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Jan 2013

Volume 25, Issue 1, Articles (01xxxx)

Issue Cover Spotlight Figure

Phys. Fluids 25, 015107 (2013); http://dx.doi.org/10.1063/1.4774338 (18 pages)

W. Cabot and Ye Zhou
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Announcement: The 2012 François Naftali Frenkiel Award for Fluid Mechanics

The Editors

Phys. Fluids 25, 010201 (2013); http://dx.doi.org/10.1063/1.4767533 (2 pages)

Online Publication Date: 2 January 2013

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Abstract Unavailable
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01.10.Cr Announcements, news, and awards
68.03.Cd Surface tension and related phenomena
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Referee Acknowledgment for 2012

John Kim and Gary Leal, Editors

Phys. Fluids 25, 010202 (2013); http://dx.doi.org/10.1063/1.4783618 (7 pages)

Online Publication Date: 23 January 2013

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Abstract Unavailable
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01.30.-y Physics literature and publications
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Intermittency and local dissipation scales under strong mean shear

Khandakar Niaz Morshed, Subhas Karan Venayagamoorthy, and Lakshmi Prasad Dasi

Phys. Fluids 25, 011701 (2013); http://dx.doi.org/10.1063/1.4774039 (6 pages) | Cited 1 time

Online Publication Date: 9 January 2013

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We experimentally probe the local dissipation scale distribution Q(η) and temporal fluctuations of the turbulent kinetic energy dissipation rate ε in the strongly anisotropic flow past a backward facing step. A shift in Q(η) and corresponding reduction in the relative intermittency of ε is observed with increasing mean shear S. We offer physical arguments to elucidate the role of strong shear on the small-scale structure. A local mean-shear dissipation Reynolds number, ReS ≡ ⟨ε⟩/(S2ν), is proposed that may define a family of universal small-scale structures of turbulence.
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47.27.nd Channel flow
47.80.Jk Flow visualization and imaging
47.60.Dx Flows in ducts and channels
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back to top Biofluid Mechanics

Mechanics of swimming of multi-body bacterial swarmers using non-labeled cell tracking algorithm

Kiran Phuyal and Min Jun Kim

Phys. Fluids 25, 011901 (2013); http://dx.doi.org/10.1063/1.4774041 (9 pages)

Online Publication Date: 14 January 2013

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To better understand the survival strategy of bacterial swarmers and the mechanical advantages offered by the linear chain (head-tail) attachment of the multiple bacterial bodies in an individual swarmer cell at low Reynolds number, a non-labeled cell tracking algorithm was used to quantify the mechanics of multi-body flagellated bacteria, Serratia marcescens, swimming in a motility buffer that originally exhibited the swarming motility. Swarming is a type of bacterial motility that is characterized by the collective coordinated motion of differentiated swarmer cells on a two-dimensional surface such as agar. In this study, the bacterial swarmers with multiple cell bodies (2, 3, and 4) were extracted from the swarm plate, and then tracked individually after resuspending in the motility medium. Their motion was investigated and compared with individual undifferentiated swimming bacterial cells. The swarmers when released into the motility buffer swam actively without tumbles. Their speeds, orientations, and the diffusive properties were studied by tracking the individual cell trajectories over a short distance in two-dimensional field when the cells are swimming at a constant depth in a bulk aqueous environment. At short time scales, the ballistic trajectory was dominant for both multi-body swarmers and undifferentiated cells.
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87.17.Rt Cell adhesion and cell mechanics
87.17.Jj Cell locomotion, chemotaxis

Hydrodynamic interaction of oblique sheets in tandem arrangement

Bo Yin and Haoxiang Luo

Phys. Fluids 25, 011902 (2013); http://dx.doi.org/10.1063/1.4774345 (15 pages)

