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Aug 2009

Volume 21, Issue 8, Articles (08xxxx)

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Phys. Fluids 21, 082103 (2009); http://dx.doi.org/10.1063/1.3207884 (8 pages)

J. Bico, J. Ashmore-Chakrabarty, G. H. McKinley, and H. A. Stone
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Motion of a vortex ring in a simple shear flow

M. Cheng, J. Lou, and T. T. Lim

Phys. Fluids 21, 081701 (2009); http://dx.doi.org/10.1063/1.3196903 (4 pages) | Cited 4 times

Online Publication Date: 5 August 2009

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The motion and deformation of a vortex ring in a linear or simple shear flow have been simulated numerically by using the lattice Boltzmann method with multiple relaxation times. The study is motivated by a recent experiment [ T. T. Lim, K. B. Lua, and K. Thet, Phys. Fluids 20, 051701 (2008) ], which shows that a vortex ring propagating in a uniform cross flow does not experience Kutta lift and undergo tilting and deformation. The focus of the present study is to examine the effect of a simple shear in a cross flow on the motion of a vortex ring. Numerical approach is adopted here because a truly simple shear flow is difficult to generate experimentally. Our computation shows that a vortex ring tilts and deforms in a simple shear flow, and the tilting can be attributed to the modification of the vorticity distribution of the vortex ring as a result of the entrainment of background vorticity by the vortex core. It is further shown that although the shear in the flow has the tendency to elongate the vortex ring, the tilting angle of the ring increases with the shear ratio.
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47.32.cf Vortex reconnection and rings
47.32.cd Vortex stability and breakdown
47.11.Qr Lattice gas

The behavior of subgrid-scale models near the turbulent/nonturbulent interface in jets

Carlos B. da Silva

Phys. Fluids 21, 081702 (2009); http://dx.doi.org/10.1063/1.3204229 (4 pages) | Cited 11 times

Online Publication Date: 10 August 2009

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The behavior of subgrid-scale models near the turbulent/nonturbulent interface in jets is analyzed by using direct numerical simulation and large-eddy simulation (LES). The subgrid scales of motion near this region are far from equilibrium and contain an important fraction of the total kinetic energy. The Smagorinsky constant CS needs to be corrected near the jet edge and the method used to obtain the dynamic Smagorinsky constant CD is not able to cope with the intermittent nature of this region. A priori tests and LES show that near the jet edge the Smagorinsky model is superior both to the dynamic Smagorinsky and to the gradient models.
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47.11.-j Computational methods in fluid dynamics
47.27.E- Turbulence simulation and modeling
47.27.-i Turbulent flows
47.60.Kz Flows and jets through nozzles

Coupled flutter of parallel plates

Lionel Schouveiler and Christophe Eloy

Phys. Fluids 21, 081703 (2009); http://dx.doi.org/10.1063/1.3204672 (4 pages) | Cited 5 times

Online Publication Date: 12 August 2009

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Experimental visualizations of the coupled flutter of an assembly of two, three, and four flexible parallel cantilevered plates immersed in an axial uniform flow are presented. Depending on the flow velocity, on the interplate distance, and on the plate length, different coupled modes are observed. Selected modes and the associated thresholds and frequencies are compared with the results of a linear stability analysis.
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47.27.N- Wall-bounded shear flow turbulence

Turbulence-induced secondary motion in a buoyancy-driven flow in a circular pipe

Yannick Hallez and Jacques Magnaudet

Phys. Fluids 21, 081704 (2009); http://dx.doi.org/10.1063/1.3213246 (4 pages) | Cited 4 times

Online Publication Date: 25 August 2009

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We analyze the results of a direct numerical simulation of the turbulent buoyancy-driven flow that sets in after two miscible fluids of slightly different densities have been initially superimposed in an unstable configuration in an inclined circular pipe closed at both ends. In the central region located midway between the end walls, where the flow is fully developed, the resulting mean flow is found to exhibit nonzero secondary velocity components in the tube cross section. We present a detailed analysis of the generation mechanism of this secondary flow which turns out to be due to the combined effect of the lateral wall and the shear-induced anisotropy between the transverse components of the turbulent velocity fluctuations.
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47.27.N- Wall-bounded shear flow turbulence
47.27.E- Turbulence simulation and modeling
47.27.-i Turbulent flows
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back to top Biofluid Mechanics

