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Mar 2005

Volume 17, Issue 3, Articles (03xxxx)

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Preface: Biofluid mechanics

James B. Grotberg

Phys. Fluids 17, 031401 (2005); http://dx.doi.org/10.1063/1.1862617 (1 page)

Online Publication Date: 22 February 2005

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Abstract Unavailable
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01.30.-y Physics literature and publications
87.19.U- Hemodynamics
87.19.Wx Pneumodyamics, respiration

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); http://dx.doi.org/10.1063/1.1829972 (3 pages) | Cited 4 times

Online Publication Date: 22 February 2005

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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.U- Hemodynamics
87.19.Wx Pneumodyamics, respiration
87.17.Jj Cell locomotion, chemotaxis
47.55.Kf Particle-laden flows
47.35.-i Hydrodynamic waves
47.60.-i Flow phenomena in quasi-one-dimensional systems

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

A. M. Jacob and D. P. Gaver

Phys. Fluids 17, 031502 (2005); http://dx.doi.org/10.1063/1.1862642 (11 pages) | Cited 10 times

Online Publication Date: 23 February 2005

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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.U- Hemodynamics
87.19.Wx Pneumodyamics, respiration
87.17.Aa Modeling, computer simulation of cell processes
47.55.D- Drops and bubbles
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.27.N- Wall-bounded shear flow turbulence
47.35.-i Hydrodynamic waves
47.10.-g General theory in fluid dynamics

Axisymmetric motion of a file of red blood cells through capillaries

C. Pozrikidis

Phys. Fluids 17, 031503 (2005); http://dx.doi.org/10.1063/1.1830484 (14 pages) | Cited 50 times

Online Publication Date: 23 February 2005

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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.U- Hemodynamics
87.19.Wx Pneumodyamics, respiration
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.55.Kf Particle-laden flows
47.11.-j Computational methods in fluid dynamics

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); http://dx.doi.org/10.1063/1.1830486 (14 pages) | Cited 39 times

Online Publication Date: 23 February 2005

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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 Cell locomotion, chemotaxis
47.32.-y Vortex dynamics; rotating fluids
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.50.-d Non-Newtonian fluid flows
47.10.-g General theory in fluid dynamics

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); http://dx.doi.org/10.1063/1.1862635 (21 pages) | Cited 22 times

Online Publication Date: 24 February 2005

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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.rh Fluid transport and rheology
83.80.Lz Physiological materials (e.g. blood, collagen, etc.)
87.19.U- Hemodynamics
87.19.Wx Pneumodyamics, respiration
87.10.-e General theory and mathematical aspects
47.11.-j Computational methods in fluid dynamics
83.50.Ax Steady shear flows, viscometric flow
83.50.Lh Slip boundary effects (interfacial and free surface flows)
87.15.La Mechanical properties

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); http://dx.doi.org/10.1063/1.1862631 (17 pages) | Cited 8 times

Online Publication Date: 1 March 2005

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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.U- Hemodynamics
87.19.Wx Pneumodyamics, respiration
47.11.-j Computational methods in fluid dynamics
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.20.Dr Surface-tension-driven instability
68.15.+e Liquid thin films

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

V. Suresh and J. B. Grotberg

Phys. Fluids 17, 031507 (2005); http://dx.doi.org/10.1063/1.1863853 (15 pages) | Cited 6 times

Online Publication Date: 1 March 2005

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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 α 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, α 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 α. 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, VṘ. 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 General theory in fluid dynamics
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.55.Kf Particle-laden flows
87.19.U- Hemodynamics
87.19.Wx Pneumodyamics, respiration

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); http://dx.doi.org/10.1063/1.1830485 (13 pages) | Cited 5 times

Online Publication Date: 1 March 2005

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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 ωc. A fluid velocity boundary layer develops at the outer edge of the surface layers when the dimensionless Brinkman parameter α = L/math, 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 ω<ωc or ωr( = ω/ωc)<1. However, the velocity at the tips of the structural element is π/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 α 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 Cell locomotion, chemotaxis
87.14.E- Proteins
87.17.Aa Modeling, computer simulation of cell processes
47.35.-i Hydrodynamic waves
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.27.nb Boundary layer turbulence

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); http://dx.doi.org/10.1063/1.1863278 (17 pages) | Cited 7 times

Online Publication Date: 1 March 2005

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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 Physiological materials (e.g. blood, collagen, etc.)
47.11.-j Computational methods in fluid dynamics
87.19.R- Mechanical and electrical properties of tissues and organs
83.50.-v Deformation and flow
87.17.Aa Modeling, computer simulation of cell processes

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); http://dx.doi.org/10.1063/1.1830487 (16 pages) | Cited 2 times

Online Publication Date: 1 March 2005

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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.U- Hemodynamics
87.19.Wx Pneumodyamics, respiration
47.32.C- Vortex dynamics
47.35.-i Hydrodynamic waves
47.27.T- Turbulent transport processes
47.10.-g General theory in fluid dynamics
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Predicting rogue waves in random oceanic sea states

A. L. Islas and C. M. Schober

Phys. Fluids 17, 031701 (2005); http://dx.doi.org/10.1063/1.1872093 (4 pages) | Cited 7 times

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 Ocean waves and oscillations
47.35.-i Hydrodynamic waves
47.10.-g General theory in fluid dynamics

