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May 2009

Volume 21, Issue 5, Articles (05xxxx)

Issue Cover Spotlight Figure

Phys. Fluids 21, 056602 (2009); http://dx.doi.org/10.1063/1.3140002 (10 pages)

R. D. Wordsworth
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back to top Biofluid Mechanics

Wave propagation and induced steady streaming in viscous fluid contained in a prestressed viscoelastic tube

Ye Ma and Chiu-On Ng

Phys. Fluids 21, 051901 (2009); http://dx.doi.org/10.1063/1.3139250 (25 pages) | Cited 2 times

Online Publication Date: 22 May 2009

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The oscillatory and time-mean motions induced by a propagating wave of small amplitude through a viscous incompressible fluid contained in a prestressed and viscoelastic (modeled as a Voigt material) tube are studied by a perturbation analysis based on equations of motion in the Lagrangian system. The classical problem of oscillatory viscous flow in a flexible tube is re-examined in the contexts of blood flow in arteries or pulmonary gas flow in airways. The wave kinematics and dynamics, including wavenumber, wave attenuation, velocity, and stress fields, are found as analytical functions of the wall and fluid properties, prestress, and the Womersley number for the cases of a free or tethered tube. On extending the analysis to the second order in terms of the small wave steepness, it is shown that the time-mean motion of the viscoelastic tube with sufficient strength is short lived and dies out quickly as a limit of finite deformation is approached. Once the tube has attained its steady deformation, the steady streaming in the fluid can be solved analytically. Results are generated to illustrate the combined effects on the first-order oscillatory flow and the second-order steady streaming due to elasticity, viscosity, and initial stresses of the wall. The present model as applied to blood flow in arteries and gas flow in pulmonary airways during high-frequency ventilation is examined in detail through comparison with models in the literature.
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87.19.U- Hemodynamics
87.19.Wx Pneumodyamics, respiration
87.85.gf Fluid mechanics and rheology
47.60.Dx Flows in ducts and channels
47.50.-d Non-Newtonian fluid flows
back to top Micro- and Nanofluid Mechanics

Time dependence of effective slip on textured hydrophobic surfaces

R. N. Govardhan, G. S. Srinivas, A. Asthana, and M. S. Bobji

Phys. Fluids 21, 052001 (2009); http://dx.doi.org/10.1063/1.3127123 (8 pages) | Cited 7 times

Online Publication Date: 6 May 2009

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In this paper, we present results on water flow past randomly textured hydrophobic surfaces with relatively large surface features of the order of 50 μm. Direct shear stress measurements are made on these surfaces in a channel configuration. The measurements indicate that the flow rates required to maintain a shear stress value vary substantially with water immersion time. At small times after filling the channel with water, the flow rates are up to 30% higher compared with the reference hydrophilic surface. With time, the flow rate gradually decreases and in a few hours reaches a value that is nearly the same as the hydrophilic case. Calculations of the effective slip lengths indicate that it varies from about 50 μm at small times to nearly zero or “no slip” after a few hours. Large effective slip lengths on such hydrophobic surfaces are known to be caused by trapped air pockets in the crevices of the surface. In order to understand the time dependent effective slip length, direct visualization of trapped air pockets is made in stationary water using the principle of total internal reflection of light at the water-air interface of the air pockets. These visualizations indicate that the number of bright spots corresponding to the air pockets decreases with time. This type of gradual disappearance of the trapped air pockets is possibly the reason for the decrease in effective slip length with time in the flow experiments. From the practical point of usage of such surfaces to reduce pressure drop, say, in microchannels, this time scale of the order of 1 h for the reduction in slip length would be very crucial. It would ultimately decide the time over which the surface can usefully provide pressure drop reductions.
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47.45.Gx Slip flows and accommodation
47.60.Dx Flows in ducts and channels
Author Select

Huge reduction in pressure drop of water, glycerol/water mixture, and aqueous solution of polyethylene oxide in high speed flows through micro-orifices

Tomiichi Hasegawa, Akiomi Ushida, and Takatsune Narumi

Phys. Fluids 21, 052002 (2009); http://dx.doi.org/10.1063/1.3129592 (9 pages) | Cited 12 times