Linear stability analysis of gyrotactic plumes

S. Ghorai and R. Singh

Phys. Fluids 21, 081901 (2009); http://dx.doi.org/10.1063/1.3206730 (9 pages) | Cited 1 time

Online Publication Date: 19 August 2009

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Bioconvection occurs as the result of the collective behavior of many micro-organisms swimming in a fluid and is realized as patterns similar to those of thermal convection, which occur when a layer of fluid is heated from below. We consider the phenomenon of pattern formation due to gyrotaxis, an orientation mechanism which results from the balance of gravitational and viscous torques acting on bottom-heavy micro-organisms. Using the continuum model of Pedley et al. [“The growth of bioconvection patterns in a uniform suspension of gyrotactic micro-organisms,” J. Fluid Mech. 195, 223 (1988) ], the linear stability of a gyrotactic plume (descending line of concentrated micro-organisms) is investigated. Linear stability analysis predicts that a plume is always unstable to both the varicose and meandering modes. The growth rates of these instability modes and their dependence on parameter values are investigated. Comparisons are made with the experimental and numerical results.
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47.63.Gd Swimming microorganisms
47.20.-k Flow instabilities

Approximate behavior of arbitrarily unsteady laminar flow in long, straight, flexible tubes

G. J. Brereton

Phys. Fluids 21, 081902 (2009); http://dx.doi.org/10.1063/1.3205099 (16 pages) | Cited 1 time

Online Publication Date: 26 August 2009

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Analytical solutions have been obtained for laminar flows in long, straight tubes with linearly elastic walls that undergo arbitrary spatial/temporal unsteadiness from a known initial state. These initial-boundary value solutions express quantities such as the momentary wall deflection, flow rate, and wall shear stress as functionals of the pressure field’s history under the assumptions that unsteady effects propagate as long-wavelength disturbances at a constant wave speed and produce changes in the wall shear stress that are significantly less than in the pressure. These solutions are particularly useful for analysis of pulsatile periodic and aperiodic flows that come to rest before restarting, for which existing continuously unsteady analytical solutions do not apply. When the arbitrary unsteadiness is given the particular form of a sinusoidally varying pressure field that starts from rest at time zero, the long-time behavior of these approximate solutions is in excellent agreement with existing analytical solutions for continuously unsteady flow at all but low values of the Womersley frequency parameter.
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47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.27.N- Wall-bounded shear flow turbulence
47.60.Dx Flows in ducts and channels
back to top Micro- and Nanofluid Mechanics

Extending the Navier–Stokes solutions to transition regime in two-dimensional micro- and nanochannel flows using information preservation scheme

Ehsan Roohi and Masoud Darbandi

Phys. Fluids 21, 082001 (2009); http://dx.doi.org/10.1063/1.3177351 (12 pages) | Cited 16 times

Online Publication Date: 5 August 2009

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The kinetic-theory-based numerical schemes, such as direct simulation Monte Carlo (DSMC) and information preservation (IP), can be readily used to solve transition flow regimes. However, their high computational cost still promotes the researchers to extend the Navier–Stokes (NS) equations beyond the slip flow and to the transition regime applications. Evidently, a suitable extension would accurately predict both the local velocity profiles and the mass flow rate magnitude as well as the streamwise pressure distribution. The second-order slip velocity model derived from kinetic theory can provide relatively accurate velocity profiles up to a Knudsen (Kn) number of around 0.5; however, its mass flow rate accuracy decreases as Knudsen number approaches the upper bound. One remedy is to consider the rarefaction effects in calculating the NS viscosity coefficient. In this work, we use the shear stress distribution derived from our IP simulations, extend an analytical expression for the viscosity coefficient, impose it in the NS equations, and evaluate it via solving the transition regime. Using the new viscosity coefficient, we also derive an analytical expression for the mass flow rate, which provides accurate solutions for Kn<0.5 and even beyond in micro- and nanochannel flows. We also show that the obtained streamwise pressure distribution agrees well with that of the DSMC-IP in this range. The current study is concerned with low speed diatomic gas flow through two-dimensional micro- and nanochannels.
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47.61.Fg Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)
47.45.-n Rarefied gas dynamics
47.10.ad Navier-Stokes equations
47.61.Cb Non-continuum effects
back to top Interfacial Flows