Online Publication Date: 17 January 2013

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Vortex-induced vibration of thin structures attached with piezoelectric materials has recently been explored for its potential application in energy harvesting from a flow. In this work, we numerically simulate the hydrodynamic interaction of two elastic sheets in tandem arrangement, and we study the mechanism of system resonance, at which both sheets are excited and experience greatly increased oscillations as compared to the single sheet with identical properties. The sheets are mounted obliquely to the flow to facilitate vortex shedding. The separation distance between the sheets is systematically varied, and the resonance is found within a range that depends on the mass ratio of the sheets. In contrast with two elastically mounted cylinders oscillating in the transverse direction and experiencing a similar group behavior, the resonance occurs in the present study even when the free stream does not directly impinge on the rear sheet. Further study shows that the resonance is caused by the vortex-vortex and vortex-sheet interactions that adjust the oscillation frequency and modify the magnitude/phase-shift of the hydrodynamic force on the sheets. Implication of the study on multiple sheets in tandem arrangement is also discussed.
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47.32.cb Vortex interactions
02.60.Cb Numerical simulation; solution of equations
47.11.-j Computational methods in fluid dynamics
back to top Micro- and Nanofluid Mechanics

Diffusiophoretic self-propulsion of colloids driven by a surface reaction: The sub-micron particle regime for exponential and van der Waals interactions

Nima Sharifi-Mood, Joel Koplik, and Charles Maldarelli

Phys. Fluids 25, 012001 (2013); http://dx.doi.org/10.1063/1.4772978 (34 pages)

Online Publication Date: 8 January 2013

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Diffusiophoresis is a mechanism for propelling colloid particles in a liquid in which the driving force for the motion derives from intermolecular interactions between solute molecules surrounding the particle and the colloid itself. When solutes are asymmetrically distributed around the particle, the solutal interactions exerted on the colloid are unbalanced, and the particle is propelled. In self-diffusiophoresis, the particle itself creates the asymmetric distribution as a means of autonomous motion (a motor). Experiments implement the asymmetric production of a solutal concentration gradient by functionalizing one side of the colloid with a catalyst, which converts a reactant solute into a product. Previous hydrodynamic models of this design have assumed the length scale L of the intermolecular interaction (typically of order 1−10 nm) to be much smaller than the colloid radius, a (order 1 μm), L/a < 1. In this limit, assuming the catalytic reaction produces a constant flux of solute, and convective effects are negligible, the self-diffusiophoretic velocity is to leading order independent of a. Anticipating future experiments on nanosized motors (a=O(10−100 nm)), numerical solutions are presented for the velocity up to order one in L/a, and an integral asymptotic approximation is constructed accurate for L/a less than 0.1. Three intermolecular interactions are examined, a hard sphere excluded volume potential, an exponential interaction and a long-range van der Waals attraction, which is computed by pairwise additivity and formulated to include the attraction of the solvent with the colloid. For each interaction, the velocity decreases as the colloid radius decreases with the interaction parameters constant. For small L/a, velocity for the exponential potential decreases with an order one correction in L/a while this correction is logarithmic for the van der Waals potential. A curve for velocity as a function of a is constructed for the van der Waals interaction in terms of the pairwise interaction parameters of the colloid with the solute and solvent.
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82.70.Dd Colloids
02.60.Cb Numerical simulation; solution of equations
47.55.-t Multiphase and stratified flows
47.70.Fw Chemically reactive flows
47.80.Jk Flow visualization and imaging
82.33.Nq Reactions in micells
back to top Interfacial Flows

Assessment of the role of axial vorticity in the formation of particle accumulation structures in supercritical Marangoni and hybrid thermocapillary-rotation-driven flows

Marcello Lappa

Phys. Fluids 25, 012101 (2013); http://dx.doi.org/10.1063/1.4769754 (11 pages) | Cited 1 time

Online Publication Date: 2 January 2013

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Evidence is provided that when the so-called phenomenon of particle accumulation structure (PAS) occurs, extended regions exist where ½ of the axial component of vorticity matches the angular frequency of the traveling wave produced by the instability of the Marangoni flow. Several cases are considered in which such axial component is varied by “injecting” vorticity into the system via rotation of one of its endwalls. The results show that both the resulting PAS lines and the trajectories of related solid particles undergo significant changes under the influence of imposed rotation. By analysis of such findings, a validation and a generalization/extension of the so-called “phase-locking” model are provided.
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47.32.Ef Rotating and swirling flows
47.55.Kf Particle-laden flows
47.55.nb Capillary and thermocapillary flows
47.55.pf Marangoni convection
47.10.ad Navier-Stokes equations
47.32.cd Vortex stability and breakdown

Runup and boundary layers on sloping beaches

G. K. Pedersen, E. Lindstrøm, A. F. Bertelsen, A. Jensen, D. Laskovski, and G. Sælevik

Phys. Fluids 25, 012102 (2013); http://dx.doi.org/10.1063/1.4773327 (23 pages)

