerning the validity of one-dimensional average models in the description of charged jets. To that end, a temporal linear modal stability analysis is carried out of poor-conductor viscous liquid jets flowing relatively to a steady radial electric field. Only axisymmetric perturbations, leading to highest quality aerosols, are considered. A grounded coaxial electrode is located at variable distance. Most available studies in the literature are restricted to the perfect-conductor limit, while the present contribution is an extension to moderate and low electrical conductivity and permittivity jets, in an effort to describe a situation increasingly prevalent in the sector of small-scale free-surface flows. The influence of the electrode distance b, a parameter alpha defined as the ratio of the electric relaxation time scale to the capillary time scale, and the relative permittivity beta on the growth rate has been explored yielding results on the stability spectrum. In addition, arbitrary viscosity and electrification parameters are contemplated. In a wide variety of situations, the perfect-conductor limit provides a good approximation; however, the influence of alpha and beta on the growth rate and most unstable wavelength cannot be neglected in the general case. An interfacial boundary layer in the axial velocity profile occurs in the low-viscosity limit, but this boundary layer tends to disappear when alpha or beta are large enough. The use of a one-dimensional (1D) averaged model as an alternative to the 3D approach provides a helpful shortcut and a complementary insight on the nature of the jet's perturbative behavior. Lowest-order 1D approximations (average model), of widespread application in the literature of electrified jets, are shown to be inaccurate in low-viscosity imperfect-conductor jets.
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47.11.+j, 47.27.Wg, 47.65.+a, 47.20.Gv, 47.20.Ma, 47.55.Kf

Nucleation and spinodal decomposition of liquid mixtures

Andrea G. Lamorgese and Roberto Mauri

Phys. Fluids 17, 034107 (2005) (10 pages)

Online Publication Date: 1 March 2005

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We simulated the phase segregation of a metastable deeply quenched binary mixture. Our theoretical approach follows the diffuse interface model, where convection and diffusion are coupled via a nonequilibrium capillary force, expressing the tendency of the demixing system to minimize its free energy. As this driving force induces a material flux which, for liquid mixtures, is much larger than that due to pure molecular diffusion, the ratio of thermal to viscous forces is assumed to be of order 103, in agreement with experimental data. Using a pseudospectral method, we integrated the equations of motion in two dimensions, showing that the metastability of the system can be characterized through a critical radius, as in Gibbs' treatment, or through the (finite) intensity of a white noise superposed on the initial uniform concentration field. This critical intensity grows exponentially as the mean composition of the mixture approaches its equilibrium value. In addition we showed that, in general, the value of the critical radius decreases as the number density of the nucleating drops becomes very large, so that nuclei have the chance to coalesce and grow before being reabsorbed.
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47.55.Dz, 47.27.Te, 47.35.+i, 64.75.+g, 66.10.Cb

Turbulent Flows

Modeling return to isotropy using kinetic equations

Blair Perot and Chris Chartrand

Phys. Fluids 17, 035101 (2005) (18 pages)

Online Publication Date: 28 January 2005

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Kinetic equations modeling the behavior of the velocity probability density function (PDF) in homogeneous anisotropic decaying turbulence are hypothesized and their implications for return-to-isotropy are investigated. Anisotropic turbulent decay is a parametrically simple but theoretically complex turbulent flow that is dominated by nonlinear interactions. The physical implications of the Bhatnagar–Gross–Krook model, a relaxation model, and the Fokker–Planck model for the "collision" term in the PDF evolution equation are analyzed in detail. Using fairly general assumptions about the physics, three different parameter-free return-to-isotropy models are proposed. These models are compared with experimental data, classical models, and analytical limits. The final model expression is particularly interesting, and can easily be implemented in classic Reynolds stress transport models.
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47.27.Eq, 47.27.Gs, 47.11.+j

Experimental support for Townsend's Reynolds number similarity hypothesis on rough walls

Karen A. Flack, Michael P. Schultz, and Thomas A. Shapiro

Phys. Fluids 17, 035102 (2005) (9 pages)

Online Publication Date: 28 January 2005

Full Text: PDF (153 kB)

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The Reynolds number similarity hypothesis of Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, UK, 1976)] states that the turbulence beyond a few roughness heights from the wall is independent of the surface condition. The underlying assumption is that the boundary layer thickness delta is large compared to the roughness height k. This hypothesis was tested experimentally on two types of three-dimensional rough surfaces. Boundary layer measurements were made on flat plates covered with sand grain and woven mesh roughness in a closed return water tunnel at a momentum thickness Reynolds number Retheta of ~14  000. The boundary layers on the rough walls were in the fully rough flow regime (k<sub>s</sub><sup>+</sup>>=100) with the ratio of the boundary layer thickness to the equivalent sand roughness height delta/ks greater than 40. The results show that the mean velocity profiles for rough and smooth walls collapse well in velocity defect form in the overlap and outer regions of the boundary layer. The Reynolds stresses for the two rough surfaces agree well throughout most of the boundary layer and collapse with smooth wall results outside of 3ks. Higher moment turbulence statistics and quadrant analysis also indicate the differences in the rough wall boundary layers are confined to y<5ks. The present results provide support for Townsend's Reynolds number similarity hypothesis for uniform three-dimensional roughness in flows where delta/ks>=40.
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47.27.Nz

Droplet distributions at the liquid core of a turbulent spray

Sam S. Yoon

Phys. Fluids 17, 035103 (2005) (24 pages)