Stability of gravity-capillary waves generated by a moving pressure disturbance in water of finite depth

Roger Grimshaw, Montri Maleewong, and Jack Asavanant

Phys. Fluids 21, 082101 (2009); http://dx.doi.org/10.1063/1.3207024 (10 pages) | Cited 6 times

Online Publication Date: 13 August 2009

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In previous work, we investigated two-dimensional steady gravity-capillary waves generated by a localized pressure distribution moving with a constant speed U in water of finite depth h. Localized solitary waves can only exist in subcritical flows where the Froude number F = U/(gh)1/2<1, and were found using a combination of numerical simulations of the fully nonlinear inviscid, irrotational equations, and analytically from a weakly nonlinear long-wave model, the steady forced Korteweg–de Vries equation. The solution branches depended on three parameters, the Froude number, F<1, the Bond number, τ>1/3, and the magnitude and sign of the pressure distribution, ϵ. In this paper, we examine the two-dimensional stability of these waves using numerical simulations of the fully nonlinear unsteady equations. The results are favorably compared to analogous numerical solutions of the unsteady forced Korteweg–de Vries equation. We find that for ϵ>0, the small-amplitude steady depression wave is stable whereas the large-amplitude steady depression wave is unstable. The depression wave with a dimple at its crest, which occurs only when ϵ<0 is unstable, but the small-amplitude elevation wave with ϵ<0 is stable.
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47.35.Bb Gravity waves
47.35.Fg Solitary waves
47.35.Pq Capillary waves
47.20.-k Flow instabilities
47.10.-g General theory in fluid dynamics

The Richtmyer–Meshkov instability in magnetohydrodynamics

V. Wheatley, R. Samtaney, and D. I. Pullin

Phys. Fluids 21, 082102 (2009); http://dx.doi.org/10.1063/1.3194303 (13 pages) | Cited 1 time

Online Publication Date: 25 August 2009

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In ideal magnetohydrodynamics (MHD), the Richtmyer–Meshkov instability can be suppressed by the presence of a magnetic field. The interface still undergoes some growth, but this is bounded for a finite magnetic field. A model for this flow has been developed by considering the stability of an impulsively accelerated, sinusoidally perturbed density interface in the presence of a magnetic field that is parallel to the acceleration. This was accomplished by analytically solving the linearized initial value problem in the framework of ideal incompressible MHD. To assess the performance of the model, its predictions are compared to results obtained from numerical simulation of impulse driven linearized, shock driven linearized, and nonlinear compressible MHD for a variety of cases. It is shown that the analytical linear model collapses the data from the simulations well. The predicted interface behavior well approximates that seen in compressible linearized simulations when the shock strength, magnetic field strength, and perturbation amplitude are small. For such cases, the agreement with interface behavior that occurs in nonlinear simulations is also reasonable. The effects of increasing shock strength, magnetic field strength, and perturbation amplitude on both the flow and the performance of the model are investigated. This results in a detailed exposition of the features and behavior of the MHD Richtmyer–Meshkov flow. For strong shocks, large initial perturbation amplitudes, and strong magnetic fields, the linear model may give a rough estimate of the interface behavior, but it is not quantitatively accurate. In all cases examined the accuracy of the model is quantified and the flow physics underlying any discrepancies is examined.
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.40.Nm Shock wave interactions and shock effects
47.11.-j Computational methods in fluid dynamics

Rolling stones: The motion of a sphere down an inclined plane coated with a thin liquid film

J. Bico, J. Ashmore-Chakrabarty, G. H. McKinley, and H. A. Stone

Phys. Fluids 21, 082103 (2009); http://dx.doi.org/10.1063/1.3207884 (8 pages) | Cited 3 times