Online Publication Date: 8 January 2013

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The present study is devoted to discrepancies between experimental and theoretical runup heights on an inclined plane, which have occasionally been reported in the literature. In a new study on solitary wave-runup on moderately steep slopes, in a wave tank with 20 cm water depth, detailed observations are made for the shoreline motion and velocity profiles during runup. The waves are not breaking during runup, but they do break during the subsequent draw-down. Both capillary effects and viscous boundary layers are detected. In the investigated cases the onshore flow is close to the transitional regime between laminar and turbulent boundary layers. The flow behaviour depends on the amplitude of the incident wave and the location on the beach. Stable laminar flow, fluctuations (Tollmien-Schlichting waves), and formation of vortices are all observed. Comparison with numerical simulations showed that the experimental runup heights were markedly smaller than predictions from inviscid theory. The observed and computed runup heights are discussed in the context of preexisting theory and experiments. Similar deviations are apparent there, but have often been overlooked or given improper physical explanations. Guided by the absence of turbulence and irregular flow features in parts of the experiments we apply laminar boundary layer theory to the inundation flow. Outer flows from potential flow models are inserted in a nonlinear, numerical boundary layer model. Even though the boundary layer model is invalid near the moving the shoreline, the computed velocity profiles are found to compare well with experiments elsewhere, until instabilities are observed in the measurements. Analytical, linear boundary layer solutions are also derived both for an idealized swash zone motion and a polynomial representation of the time dependence of the outer flow. Due to lacking experimental or theoretical descriptions of the contact point dynamics no two-way coupling of the boundary layer model and the inviscid runup models is attempted. Instead, the effect of the boundary layer on the maximum runup is estimated through integrated losses of onshore volume transport and found to be consistent with the differences between inviscid theory and experiments.
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47.35.Fg Solitary waves
47.35.Pq Capillary waves
47.11.-j Computational methods in fluid dynamics
47.15.Cb Laminar boundary layers
47.27.nb Boundary layer turbulence
47.32.C- Vortex dynamics

Temporal instability analysis of inviscid compound jets falling under gravity

Muhammad Mohsin, Jamal Uddin, Stephen P. Decent, and Muhammad F. Afzaal

Phys. Fluids 25, 012103 (2013); http://dx.doi.org/10.1063/1.4775792 (16 pages)

Online Publication Date: 18 January 2013

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Compound liquid jets can be used in a variety of industrial applications ranging from capsule production in pharmaceutics to enhance printing methods in ink-jet printing. An appreciation of how instability along compound jets can lead to breakup and droplet formation is thus critical in many fields in science and engineering. In this paper, we perform a theoretical analysis to examine the instability of an axisymmetric inviscid compound liquid jet which falls vertically under the influence of gravity. We use a long-wavelength, slender-jet asymptotic expansion to reduce the governing equations of the problem into a set of one-dimensional partial differential equations, which describe the evolution of the leading-order axial velocity of the jet as well as the radii of both the inner and the outer interfaces. We first determine the steady-state solutions of the one-dimensional model equations and then we perform a linear temporal instability analysis to obtain a dispersion relation, which gives us useful information about the maximum growth rate and the maximum wavenumber of the imposed wave-like disturbance. We use our results to estimate the location and qualitative nature of breakup and then compare our results with numerical simulations.
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47.20.Cq Inviscid instability
47.35.-i Hydrodynamic waves
47.55.db Drop and bubble formation
47.55.df Breakup and coalescence
02.30.Jr Partial differential equations
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Dynamical behavior of electrified pendant drops

C. Ferrera, J. M. López-Herrera, M. A. Herrada, J. M. Montanero, and A. J. Acero

Phys. Fluids 25, 012104 (2013); http://dx.doi.org/10.1063/1.4776238 (16 pages)

