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Dec 2011

Volume 23, Issue 12, Articles (12xxxx)

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Phys. Fluids 23, 123101 (2011); http://dx.doi.org/10.1063/1.3659140 (11 pages)

Julia Nase, Didi Derks, and Anke Lindner
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Announcement: New Format for Physics of Fluids

John Kim and L. Gary Leal

Phys. Fluids 23, 120201 (2011); http://dx.doi.org/10.1063/1.3659023 (1 page)

Online Publication Date: 14 December 2011

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Abstract Unavailable
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99.10.Np Editorial note
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A new unstable mode in the wake of a circular cylinder

Abhishek Verma and Sanjay Mittal

Phys. Fluids 23, 121701 (2011); http://dx.doi.org/10.1063/1.3664869 (4 pages)

Online Publication Date: 2 December 2011

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The flow past a circular cylinder looses stability at Re ∼ 47, via the primary wake (PW) mode. Linear stability analysis of the steady base flow, in two dimensions, is conducted using a stabilized finite element formulation. A new mode, referred to as the secondary wake (SW) mode, is discovered which is found to be unstable for Re ≥ 110.8. The relative roles of the PW and SW mode in the development of Karman vortex shedding are also investigated.
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47.27.wb Turbulent wakes
47.32.cd Vortex stability and breakdown
47.11.Fg Finite element methods

The relationship between the velocity skewness and the amplitude modulation of the small scale by the large scale in turbulent boundary layers

Romain Mathis, Ivan Marusic, Nicholas Hutchins, and K. R. Sreenivasan

Phys. Fluids 23, 121702 (2011); http://dx.doi.org/10.1063/1.3671738 (4 pages)

Online Publication Date: 23 December 2011

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A defining feature of the inner-outer interactions in wall-bounded turbulent flows is the imprint of the outer large-scale motions on the inner small scale. Recently, Mathis et al. [“Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers,” J. Fluid Mech. 628, 311 (2009)] quantified this imprint by applying the Hilbert transform to small-scale components of the fluctuating streamwise velocity, u. They found that the wall-normal profile of the amplitude modulation between the large scale and the envelope of the small scale exhibits strong resemblance to the skewness profile of u. In this study, we assess this apparent relationship and show that the Reynolds number trend in the skewness profile of u is strongly related to the amplitude modulation effect of the small scales by the large. This observation also leads to an alternative diagnostic for the amplitude modulation effect, which is one component of the skewness factor based on a scale decomposition.
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47.27.nb Boundary layer turbulence
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
02.30.Uu Integral transforms
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back to top Biofluid Mechanics

The dynamics of a vesicle in a wall-bound shear flow

Hong Zhao, Andrew P. Spann, and Eric S. G. Shaqfeh

Phys. Fluids 23, 121901 (2011); http://dx.doi.org/10.1063/1.3669440 (12 pages) | Cited 1 time

Online Publication Date: 14 December 2011

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The three-dimensional dynamics of a lipid vesicle in a wall-bound shear flow is simulated by a Stokes-flow boundary integral equation method. When the vesicle is far away from the wall, the wall induces a lift velocity that is proportional to the wall normal component of the particle stresslet and is inversely proportional to the square of its centroid height. When the vesicle is in close contact with the wall under the action of gravity, its bottom surface height scales linearly with the shear rate, with a scaling constant that depends strongly on its nonsphericity. The numerical results are in quantitative agreement with the experimental measurements. The wall boundary causes the particle shear stress and normal stress differences to increase, but the effect diminishes when the centroid height is more than twice the vesicle radius. The simulation shows that the presence of the wall delays the transition (i.e., creates higher critical viscosity ratios) from the tank-treading motion to trembling and tumbling.
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47.55.Kf Particle-laden flows
02.30.Rz Integral equations
47.11.-j Computational methods in fluid dynamics

Correlations and fluctuations of stress and velocity in suspensions of swimming microorganisms

Patrick T. Underhill and Michael D. Graham

Phys. Fluids 23, 121902 (2011); http://dx.doi.org/10.1063/1.3670420 (15 pages)