Online Publication Date: 7 May 2009

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Microfluid mechanics is one of the most exciting research areas in modern fluid mechanics and fluid engineering because of its many potential industrial and biological applications. In the present study, pressure drops (PDs) were measured for water, a 50/50 glycerol/water mixture, and a 0.1% aqueous solution of polyethylene oxide (PEO) 8000 flowing at high velocities through various sizes of micro-orifice. It was found that the measured PD of water and the glycerol/water mixture agrees with the prediction of the Navier–Stokes equation for orifices 100 and 400 μm in diameter, but it is lower for orifices less than 50 μm in diameter. In particular, the measured maximum PD was almost two orders of magnitude lower than the prediction for the 10 and 5 μm diameter orifices. The glycerol/water mixture, possessing a viscosity ten times higher than water, provided nearly the same PDs as water when the reduction was generated. The solution of PEO produced a lower PD than water and the glycerol/water mixture except for the 400 μm diameter orifice. Several factors, including orifice shape, deformation of orifice foil, wall slip, transition, cavitation, and elasticity were considered but the evidence suggests that the reduction in PD may be caused by wall slip or the elasticity induced in a flow of high elongational rate.
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47.60.Dx Flows in ducts and channels
47.55.D- Drops and bubbles
47.85.Np Fluidics
47.10.A- Mathematical formulations
66.20.-d Viscosity of liquids; diffusive momentum transport
47.50.-d Non-Newtonian fluid flows

Gravity-driven slug motion in capillary tubes

Ivan Lunati and Dani Or

Phys. Fluids 21, 052003 (2009); http://dx.doi.org/10.1063/1.3125262 (9 pages) | Cited 2 times

Online Publication Date: 14 May 2009

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The velocity of a liquid slug falling in a capillary tube is lower than predicted for Poiseuille flow due to presence of menisci, whose shapes are determined by the complex interplay of capillary, viscous, and gravitational forces. Due to the presence of menisci, a capillary pressure proportional to surface curvature acts on the slug and streamlines are bent close to the interface, resulting in enhanced viscous dissipation at the wedges. To determine the origin of drag-force increase relative to Poiseuille flow, we compute the force resultant acting on the slug by integrating Navier–Stokes equations over the liquid volume. Invoking relationships from differential geometry we demonstrate that the additional drag is due to viscous forces only and that no capillary drag of hydrodynamic origin exists (i.e., due to hydrodynamic deformation of the interface). Requiring that the force resultant is zero, we derive scaling laws for the steady velocity in the limit of small capillary numbers by estimating the leading order viscous dissipation in the different regions of the slug (i.e., the unperturbed Poiseuille-like bulk, the static menisci close to the tube axis and the dynamic regions close to the contact lines). Considering both partial and complete wetting, we find that the relationship between dimensionless velocity and weight is, in general, nonlinear. Whereas the relationship obtained for complete-wetting conditions is found in agreement with the experimental data of Bico and Quéré [ J. Bico and D. Quéré, J. Colloid Interface Sci. 243, 262 (2001) ], the scaling law under partial-wetting conditions is validated by numerical simulations performed with the Volume of Fluid method. The simulated steady velocities agree with the behavior predicted by the theoretical scaling laws in presence and in absence of static contact angle hysteresis. The numerical simulations suggest that wedge-flow dissipation alone cannot account for the entire additional drag and that the non-Poiseuille dissipation in the static menisci (not considered in previous studies) has to be considered for large contact angles.
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47.55.nb Capillary and thermocapillary flows
47.35.Bb Gravity waves
47.60.Dx Flows in ducts and channels
47.10.ad Navier-Stokes equations
68.08.Bc Wetting
68.03.Cd Surface tension and related phenomena

Chaotic mixing in electro-osmotic flows driven by spatiotemporal surface charge modulation

Chih-Chang Chang and Ruey-Jen Yang

Phys. Fluids 21, 052004 (2009); http://dx.doi.org/10.1063/1.3139162 (15 pages) | Cited 4 times

Online Publication Date: 18 May 2009

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This paper presents an investigation into chaotic mixing in an electro-osmotic flow through a microchannel. In the mixing system, the continuous throughput flow has the form of a pluglike electro-osmotic flow induced by a permanent surface charge on the wall surface, while electro-osmotic flows contributed by spatiotemporal surface charge variations act as a perturbed flow. The spatiotemporal surface charge variations are achieved using the field-effect control method. The analyses consider two different spatiotemporal surface charge modulation schemes, designated as “MS I” and “MS II,” respectively. It is shown that both modulation schemes prompt the crossing of the flow streamlines at different instances in time and produce a chaotic mixing effect. Utilizing the thin double layer assumption, the study commences by solving the biharmonic equation for the electro-osmotic flow fields analytically. The mixing phenomena induced by the two modulation schemes are then analyzed using the Lagrangian particle tracing method. Finally, the mixing performances of the two schemes are evaluated analytically using the Poincaré section method, the finite-time Lyapunov exponent (FTLE) technique, and a stretching value distribution analysis method, respectively. It is found that the mean FTLE combined with the coefficient of variance of the FTLE distribution provides the most suitable criterion for obtaining quantitative estimates of the mixing performance and therefore provides a feasible means of estimating the amplitude and time-switching period of the perturbed flows which optimize the mixing performance. The validity of the analytical results is confirmed via a comparison with the results obtained from the back-trace imaging method and direct numerical simulations based on a species convection-diffusion equation, respectively. In addition, the direct numerical simulation results show that the dimensionless mixing length and dimensionless mixing time required to achieve a 90% mixing both vary as a logarithmic function of the Péclet number when the mixing system is in a nearly fully chaotic state.
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47.52.+j Chaos in fluid dynamics
47.60.Dx Flows in ducts and channels
47.11.-j Computational methods in fluid dynamics
87.50.ch Electrophoresis/dielectrophoresis and other mechanical effects