Online Publication Date: 22 January 2013

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The electrohydrodynamic response of low-conductivity pendant drops to a step change in the electric field magnitude was examined both numerically and experimentally. Both the leaky-dielectric and perfect-conductor models were solved in the simulations. Experiments were conducted to precisely measure the drop interface shape as a function of time. The drop oscillated for applied voltages smaller than a critical value which depended on the rest of governing parameters. It stretched and subsequently emitted a microjet from its tip for electric potentials above that critical value. The perfect-conductor model described accurately the oscillations of subcritical drops. This model also provided satisfactory results for the prejetting regime in the supercritical case. We found a good agreement between the leaky-dielectric model and the experiments for the drop-jet transitional region, despite the fact that the tip streaming arose on a time scale much shorter than the electric relaxation time. This result shows the capability of the leaky-dielectric model to describe the flow in this singular region. The numerical simulations allowed us to describe the pressure and velocity fields in the transitional region.
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47.55.db Drop and bubble formation
47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.80.-v Instrumentation and measurement methods in fluid dynamics
47.11.-j Computational methods in fluid dynamics

Effect of pre-impingement length and misalignment in the hydrodynamics of multijet impingement atomization

M. R. O. Panão and J. M. D. Delgado

Phys. Fluids 25, 012105 (2013); http://dx.doi.org/10.1063/1.4774347 (11 pages)

Online Publication Date: 29 January 2013

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The multijet impingement atomization strategy is proposed as a competitive one in designing atomizers with relatively simple geometries, producing sprays from the impact of multiple jets at low-flow rate conditions (<1.5 l/min). Most theoretical studies have been made for the spray produced by the impact of two jets. However, there are two important geometric issues related with the atomizer design, scarcely approached in the literature, which are the pre-impingement length of jets before impact and jet misalignment. This work analyses the influence of these parameters on the structure of the liquid sheet as well as on drop size. First, the liquid sheet structure has two hydrodynamic regimes: closed-rim and open-rim. The results evidence that higher pre-jet-impingement distances influence only the open-rim regime, namely, producing shorter liquid sheet breakup lengths, smaller drop sizes, and more droplets. The jet misalignment elongates the liquid sheet in the closed-rim regime, and anticipates breakup in the open-rim regime.
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47.55.nm Curtains/sheets
47.57.-s Complex fluids and colloidal systems
47.55.df Breakup and coalescence
back to top Viscous and Non-Newtonian Flows

Velocity relaxation of an ellipsoid immersed in a viscous incompressible fluid

B. U. Felderhof

Phys. Fluids 25, 013101 (2013); http://dx.doi.org/10.1063/1.4774331 (13 pages)

Online Publication Date: 14 January 2013

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The motion of an ellipsoid in a viscous incompressible fluid, caused by a small time-dependent applied force, is studied on the basis of the linearized Navier-Stokes equations in terms of the frequency-dependence of the friction tensor. The asymptotic behavior of the hydrodynamic force at high frequency contains a term linear in frequency, with an added mass coefficient, and a term proportional to the square root of frequency, with a Basset coefficient. The latter is calculated from an expression derived by Batchelor [An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 1967)]. A simple approximate three-pole expression is proposed for the frequency-dependent admittance for each principal direction, embodying added mass, particle mass, the steady state friction coefficient, and the Basset coefficient. It is suggested that a remaining unknown coefficient in the expression be determined by experiment, computer simulation, or numerical solution of an integral equation derived by Pozrikidis [“A study of linearized oscillatory flow past particles by the boundary-integral method,” J. Fluid Mech. 202, 17 (1989)10.1017/S0022112089001084].
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47.10.ad Navier-Stokes equations
02.30.Rz Integral equations
02.60.Nm Integral and integrodifferential equations

Short time dynamics of viscous drop spreading

A. Eddi, K. G. Winkels, and J. H. Snoeijer

Phys. Fluids 25, 013102 (2013); http://dx.doi.org/10.1063/1.4788693 (10 pages)

Online Publication Date: 31 January 2013

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Liquid drops start spreading directly after coming into contact with a solid substrate. Although this phenomenon involves a three-phase contact line, the spreading motion can be very fast. We experimentally study the initial spreading dynamics, characterized by the radius of the wetted area, for viscous drops. Using high-speed imaging with synchronized bottom and side views gives access to 6 decades of time resolution. We show that short time spreading does not exhibit a pure power-law growth. Instead, we find a spreading velocity that decreases logarithmically in time, with a dynamics identical to that of coalescing viscous drops. Remarkably, the contact line dissipation and wetting effects turn out to be unimportant during the initial stages of drop spreading.
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47.55.df Breakup and coalescence
47.80.Jk Flow visualization and imaging
68.08.Bc Wetting
66.20.Ej Studies of viscosity and rheological properties of specific liquids