Online Publication Date: 27 December 2011

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Active systems, which are driven out of equilibrium, can produce long range correlations and large fluctuations that are not restricted by the fluctuation-dissipation theorem. We consider here the fluctuations and correlations in suspensions of swimming microorganisms that interact hydrodynamically. Modeling the organisms as force dipoles in Stokes flow and considering run-and-tumble and rotational diffusion models of their orientational dynamics allow derivation of closed form results for the stress fluctuations in the long-wave limit. Both of these models lead to Lorentzian distributions, in agreement with some experimental data. These fluctuations are not restricted by the fluctuation-dissipation theorem, as is explicitly verified by comparing the fluctuations with the viscosity of the suspension. In addition to the stress fluctuations in the suspension, we examine correlations between the organisms. Because of the hydrodynamic interactions, the velocities of two organisms are correlated even if the positions and orientations are uncorrelated. We develop a theory of the velocity correlations in this limit and compare with the results of computer simulations. We also formally include orientational correlations in the theory; and comparing with simulations, we are able to show that these are important even in the dilute limit and are responsible in large part for the velocity correlations. While the orientation correlations cannot as yet be predicted from this theory, by inserting the results from simulations into the theory it is possible to properly determine the form of the swimmer velocity correlations. These correlations of orientations are also the key to understanding the spatial correlations of the fluid velocity. Through simulations we show that the orientational correlations decay as r−2 with distance—inserting this dependence into the theory leads to a logarithmic dependence of the velocity fluctuations on the size of the system.
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87.85.gj Movement and locomotion
82.70.Kj Emulsions and suspensions
47.57.eb Diffusion and aggregation
47.32.Ef Rotating and swirling flows
47.10.ad Navier-Stokes equations
47.63.Gd Swimming microorganisms
back to top Micro- and Nanofluid Mechanics

Interaction of a liquid flow around a micropillar with a gas jet

D. Elcock, J. Jung, C.-J. Kuo, M. Amitay, and Y. Peles

Phys. Fluids 23, 122001 (2011); http://dx.doi.org/10.1063/1.3662436 (14 pages)

Online Publication Date: 9 December 2011

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An experimental study was conducted to investigate two-phase flow characteristics resulting from gas jet injection into a 225 μm high by 1500 μm wide microchannel. The jet was injected from a 25 μm wide slit on the downstream side of a 150 μm diameter pillar. The liquid Reynolds number (Re = ρUD/μ) based on pillar diameter ranged from 100 to 700, and the average gas momentum coefficient (ρjetUjetAjet/ρmainUmainAref), defined as the ratio of gas momentum to liquid momentum, ranged from 1.6 × 10−5 to 3.368 × 10−1. Flow visualization, micro particle image velocimetry (μPIV), and micro particle tracing velocimetry (μPTV) were used to elucidate the two-phase flow patterns, liquid velocity field, and bubble dynamics. Two modes of gas jets were observed in which bubbles either formed and detached at the pillar or formed an attached ligament that sheared bubbles from its trailing edge. The modes were determined to be primarily Reynolds number dependent. Both modes were observed to positively affect turbulent kinetic energy in the microchannel. The momentum coefficient of the gas jet had the most significant effect at low Reynolds numbers, when bubble formation took place at the pillar.
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47.55.Ca Gas/liquid flows
47.55.dd Bubble dynamics
47.61.Jd Multiphase flows
47.60.Dx Flows in ducts and channels
47.27.nd Channel flow
47.27.wg Turbulent jets

Dipolophoresis of interacting conducting nano-particles of finite electric double layer thickness

Touvia Miloh

Phys. Fluids 23, 122002 (2011); http://dx.doi.org/10.1063/1.3671681 (14 pages) | Cited 1 time

Online Publication Date: 30 December 2011

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A general integral method is presented for calculating the dipolophoretic velocities of two interacting, ideally polarizable colloids of arbitrary electric double layer thickness under weak AC electric forcing. The 12 non-linear mobilities are comprised of induced-charge-electrophoresis (ICEP), dielectrophoresis (DEP), and Faxén-Stokes contributions. The explicit integral scheme, based on the Teubner [J. Chem. Phys. 76, 5564 (1982)] formulation, is demonstrated for the case of two-sphere interaction. Further simplifications using the remote-sphere approximation are employed and the asymptotic results thus obtained are compared against those recently obtained by Saintillan [Phys. Fluids 20, 067104 (2008)] and extend the latter for finite Debye scales and forcing frequencies. It is also shown that the same methodology can be used to determine the mobility of a polarized particle in the proximity of an insulating or conducting plane boundary. The case of a spherical colloid near an uncharged insulating planar wall is of special interest and by using the Lorentz image solution, we readily recover the large-spacing approximation of Yariv [Proc. R. Soc. A. London Ser. A 465, 709 (2009)] as a limiting case.
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
02.30.Rz Integral equations
82.70.Dd Colloids
47.57.jd Electrokinetic effects
82.45.-h Electrochemistry and electrophoresis
back to top Interfacial Flows