Online Publication Date: 28 January 2005

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Initial droplet distributions at the liquid core are examined for various Weber number and pulsing conditions. While experimental investigation in the liquid core region is nearly impossible due to difficulty in the optical access to the region, the distribution at the region is investigated computationally, and typical droplet distributions are identified. It is found that the Nukiyama–Tanasawa and log-normal distributions can best describe the droplet size and velocity distributions, respectively. By comparing computational results obtained at the liquid core (0<x<8  mm) and experimental data collected at x = 48  mm, it is suspected that the droplet gradation occurs immediately after droplets are separated from the liquid core. Thus, the distribution shape changes rapidly in both axial and radial directions. Such droplet–gradation behavior is numerically confirmed when the Nukiyama–Tanasawa droplet size distribution is used as an initial condition for the stochastic separated flow model. When the jet velocity is increased, the width of the droplet-size distribution becomes narrower, while the droplet velocity distribution becomes broader. Possible physical mechanism for that behavior is discussed in detail. Pulsing injection prominently influences the external spray shape near the nozzle exit. However, the overall droplet size and velocity distributions of the liquid core due to the pulsing injection are relatively insignificant for a turbulent spray in the atomization regime.
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47.55.Dz, 47.55.Kf, 47.27.Nz, 47.27.Wg, 47.60.+i, 47.32.Ff, 47.35.+i, 47.27.Eq, 47.10.+g

One-particle two-time diffusion in three-dimensional homogeneous isotropic turbulence

D. R. Osborne, J. C. Vassilicos, and J. D. Haigh

Phys. Fluids 17, 035104 (2005) (11 pages)

Online Publication Date: 28 January 2005

Full Text: PDF (162 kB)

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A model of turbulence based on a summation of Fourier modes with an imposed turbulent energy spectrum, E(k)~k–p, is used to investigate the characteristics of one-particle diffusion in turbulent flow. The model is described and the general Eulerian field is investigated. Using a number of Lagrangian statistical measures the results from the model are compared with laboratory experiments [N. Mordant, P. Metz, O. Michel, and J.-F. Pinton, "Measurement of Lagrangian velocity in fully developed turbulence," Phys. Rev. Lett. 87, 214501 (2001)]. The correlation structure and spectral properties of the real and modeled fields agree well under certain time dependency conditions. The correlation signature of Lagrangian accelerations is shown to reflect the persistence of the underlying streamline structure. Intermittency may influence these correlations but is not their primary cause.
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47.27.Eq, 47.27.Qb, 47.27.Gs, 47.11.+j, 47.55.Kf

The influence of turbulence on a columnar vortex

Naoya Takahashi, Hiroyuki Ishii, and Takeshi Miyazaki

Phys. Fluids 17, 035105 (2005) (14 pages)

Online Publication Date: 8 February 2005

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The interaction between a columnar vortex and external turbulence is investigated numerically. A Lamb–Oseen vortex is immersed in an initially isotropic homogeneous turbulence field, which itself is produced numerically by a direct numerical simulation of decaying turbulence. The formation of inhomogeneous fine turbulent eddies around the columnar vortex and the vortex-core deformations are studied in detail by visualizing the flow field. The initially random turbulent eddies (worms) are wrapped around the columnar vortex and become spirals. Statistical quantities, such as two-point-energy spectra and two-point-enstrophy spectra, are evaluated and compared with the theoretical predictions from rapid distortion theory. The axial velocity correlation dominates near the vortex surface, whereas the radial velocity correlation becomes larger where the worms are wrapped. Where the columnar vortex is strong compared with the external turbulence, external velocity disturbances are blocked by the vortex and they cannot penetrate into the vortex core directly, whereas various types of vortex waves (Kelvin waves) are excited.
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47.27.Eq, 47.32.Cc, 47.27.Gs, 47.11.+j

Viscoelastic effects on higher order statistics and on coherent structures in turbulent channel flow

Kostas D. Housiadas, Antony N. Beris, and Robert A. Handler

Phys. Fluids 17, 035106 (2005) (20 pages)

Online Publication Date: 8 February 2005

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In this work we study, using the results of direct numerical simulations [Housiadas and Beris, "Polymer-induced drag reduction: Viscoelastic and inertia effects of the variations in viscoelasticity and inertia," Phys. Fluids 15, 2369 (2003)], the effects of changes in the flow viscoelasticity and the friction Reynolds number on several higher order statistics of turbulence, such as the Reynolds stress, the enstrophy, the averaged equations for the conformation tensor, as well as on the coherent structures through a Karhunen–Loeve (K-L) analysis and selected flow and conformation visualizations. In particular, it is shown that, as the zero friction Weissenberg number Wetau0 increases (for a constant zero friction Reynolds number Retau0) dramatic reductions take place in many terms in the averaged equations for the Reynolds stresses and in all terms of the averaged enstrophy equations. From a Karhunen–Loeve analysis of the eigenmodes of the flow we saw that the presence of viscoelasticity increases significantly the coherence and energy content of the first few modes. The K-L dimension of the flow at Wetau0 = 125 is fully one order of magnitude lower than its Newtonian counterpart. As far as the effect of viscoelasticity is concerned, it is manifested primarily by changes in the boundary layer, which are mostly accomplished by Wetau0 = 50–62.5. In comparison, increasing the Retau0, from 125 to 590, induces significant changes in various terms in the budgets, despite the fact that the drag reduction remains practically the same over that range. However, the near the wall region seems to change significantly only up to Retau0 = 395, with few changes observed upon a further increase to Retau0 = 590.
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47.60.+i, 47.50.+d, 47.11.+j, 47.80.+v, 47.27.Nz