An actuated elastic sheet interacting with passive and active structures in a viscoelastic fluid

J. C. Chrispell, L. J. Fauci, and M. Shelley

Phys. Fluids 25, 013103 (2013); http://dx.doi.org/10.1063/1.4789410 (16 pages)

Online Publication Date: 31 January 2013

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We adapt the classic Taylor swimming sheet set-up to investigate both the transient and long-time dynamics of an actuated elastic sheet immersed in a viscoelastic fluid as it interacts with neighboring structures. While the preferred kinematics of the sheet are specified, the flexible sheet interacts with the surrounding fluid and other structures, and its realized kinematics emerges from this coupling. We use an immersed boundary framework to evolve the Oldroyd-B/Navier-Stokes equations and capture the spatial and temporal development of viscoelastic stresses and sheet shape. We compare the dynamics when the actuated sheet swims next to a free elastic membrane, with and without bending rigidity, and next to a fixed wall. We demonstrate that the sheets can exploit the neighboring structures to enhance their swimming speed and efficiency, and also examine how this depends upon fluid viscoelasticity. When the neighboring structure is likewise an actuated elastic sheet, we investigate the viscoelastic dynamics of phase-locking.
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47.63.Gd Swimming microorganisms
47.50.Cd Modeling
47.10.ad Navier-Stokes equations
83.60.Bc Linear viscoelasticity
back to top Particulate, Multiphase, and Granular Flows

Preferential concentration and settling of heavy particles in homogeneous turbulence

A. Dejoan and R. Monchaux

Phys. Fluids 25, 013301 (2013); http://dx.doi.org/10.1063/1.4774339 (16 pages)

Online Publication Date: 16 January 2013

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Voronoï diagrams are used to analyze one-way coupling direct numerical simulation data of heavy particles settling in homogeneous turbulence. Preferential concentration and clustering of the inertial particles are analyzed for an extended range of particle Stokes and Rouse numbers. Influence of preferential concentration on the settling velocity enhancement is addressed from statistics of particle and flow field quantities conditioned on the local concentration. While gravity is found to have almost no influence on the global characteristics of preferential concentration, the conditional statistics bring out a refined preferential sampling of the flow field resulting from the gravitational effects. This preferential sampling shows that beside the descending fluid velocity contribution, the settling velocity is further increased by the descending fluid acceleration. This effect cannot be detected from global estimations of the particle concentration field. A 2D analysis of the Voronoï cells is also presented to investigate their shape and orientation. It is found that clusters can be represented as 2D elongated manifolds. Their shape is shown to be similar in zero and non-zero gravity fields while Voronoï cells tend to be more elongated for Stokes numbers around unity. Under the gravity effects, they tend to be preferentially oriented perpendicularly to the gravitational axis.
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47.27.Gs Isotropic turbulence; homogeneous turbulence
47.55.Kf Particle-laden flows
02.60.Cb Numerical simulation; solution of equations
47.10.ad Navier-Stokes equations
47.27.eb Statistical theories and models
47.27.ek Direct numerical simulations

Bubble motion and size variation during thermal migration with phase change

A. K. Nurse, G. B. McFadden, and S. R. Coriell

Phys. Fluids 25, 013302 (2013); http://dx.doi.org/10.1063/1.4774329 (21 pages)

Online Publication Date: 29 January 2013

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An analysis of the motion of a spherical bubble in a two-phase (fluid-fluid), single component system with a vertical linear temperature gradient is presented. The model for the migration of an immiscible bubble under the effects of buoyancy and thermocapillarity, considered by Young et al. [“The motion of bubbles in a vertical temperature gradient,” J. Fluid Mech. 6, 350–356 (1959)], is modified to allow for phase change at the bubble surface. We allow the possibility of both translation of the bubble in the vertical direction and the change of bubble radius with time. Depending on the material parameters, the thermocapillary and buoyancy effects that govern the migration of an immiscible bubble can be overwhelmed by the effects of latent heat generation, resulting in a change in the mechanism driving the motion. For a water-steam system, conditions are determined for a stationary bubble in which the effects of buoyancy and thermal migration are balanced. The linear stability of the bubble is considered, and conditions are determined that correspond to small-amplitude oscillations of the position and radius of the bubble. A weakly nonlinear analysis of the solution in the vicinity of the unstable solution is performed, and the results are compared with a numerical solution of the nonlinear equations.
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47.55.dm Thermocapillary effects
47.55.nb Capillary and thermocapillary flows
02.30.Hq Ordinary differential equations
02.60.Lj Ordinary and partial differential equations; boundary value problems
47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)