Rarefied gas flow in microtubes at different inlet-outlet pressure ratios

Z. Yang and S. V. Garimella

Phys. Fluids 21, 052005 (2009); http://dx.doi.org/10.1063/1.3139310 (15 pages) | Cited 1 time

Online Publication Date: 27 May 2009

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A model is developed for rarefied gas flow in long microtubes with different inlet-outlet pressure ratios at low Mach numbers. The model accounts for significant changes in Knudsen number along the length of the tube and is therefore applicable to gas flow in long tubes encountering different flow regimes along the flow length. Predictions from the model show good agreement with experimental measurements of mass flow rate, pressure drop, and inferred streamwise pressure distribution obtained under different flow conditions and offer a better match with experiments than do those from a conventional slip flow model.
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47.45.Gx Slip flows and accommodation
47.40.-x Compressible flows; shock waves
47.60.Dx Flows in ducts and channels
47.61.Fg Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)
47.85.Gj Aerodynamics
47.85.Np Fluidics
back to top Interfacial Flows

Evaporation of a thin droplet on a thin substrate with a high thermal resistance

G. J. Dunn, S. K. Wilson, B. R. Duffy, and K. Sefiane

Phys. Fluids 21, 052101 (2009); http://dx.doi.org/10.1063/1.3121214 (7 pages) | Cited 8 times

Online Publication Date: 6 May 2009

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A mathematical model for the quasisteady evaporation of a thin liquid droplet on a thin substrate that incorporates the dependence of the saturation concentration of vapor at the free surface of the droplet on temperature is used to examine an atypical situation in which the substrate has a high thermal resistance relative to the droplet (i.e., it is highly insulating and/or is thick relative to the droplet). In this situation diffusion of heat through the substrate is the rate-limiting evaporative process and at leading order the local mass flux is spatially uniform, the total evaporation rate is proportional to the surface area of the droplet, and the droplet is uniformly cooled. In particular, the qualitative differences between the predictions of the present model in this situation and those of the widely used “basic” model in which the saturation concentration is independent of temperature are highlighted.
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47.55.D- Drops and bubbles
64.70.fm Thermodynamics studies of evaporation and condensation
68.03.Fg Evaporation and condensation of liquids

Sloshing of a layered fluid with a free surface as a Hamiltonian system

G. Sciortino, C. Adduce, and M. La Rocca

Phys. Fluids 21, 052102 (2009); http://dx.doi.org/10.1063/1.3121304 (16 pages)

Online Publication Date: 6 May 2009

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The aim of this paper is the investigation of a layered sloshing fluid system using both a new Hamiltonian mathematical model and new laboratory experiments. The mathematical model is defined for a cylindrical tank with an arbitrary shape and subjected to an arbitrary rigid motion. The model consists of a pure evolution system of partial differential first order equations in the canonical four unknowns: water elevation at the upper free surface and at the separation surface and the gap in momentum potential density computed at each fluid surface. The system of equations is obtained by avoiding the construction of the Hamiltonian and its variational derivatives. An important advantage of this formulation, with respect to the Lagrangian formulation, is that the nonevolution constraint, which imposes for each fluid the same velocity component along the normal direction of the separation surface, is fulfilled by the model itself. The model implementation needs to define the so-called Neumann–Dirichlet operators, which are computed by an efficient algorithm, for any instantaneous configuration of the two fluid domains. A numerical integration of the model is performed by a suitable Galerkin projection of the evolution equations. New laboratory experiments, simulating the sloshing of a layered fluid system, inside a tank with a squared cross section, were performed. The experiments, with a two-dimensional sloshing, were carried out by varying the forcing frequency, the oscillation amplitude and the ratio of the two fluids’ depths. In some experiments, a traveling wave, with a shape similar to a moving hydraulic jump, was observed at the separation surface. Measurements of the space-time evolution of both the free and the separation surfaces were performed and compared with the model’s predictions. A good agreement between the model predictions and laboratory measurements is found, even for strong nonlinear cases such as the traveling wave.
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47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.11.-j Computational methods in fluid dynamics
47.35.-i Hydrodynamic waves

Inertia dominated drop collisions. I. On the universal flow in the lamella

Ilia V. Roisman, Edin Berberović, and Cam Tropea

Phys. Fluids 21, 052103 (2009); http://dx.doi.org/10.1063/1.3129282 (10 pages) | Cited 22 times