Large-eddy simulation of low frequency oscillations of the Dean vortices in turbulent pipe bend flows

F. Rütten, W. Schröder, and M. Meinke

Phys. Fluids 17, 035107 (2005) (11 pages)

Online Publication Date: 9 February 2005

Full Text: PDF (364 kB)

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Large-eddy simulations are performed to investigate turbulent flows through 90° pipe bends that feature unsteady flow separation, unstable shear layers, and an oscillation of the Dean vortices. Single bends with curvature radii of one- and three-pipe diameters are considered at the Reynolds number range 5000–27 000. The numerically computed distributions of the time-averaged velocities, Reynolds stress components, and power spectra of the velocities are validated by comparison with particle image velocimetry measurements. The power spectra of the overall forces onto the pipe walls are determined. The spectra exhibit a distinct peak in the high frequency range that is ascribed to vortex shedding at the inner side of the bends and shear layer instability. At the largest Reynolds number the spectra also exhibit an oscillation at a frequency much lower than that commonly observed at vortex shedding from separation. It turns out that the associated flow pattern is similar to the swirl switching phenomenon earlier found in experimental studies with which the present results are compared. It is shown that the low frequency oscillation perceptible on the entire wall is caused by the two Dean vortices whose strength vary in time and which as such alternately dominate the flow field.
Show PACS
47.27.Nz, 47.27.Eq, 47.32.Cc, 47.60.+i, 47.35.+i, 47.20.Ft, 47.54.+r, 47.11.+j, 47.32.Ff

Commutator errors in the filtering approach to large-eddy simulation

Fedderik van der Bos and Bernard J. Geurts

Phys. Fluids 17, 035108 (2005) (20 pages)

Online Publication Date: 9 February 2005

Full Text: PDF (351 kB)

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We analyze the large-eddy equations that are obtained from the application of a spatially nonuniform filter to the Navier–Stokes equations. Next to the well-known turbulent stress tensor a second group of subgrid terms arises; the so-called commutator errors. These additional subgrid terms emerge in the large-eddy equations solely as a consequence of the nonuniformity of the filter. We compare the magnitude of the divergence of the turbulent stress tensor with that of the commutator errors and pay attention to the role of the explicit filter that is adopted. It is shown that the turbulent stress contributions and the commutator errors display the same scaling behavior on the filter width and its derivative. Correspondingly, the use of higher-order filters is shown not only to decrease the commutator errors but likewise the turbulent stresses are uniformly reduced with increasing filter order. In addition, we establish that skewness of the spatial filter has a strong influence on the magnitude of the commutator errors while leaving the turbulent stress contributions roughly unaltered. The analysis of the order of magnitude of the various terms provides an impression of the flow conditions and filter width nonuniformities which necessitate explicit commutator-error modeling next to the more traditional turbulent stress subgrid modeling. Some explicit models for the commutator errors are put forward and an a priori assessment of these commutator-error models in turbulent mixing layers is obtained. Generalized similarity models appear promising in this respect and display high correlation with the exact commutator errors.
Show PACS
47.27.Eq, 47.10.+g

A dynamic nonlinear subgrid-scale stress model

Bing-Chen Wang and Donald J. Bergstrom

Phys. Fluids 17, 035109 (2005) (15 pages)

Online Publication Date: 16 February 2005

Full Text: PDF (244 kB)

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In this paper, a dynamic subgrid scale (SGS) stress model based on Speziale's quadratic nonlinear constitutive relation [C. G. Speziale, J. Fluid Mech. 178, 459 (1987); T. B. Gatski and C. G. Speziale, J. Fluid Mech. 254, 59 (1993)] is proposed, which includes the conventional dynamic SGS model as its first-order approximation. The closure method utilizes both the symmetric and antisymmetric parts of the resolved velocity gradient, and allows for a nonlinear anisotropic representation of the SGS stress tensor. Unlike the conventional Smagorinsky type modeling approaches, the proposed model does not require an alignment between the SGS stress tensor and the resolved strain rate tensor. It exhibits significant flexibility in self-calibration of the model coefficients, and local stability without the need for plane averaging to avoid excessive backscatter of SGS turbulence kinetic energy and potential modeling singularity problems. It also allows for variable tensorial geometric relations between the SGS stress and its constituent terms, and reflects both forward and backward scatters of SGS turbulence kinetic energy between the filtered and subgrid scales of motions. Turbulent Couette flow for Reynolds numbers (based on channel height and one half the velocity difference between the two plates) of 2600 and 4762 was used in numerical simulations to validate the proposed approach.
Show PACS
47.27.Eq, 47.11.+j, 47.32.-y

Use of the 4/5 Kolmogorov equation for describing some characteristics of fully developed turbulence

V. I. Tatarskii

Phys. Fluids 17, 035110 (2005) (12 pages)

Online Publication Date: 16 February 2005

Full Text: PDF (187 kB)