Asymptotic behavior of a retracting two-dimensional fluid sheet

Leonardo Gordillo, Gilou Agbaglah, Laurent Duchemin, and Christophe Josserand

Phys. Fluids 23, 122101 (2011); http://dx.doi.org/10.1063/1.3663577 (14 pages)

Online Publication Date: 7 December 2011

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Two-dimensional (2D) capillary retraction of a viscous liquid film is studied using numerical and analytical approaches for both diphasic and free surface flows. Full 2D Navier-Stokes equations are integrated numerically for the diphasic case, while one-dimensional (1D) free surface model equations are used for free surface flows. No pinch-off is observed in the film in any of these cases. By means of an asymptotic matching method on the 1D model, we derive an analytical expansion of the film profile for large times. Our analysis shows that three regions with different timescales can be identified during retraction: the rim, the film, and an intermediate domain connecting these two regions. The numerical simulations performed on both models show good agreement with the analytical results. Finally, we report the appearance of an instability in the diphasic retracting film for small Ohnesorge number. We understand this as a Kelvin-Helmholtz instability arising due to the formation of a shear layer in the neck region during the retraction.
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68.15.+e Liquid thin films
02.60.Cb Numerical simulation; solution of equations
47.10.ad Navier-Stokes equations
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.55.nb Capillary and thermocapillary flows

Gravity-driven flow over heated, porous, wavy surfaces

K. A. Ogden, S. J. D. D’Alessio, and J. P. Pascal

Phys. Fluids 23, 122102 (2011); http://dx.doi.org/10.1063/1.3667267 (19 pages)

Online Publication Date: 16 December 2011

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The method of weighted residuals for thin film flow down an inclined plane is extended to include the effects of bottom waviness, heating, and permeability in this study. A bottom slip condition is used to account for permeability and a constant temperature bottom boundary condition is applied. A weighted residual model (WRM) is derived and used to predict the combined effects of bottom waviness, heating, and permeability on the stability of the flow. In the absence of bottom topography, the results are compared to theoretical predictions from the corresponding Benney equation and also to existing Orr-Sommerfeld predictions. The excellent agreement found indicates that the model does faithfully predict the theoretical critical Reynolds number, which accounts for heating and permeability, and these effects are found to destabilize the flow. Floquet theory is used to investigate how bottom waviness influences the stability of the flow. Finally, numerical simulations of the model equations are also conducted and compared with numerical solutions of the full Navier-Stokes equations for the case with bottom permeability. These results are also found to agree well, which suggests that the WRM remains valid even when permeability is included.
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47.56.+r Flows through porous media
02.60.Cb Numerical simulation; solution of equations
47.10.ad Navier-Stokes equations
47.20.-k Flow instabilities
47.45.Gx Slip flows and accommodation

On the validity of a universal solution for viscous capillary jets

J. M. Montanero, M. A. Herrada, C. Ferrera, E. J. Vega, and A. M. Gañán-Calvo

Phys. Fluids 23, 122103 (2011); http://dx.doi.org/10.1063/1.3670007 (12 pages)

Online Publication Date: 16 December 2011

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In this paper, we assess the validity of a universal solution based on the slenderness approximation to describe the velocity and shape of viscous capillary jets produced by two very different mechanisms: the action of the constant gravity force and the focusing effect of a coflowing gas stream. In the gravitational case, the jet’s velocity distribution given by the universal solution is compared with that calculated numerically from the Navier-Stokes equations. The universal solution provides remarkably good predictions for the wide range of parameters considered in this work. Its accuracy generally improves as the Reynolds number increases and/or the Froude number decreases, probably because the jet viscous region decreases in this case. The flow focusing method was examined experimentally by acquiring and processing images of the tapering liquid meniscus formed between the feeding capillary and the discharge orifice. In this case, the universal solution provides satisfactory results for sufficiently slender liquid meniscus (i.e., for sufficiently large liquid viscosities and flow rates and small applied pressure drops), provided that the ratio capillary-to-orifice distance H to orifice diameter D takes sufficiently small values. If these conditions are not satisfied, the universal solution underestimates the jet radius close to the feeding capillary, but it still provides accurate predictions beyond the discharge orifice. For small H/D values, the accuracy of the universal solution is mainly limited by radial momentum effects associated with the sharp contraction of the meniscus shape, which becomes less slender as the liquid viscosity and flow rate decrease, or the pressure drop increases. For large H/D values, the driving force significantly deviates from its assumed constant value in the universal solution, giving rise to larger discrepancies between that solution and the experimental results even for slender shapes.
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47.60.Kz Flows and jets through nozzles
47.80.Jk Flow visualization and imaging
47.10.ad Navier-Stokes equations
02.60.-x Numerical approximation and analysis
66.20.-d Viscosity of liquids; diffusive momentum transport
02.60.Cb Numerical simulation; solution of equations