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); http://dx.doi.org/10.1063/1.1863332 (4 pages) | Cited 19 times

Online Publication Date: 22 February 2005

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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 θ from vertical. Three flow regimes are observed: starting from vertical, Vf first increases with θ, reaches a plateau and then decreases again. In the first regime, Vf is controlled by segregation and mixing effects, respectively, increasing and decreasing with θ. 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 θ, 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 Flow phenomena in quasi-one-dimensional systems
47.55.Kf Particle-laden flows

Computer simulations of the collapse of a granular column

Roberto Zenit

Phys. Fluids 17, 031703 (2005); http://dx.doi.org/10.1063/1.1862240 (4 pages) | Cited 24 times

Online Publication Date: 23 February 2005

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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 Particle-laden flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.11.-j Computational methods in fluid dynamics

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

Oleg A. Likhachev and Jeffrey W. Jacobs

Phys. Fluids 17, 031704 (2005); http://dx.doi.org/10.1063/1.1863276 (3 pages) | Cited 3 times

Online Publication Date: 23 February 2005

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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.C- Vortex dynamics
47.55.D- Drops and bubbles
47.10.-g General theory in fluid dynamics
47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.55.Kf Particle-laden flows
47.35.-i Hydrodynamic waves

Spiral shear layers: Roll-up and incipient instability

Christophe Lepage, Thomas Leweke, and Alberto Verga

Phys. Fluids 17, 031705 (2005); http://dx.doi.org/10.1063/1.1863249 (4 pages)

Online Publication Date: 1 March 2005

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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.C- Vortex dynamics
47.11.-j Computational methods in fluid dynamics
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.27.N- Wall-bounded shear flow turbulence
47.53.+n Fractals in fluid dynamics

The existence of vortices in the wakes of simulated raindrops

J. R. Saylor and B. K. Jones

Phys. Fluids 17, 031706 (2005); http://dx.doi.org/10.1063/1.1874192 (4 pages) | Cited 8 times

Online Publication Date: 1 March 2005

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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 General theory in fluid dynamics
47.32.C- Vortex dynamics
47.27.wb Turbulent wakes
47.55.D- Drops and bubbles
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.35.-i Hydrodynamic waves

Turbulence in dilute polymer solutions

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

Phys. Fluids 17, 031707 (2005); http://dx.doi.org/10.1063/1.1864133 (4 pages) | Cited 18 times

Online Publication Date: 1 March 2005

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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 Isotropic turbulence; homogeneous turbulence
47.50.-d Non-Newtonian fluid flows
47.32.C- Vortex dynamics
47.55.Kf Particle-laden flows
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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); http://dx.doi.org/10.1063/1.1850691 (7 pages) | Cited 20 times

Online Publication Date: 4 February 2005

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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 Turbulent jets
47.55.Kf Particle-laden flows
47.55.D- Drops and bubbles
47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.20.Dr Surface-tension-driven instability
47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.20.Gv Viscous and viscoelastic instabilities
47.10.-g General theory in fluid dynamics

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

A. Kerem Uguz and R. Narayanan

Phys. Fluids 17, 032102 (2005); http://dx.doi.org/10.1063/1.1846791 (7 pages)

Online Publication Date: 8 February 2005

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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 General theory in fluid dynamics
47.20.Cq Inviscid instability
47.55.Kf Particle-laden flows
81.10.Fq Growth from melts; zone melting and refining

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

Michael A. Rother and Robert H. Davis

Phys. Fluids 17, 032103 (2005); http://dx.doi.org/10.1063/1.1856532 (12 pages) | Cited 3 times

Online Publication Date: 9 February 2005

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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.D- Drops and bubbles
02.30.Rz Integral equations

Electrically induced pattern formation in thin leaky dielectric films

R. V. Craster and O. K. Matar

Phys. Fluids 17, 032104 (2005); http://dx.doi.org/10.1063/1.1852459 (17 pages) | Cited 35 times

Online Publication Date: 9 February 2005

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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 Pattern selection; pattern formation
47.10.-g General theory in fluid dynamics
77.84.Nh Liquids, emulsions, and suspensions; liquid crystals
77.55.-g Dielectric thin films
68.15.+e Liquid thin films
47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.20.Gv Viscous and viscoelastic instabilities

Enhanced damping of capillary bridge oscillations using velocity feedback

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

Phys. Fluids 17, 032105 (2005); http://dx.doi.org/10.1063/1.1859191 (11 pages) | Cited 4 times

Online Publication Date: 16 February 2005

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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 Hydrodynamic waves

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

Thomas Boeck and Stéphane Zaleski

Phys. Fluids 17, 032106 (2005); http://dx.doi.org/10.1063/1.1862234 (11 pages) | Cited 11 times

Online Publication Date: 24 February 2005

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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 Particle-laden flows
47.27.nb Boundary layer turbulence
47.20.Gv Viscous and viscoelastic instabilities
47.20.Cq Inviscid instability
47.35.-i Hydrodynamic waves

On-shell description of stationary flames

Kirill A. Kazakov

Phys. Fluids 17, 032107 (2005); http://dx.doi.org/10.1063/1.1864132 (15 pages) | Cited 9 times

Online Publication Date: 1 March 2005

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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 θ→1 where θ 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 Chemically reactive flows
47.32.C- Vortex dynamics
47.10.-g General theory in fluid dynamics
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