Online Publication Date: 11 May 2009

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This study is devoted to the analysis of inertia dominated axisymmetric drop collisions with a dry substrate or with another liquid drop. All the previous theoretical and semiempirical models of drop collisions are based on the assumption that the flow in the lamella and its thickness are determined by the impact conditions, mainly by the Reynolds and Weber numbers. In this study the existing experimental data are compared to existing and new numerical simulations for the shape of the lamella generated at the early times of drop impact for various impact conditions. The results show that if the Reynolds and Weber numbers are high enough, the evolution of the lamella thickness almost does not depend on the viscosity and surface tension. Therefore these results completely change our understanding of the flow generated by drop collisions. Moreover, we demonstrate that the theoretical models based on the approximation of the shape of the deforming drop by a disk and the models based on the energy balance approach are not correct. Finally, universal dimensionless distributions for the lamella thickness, velocity, and pressure are obtained from the numerical simulations of drop impact onto a symmetry plane (associated with the binary drop collisions). These universal distributions are valid for high impact Weber and Reynolds numbers.
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47.55.dr Interactions with surfaces
47.15.Cb Laminar boundary layers
47.11.-j Computational methods in fluid dynamics
68.05.-n Liquid-liquid interfaces
68.08.-p Liquid-solid interfaces

Inertia dominated drop collisions. II. An analytical solution of the Navier–Stokes equations for a spreading viscous film

Ilia V. Roisman

Phys. Fluids 21, 052104 (2009); http://dx.doi.org/10.1063/1.3129283 (11 pages) | Cited 20 times

Online Publication Date: 11 May 2009

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This study is devoted to a theoretical description of an unsteady laminar viscous flow in a spreading film of a Newtonian fluid. Such flow is generated by normal drop impact onto a dry substrate with high Weber and Reynolds numbers. An analytical self-similar solution for the viscous flow in the spreading drop is obtained which satisfies the full Navier–Stokes equations. The characteristic thickness of a boundary layer developed near the wall uniformly increases as a square root of time. An expression for the thickness of the boundary layer is used for the estimation of the residual film thickness formed by normal drop impact and the maximum spreading diameter. The theoretical predictions agree well with the existing experimental data. A possible explanation of the mechanism of formation of an uprising liquid sheet leading to splash is also proposed.
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47.55.dr Interactions with surfaces
47.10.ad Navier-Stokes equations
47.15.Cb Laminar boundary layers
47.55.nd Spreading films

The effective slip length and vortex formation in laminar flow over a rough surface

Anoosheh Niavarani and Nikolai V. Priezjev

Phys. Fluids 21, 052105 (2009); http://dx.doi.org/10.1063/1.3121305 (10 pages) | Cited 5 times

Online Publication Date: 11 May 2009

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The flow of viscous incompressible fluid over a periodically corrugated surface is investigated numerically by solving the Navier–Stokes equation with the local slip and no-slip boundary conditions. We consider the effective slip length which is defined with respect to the level of the mean height of the surface roughness. With increasing corrugation amplitude the effective no-slip boundary plane is shifted toward the bulk of the fluid, which implies a negative effective slip length. The analysis of the wall shear stress indicates that a flow circulation is developed in the grooves of the rough surface provided that the local boundary condition is no-slip. By applying a local slip boundary condition, the center of the vortex is displaced toward the bottom of the grooves and the effective slip length increases. When the intrinsic slip length is larger than the corrugation amplitude, the flow streamlines near the surface are deformed to follow the boundary curvature, the vortex vanishes, and the effective slip length saturates to a constant value. Inertial effects promote vortex flow formation in the grooves and reduce the effective slip length.
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47.45.Gx Slip flows and accommodation
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.32.-y Vortex dynamics; rotating fluids
83.50.Rp Wall slip and apparent slip
47.10.ad Navier-Stokes equations

Nonlinear regimes of anticonvection, thermocapillarity, and Rayleigh–Benard convection in two-layer systems

Ilya B. Simanovskii, Antonio Viviani, Frank Dubois, and Jean–Claude Legros

Phys. Fluids 21, 052106 (2009); http://dx.doi.org/10.1063/1.3139264 (11 pages) | Cited 1 time

Online Publication Date: 18 May 2009

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The nonlinear regimes of anticonvection and Rayleigh–Benard convection in a two-layer system with periodic boundary conditions on lateral walls in the presence of the interfacial heat release are studied. The region where anticonvective and the Rayleigh–Benard instability mechanisms act simultaneously is considered. The influence of the thermocapillary effect on anticonvective and Rayleigh–Benard flows, is investigated. New types of nonlinear traveling waves and modulated traveling waves are found.
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47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.55.N- Interfacial flows

Characterization of string cavitation in large-scale Diesel nozzles with tapered holes