Online Publication Date: 26 August 2009

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A spherical bead deposited on a smooth tilted dry plane wall rolls down the slope under the uniform acceleration of gravity. We describe an analogous experiment conducted using a plane wall that is coated with a thin layer (of order 50–100 μm) of a viscous liquid. The steady motion of the sphere under gravity involves a combination of rotation and sliding. We examine the dependence of the experimentally observed steady translational and rotational speeds on the physical parameters in the system. In particular, the interplay between viscous forces and interfacial forces leads to nontrivial exponents for the scaling of the speeds with the characteristics of the sphere and the viscous liquid. The overhang situation, in which the sphere rolls down the underside of an inclined lubricated plane, is also examined. In this case, the steady motion is still observed for a certain range of angles and bead sizes; that is, the sphere does not always detach from the surface. The adhesive force arises dynamically from the motion of the sphere and can exceed classical quasistatic capillary forces. Such a force should also play a role in other problems of lubrication mechanics such as humid granular flows.
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46.55.+d Tribology and mechanical contacts
47.57.Gc Granular flow

Separation of sheet flow on the surface of a circular cylinder

Hiroshi Isshiki, Bum-Sang Yoon, and Deuk-Joon Yum

Phys. Fluids 21, 082104 (2009); http://dx.doi.org/10.1063/1.3210762 (7 pages) | Cited 1 time

Online Publication Date: 28 August 2009

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The shape of a spout of a pot is very important for the liquid to flow smoothly from the pot. This is known as the “teapot effect.” Separation of flow must take place at the tip of the spout. Separation of sheet flow on the surface of a circular cylinder may provide an explanation as to why pot spouts have such a unique shape. As can be easily observed by a simple experiment, separation of sheet flow from the surface of a circular cylinder is a very interesting phenomenon beyond intuition. In the nonviscous case, the flow released at the top of the surface may proceed completely around the surface and come back to the flow start point without separation. In the present paper, effects of gravity and viscosity on sheet flow are theoretically explained and the theory is verified by experiments. The results of the theoretical model proposed in the present study were very similar to the experimental measurements. In the present study, the effects of viscosity on sheet flow on a circular cylinder, the location of flow separation, and other associated responses were investigated.
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47.32.Ff Separated flows
47.60.-i Flow phenomena in quasi-one-dimensional systems

On the breakup of fluid rivulets

Javier A. Diez, Alejandro G. González, and Lou Kondic

Phys. Fluids 21, 082105 (2009); http://dx.doi.org/10.1063/1.3211248 (15 pages) | Cited 9 times

Online Publication Date: 31 August 2009

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We study the stability of rivulets on horizontal substrates. The implemented model includes the effects of capillarity, fluid-solid interaction, and gravity if appropriate, within the framework of the lubrication approximation. We find that the results compare favorably with those in literature, in the regime where previous analyses are valid. By isolating the effect of van der Waals interactions for nanoscale rivulets, and of gravity for macrosize rivulets, we are able to analyze the influence of these forces on the stability. We discuss in detail the scaling of the emerging wavelengths (distance between drops formed after the breakup process) with the rivulet cross-sectional area. Perhaps surprisingly, we uncover close connection between this scaling and the one for the breakup of a free-space fluid jet (Rayleigh–Plateau instability). Finally, we consider rivulets of finite length and find that the finite size effects are considerably different from the ones obtained previously for semi-infinite fluid films.
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47.20.-k Flow instabilities
47.55.D- Drops and bubbles
47.15.Uv Laminar jets
back to top Viscous and Non-Newtonian Flows

Influence of miscible viscous fingering of finite slices on an adsorbed solute dynamics

M. Mishra, M. Martin, and A. De Wit

Phys. Fluids 21, 083101 (2009); http://dx.doi.org/10.1063/1.3200870 (10 pages) | Cited 4 times

Online Publication Date: 5 August 2009

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Viscous fingering (VF) between miscible fluids of different viscosities can affect the dispersion of finite width samples in porous media. We investigate here the influence of such VF due to a difference between the viscosity of the displacing fluid and that of the sample solvent on the spatiotemporal dynamics of the concentration of a passive solute initially dissolved in the injected sample and undergoing adsorption on the porous matrix. Such a three component system is modeled using Darcy’s law for the fluid velocity coupled to mass-balance equations for the sample solvent and solute concentrations. Depending on the conditions of adsorption, the spatial distribution of the solute concentration can either be deformed by VF of the sample solvent concentration profiles or disentangle from the fingering zone. In the case of deformation by fingering, a parametric study is performed to analyze the influence of parameters such as the log-mobility ratio, the ratio of dispersion coefficients, the sample length, and the adsorption retention parameter k′ on the widening of the solute concentration peak. The results highlight experimental evidences obtained recently in reversed-phase liquid chromatography.
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66.20.-d Viscosity of liquids; diffusive momentum transport
68.43.-h Chemisorption/physisorption: adsorbates on surfaces
47.56.+r Flows through porous media
64.75.Bc Solubility