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The Kolmogorov equation, which relates the second-order structure function Dll(r) and the third-ordrer structure function Dlll(r), may be presented as a closed linear integrodifferential equation for the probability distribution function W(U,r) of longitudinal velocity difference U. In general, without any restrictions, the function of two variables W(U,r) may be presented as [Dll(r)]–1/2F(U/sqrt(D[sub ll](r)),r). As a first approximation, we neglect dependence of F on the second argument r. In this approximation (self-similarity of the probability density function), the integrodifferential equation for W reduces to the ordinary nonlinear differential equation for Dll(r). It follows from this equation that for r-->[infinity] the function Dll(r)~r2/3. This consideration does not use the 1941 Kolmogorov hypothesis that is based on dimension analysis. Any deviations from the 2/3 law, including intermittency effects, must be related to the violation of the above-mentioned self-similarity of W, i.e., with the additional dependence of F on the second argument r. On the basis of experimental data, we suggest a simple model of W, which allows us to describe deviations from the 2/3 law, caused by intermittency, and describe the local exponents kappa in the structure functions <|U(r)|rho>~rkappa(rho) for moderate rho. The so called "bottleneck effect" also can be described by 4/5 Kolmogorov equation.
Show PACS
47.27.Eq, 47.10.+g, 02.50.Ng

Experimental studies of occupation and transit times in turbulent flows

J. Berg Jørgensen, J. Mann, S. Ott, H. L. Pécseli, and J. Trulsen

Phys. Fluids 17, 035111 (2005) (12 pages)

Online Publication Date: 1 March 2005

Full Text: PDF (213 kB)

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The motion of passively advected particles is studied experimentally in approximately homogeneous and isotropic turbulent flows. The turbulence is generated in water by two moving grids. The simultaneous trajectories of many small passively advected, neutrally buoyant polystyrene particles are followed in time by a particle tracking technique. We estimate the probability distribution of the transit times of such particles in spherical volumes with given radius. A particle which is passively advected by the flow is selected to define the center of a reference sphere, with the transit time being defined as the difference between entrance and exit times of surrounding particles advected through this sphere by the turbulent motions. Simple scaling laws are obtained for the probability density of the transit times in terms of the basic properties of the turbulent flow and the geometry. Also other formulations of the problem have been considered, by assuming, for instance, that particle positions are uniformly distributed within the reference sphere, and then determine the statistical distribution of the time they subsequently spend inside the sphere, i.e., their occupation time. These problems have Eulerian counterparts, and they were analyzed as well. In the present formulation, we find that the results of the analysis are relevant for understanding certain details in the feeding rate of microorganisms in turbulent waters, for instance.
Show PACS
47.27.Eq, 47.27.Gs, 47.55.Kf, 47.10.+g

A numerical study of the alpha model for two-dimensional magnetohydrodynamic turbulent flows

Pablo D. Mininni, David C. Montgomery, and Annick G. Pouquet

Phys. Fluids 17, 035112 (2005) (17 pages)

Online Publication Date: 1 March 2005

Full Text: PDF (327 kB)

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We explore some consequences of the "alpha model," also called the "Lagrangian-averaged" model, for two-dimensional incompressible magnetohydrodynamic (MHD) turbulence. This model is an extension of the smoothing procedure in fluid dynamics, which filters velocity fields locally while leaving their associated vorticities unsmoothed, and has proved useful for high Reynolds number turbulence computations. We consider several known effects (selective decay, dynamic alignment, inverse cascades, and the probability distribution functions of fluctuating turbulent quantities) in magnetofluid turbulence and compare the results of numerical solutions of the primitive MHD equations with their alpha-model counterparts' performance for the same flows, in regimes where available resolution is adequate to explore both. The hope is to justify the use of the alpha model in regimes that lie outside currently available resolution, as will be the case in particular in three-dimensional geometry or for magnetic Prandtl numbers differing significantly from unity. We focus our investigation, using direct numerical simulations with a standard and fully parallelized pseudospectral method and periodic boundary conditions in two space dimensions, on the role that such a modeling of the small scales using the Lagrangian-averaged framework plays in the large-scale dynamics of MHD turbulence. Several flows are examined, and for all of them one can conclude that the statistical properties of the large-scale spectra are recovered, whereas small-scale detailed phase information (such as, e.g., the location of structures) is lost.
Show PACS
47.27.Eq, 47.65.+a, 47.55.Kf, 47.32.Cc, 47.10.+g

Sensitivity of spectral variational multiscale methods for large-eddy simulation of isotropic turbulence

P. Sagaut and V. Levasseur

Phys. Fluids 17, 035113 (2005) (11 pages)

Online Publication Date: 1 March 2005

Full Text: PDF (161 kB)

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Subgrid closures in the Fourier space belonging to the variational multiscale method proposed by Hughes are investigated in the case of the incompressible freely evolving isotropic turbulence in the limit of an infinite Reynolds number. Sensitivity to the closure used at small scales is shown to be high, and different hybrid spectral closures proposed in the present study which explicitly account for the computed kinetic energy spectrum shape yield good results. The original formulation of the method is observed to suffer from an unphysical energy pile-up in the large scales, which arises from the fact that the kinetic energy transfers associated with distant triadic interactions are neglected. The use of a nonorthogonal operator to define the resolved large and small scales is proved to alleviate this problem, yielding an accurate and robust spectral variational multiscale methods for high Reynolds number flows.
Show PACS
47.27.Eq, 47.27.Gs, 47.27.Jv, 47.10.+g

Numerical study of the decay of enstrophy in a two-dimensional Navier–Stokes fluid in the limit of very small viscosities

Pablo Dmitruk and David C. Montgomery

Phys. Fluids 17, 035114 (2005) (5 pages)

Online Publication Date: 1 March 2005

Full Text: PDF (79 kB)