Chaotic rotation of inertial spheroids in oscillating shear flow

Christopher Nilsen and Helge I. Andersson

Phys. Fluids 25, 013303 (2013); http://dx.doi.org/10.1063/1.4789376 (12 pages)

Online Publication Date: 31 January 2013

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The rotation of prolate spheroidal particles is studied in the flow-gradient plane of an oscillating creeping shear flow. Chaotic dynamics is observed for particles with strong inertia, and spheroids with aspect ratio 3:1 are seen to be the most prone to chaotic rotation. This makes the particles’ long-term behaviour unpredictable, and also affects the particles’ average statistics, such as the rotation energy. Chaos is only seen for Stokes numbers larger than a certain critical value, always greater than the Stokes number for which the particle rotation period in a constant shear rate transitions from long to short. This is because both inertial and nonlinear effects need to be significant for chaos to emerge.
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47.55.Kf Particle-laden flows
47.52.+j Chaos in fluid dynamics
47.15.St Free shear layers
back to top Laminar Flows

On the lock-on of vortex shedding to oscillatory actuation around a circular cylinder

Phillip M. Munday and Kunihiko Taira

Phys. Fluids 25, 013601 (2013); http://dx.doi.org/10.1063/1.4772977 (13 pages)

Online Publication Date: 2 January 2013

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We numerically investigate the influence of sinusoidal flow control on the von Kármán vortex shedding behind a circular cylinder in two-dimensional flow. Actuator location, direction, frequency, and amplitude are varied to examine their effects on the wake and the corresponding change in drag on the cylinder. We place focus on the conditions for which the cylinder wake locks onto the actuation frequency. The lock-on region is found to be consistent with stability horns observed in oscillator dynamics. Under certain conditions, the actuation reduces drag by elongating the wake structure to appear more streamlined than the wake without flow control. In other cases, the use of actuation led to less streamlined wakes, resulting in no significant drag reduction or for some instances in a drag increase. Purely steady and oscillatory actuation components are examined to highlight their individual influence on the lock-on and drag characteristics. We also note that low frequency oscillations are observed for cases in the neighborhood of the lock-on boundaries due to the competition between low and high-drag states.
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47.85.lb Drag reduction
02.60.-x Numerical approximation and analysis
47.32.cd Vortex stability and breakdown

Effect of acoustic coupling on power-law flame acceleration in spherical confinement

V’yacheslav Akkerman and Chung K. Law

Phys. Fluids 25, 013602 (2013); http://dx.doi.org/10.1063/1.4773196 (12 pages) | Cited 1 time

Online Publication Date: 7 January 2013

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A model describing acoustically-generated parametric instability in a spherical chamber is developed for quasi-one-dimensional, low-Mach number flames. We demonstrate how sound waves generated by a centrally-ignited, outwardly-propagating accelerating flamefront can be incorporated into an existing theory of self-similar flame acceleration in free space [V. Akkerman, C. K. Law, and V. Bychkov, “Self-similar accelerative propagation of expanding wrinkled flames and explosion triggering,” Phys. Rev. E 83, 026305 (2011)]10.1103/PhysRevE.83.026305. Being reflected from the chamber wall, flame-generated acoustics interact with the flamefront and the attendant hydrodynamic flamefront cellular instability. This in turn affects the subsequent flame morphology and propagation speed. It is shown that the acoustics modify the power-law flame acceleration, concomitantly facilitating or inhibiting the transition to detonation in confinement, which allows reconciliation of a discrepancy in experimental measurements of different groups.
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47.70.Pq Flames; combustion
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.20.-k Flow instabilities
47.40.Rs Detonation waves
47.53.+n Fractals in fluid dynamics
47.70.Fw Chemically reactive flows
back to top Instability and Transition

Detailed analysis of the vibration induced instability of a liquid film flow

H. Garih, A. Strzelecki, G. Casalis, and J. L. Estivalezes

Phys. Fluids 25, 014101 (2013); http://dx.doi.org/10.1063/1.4773598 (17 pages)