Enhancement of transport from drops by steady and modulated electric fields

C. I. Christov and G. M. Homsy

Phys. Fluids 21, 083102 (2009); http://dx.doi.org/10.1063/1.3179555 (13 pages) | Cited 3 times

Online Publication Date: 13 August 2009

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We consider the problem of transport of heat or mass from circulating droplets that are both settling and subject to an axial electric field. The electric field can be either steady or oscillatory in time and drives an electrohydrodynamic flow, called the Taylor circulation, which augments the Hadamard circulation caused by steady translation. The problem is governed by four dimensionless groups: the Peclet number Pe, the dimensionless amplitudes of both the steady and unsteady electric field, and the dimensionless frequency ω of the modulation. The convective diffusion equation is solved numerically by an efficient finite-difference scheme that allows a wide range of parameters—in particular, very large Peclet numbers—to be covered. The results are characterized by the asymptotic rate of extraction of heat or mass from the droplet, which is found to be exponential in time. The enhancement factor, defined as the ratio of this rate to that of a stagnant drop, is studied as a function of parameters. For steady drops, we find that transport remains diffusion controlled, but the enhancement factor is significantly higher with the Taylor flow than without. For modulated electric field the enhancement factor is not a simple function of parameters and exhibits spectral “resonant peaks” at particular values of ω for which the enhancement factor is extremely large. Movies of the simulations are used to study the underlying time-periodic spatial structures of the concentration field (so-called strange eigenmodes) and the complex time dependence that is responsible for these resonances.
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.55.D- Drops and bubbles
47.55.P- Buoyancy-driven flows; convection
66.10.C- Diffusion and thermal diffusion

Reduction of the loads on a cylinder undergoing harmonic in-line motion

Osama A. Marzouk and Ali H. Nayfeh

Phys. Fluids 21, 083103 (2009); http://dx.doi.org/10.1063/1.3210774 (13 pages) | Cited 1 time

Online Publication Date: 19 August 2009

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We use the finite-difference computational fluid dynamics method to study in detail the flow field around a circular cylinder in a uniform stream while undergoing in-line harmonic motion. For a given motion amplitude, there exists a critical forcing frequency below which the lift and drag can be period-n, quasiperiodic, or chaotic. Similarly, for a given frequency, there exists a critical amplitude below which the lift and drag can be period-n, quasiperiodic, or chaotic. Above these critical conditions, the lift and drag are synchronous with the forcing. The lift nearly vanishes and the mean drag drops and saturates at a value that is independent of the driving frequency, whereas the oscillatory drag quadratically depends on it. We relate these features to changes in the wake and the surface-pressure distribution. We examine the influence of the Reynolds number on these critical frequency and amplitude. Second- and higher-order spectral analyses show remarkable changes in the linear and quadratic coupling between the lift and drag when synchronization takes place; it destroys the two-to-one coupling between them in the cases of no motion and synchronization due to cross-flow motion.
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47.35.Lf Wave-structure interactions
47.27.wb Turbulent wakes
47.32.-y Vortex dynamics; rotating fluids
47.11.Bc Finite difference methods
back to top Particulate, Multiphase, and Granular Flows

A numerical investigation of the rheology of sheared fiber suspensions

Stefan B. Lindström and Tetsu Uesaka

Phys. Fluids 21, 083301 (2009); http://dx.doi.org/10.1063/1.3195456 (18 pages) | Cited 3 times

Online Publication Date: 3 August 2009

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Particle-level simulations are performed to study the rheology of monodispersed non-Brownian fibers suspended in a Newtonian fluid in shear flow. The effects of fiber aspect ratio, concentration, and interparticle friction on the stress tensor of the suspension in the steady state and on the tendency of fiber agglomeration are investigated. Semiempirical expressions for the steady state apparent shear viscosity and the steady state first and second normal stress difference were obtained for the case of well dispersed suspensions in the nonconcentrated regimes. The simulation predictions of the specific viscosity were in fair agreement with previous experimental investigations.
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47.57.E- Suspensions
82.70.Kj Emulsions and suspensions
83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
47.11.-j Computational methods in fluid dynamics
83.50.Ax Steady shear flows, viscometric flow
66.20.-d Viscosity of liquids; diffusive momentum transport