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The rate of enstrophy decay in two-dimensional Navier–Stokes turbulence is explored numerically with high resolution pseudospectral simulations. Initial conditions and all other physical parameters are held fixed while viscosity is decreased through about three orders of magnitude, while increasing the numerical resolution as required to resolve the smallest scales that develop. The attempt is to discern whether or not a regime is being approached in which the behavior of the vorticity decay could be approximated as ideal and nondissipative. Although the enstrophy decay shows a (logarithmic) tendency to go to zero as the viscosity is decreased, at fixed times, the extrapolated values of viscosity to approach a zero enstrophy decay regime lie many orders of magnitude out of our currently available numerical resolution.
Show PACS
47.27.Eq, 47.32.Cc, 47.11.+j

Compressible Flows

On the Rayleigh–Bénard problem in the continuum limit

Avshalom Manela and Itzchak Frankel

Phys. Fluids 17, 036101 (2005) (7 pages)

Online Publication Date: 16 February 2005

Full Text: PDF (272 kB)

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The transition to convection in the Rayleigh–Bénard problem at small Knudsen numbers is studied via a linear temporal stability analysis of the compressible "slip-flow" problem. No restrictions are imposed on the magnitudes of temperature difference and compressibility-induced density variations. The dispersion relation is calculated by means of a Chebyshev collocation method. The results indicate that occurrence of instability is limited to small Knudsen numbers (Kn<~0.03) as a result of the combination of the variation with temperature of fluid properties and compressibility effects. Comparison with existing direct simulation Monte Carlo and continuum nonlinear simulations of the corresponding initial-value problem demonstrates that the present results correctly predict the boundaries of the convection domain. The linear analysis thus presents a useful alternative in studying the effects of various parameters on the onset of convection, particularly in the limit of arbitrarily small Knudsen numbers.
Show PACS
47.45.Gx, 47.40.-x, 47.10.+g, 47.27.Te, 47.20.-k

Film cooling effectiveness on a large angle blunt cone flying at hypersonic speed

Niranjan Sahoo, Vinayak Kulkarni, S. Saravanan, G. Jagadeesh, and K. P. J. Reddy

Phys. Fluids 17, 036102 (2005) (11 pages)

Online Publication Date: 23 February 2005

Full Text: PDF (322 kB)

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Effectiveness of film cooling technique to reduce convective heating rates for a large angle blunt cone flying at hypersonic Mach number and its effect on the aerodynamic characteristics is investigated experimentally by measuring surface heat-transfer rates and aerodynamic drag coefficient simultaneously. The test model is a 60° apex-angle blunt cone with an internally mounted accelerometer balance system for measuring aerodynamic drag and an array of surface mounted platinum thin film gauges for measuring heat-transfer rates. The coolant gas (air, carbon dioxide, and/or helium) is injected into the hypersonic flow at the nose of the test model. The experiments are performed at a flow free stream Mach number of 5.75 and 0° angle of attack for stagnation enthalpies of 1.16  MJ/kg and 1.6  MJ/kg with and without gas injection. About 30%–45% overall reduction in heat-transfer rates is observed with helium as coolant gas except at stagnation regions. With all other coolants, the reduction in surface heat-transfer rate is between 10%–25%. The aerodynamic drag coefficient is found to increase by 12% with helium injection whereas with other gases this increase is about 27%.
Show PACS
47.27.Te, 47.40.Ki, 47.85.Gj

Geophysical Flows

Numerical simulations of high density ratio lock-exchange flows

Jocelyn Étienne, Emil J. Hopfinger, and Pierre Saramito

Phys. Fluids 17, 036601 (2005) (12 pages)

Online Publication Date: 28 January 2005

Full Text: PDF (598 kB)

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In this paper direct numerical simulations of exchange flows of large density ratios are presented and are compared with experiments by Gröbelbauer et al. [J. Fluid Mech. 250, 669 (1993)]. These simulations, which make use of a dynamic mesh adaptation technique, cover the whole density ratio range of the experiments and very good agreement with the experimental front velocities and the Froude number variations is obtained. Moreover, in order to establish more definitely the Froude number dependency on density ratio, the simulations were carried up to ratios of 100 compared with 21.6 accessible in experiments. An empirical law for the dense front Froude number as a function of the density parameter is proposed. The mathematical difficulty of the problem is discussed. This difficulty arises because, when the density ratio is large, the existence of a solution is dependent on a compatibility condition between the diffusion and viscous terms model. Moreover, a specific numerical technique is required to treat the finite, nonuniform divergence of the mass-averaged velocity field described by the continuity equation.
Show PACS
47.11.+j, 47.60.+i, 47.55.Kf, 47.32.Cc

Coupling or decoupling bed and flow dynamics: Fast and slow sediment waves at high Froude numbers

Marco Colombini and Alessandro Stocchino

Phys. Fluids 17, 036602 (2005) (9 pages)

Online Publication Date: 4 February 2005

Full Text: PDF (502 kB)

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The effect of coupling or decoupling bed and flow dynamics is analyzed in the framework of a linear analysis of the stability of a uniform, rotational, two-dimensional flow in an infinitely wide channel with a bed composed by incoherent sediments. It is shown that results obtained with the coupled analysis in term of instability of slow sediment waves of the dune/antidune kind are quite similar to the results obtained making use of the "quasisteady hypothesis," which forms the basis of most of the existing linear stability analyses of bedforms and formally justifies the decoupling procedure. Small differences can be observed, for Froude numbers of O(1), in the surroundings of the marginal curves that bound the instability regions, mainly due to the removal of the artificial resonance that is introduced in the analysis when the quasisteady hypothesis is enforced. The decoupled approach, however, completely wipes out a mode of instability associated with fast-moving sediment waves, which appear at high Froude numbers in connection with the formation of roll waves on the free surface. This mode of instability, characterized by large wavelengths, is shown to coexist with the slower, shorter antidune mode.
Show PACS
47.11.+j, 47.32.-y, 47.55.Mh, 47.20.-k, 47.35.+i, 47.60.+i