Online Publication Date: 14 January 2013

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The problem of the vibration induced instability of a liquid film flow is formulated, thanks to a linear approach. For the solution of the problem, the disturbances are expanded using a spectral method based on Chebyshev polynomials leading to a system of ordinary differential equations. This system is solved by using Floquet theory. The natural and vibration induced instabilities are studied in terms of frequency, temporal growth rate, and eigenfunction. Numerical results show that the mean flow velocity alters the surface wave frequency, which is not predictable by Mathieu's equation model (which assumes that the fluid is at rest). Above a threshold amplitude, multiple vibration induced instability modes are triggered. At specific amplitudes above the latter, two wavenumbers coexist at the free surface. A relation between the eigenfunction shape and the instability mode is observed.
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47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.35.-i Hydrodynamic waves
47.55.nd Spreading films
68.15.+e Liquid thin films
02.70.Hm Spectral methods
47.11.Kb Spectral methods

Oscillations and translation of a free cylinder in a viscous confined flow

Maria Veronica D’Angelo, Jean-Pierre Hulin, and Harold Auradou

Phys. Fluids 25, 014102 (2013); http://dx.doi.org/10.1063/1.4775385 (15 pages)

Online Publication Date: 22 January 2013

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An oscillatory instability has been observed experimentally on an horizontal cylinder free to move and rotate between two parallel vertical walls of distance H. The vertical motion of the cylinder, its rotation about its axis, and its transverse motion across the gap have been investigated as a function of its diameter D, its density ρs, of the mean vertical velocity U of the fluid, and of its viscosity ν. The relevant Reynolds number Re is shown to be based on the cell aperture H and on the relative velocity Vr between the fluid and the cylinder. For a blockage ratio D/H above 0.5 and Re above 20, oscillations of the rolling angle of the cylinder about its axis and of its transverse coordinate in the gap were observed together with periodic variations of the vertical velocity. For a given fluid-cylinder pair, the relative velocity Vr as well as the frequency f and the amplitude of the transverse velocity for these oscillations are nearly independent of the flow velocity U. For given cylinder density and fluid characteristics, f is also nearly independent of the ratio D/H in the range investigated. The oscillations could be observed down to values of Re as low as 30: this is lower than usual values for vortex shedding in confined geometries, which suggests that one might deal with a different instability mechanism.
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47.32.Ef Rotating and swirling flows
47.15.Fe Stability of laminar flows
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.32.cd Vortex stability and breakdown

Asymmetric Rayleigh-Taylor and double-diffusive fingers in reactive systems

L. Lemaigre, M. A. Budroni, L. A. Riolfo, P. Grosfils, and A. De Wit

Phys. Fluids 25, 014103 (2013); http://dx.doi.org/10.1063/1.4774321 (18 pages)

Online Publication Date: 25 January 2013

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Buoyancy-driven flows induced by the hydrodynamic Rayleigh-Taylor or double-diffusive instabilities develop symmetrically around the initial contact line when two solutions of given solutes with different densities are put in contact in the gravitational field. If the solutes affecting the densities of these solutions are involved in chemical reactions, changes in composition due to the underlying reaction-diffusion processes can modify the density profile in space and time, and affect the hydrodynamic patterns. In particular, if the density difference between the two reactant solutions is not too large, the resulting chemo-hydrodynamic patterns are asymmetric with regard to the initial contact line. We quantify both experimentally and numerically this asymmetry showing that fingers here preferentially develop above the reaction zone and not across the mixing zone as in the non reactive situation. In some cases, the reaction can even lead to the onset of a secondary double-diffusive instability between the product of the reaction, dynamically generated in situ, and one of the reactants.
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47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.54.Bd Theoretical aspects
47.54.De Experimental aspects
47.70.Fw Chemically reactive flows
02.60.-x Numerical approximation and analysis

Manipulation of instabilities in core-annular flows using a deformable solid layer

Gaurav and V. Shankar

Phys. Fluids 25, 014104 (2013); http://dx.doi.org/10.1063/1.4788712 (21 pages)