Sustained inertial-capillary oscillations and jet formation in displacement flow in a tube

Yi Sui and Peter D. M. Spelt

Phys. Fluids 23, 122104 (2011); http://dx.doi.org/10.1063/1.3670010 (11 pages)

Online Publication Date: 16 December 2011

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We study inertial effects in the displacement of a fluid in a capillary by a more viscous fluid, using a numerical method. A level-set approach is employed to track the meniscus, and a Navier slip boundary condition is imposed in order to alleviate a stress singularity at the moving contact line. Various flow regimes are identified with a Reynolds number and a capillary number as the main parameters. At relatively low Reynolds number, the meniscus forms a steady shape, and the interfacial curvature at the tube centre can change from being concave to convex upon increasing the Reynolds number if the displacing fluid is wetting to the tube surface. For wetting displacing fluids, beyond a critical Reynolds number, a quasi-steady solution is no longer found: instead, the interface undergoes non-dampened periodic oscillations and, at even larger values of the Reynolds number, quasi-periodically, and the interface evolves from simple wavy shapes to complex shapes with multiple wavy units. This oscillating state is observed for sufficiently small contact angle values defined from the displacing fluid (<80°). Beyond a second critical Reynolds number, the displacing fluid forms a jet and the meniscus advances with a nearly constant speed which decreases with Re. This is also observed at large contact angle values. In a developing jet, however, the interface shape remains partially quasi-steady, near the contact line region and the tube centre. The flow behaviour is shown to be robust over a range of other governing parameters, including the capillary number and the slip length. The potential implications of the work on network models of two-phase flow through porous media are discussed.
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47.45.Gx Slip flows and accommodation
47.10.ad Navier-Stokes equations
47.60.Dx Flows in ducts and channels
68.08.Bc Wetting
68.03.Cd Surface tension and related phenomena
47.56.+r Flows through porous media

Formation of organized nanostructures from unstable bilayers of thin metallic liquids

Mikhail Khenner, Sagar Yadavali, and Ramki Kalyanaraman

Phys. Fluids 23, 122105 (2011); http://dx.doi.org/10.1063/1.3665618 (14 pages)

Online Publication Date: 20 December 2011

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Dewetting of pulsed-laser irradiated, thin (<20 nm), optically reflective metallic bilayers on an optically transparent substrate with a reflective support layer is studied within the lubrication equations model. A steady-state bilayer film thickness (h) dependent temperature profile is derived based on the mean substrate temperature estimated from the elaborate thermal model of transient heating and melting/freezing. Large thermocapillary forces are observed along the plane of the liquid-liquid and liquid-gas interfaces due to this h-dependent temperature, which, in turn, is strongly influenced by the h-dependent laser light reflection and absorption. Consequently the dewetting is a result of the competition between thermocapillary and intermolecular forces. A linear analysis of the dewetting length scales established that the non-isothermal calculations better predict the experimental results as compared to the isothermal case within the bounding Hamaker coefficients. Subsequently, a computational non-linear dynamics study of the dewetting pathway was performed for Ag/Co and Co/Ag bilayer systems to predict the morphology evolution. We found that the systems evolve towards formation of different morphologies, including core-shell, embedded, or stacked nanostructure morphologies.
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47.55.Hd Stratified flows
47.55.nb Capillary and thermocapillary flows
68.08.Bc Wetting
68.15.+e Liquid thin films
47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.55.Ca Gas/liquid flows

Surfactant-driven dynamics of liquid lenses

George Karapetsas, Richard V. Craster, and Omar K. Matar

Phys. Fluids 23, 122106 (2011); http://dx.doi.org/10.1063/1.3670009 (16 pages)