M. Gavaises, A. Andriotis, D. Papoulias, N. Mitroglou, and A. Theodorakakos

Phys. Fluids 21, 052107 (2009); http://dx.doi.org/10.1063/1.3140940 (9 pages) | Cited 1 time

Online Publication Date: 21 May 2009

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The cavitation structures formed inside enlarged transparent replicas of tapered Diesel valve covered orifice nozzles have been characterized using high speed imaging visualization. Cavitation images obtained at fixed needle lift and flow rate conditions have revealed that although the conical shape of the converging tapered holes suppresses the formation of geometric cavitation, forming at the entry to the cylindrical injection hole, string cavitation has been found to prevail, particularly at low needle lifts. Computational fluid dynamics simulations have shown that cavitation strings appear in areas where large-scale vortices develop. The vortical structures are mainly formed upstream of the injection holes due to the nonuniform flow distribution and persist also inside them. Cavitation strings have been frequently observed to link adjacent holes while inspection of identical real-size injectors has revealed cavitation erosion sites in the area of string cavitation development. Image postprocessing has allowed estimation of their frequency of appearance, lifetime, and size along the injection hole length, as function of cavitation and Reynolds numbers and needle lift.
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47.55.D- Drops and bubbles
47.60.Kz Flows and jets through nozzles
47.32.-y Vortex dynamics; rotating fluids
47.80.Jk Flow visualization and imaging
47.11.-j Computational methods in fluid dynamics
back to top Viscous and Non-Newtonian Flows

Abrupt contraction flow of magnetorheological fluids

P. Kuzhir, M. T. López-López, and G. Bossis

Phys. Fluids 21, 053101 (2009); http://dx.doi.org/10.1063/1.3125947 (13 pages) | Cited 5 times

Online Publication Date: 6 May 2009

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Contraction and expansion flows of magnetorheological fluids occur in a variety of smart devices. It is important therefore to learn how these flows can be controlled by means of applied magnetic fields. This paper presents a first investigation into the axisymmetric flow of a magnetorheological fluid through an orifice (so-called abrupt contraction flow). The effect of an external magnetic field, longitudinal or transverse to the flow, is examined. In experiments, the pressure-flow rate curves were measured, and the excess pressure drop (associated with entrance and exit losses) was derived from experimental data through the Bagley correction procedure. The effect of the longitudinal magnetic field is manifested through a significant increase in the slope of the pressure-flow rate curves, while no discernible yield stress occurs. This behavior, observed at shear Mason numbers 10<Mnshear<100, is interpreted in terms of an enhanced extensional response of magnetorheological fluids accompanied by shrinkage of the entrance flow into a conical funnel. At the same range of Mason numbers, the transverse magnetic field appears not to influence the pressure drop. This can be explained by a total destruction of magnetic particle aggregates by large hydrodynamic forces acting on them when they are perpendicular to the flow. To support these findings, we have developed a theoretical model connecting the microstructure of the magnetorheological fluid to its extensional rheological properties and predicting the pressure-flow rate relations through the solution of the flow equations. In the case of the longitudinal magnetic field, our model describes the experimental results reasonably well.
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47.65.Cb Magnetic fluids and ferrofluids

Dissipation in quasi-two-dimensional flowing foams

Christophe Raufaste, Amandine Foulon, and Benjamin Dollet

Phys. Fluids 21, 053102 (2009); http://dx.doi.org/10.1063/1.3142502 (9 pages) | Cited 5 times

Online Publication Date: 26 May 2009

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The dissipation between two-dimensional (2D) monolayers of bubbles, the so-called quasi-2D foams, and a wall is investigated in two setups: a “liquid pool” system, where the foam is confined between a soap solution and a glass coverslip, and a Hele-Shaw cell, where the foam occupies the narrow gap between two plates. This experimental study reports dissipation measurements for mobile gas/liquid interfaces (free shear boundary condition) over a large range of parameters: in the liquid pool system, velocity and bubble area; in the Hele-Shaw cell, velocity and liquid fraction. The effect of the latter quantity is measured for the first time over more than three orders of magnitude. A full comparison between our results and other experimental studies is proposed and enables to rescale all measurements on a single master curve. It shows that for mobile gas/liquid interfaces, the existing models systematically underestimate the dissipation in flowing foams. This is quantified by a discrepancy factor ξ, ratio of the experimental dissipation measurements to the theoretical predictions, which scales as ξ = 1.4(RP/math)−0.5 with RP the Plateau border radius and A the bubble area, showing that the discrepancy is higher for dry foams.
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47.57.Bc Foams and emulsions
47.55.dd Bubble dynamics
47.55.Ca Gas/liquid flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
back to top Particulate, Multiphase, and Granular Flows

Peristaltic particle transport using the lattice Boltzmann method

Kevin Connington, Qinjun Kang, Hari Viswanathan, Amr Abdel-Fattah, and Shiyi Chen