Others

Numerical simulation of finite Reynolds number suspension drops settling under gravity

Thorsten Bosse, Leonhard Kleiser, Carlos Härtel, and Eckart Meiburg

Phys. Fluids 17, 037101 (2005) (17 pages)

Online Publication Date: 2 February 2005

Full Text: PDF (2100 kB)

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A suspension drop is a swarm of particles that are suspended in initially still fluid. When settling under the influence of gravity a suspension drop may undergo a complex shape evolution including the formation of a torus and eventual disintegration. In the present work the settling process of initially spherical suspension drops is investigated numerically for low and moderate drop Reynolds numbers Red. In the simulations a pseudospectral method is used for the liquid phase combined with a Lagrangian point-particle model for the particulate phase. In the case of low Reynolds numbers (Red<1) the suspension drop retains a roughly spherical shape while settling. A few particles leak away into a tail emanating from the rear of the drop. Due to the use of periodic boundaries a hindered settling effect is observed: the drop settling velocity is decreased compared to a suspension drop in infinite fluid. In the Reynolds number range 1<=Red<=100 the suspension drop deforms into a torus that eventually becomes unstable and breaks up into a number of secondary blobs. This Reynolds number range has not been investigated systematically in previous studies and is the focus of the present work. It is shown that the number of secondary blobs is primarily determined by the Reynolds number and the particle distribution inside the initial drop. An increased number of particles making up the suspension, i.e., a finer drop discretization, may result in a delayed torus disintegration with a larger number of secondary blobs. The influence of the initial particle distribution as a source of (natural) perturbations and the effect of initially imposed (artificial) shape perturbations on the breakup process are examined in detail. To gain a better understanding of the substructural effects (inside the suspension) leading to torus breakup, the particle field is analyzed from a spectral point of view. To this end, the time evolution of the Fourier coefficients associated with the particle distribution in the azimuthal direction of the torus is studied.
Show PACS
47.55.Dz, 47.11.+j, 47.55.Kf, 47.15.Pn

The McCormack model for gas mixtures: Plane Couette flow

R. D. M. Garcia and C. E. Siewert

Phys. Fluids 17, 037102 (2005) (6 pages)

Online Publication Date: 4 February 2005

Full Text: PDF (71 kB)

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An analytical version of the discrete-ordinates method is used to establish a concise and particularly accurate solution to the problem of plane Couette flow for a binary gas mixture described by the McCormack kinetic model. The solution yields, for the general (specular-diffuse) case of Maxwell boundary conditions for each of the two species, the velocity, heat-flow, and shear-stress profiles for both types of particles, as well as the particle-flow and heat-flow rates associated with each of the two species of gas particles. Highly accurate numerical results are reported for the case of a helium–argon mixture confined between molybdenum and tantalum plates. The algorithm is considered especially easy to use, and the developed (FORTRAN) code requires typically less than a second on a 2.2  GHz Pentium 4 machine to compute all quantities of interest with at least five figures of accuracy.
Show PACS
47.11.+j, 47.45.-n, 47.10.+g, 47.15.-x, 47.55.Kf, 47.60.+i, 47.40.-x, 47.27.Te

Geometric collision rates and trajectories of cloud droplets falling into a Burgers vortex

Reginald J. Hill

Phys. Fluids 17, 037103 (2005) (23 pages)

Online Publication Date: 22 February 2005

Full Text: PDF (4603 kB)

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Droplet velocities, concentrations, and geometric collision rates are calculated for droplets falling into Burgers vortices as a step toward understanding the role of turbulence-induced collisions of cloud water droplets. The Burgers vortex is an often used model of vortices in high Reynolds number turbulence. Droplet radii considered are 10, 20, and 40  µm; those radii are relevant to warm rain initiation. A method of calculating the concentrations of droplets along their trajectories by means of differential geometry is derived and implemented. A generalization of the rate of geometrical collisions of inertial particles is derived; the formulation applies for any local vorticity and rate of strain, and the classic collision-rate formula is obtained in the process. The relative velocities of droplets of different radii and their spatial variation of concentration affects spatial variation of collision rate; greater variation exists for a stronger vortex. The physical effects included in the droplet equation of motion are inertia, gravity, viscous drag, pressure and shear stress, added mass, the history integral, and the lift force. The lift force requires calculation of droplet angular velocity, the equation for which contains rotational inertial and viscous drag. An initial condition is found that does not cause an impulse in the history integral. The important terms in the droplets' equations of motion are found such that simpler approximate equations can be used. It is found that the lift force is negligible, the history integral is not. For smaller droplets in regions of lower vorticity, the time derivative of the difference of slip velocity and gravitationally induced drift velocity may be neglected. The present study suggests that acceleration-induced coalescence is most significant for droplets that are entrained into or formed within an intensifying vortex as distinct from falling toward the vortex.
Show PACS
92.60.Nv, 92.60.Ek, 47.32.Cc, 47.55.Dz, 47.55.Kf, 47.45.Gx, 47.27.-i

Thermodiffusion in ferrofluids in the presence of a magnetic field

T. Voelker and S. Odenbach

Phys. Fluids 17, 037104 (2005) (6 pages)