Online Publication Date: 22 December 2011

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Sessile liquid lenses spreading over a fluid layer, in the presence of Marangoni stresses due to surfactants, show a surprisingly wide range of interesting behaviour ranging from complete spreading of the lens, to spreading followed by retraction, to sustained pulsating oscillations. Models for the spreading process, the effects of surfactant at the moving contact line, sorption kinetics above and below the critical micelle concentration, are all incorporated into the modelling. Numerical results cast light upon the physical processes that drive these phenomena, and the regular oscillatory beating of lenses is shown to occur in specific limits.
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47.55.dk Surfactant effects
68.03.Cd Surface tension and related phenomena
68.08.Bc Wetting
82.70.Dd Colloids
82.70.Uv Surfactants, micellar solutions, vesicles, lamellae, amphiphilic systems, (hydrophilic and hydrophobic interactions)
47.57.J- Colloidal systems

Scaling percolation in thin porous layers

E. F. Médici and J. S. Allen

Phys. Fluids 23, 122107 (2011); http://dx.doi.org/10.1063/1.3670017 (9 pages)

Online Publication Date: 23 December 2011

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Percolation in porous media is a complex process that depends on the flow rate, material, and fluids properties as well as the boundary conditions. Traditional methods of characterizing percolation rely upon visual observation of a flow pattern or a pressure-saturation relation valid only in the limit of no flow. In this paper, the dynamics of fluid percolation in thin porous media is approached through a new scaling. This new scaling in conjunction with the capillary number and the viscosity ratio has resulted in a linear non-dimensional correlation of the percolation pressure and wetted area in time unique to each porous media. The effect of different percolation flow patterns on the dynamic pressure-saturation relation can be condensed into a linear correlation using this scaling. The general trend and implications of the scaling have been analyzed using an analytical model of a fluid percolating between two parallel plates and by experimental testing on thin porous media. Cathode porous transport layers (PTLs), also known as gas diffusion layers, of a proton exchange membrane (PEM) fuel cell having different morphological and wetting properties were tested under drainage conditions. Images of the fluid percolation evolution and the percolation pressure in the PTLs were simultaneously recorded. A unique linear correlation is obtained for each type of PTL samples using the new scaling. The correlation derived from this new scaling can be used to quantitatively characterize porous media with respect to percolation. While the characterization method discussed herein was developed for the study of porous materials used in PEM fuel cells, the method and scaling are applicable to any porous media.
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47.56.+r Flows through porous media
47.54.Bd Theoretical aspects
68.08.Bc Wetting
82.47.Gh Proton exchange membrane (PEM) fuel cells
47.60.Dx Flows in ducts and channels

Wicking flow through microchannels

Hadi Mehrabian, Peng Gao, and James J. Feng

Phys. Fluids 23, 122108 (2011); http://dx.doi.org/10.1063/1.3671739 (14 pages)

Online Publication Date: 27 December 2011

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We report numerical simulations of wicking through micropores of two types of geometries, axisymmetric tubes with contractions and expansions of the cross section, and two-dimensional planar channels with a Y-shaped bifurcation. The aim is to gain a detailed understanding of the interfacial dynamics in these geometries, with an emphasis on the motion of the three-phase contact line. We adopt a diffuse-interface formalism and use Cahn-Hilliard diffusion to model the moving contact line. The Stokes and Cahn-Hilliard equations are solved by finite elements with adaptive meshing. The results show that the liquid meniscus undergoes complex deformation during its passage through contraction and expansion. Pinning of the interface at protruding corners limits the angle of expansion into which wicking is allowed. For sufficiently strong contractions, the interface negotiates the concave corners, thanks to its diffusive nature. Capillary competition between branches downstream of a Y-shaped bifurcation may result in arrest of wicking in the wider branch. Spatial variation of wettability in one branch may lead to flow reversal in the other.
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47.60.Dx Flows in ducts and channels
47.11.-j Computational methods in fluid dynamics
47.55.nb Capillary and thermocapillary flows
02.60.Cb Numerical simulation; solution of equations
68.08.Bc Wetting
47.10.ad Navier-Stokes equations
back to top Viscous and Non-Newtonian Flows

Dynamic evolution of fingering patterns in a lifted Hele–Shaw cell

Julia Nase, Didi Derks, and Anke Lindner

Phys. Fluids 23, 123101 (2011); http://dx.doi.org/10.1063/1.3659140 (11 pages)