Phys. Fluids 21, 053301 (2009); http://dx.doi.org/10.1063/1.3111782 (16 pages) | Cited 10 times

Online Publication Date: 6 May 2009

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Peristaltic transport refers to a class of internal fluid flows where the periodic deformation of flexible containing walls elicits a non-negligible fluid motion. It is a mechanism used to transport fluid and immersed solid particles in a tube or channel when it is ineffective or impossible to impose a favorable pressure gradient or desirous to avoid contact between the transported mixture and mechanical moving parts. Peristaltic transport occurs in many physiological situations and has myriad industrial applications. We focus our study on the peristaltic transport of a macroscopic particle in a two-dimensional channel using the lattice Boltzmann method. We systematically investigate the effect of variation of the relevant dimensionless parameters of the system on the particle transport. We find, among other results, a case where an increase in Reynolds number can actually lead to a slight increase in particle transport, and a case where, as the wall deformation increases, the motion of the particle becomes non-negative only. We examine the particle behavior when the system exhibits the peculiar phenomenon of fluid trapping. Under these circumstances, the particle may itself become trapped where it is subsequently transported at the wave speed, which is the maximum possible transport in the absence of a favorable pressure gradient. Finally, we analyze how the particle presence affects stress, pressure, and dissipation in the fluid in hopes of determining preferred working conditions for peristaltic transport of shear-sensitive particles. We find that the levels of shear stress are most hazardous near the throat of the channel. We advise that shear-sensitive particles should be transported under conditions where trapping occurs as the particle is typically situated in a region of innocuous shear stress levels.
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47.60.Dx Flows in ducts and channels
47.57.Gc Granular flow
47.11.Qr Lattice gas

Particle migration and suspension structure in steady and oscillatory plane Poiseuille flow

K. Yapici, R. L. Powell, and R. J. Phillips

Phys. Fluids 21, 053302 (2009); http://dx.doi.org/10.1063/1.3119802 (16 pages) | Cited 11 times

Online Publication Date: 13 May 2009

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A structure-tensor-based model is used to compute the microstructure and velocity field of concentrated suspensions of hard spheres in a fully developed, pressure-driven channel flow. The model is comprised of equations governing conservation of mass and momentum in the bulk suspension, conservation of particles, and conservation of momentum in the particle phase. The equations governing the relation between structure and stress in hard-sphere suspensions were developed previously and were shown to reproduce quantitatively results obtained by Stokesian dynamics simulations of linear shear flows. In nonhomogeneous, pressure-driven flows, the divergence of the particle contribution to the stress is nonzero and acts as a body force that causes particles to migrate across streamlines. Under steady conditions, the model predicts that the resulting migration causes particles to move to the center of the channel, where the concentration approaches the maximum packing for hard-sphere suspensions. In oscillatory flow, the behavior depends strongly on the amplitude of the strain. For oscillations with large strains, the particles migrate to the channel center. However, when the strain is small, the maximum concentration is located either at a position between the channel center and walls or, in the limit of very small strains, at the wall. The migration to the wall induced by small-strain oscillation occurs in conjunction with the suspension microstructure becoming ordered. This behavior agrees qualitatively with experimental observations reported in the literature. However, the predicted rate of migration toward the wall in the simulations is significantly slower than what is observed experimentally.
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47.60.Dx Flows in ducts and channels
47.57.E- Suspensions
47.11.-j Computational methods in fluid dynamics

Dissipative-particle dynamics simulations of flow over a stationary sphere in compliant channels

Harinath Reddy and John Abraham

Phys. Fluids 21, 053303 (2009); http://dx.doi.org/10.1063/1.3134044 (10 pages)

Online Publication Date: 13 May 2009

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Dissipative-particle dynamics (DPD), a particle-based fluid-simulation approach, is employed to simulate isothermal pressure-driven flow across a sphere in compliant cylindrical channels. The sphere is represented by frozen DPD particles, while the surrounding fluid is modeled using simple fluid particles. The channel walls are made up of interconnected finite extensible nonlinear elastic bead-spring chains. The wall particles at the inlet and outlet ends of the channel are frozen so as to hinge the channel. The model is assessed for accuracy by computing the drag coefficient CD in shear flow past a uniform sphere in unbounded flow, and comparing the results with those from correlations in literature. The effect of the aspect ratio λ of the channel, i.e., the ratio of the sphere diameter d to the channel diameter D, on the drag force FD on the sphere is investigated, and it is found that FD decreases as λ decreases toward the values predicted by the correlations as λ approaches zero. The effect of the elasticity of the wall is also studied. It is observed that as the wall becomes more elastic, there is a decrease in FD on the sphere.
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47.60.Dx Flows in ducts and channels
47.50.Cd Modeling
47.11.-j Computational methods in fluid dynamics
back to top Laminar Flows
Author Select