Online Publication Date: 24 February 2005

Full Text: PDF (102 kB)

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Investigations were made to investigate the thermodiffusion process (Soret effect) of magnetic particles in a ferrofluid under the influence of a magnetic field. The so-called magnetic Soret effect was theoretically predicted to be two to three orders of magnitude smaller than the conventional Soret effect. In contrast, former experiments have qualitatively shown that the magnetic influence on the thermodiffusion process is much higher than the theoretical predictions for the magnetic Soret effect. However, in those experiments the influence of buoyancy and magnetic driven convection disturbed the measurement significantly. Thus it is still an open question how strong the influence of a magnetic field on thermodiffusion can be and how this influence can be explained theoretically. Therefore an experimental setup was developed which minimizes parasitic effects, simplifying the analysis of the experimental results. These results provide quantitative measures of the magnetic field dependence of the Soret effect in suspensions of magnetic nanoparticles. If this influence is taken as a magnetic Soret effect it is shown that it can even be higher than the conventional one and that its strength as well as its direction depend on the magnetic field strength and its relative alignment to the temperature gradient in the fluid.
Show PACS
47.27.Te, 47.55.Kf, 47.32.Ff, 47.65.+a, 47.10.+g
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BRIEF COMMUNICATIONS

Asymptotic analysis of liquid films dip-coated onto chemically micropatterned surfaces

Jeffrey M. Davis

Phys. Fluids 17, 038101 (2005) (4 pages)

Online Publication Date: 28 January 2005

Full Text: PDF (234 kB)

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The dip coating of chemically heterogeneous surfaces is a useful technique for attaining selective material deposition. For the case of vertical, wetting stripes surrounded by nonwetting regions, experiments have demonstrated that the thickness of the entrained film on the stripes is significantly different than on homogeneous surfaces because of the lateral confinement of the liquid. In the present work, the asymptotic matching of equations based on lubrication theory is used to determine the film thickness, and necessary restrictions on the capillary and Bond numbers are provided. The predictions are in excellent agreement with the existing experimental data, and the classical Landau–Levich formula for homogeneous surfaces is recovered from the analysis in the limit of very wide stripes.
Show PACS
47.10.+g, 68.15.+e, 47.70.Fw, 47.60.+i

Potential dominance of oscillating crescent waves in finite width tanks

David R. Fuhrman and Per A. Madsen

Phys. Fluids 17, 038102 (2005) (4 pages)

Online Publication Date: 2 February 2005

Full Text: PDF (189 kB)

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Recently, it has been proposed that the emergence of previously observed oscillating crescent water wave patterns, created by class II (three-dimensional) instabilities which are in principle not dominant, could in fact be explained as an artifact of a finite width tank, combined with a suppression of the class I (Benjamin–Feir) instability. Within this context, we investigate quantitatively the dominance of class II deep water wave instabilities for particular transversal wavenumbers, and it is shown that the regions where non-phase-locked (oscillating) crescent wave patterns are locally dominant is surprisingly large, particularly for low to moderate wave steepness. This is an important realization for both experimentalists and numerical modelers currently studying these phenomena.
Show PACS
47.35.+i, 47.20.Lz

Scalar-threshold dependence and internal dynamics in turbulent jets

Roberto C. Aguirre and Haris J. Catrakis

Phys. Fluids 17, 038103 (2005) (4 pages)

Online Publication Date: 4 February 2005

Full Text: PDF (276 kB)

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The scalar-threshold dependence of internal interfaces in turbulent jets is examined above the mixing transition with an experimental database generated from high-resolution three-dimensional space-time measurements using laser-induced fluorescence and digital-imaging techniques. Quadratic dependence on scalar threshold is found for the volume of fluid enclosed by internal interfaces over a wide range of thresholds. Linear dependence on scalar threshold is found for the interfacial surface area over the same range of thresholds. The observed behavior can be accounted for by physical modeling based on the dynamics of internal large-scale well-mixed regions.
Show PACS
47.27.Eq, 47.27.Wg, 47.11.+j, 47.27.Qb, 47.55.Kf

Flight in a viscous fluid: Asymptotic theory of the vortex wake

Yakov Afanasyev

Phys. Fluids 17, 038104 (2005) (4 pages)

Online Publication Date: 8 February 2005

Full Text: PDF (288 kB)

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Solutions for the three-dimensional distributions of vorticity in the wake behind localized forces moving in a viscous fluid are obtained. The forces simulate the drag, thrust, and lift forces applied on the fluid by a flying animal such as a small insect. Concentrated vortex tubes in the wake are also illustrated in a visualization experiment where a "virtual" insect is modeled using the electromagnetic method of forcing.
Show PACS
47.11.+j, 47.32.Cc, 47.27.Vf, 47.40.-x, 87.19.St

Simulations of starting gas jets at low Mach numbers

Immaculada Iglesias, Marcos Vera, Antonio L. Sánchez, and Amable Liñán

Phys. Fluids 17, 038105 (2005) (4 pages)

Online Publication Date: 8 February 2005

Full Text: PDF (85 kB)