Drag on random assemblies of spheres in shear-thinning and thixotropic liquids

J. J. Derksen

Phys. Fluids 21, 083302 (2009); http://dx.doi.org/10.1063/1.3200946 (9 pages) | Cited 3 times

Online Publication Date: 5 August 2009

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The flow and resulting drag force in suspensions consisting of monodisperse, solid spheres, and non-Newtonian liquids have been studied via direct numerical simulations. The liquids are purely viscous (i.e., nonelastic) with shear thinning and/or thixotropic (time-dependent) behavior. The configuration of spheres is static. The interstitial liquid flow is solved by means of the lattice-Boltzmann method. Only creeping flow conditions have been considered. Thixotropy enters via a network integrity parameter that relates to the local, apparent viscosity and for which a transport equation has been solved. The results show that the shear-thinning character of the liquid manifests itself more pronounced at higher solids volume fractions. Thixotropy tends to increase the drag force due to the decoupling of locations of high deformation rates and low viscosity.
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47.57.E- Suspensions
47.57.Qk Rheological aspects
47.50.-d Non-Newtonian fluid flows
47.11.Qr Lattice gas

Lateral migration of a small spherical buoyant particle in a wall-bounded linear shear flow

Fumio Takemura and Jacques Magnaudet

Phys. Fluids 21, 083303 (2009); http://dx.doi.org/10.1063/1.3206729 (7 pages) | Cited 1 time

Online Publication Date: 14 August 2009

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Lateral migration velocities of solid spherical particles suspended in a linear wall-bounded shear flow are measured for Reynolds number, Re<2 (Re = 2RU/ν, where R is the particle radius, U is the local slip velocity between the particle and the fluid, and ν is the kinematic viscosity of the suspending fluid). The velocity parallel to the wall and the distance between the particle and the wall are measured as a function of time, allowing the lateral migration velocity and the slip velocity of the particle to be determined. The measured velocities are compared to the theoretical predictions of McLaughlin [“The lift on a small sphere in wall-bounded linear shear flows,” J. Fluid Mech. 246, 249 (1993) ] and Magnaudet et al. [J. Fluid Mech. 476, 115 (2003) ] corresponding to the situation where the wall lies in the Oseen region and in the Stokes region of the flow disturbance produced by the particle, respectively. A good agreement is observed in both regimes with the corresponding prediction. The measurements are used to build an empirical fit capable of predicting the migration velocity whatever the distance between the particle and the wall.
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47.27.N- Wall-bounded shear flow turbulence
47.55.-t Multiphase and stratified flows

Removal of particles from holes in submerged plates with oscillating bubbles

Delphine Pavard, Evert Klaseboer, Siew-Wan Ohl, and Boo Cheong Khoo

Phys. Fluids 21, 083304 (2009); http://dx.doi.org/10.1063/1.3211132 (8 pages) | Cited 4 times

Online Publication Date: 18 August 2009

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This study is motivated by a common problem in submerged tubes and structures, which is the blockage of the tubes by pollutant particles or debris from the surrounding fluid. To clear the obstruction from the tube, an expanding bubble is used to propel the obstruction away from the tube (the tube is represented as a submerged transparent plate with a hole in our experiments). In some cases the obstruction removal effect is reinforced by the impacting jet of such a collapsing bubble. The bubble is generated via a simple low voltage electric spark discharge circuit. The pressure generated by the oscillating bubble effectively pushes the particle away from the tube, thereby successfully clearing the obstruction. High-speed photography is used to record and analyze the phenomenon. The speed of the particle is found to be around 1 m/s shortly after the collapse of the bubble. Interestingly, there is a clear difference between air-backed plates and water-backed plates in terms of bubble and particle dynamics. The bubbles in the current study are typically of millimeter size. Since the physics are similar for smaller bubbles, the process can possibly be downsized for other microapplications such as the removal of blood clots in vessels [ S. R. Visuri et al., U.S. Patent No. 6428531 (August 6, 2002) ].
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47.55.dd Bubble dynamics
47.80.Jk Flow visualization and imaging