Novel characteristics of valveless pumping

S. Timmermann and J. T. Ottesen

Phys. Fluids 21, 053601 (2009); http://dx.doi.org/10.1063/1.3114603 (14 pages) | Cited 1 time

Online Publication Date: 4 May 2009

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multimedia

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This study investigates the occurrence of valveless pumping in a fluid-filled system consisting of two open tanks connected by an elastic tube. We show that directional flow can be achieved by introducing a periodic pinching applied at an asymmetrical location along the tube, and that the flow direction depends on the pumping frequency. We propose a relation between wave propagation velocity, tube length, and resonance frequencies associated with shifts in the pumping direction using numerical simulations. The eigenfrequencies of the system are estimated from the linearized system, and we show that these eigenfrequencies constitute the resonance frequencies and the horizontal slope frequencies of the system; “horizontal slope frequency” being a new concept. A simple model is suggested, explaining the effect of the gravity driven part of the oscillation observed in response to the tank and tube diameter changes. Results are partly compared with experimental findings.
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47.85.L- Flow control
47.60.Dx Flows in ducts and channels
47.11.-j Computational methods in fluid dynamics
47.10.ad Navier-Stokes equations

A nonmolecular derivation of Maxwell’s thermal-creep boundary condition in gases and liquids via application of the LeChatelier–Braun principle to Maxwell’s thermal stress

Howard Brenner

Phys. Fluids 21, 053602 (2009); http://dx.doi.org/10.1063/1.3139273 (11 pages) | Cited 5 times

Online Publication Date: 20 May 2009

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According to the LeChatelier–Braun principle, when a closed quiescent system initially in an equilibrium or unstressed steady state is subjected to an externally imposed “stress” it responds in a manner tending to alleviate that stress. Use of this entropically based qualitative rule, in combination with the notion of Maxwell thermal stresses existing in nonisothermal gases and liquids, enables one to (i) derive Maxwell’s thermal-creep boundary condition prevailing at the boundary between a solid and a fluid (either gas or liquid) and (ii) rationalize the phenomenon of thermophoresis in liquids, for which, in contrast with the case of gases, an elementary explanation is currently lacking. These two objectives are achieved by quantitatively interpreting the heretofore qualitative LeChatelier–Braun notion of stress in the present context as being the fluid’s stress tensor, the latter including Maxwell’s thermal stress. In effect, thermophoretic particle motion is interpreted as the manifestation of the fluid’s attempt to expel the particle from its interior so as to alleviate the thermal stress that would otherwise ensue were the particle to remain at rest (thus obeying the traditional no slip rather than thermal-creep boundary condition) following its introduction into the previously stress-free quiescent fluid. With Kn the Knudsen number in the case of rarefied gases, Maxwell’s thermal stress constitutes a noncontinuum phenomenon of O(Kn2), whereas his thermal-creep phenomenon constitutes a continuum phenomenon of O(Kn). That these two phenomena can, nevertheless, be proved to be synonymous (in the sense, so to speak, of being two sides of the same coin), as is done in the present paper, supports the “ghost effect” findings of Sone [ Y. Sone, “Flows induced by temperature fields in a rarefied gas and their ghost effect on the behavior of a gas in the continuum limit,” Annu. Rev. Fluid Mech 32, 779 (2000) ], which, philosophically, imply the artificiality of the distinction currently existing between continuum- and noncontinuum-level phenomena.
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47.45.Gx Slip flows and accommodation
47.55.Kf Particle-laden flows
back to top Instability and Transition

Marangoni convection in a binary liquid layer with Soret effect at small Lewis number: Linear stability analysis

S. Shklyaev, A. A. Nepomnyashchy, and A. Oron

Phys. Fluids 21, 054101 (2009); http://dx.doi.org/10.1063/1.3127802 (18 pages) | Cited 6 times

Online Publication Date: 6 May 2009

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We consider surface-tension-driven convection in a layer of a binary mixture. A linear stability problem is studied in the presence of both thermocapillary and solutocapillary effects. Assuming the Lewis and Biot numbers to be small, we develop the long wave theory and find both monotonic and oscillatory modes. Three various modes of oscillatory convection exist depending on the ratio between the small parameters. In the case of finite but sufficiently small values of the Biot and Lewis numbers, linear stability thresholds are determined numerically. The numerical results agree well with those found analytically.
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47.55.pf Marangoni convection
47.20.Dr Surface-tension-driven instability
47.27.tb Turbulent diffusion
47.35.-i Hydrodynamic waves

Experimental and numerical results on three-dimensional instabilities in a rotating disk–tall cylinder flow

J. N. Sørensen, A. Yu. Gelfgat, I. V. Naumov, and R. F. Mikkelsen

Phys. Fluids 21, 054102 (2009); http://dx.doi.org/10.1063/1.3133262 (5 pages) | Cited 3 times