Online Publication Date: 7 December 2011

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We present a study on pattern formation in a Newtonian liquid during lifting of a circular Hele–Shaw cell. When a confined layer of oil is subject to such a stretch flow, air penetrates into the liquid from the sides and a fingering instability, a variant of the classical Saffman–Taylor instability, evolves. This setting has the particularity that the finger growth takes place in a conserved volume of liquid and that the dimensionless surface tension, the control parameter which governs the Saffman–Taylor instability, is changing with time. This leads to a constantly evolving pattern, which we investigate with regard to number of fingers and finger amplitude. We distinguish in the pattern at each instant growing fingers and stagnant fingers. Systematically varying the properties of the viscous oil and the geometry of the Hele–Shaw cell, we show that the number of growing fingers is at each moment well described by a simple approach based on linear stability analysis and depends only on the dimensionless surface tension. In contrast, the finger amplitude and consequently the total number of fingers (growing and stagnant fingers) depend also on the cell confinement. We demonstrate that the finger amplitude has a distinct influence on the debonding force. Higher finger amplitude and number of fingers lead to lower forces.
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47.54.Bd Theoretical aspects
47.85.L- Flow control
68.03.Cd Surface tension and related phenomena
47.20.Dr Surface-tension-driven instability

Nonlinear viscous fluid patterns in a thin rotating spherical domain and applications

Ranis N. Ibragimov

Phys. Fluids 23, 123102 (2011); http://dx.doi.org/10.1063/1.3665132 (8 pages)

Online Publication Date: 9 December 2011

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We study the nonlinear incompressible fluid flows within a thin rotating spherical shell. The model uses the two-dimensional Navier-Stokes equations on a rotating three-dimensional spherical surface and serves as a simple mathematical descriptor of a general atmospheric circulation caused by the difference in temperature between the equator and the poles. Coriolis effects are generated by pseudoforces, which support the stable west-to-east flows providing the achievable meteorological flows rotating around the poles. This work addresses exact stationary and non-stationary solutions associated with the nonlinear Navier-Stokes. The exact solutions in terms of elementary functions for the associated Euler equations (zero viscosity) found in our earlier work are extended to the exact solutions of the Navier-Stokes equations (non-zero viscosity). The obtained solutions are expressed in terms of elementary functions, analyzed, and visualized.
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47.32.Ef Rotating and swirling flows
47.54.Bd Theoretical aspects
02.30.Jr Partial differential equations
47.10.ad Navier-Stokes equations
back to top Particulate, Multiphase, and Granular Flows

Turbulence modification and heat transfer enhancement by inertial particles in turbulent channel flow

J. G. M. Kuerten, C. W. M. van der Geld, and B. J. Geurts

Phys. Fluids 23, 123301 (2011); http://dx.doi.org/10.1063/1.3663308 (8 pages)

Online Publication Date: 5 December 2011

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We present results of direct numerical simulation of turbulence modification and heat transfer in turbulent particle-laden channel flow and show an enhancement of the heat transfer and a small increase in the friction velocity when heavy inertial particles with high specific heat capacity are added to the flow. The simulations employ a coupled Eulerian-Lagrangian computational model in which the momentum and energy transfer between the discrete particles and the continuous fluid phase are fully taken into account. The effect of turbophoresis, resulting in an increased particle concentration near a solid wall due to the inhomogeneity of the wall-normal velocity fluctuations, is shown to be responsible for an increase in heat transfer. As a result of turbophoresis, the effective macroscopic transport properties in the region near the walls differ from those in the bulk of the flow. To support the turbophoresis interpretation of the enhanced heat transfer, results of simulations employing no particle-fluid coupling and simulations with two-way coupling at considerably lower specific heat, or considerably lower particle concentration are also included. The combination of these simulations allows distinguishing contributions to the Nusselt number due to mean flow, turbulent fluctuations and explicit particle effects. We observe an increase in Nusselt number by more than a factor of two for heavy inertial particles, which is the net result of a decrease in heat transfer by turbulent velocity fluctuations and a much larger increase in heat transfer stemming from the mean temperature difference between the fluid and the particles close to the walls.
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47.27.nb Boundary layer turbulence
47.27.nd Channel flow
47.27.te Turbulent convective heat transfer
47.55.Kf Particle-laden flows
47.60.Dx Flows in ducts and channels
47.27.ek Direct numerical simulations

Inertial migration of deformable capsules in channel flow

Alex Kilimnik, Wenbin Mao, and Alexander Alexeev

Phys. Fluids 23, 123302 (2011); http://dx.doi.org/10.1063/1.3664402 (6 pages)