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The starting jet produced by the impulsively started discharge of a submerged gas stream of constant velocity through a circular orifice in a plane wall is investigated by integrating numerically the axisymmetric Navier–Stokes equations for moderately large values of the jet Reynolds number. The analysis is restricted to low-Mach-number jets, for which the jet-to-ambient temperature ratio gamma= Tj/To emerges as the most relevant parameter. It is seen that the leading vortex approaches a quasisteady structure propagating at an almost constant velocity, which is larger for smaller values of gamma. The action of the baroclinic torque in regions of nonuniform temperature leads to significant vorticity production, with a constant overall rate equal to that of an inviscid starting jet.
Show PACS
47.27.Wg, 47.10.+g, 47.60.+i, 47.40.-x

Variation in the critical mass ratio of a freely oscillating cylinder as a function of Reynolds number

K. Ryan, M. C. Thompson, and K. Hourigan

Phys. Fluids 17, 038106 (2005) (4 pages)

Online Publication Date: 8 February 2005

Full Text: PDF (179 kB)

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A two-dimensional numerical investigation of the flow-induced vibration of a circular cylinder held free to oscillate transverse to the free-stream direction has been performed. The simulations were performed over a Reynolds number range Re = [30,200] and for an infinite reduced velocity. Two regions of high amplitude oscillations are observed and are referred to as the viscous and higher Reynolds number range, respectively. The viscous range was observed for Re = [40,95] and the higher Reynolds number range was observed above Re = 180. A critical mass ratio, below which appreciable amplitude oscillations are observed, is determined as a function of Reynolds number. For Reynolds numbers between the two ranges, only very small oscillations were observed for all mass ratios investigated.
Show PACS
47.35.+i, 47.10.+g

An extension of Faxen's laws for nonisothermal flow around a sphere

Aruna Mohan and Howard Brenner

Phys. Fluids 17, 038107 (2005) (4 pages)

Online Publication Date: 9 February 2005

Full Text: PDF (51 kB)

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In the presence of temperature gradients, the enforcement of the no-slip boundary condition on the velocity of a gas at its boundary with a solid leads to predictions inconsistent with experimental observations. It is known that Maxwell's [J. C. Maxwell, Philos. Trans. R. Soc. London 170, 231 (1879)] thermal slip condition must instead be applied, as, for example, in the cases of thermophoresis and thermal transpiration. In addition to gases, the motion of particles in otherwise stationary liquids has also been explained by the use of a similarly constituted thermal slip condition. We use this slip condition to generalize Faxen's laws for incompressible creeping Stokes flow around a heat-conducting sphere in the presence of temperature gradients, for the case of an arbitrary undisturbed Stokes flow far from the sphere. These laws are confirmed by showing their agreement with known results for thermophoretic particle motion. By way of illustration, Faxen's laws are used to calculate the force and torque acting on a small spherical particle in a laterally insulated capillary tube under an externally imposed temperature gradient. These results have potential applications with respect to the motion of particles in nonisothermal, fluid-filled porous media, microelectromechanical systems devices, and in aerosol technology. The basic scheme is also generally applicable to situations in which the slip is induced by other externally imposed gradients, such as in the case of electrophoretic particle motion arising from an electric potential gradient.
Show PACS
47.10.+g, 47.15.Gf, 47.55.Kf, 47.45.Gx, 47.27.Te

Axial stretching and vortex definition

J.-Z. Wu, A.-K. Xiong, and Y.-T. Yang

Phys. Fluids 17, 038108 (2005) (4 pages)

Online Publication Date: 23 February 2005

Full Text: PDF (65 kB)

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Four existing invariant criteria for defining a vortex are diagnosed analytically and demonstrated by the Burgers and Sullivan vortices. Two of the criteria are found disqualified as generally applicable, and one underestimates the core radius. The diagnosis leads to a general requirement for any possible criterion: it should be able to identify the vortex axis and allow for arbitrary axial strain.
Show PACS
47.11.+j, 47.32.Cc

Influence of variable thermal conductivity and viscosity for nonisothermal fluid flow

Ahmet Pinarbasi, Coskun Ozalp, and Selim Duman

Phys. Fluids 17, 038109 (2005) (4 pages)

Online Publication Date: 25 February 2005

Full Text: PDF (72 kB)

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This Brief Communication investigates the effect of variable viscosity and thermal conductivity of a nonisothermal, incompressible Newtonian fluid flowing under the effect of a constant pressure gradient in plane Poiseuille flow. The viscosity and thermal conductivity of the fluid exhibit linear temperature dependence and the effect of viscous heating is included in the analysis. Channel walls are kept at constant temperatures. Discretization is performed using a pseudospectral technique based on Chebyshev polynomial expansions. The resulting nonlinear, coupled boundary value problem is solved iteratively using Chebyshev pseudospectral method.
Show PACS
47.10.+g, 47.27.Te, 47.60.+i
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COMMENTS

FREE

Comment on "Thermocapillary convection due to a stationary bubble" [Phys. Fluids 16, 3131 (2004)]

Ehud Yariv

Phys. Fluids 17, 039101 (2005) (1 page)

Online Publication Date: 11 February 2005

Full Text: PDF (26 kB)

+
 Abstract Unavailable
Show PACS
47.55.Dz, 47.27.Te, 47.35.+i, 47.10.+g, 47.55.Kf
FREE

Response to "Comment on `Thermocapillary convection due to a stationary bubble'" [Phys. Fluids 17, 039101 (2005)]

R. Balasubramaniam and R. Shankar Subramanian

Phys. Fluids 17, 039102 (2005) (1 page)

Online Publication Date: 11 February 2005

Full Text: PDF (18 kB)

+
 Abstract Unavailable
Show PACS
47.55.Dz, 47.27.Te, 47.35.+i, 47.10.+g, 47.55.Kf

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