Experimental study of gravitation effects in the flow of a particle-laden thin film on an inclined plane

Thomas Ward, Chi Wey, Robert Glidden, A. E. Hosoi, and A. L. Bertozzi

Phys. Fluids 21, 083305 (2009); http://dx.doi.org/10.1063/1.3208076 (7 pages) | Cited 7 times

Online Publication Date: 20 August 2009

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The flow of viscous, particle-laden wetting thin films on an inclined plane is studied experimentally as the particle concentration is increased to the maximum packing limit. The slurry is a non-neutrally buoyant mixture of silicone oil and either solid glass beads or glass bubbles. At low concentrations (ϕ<0.45), the elapsed time versus average front position scales with the exponent predicted by Huppert [Nature (London) 300, 427 (1982) ]. At higher concentrations, the average front position still scales with the exponent predicted by Huppert on some time interval, but there are observable deviations due to internal motion of the particles. At the larger concentration values and at later times, the departure from Huppert is seen to strongly depend on total slurry volume VT, inclination angle α, density difference, and particle size range.
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47.55.Kf Particle-laden flows
82.70.Kj Emulsions and suspensions
47.57.J- Colloidal systems
47.55.D- Drops and bubbles

The coefficient of restitution for air bubbles colliding against solid walls in viscous liquids

Roberto Zenit and Dominique Legendre

Phys. Fluids 21, 083306 (2009); http://dx.doi.org/10.1063/1.3210764 (12 pages) | Cited 4 times

Online Publication Date: 20 August 2009

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The motion of air bubbles undergoing collisions with solid walls was studied experimentally. Using a high speed camera, the processes of approach, contact, and rebound were recorded for a wide range of fluid properties. The process is characterized considering a modified Stokes number, St∗ = (CAMρdeqU0)/(9μ), which compares the inertia associated with the bubble (added mass) and viscous dissipation. We found that the dependence of the coefficient of restitution, ϵ = −Ureb/U0, with the impact Stokes number can be approximated by −log ϵ ∼ (Ca/St∗)1/2, where Ca is the capillary number; this behavior is very different from that found for the case of solid spheres. Most importantly, it shows that ϵ does not depend on the approach velocity. Considering a model for the process of contact and rebound of a deformable particle, this dependence is validated. Furthermore, by comparing the experimental trajectories and velocities of the bubble approach with model predictions, it was found that the film drainage is dominated by inertial effects; viscous effects, which would dominate for the case of approaching solid particles, are of secondary importance in this case.
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47.55.dd Bubble dynamics
47.60.-i Flow phenomena in quasi-one-dimensional systems
68.08.-p Liquid-solid interfaces
back to top Laminar Flows

Natural versus forced convection in laminar starting plumes

Michael C. Rogers and Stephen W. Morris

Phys. Fluids 21, 083601 (2009); http://dx.doi.org/10.1063/1.3207837 (7 pages) | Cited 4 times

Online Publication Date: 20 August 2009

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A starting plume or jet has a well-defined, evolving head that is driven through the surrounding quiescent fluid by a localized flux of either buoyancy or momentum, or both. We studied the scaling and morphology of starting plumes produced by a constant flux of buoyant fluid from a small, submerged outlet. The plumes were laminar and spanned a wide range of plume Richardson numbers Ri. Ri is the dimensionless ratio of the buoyancy forces to inertial effects and thus our measurements crossed over the transition between buoyancy-driven plumes and momentum-driven jets. We found that the ascent velocity of the plume, nondimensionalized by Ri, exhibits a power law relationship with Re, the Reynolds number of the injected fluid in the outlet pipe. We also found that as the threshold between buoyancy-driven and momentum-driven flows was crossed, two distinct types of plume head morphologies exist: confined heads, produced in the Ri>1 regime, and dispersed heads, which are found in the Ri<1 regime. Head dispersal is caused by a breakdown of overturning motion in the head and a local Kelvin–Helmholtz instability on the exterior of the plume.
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47.55.P- Buoyancy-driven flows; convection
47.15.Uv Laminar jets
47.15.Cb Laminar boundary layers
47.15.Fe Stability of laminar flows

On the effect of Reynolds number for flow around a row of square cylinders

C. M. Sewatkar, Atul Sharma, and Amit Agrawal

Phys. Fluids 21, 083602 (2009); http://dx.doi.org/10.1063/1.3210769 (13 pages) | Cited 5 times