Online Publication Date: 5 December 2011

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Using three-dimensional computer simulations, we study the cross-stream inertial migration of neutrally buoyant deformable particles in a pressure-driven channel flow. The particles are modeled as elastic shells filled with a viscous fluid. We show that the particles equilibrate in a channel flow at off-center positions that depend on particle size, shell compliance, and the viscosity of encapsulated fluid. These equilibrium positions, however, are practically independent of the magnitude of channel Reynolds number in the range between 1 and 100. The results of our studies can be useful for sorting, focusing, and separation of micrometer-sized synthetic particles and biological cells.
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47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.60.Dx Flows in ducts and channels
47.11.-j Computational methods in fluid dynamics

Three-dimensional numerical simulation of drops suspended in Poiseuille flow at non-zero Reynolds numbers

Amireh Nourbakhsh, Saeed Mortazavi, and Yaser Afshar

Phys. Fluids 23, 123303 (2011); http://dx.doi.org/10.1063/1.3663565 (11 pages)

Online Publication Date: 7 December 2011

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A finite difference/front tracking method is used to study the motion of three-dimensional deformable drops suspended in plane Poiseuille flow at non-zero Reynolds numbers. A parallel version of the code was used to study the behavior of suspension on a reasonable grid resolution (128×128×128 grids). The viscosity and density of drops are assumed to be equal to that of the suspending medium. The effect of Capillary number, the Reynolds number, and volume fraction are studied in detail. It is found that drops with small deformation behave like rigid particles and migrate to an equilibrium position about half way between the wall and the centerline (the Segre-Silberberg effect). However, for highly deformable drops there is a tendency for drops to migrate to the middle of the channel, and the maximum concentration occurs at the centerline. The concentration profile obtained across the channel is in agreement with that measured by Kowalewski (T. A. Kowalewski, “Concentration and velocity measurement in the flow of droplet suspensions through a tube,” Exp. Fluids 2, 213 (1984)) experimentally for viscosity ratios less than or equal to one. The effective viscosity of suspension decreases with Capillary number in agreement with the creeping flow limit. Also, the effective viscosity increases with the Reynolds number of the flow.
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47.55.db Drop and bubble formation
47.55.nb Capillary and thermocapillary flows
82.70.Kj Emulsions and suspensions
47.60.Dx Flows in ducts and channels
02.70.Bf Finite-difference methods
47.11.Bc Finite difference methods

Intermittent features of inertial particle distributions in turbulent premixed flames

F. Battista, F. Picano, G. Troiani, and C. M. Casciola

Phys. Fluids 23, 123304 (2011); http://dx.doi.org/10.1063/1.3671734 (14 pages)

Online Publication Date: 30 December 2011

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Clustering is widely observed in many turbulent flows, where it results from the inability of finite inertia particles to comply with the different time scales, which characterize a turbulent field. Depending on their inertia, particles are found to be instantaneously organized in clusters, whose size depends on the Kolmogorov-Stokes number and which presumably form as a consequence of particle ejection from persistent vortical structures. In reacting flows, the abrupt acceleration of the fluid across the thin flame front due to combustion adds new and unexpected features. The particles follow such acceleration with a certain time lag which, coupled with the flame front fluctuations, gives rise to an entirely different mechanism of cluster formation. As suggested in previous studies, a possible indicator of this preferential localization is the so-called clustering index, quantifying the departure of the actual particle arrangement from the Poissonian distribution. Most of the clustering is found in the flame brush region, where it cannot be explained by the standard arguments used in cold flows. Actually, the effect is significant also for very light particles, where the simple model we propose, based on the Bray-Moss-Libby formalism, is able to account for most of the deviation from the Poissonian. When the particle inertia increases, the effect becomes larger and it is found to persist well within the region of the burned gases. The observed clustering is confirmed by a more precise analysis in terms of a generalization of the radial distribution function to inhomogeneous, anisotropic flows. The results taken from a direct numerical simulation with single step kinetics favorably compare with experiments on a premixed Bunsen turbulent flame. The present findings are expected to be of some relevance for the plenty of applications dealing with particles in presence of combustion, e.g., liquid droplet swarms for combustion temperature control, soot dynamics, or combustion-oriented particle image velocimetry.
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47.70.Pq Flames; combustion
47.70.Fw Chemically reactive flows
47.32.-y Vortex dynamics; rotating fluids
47.27.ek Direct numerical simulations
47.27.te Turbulent convective heat transfer
47.11.-j Computational methods in fluid dynamics
back to top Laminar Flows

Vortex motion around a circular cylinder

G. L. Vasconcelos, M. N. Moura, and A. M. J. Schakel

Phys. Fluids 23, 123601 (2011); http://dx.doi.org/10.1063/1.3667269 (8 pages)