Online Publication Date: 13 May 2009

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The three-dimensional axisymmetry-breaking instability of axisymmetric flow between a rotating lid and a stationary cylinder is analyzed both numerically and experimentally for the case of tall cylinders with the height/radius aspect ratio between 3.3 and 5.5. A complete stability diagram for the primary three-dimensional instability is obtained experimentally and computed numerically. The instability sets in due to different three-dimensional disturbance modes that are characterized by different azimuthal wavenumbers. The critical Reynolds numbers and associated frequencies are identified for each mode. The onset of three-dimensional flow behavior is measured by combining the high spatial resolution of particle image velocimetry and the temporal accuracy of laser Doppler anemometry. The results are compared to the numerical stability analysis. The measured onset of three dimensionality is in a good agreement with the numerical results. Disagreements observed in supercritical regimes can be explained by secondary bifurcations that are not accounted for by linear stability analysis of the primary base flow.
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47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
47.32.Ef Rotating and swirling flows
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.80.Jk Flow visualization and imaging

Metastable bouncing droplets

D. Terwagne, T. Gilet, N. Vandewalle, and S. Dorbolo

Phys. Fluids 21, 054103 (2009); http://dx.doi.org/10.1063/1.3139138 (5 pages) | Cited 3 times

Online Publication Date: 14 May 2009

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An oil droplet is placed on an oil bath at least ten times more viscous. When the oil bath is vertically shaken according to a sinusoidal motion, the droplet may bounce indefinitely on the bath. This sustained bouncing mode is stable when the forcing acceleration is higher than a threshold value. On the other hand, the time of subsidence of the droplet on the bath is finite at weaker accelerations. The lifetime of bouncing droplets is measured for various viscosities and forcing parameters. The finiteness of the lifetime is correlated with the evolution of the interference fringe pattern made by the air film squeezed between the droplet and the bath when lighted by a monochromatic light. Finally, a model based on a combination of lubrication theory and droplet deformations rationalizes the experimental results.
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47.55.D- Drops and bubbles
68.03.-g Gas-liquid and vacuum-liquid interfaces
66.20.-d Viscosity of liquids; diffusive momentum transport
47.85.mf Lubrication flows

Drag and flow reversal in mixed convection past a heated sphere

Miroslav Kotouč, Gilles Bouchet, and Jan Dušek

Phys. Fluids 21, 054104 (2009); http://dx.doi.org/10.1063/1.3139304 (14 pages) | Cited 4 times

Online Publication Date: 18 May 2009

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Axisymmetric simulation of mixed convection past a heated sphere presented in a recent paper of Mograbi and Bar-Ziv [J. Aerosol Sci. 36, 387 (2005) ] reveals a “huge” recirculation in the opposing flow configuration at very small Reynolds numbers and at Richardson numbers exceeding unity, the size of which seems to adjust to a computational domain of any size. In this paper we show that, for Reynolds numbers as low as one, the flow is nonaxisymmetric and that its three dimensionality brings the recirculation within finite bounds. At higher Reynolds numbers (Re), the cases of Re = 10 and 100 are considered at a fixed Prandtl number of 0.72. The flow becomes very soon not only three dimensional but also chaotic. Especially at higher Reynolds numbers (100), the arising convective structures do not resist the opposing flow and do not travel upstream more than several sphere diameters.
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47.27.te Turbulent convective heat transfer
47.52.+j Chaos in fluid dynamics
47.27.E- Turbulence simulation and modeling

Elephant modes and low frequency unsteadiness in a high Reynolds number, transonic afterbody wake

Philippe Meliga, Denis Sipp, and Jean-Marc Chomaz

Phys. Fluids 21, 054105 (2009); http://dx.doi.org/10.1063/1.3139309 (7 pages) | Cited 4 times

Online Publication Date: 20 May 2009

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Experiments and large eddy numerical simulation of a fully turbulent afterbody flow in the high subsonic regime, typical of that developing in the wake of a space launcher, exhibit a large-scale low frequency oscillation of the wake. In the present paper, we investigate to what extent the existence of the synchronized oscillations can be interpreted, at the high Reynolds numbers prevailing in this class of flows, by a local stability analysis of the mean flow, as measured in experiments or computed in numerical simulations. This analysis shows the presence of a pocket of absolute instability in the near wake, slightly detached from the body. The global frequency is strikingly well predicted by the absolute frequency at the upstream station of marginal absolute instability, this frequency selection being in agreement with the theory of nonlinear global modes. This result strongly suggests that a so-called elephant mode is responsible for the intense oscillations observed in the lee of space launcher configurations.
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47.20.-k Flow instabilities
47.27.E- Turbulence simulation and modeling
47.40.Dc General subsonic flows
47.40.Hg Transonic flows
47.15.Tr Laminar wakes
47.11.-j Computational methods in fluid dynamics
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