Online Publication Date: 24 August 2009

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Flow across a row of identical square cylinders placed side-by-side has been found to show interesting flow patterns which have complex characteristics depending upon the spacing (s/d) between the cylinders and the Reynolds number (Re). The combined effects of cylinder spacing and Reynolds number on the flow across a row of cylinders are numerically studied for 30 ≤ Re ≤ 140 and 1.0 ≤ s/d ≤ 4.0, where s is the surface-to-surface distance between two cylinders and d is the size of cylinder. It is found that the critical Reynolds number for the onset of vortex shedding increases with increase in gap ratio. The Reynolds number is found to have a strong effect on the flow especially at s/d = 3.0,4.0. Secondary frequency in the signal for lift and drag coefficients significantly contributes to the forces experienced by the cylinders. It is observed that at s/d = 3.0,4.0 the secondary frequency disappears at larger Reynolds number and the primary frequency dominates the flow. This means that the interaction of the wakes behind the cylinders at these gap ratios weakens with an increase in the Reynolds number. It is proposed that wake interaction is strongly influenced by the jets in the gap region, the nature of which alters with spacing and Reynolds number. This is confirmed by computing the average wake size as a function of Reynolds number. Based on this, two critical gap ratios, 2.0 and 4.0 for the range of Reynolds number under consideration are proposed. These gap ratios separate synchronous, quasiperiodic-I and quasiperiodic-II flow regimes depending on the Reynolds number. The mechanism of wake interaction has been studied to bring out these critical gap ratios.
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47.27.wb Turbulent wakes
47.35.Lf Wave-structure interactions
47.32.-y Vortex dynamics; rotating fluids
47.27.wg Turbulent jets

Large Rayleigh number thermal convection: Heat flux predictions and strongly nonlinear solutions

Gregory P. Chini and Stephen M. Cox

Phys. Fluids 21, 083603 (2009); http://dx.doi.org/10.1063/1.3210777 (15 pages)

Online Publication Date: 26 August 2009

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We investigate the structure of strongly nonlinear Rayleigh–Bénard convection cells in the asymptotic limit of large Rayleigh number and fixed, moderate Prandtl number. Unlike the flows analyzed in prior theoretical studies of infinite Prandtl number convection, our cellular solutions exhibit dynamically inviscid constant-vorticity cores. By solving an integral equation for the cell-edge temperature distribution, we are able to predict, as a function of cell aspect ratio, the value of the core vorticity, details of the flow within the thin boundary layers and rising/falling plumes adjacent to the edges of the convection cell, and, in particular, the bulk heat flux through the layer. The results of our asymptotic analysis are corroborated using full pseudospectral numerical simulations and confirm that the heat flux is maximized for convection cells that are roughly square in cross section.
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47.27.te Turbulent convective heat transfer
47.32.-y Vortex dynamics; rotating fluids
47.27.nb Boundary layer turbulence
02.60.Nm Integral and integrodifferential equations

Influence of fiber orientation on the transverse permeability of fibrous media

M. A. Tahir and H. Vahedi Tafreshi

Phys. Fluids 21, 083604 (2009); http://dx.doi.org/10.1063/1.3211192 (5 pages) | Cited 21 times

Online Publication Date: 28 August 2009

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In this work, we study the influence of in-plane and through-plane fiber orientations on a fibrous medium’s transverse permeability. Three-dimensional virtual geometries resembling the microstructure of fibrous media with different fiber orientations are developed to be utilized in permeability calculations conducted by numerically solving the Stokes equations in the void space between fibers. Results of our simulations are compared to existing experimental and analytical studies from literature and excellent agreement is observed. We, in particular, demonstrate that the transverse permeability of a fibrous medium is independent of in-plane fiber orientation but increases with increasing deviation of the fibers’ through-plane angle from zero. Our findings somewhat disagree with some of the conclusions made by Stylianopoulos et al. [Phys. Fluids 20, 123601 (2008)] .
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47.56.+r Flows through porous media
81.05.Rm Porous materials; granular materials
61.43.Gt Powders, porous materials
47.11.-j Computational methods in fluid dynamics
47.10.A- Mathematical formulations
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