Online Publication Date: 9 December 2011

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The motion of a pair of counter-rotating point vortices placed in a uniform flow around a circular cylinder forms a rich nonlinear system that is often used to model vortex shedding. The phase portrait of the Hamiltonian governing the dynamics of a vortex pair that moves symmetrically with respect to the centerline—a case that can be realized experimentally by placing a splitter plate in the center plane—is presented. The analysis provides new insights and reveals novel dynamical features of the system, such as a nilpotent saddle point at infinity whose homoclinic orbits define the region of nonlinear stability of the so-called Föppl equilibrium. It is pointed out that a vortex pair properly placed downstream can overcome the cylinder and move off to infinity upstream. In addition, the nonlinear dynamics resulting from antisymmetric perturbations of the Föppl equilibrium is studied and its relevance to vortex shedding discussed.
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47.32.Ef Rotating and swirling flows
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
47.32.cd Vortex stability and breakdown

Laminar flow of a gas in a tube with large temperature differences

F. J. Higuera

Phys. Fluids 23, 123602 (2011); http://dx.doi.org/10.1063/1.3667270 (4 pages)

Online Publication Date: 9 December 2011

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The laminar low Mach number flow of a gas in a tube is analyzed for very small and very large values of the inlet-to-wall temperature ratio. When this ratio tends to zero, pressure forces confine the cold gas to a thin core around the axis of the tube. This core is neatly bounded by an ablation front that consumes it at a finite distance from the tube inlet. When the temperature ratio tends to infinity, the temperature of the gas increases smoothly from the wall to the axis of the tube and the shear stress and heat flux are positive at the wall despite the fact that the viscosity and thermal conductivity of the gas scaled with their inlet values tend to zero at the wall.
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47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.60.Dx Flows in ducts and channels
47.40.-x Compressible flows; shock waves
51.20.+d Viscosity, diffusion, and thermal conductivity
47.15.Cb Laminar boundary layers
back to top Instability and Transition

A simple analytic approximation to the Rayleigh-Bénard stability threshold

Andrea Prosperetti

Phys. Fluids 23, 124101 (2011); http://dx.doi.org/10.1063/1.3662466 (8 pages)

Online Publication Date: 7 December 2011

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The Rayleigh-Bénard linear stability problem is solved by means of a Fourier series expansion. It is found that truncating the series to just the first term gives an excellent explicit approximation to the marginal stability relation between the Rayleigh number and the wave number of the perturbation. Where the error can be compared with published exact results, it is found not to exceed a few percent over the entire wave number range. Several cases with no-slip boundaries of equal or unequal thermal conductivities are considered explicitly.
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47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.55.pb Thermal convection
02.30.Lt Sequences, series, and summability
02.60.Gf Algorithms for functional approximation
47.11.-j Computational methods in fluid dynamics

Interaction of viscous and inviscid instability modes in separation–bubble transition

Joshua R. Brinkerhoff and Metin I. Yaras

Phys. Fluids 23, 124102 (2011); http://dx.doi.org/10.1063/1.3666844 (11 pages)

Online Publication Date: 14 December 2011

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This paper describes numerical simulations that are used to examine the interaction of viscous and inviscid instability modes in laminar-to-turbulent transition in a separation bubble. The results of a direct numerical simulation are presented in which separation of a laminar boundary-layer occurs in the presence of an adverse streamwise pressure gradient. The simulation is performed at low freestream-turbulence levels and at a flow Reynolds number and pressure distribution approximating those typically encountered on the suction side of low-pressure turbine blades in a gas-turbine engine. The simulation results reveal the development of a viscous instability upstream of the point of separation which produces streamwise-oriented vortices in the attached laminar boundary layer. These vortices remain embedded in the flow downstream of separation and are carried into the separated shear layer, where they are amplified by the local adverse pressure-gradient and contribute to the formation of coherent hairpin-like vortices. A strong interaction is observed between these vortices and the inviscid instability that typically dominates the shear layer in the separated zone. The interaction is noted to determine the spanwise extent of the vortical flow structures that periodically shed from the downstream end of the separated shear layer. The structure of the shed vortical flow structures is examined and compared with the coherent structures typically observed within turbulent boundary layers.
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47.15.Fe Stability of laminar flows
47.27.Cn Transition to turbulence
47.55.dd Bubble dynamics
47.15.ki Inviscid flows with vorticity
47.32.C- Vortex dynamics
47.27.ek Direct numerical simulations
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