Online Publication Date: 29 January 2013

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The stability of core-annular flow (CAF) of two immiscible fluids surrounded by a soft, deformable solid layer is analyzed to examine the role of solid deformability on the interfacial instabilities in the CAF, using both low-wavenumber asymptotic analysis and numerical solutions by considering axisymmetric perturbations. For CAF in a rigid tube, two qualitatively distinct mechanisms due to capillary forces and viscosity stratification destabilize the interface between the two fluids. We show using a low-wavenumber analysis that the deformability of the solid layer has a stabilizing effect when the more viscous liquid is in the annular region, while it is destabilizing when the less viscous fluid is in the annular region. When the more viscous fluid is in the annulus, our numerical results demonstrate that by tuning the shear modulus of the solid layer, it is possible to maintain a stable core-annular flow (otherwise unstable in a rigid tube), where perturbations with all wavelengths are stable. For the same configuration, when the radius of the core fluid becomes small, we also find that it is possible to restrict the length scale of the instability to a small band of wavelengths. When the less viscous fluid is in the annulus, we show that the CAF (otherwise stable in a rigid tube) could be destabilized by solid deformability. Both these predictions, viz., suppression or enhancement of instability of the liquid-liquid interface by wall deformability could be potentially exploited in microfluidic drop formation applications that seek to control and manipulate the instability of the interface.
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47.55.Hd Stratified flows
47.55.nb Capillary and thermocapillary flows
47.60.Dx Flows in ducts and channels
46.25.-y Static elasticity
47.11.-j Computational methods in fluid dynamics
47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)

Three-dimensional transition of vortex shedding flow around a circular cylinder at right and oblique attacks

Ming Zhao, Jitendra Thapa, Liang Cheng, and Tongming Zhou

Phys. Fluids 25, 014105 (2013); http://dx.doi.org/10.1063/1.4788934 (20 pages)

Online Publication Date: 29 January 2013

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Vortex shedding from an inclined circular cylinder at low values of Reynolds number (Re) is investigated numerically. The aim of the study is to investigate the effect of cylinder oblique angle on the transition from two-dimensionality (2D) to three-dimensionality (3D) of the wake flow. The Navier-Stokes equations are solved by the Petrov-Galerkin finite element method for Reynolds numbers ranging from 100 to 1000 and the flow attack angles of α = 0° and 45°. For the right attack angle case (α = 0°), the predicted wavy spanwise vortices in the early stage of the transition mode A, the vortex dislocation in the late stage of the transition mode A and the streamwise-vortex dominant wake flow structure in the transition mode B are found to agree well with independent experimental observations and measurements. The transition from 2D to 3D at α = 45° was found distinctively different from that at α = 0°. For α = 45°, no clear-cut transition modes are observed. The wake is characterized by wavy spanwise vortices close to the lower boundary of the transition Reynolds number regime, which are similar to those in the early stage of the transition mode A at α = 0°. The vortex-dislocation in the transition mode A was not observed at α = 45°. It appears that the fluid flow in the spanwise direction in the primary vortices at α = 45° does not allow the instability to sustain at a specific spanwise location and trigger the vortex dislocation. Although the wake flow structure is different, the variation of the normal Strouhal number with the normal Reynolds number (both based on the velocity component perpendicular to the cylinder span) at α = 45° is close to that at α = 0° in the transitional Reynolds number regime. The root mean square of the lift coefficient normalized by the velocity component perpendicular to the axial direction of the cylinder at α = 45° is about 20% to 25% larger than that at α = 0° in the Reynolds number regime between 250 and 500.
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47.32.C- Vortex dynamics
47.15.Tr Laminar wakes
47.10.ad Navier-Stokes equations
47.11.Fg Finite element methods
02.70.Dh Finite-element and Galerkin methods

Singularity formation and nonlinear evolution of a viscous vortex sheet model

Sung-Ik Sohn

Phys. Fluids 25, 014106 (2013); http://dx.doi.org/10.1063/1.4789460 (18 pages)

Online Publication Date: 30 January 2013

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We study Dhanak's model [J. Fluid Mech. 269, 265 (1994)]10.1017/S0022112094001552 of a viscous vortex sheet in the sharp limit, to investigate singularity formations and present nonlinear evolutions of the sheets. The finite-time singularity does not disappear by giving viscosity to the vortex sheet, but is delayed. The singularity in the sharp viscous vortex sheet is found to be different from that of the inviscid sheet in several features. A discontinuity in the curvature is formed in the viscous sheet, similarly as the inviscid sheet, but a cusp in the vortex sheet strength is less sharpened by viscosity. Exponential decay of the Fourier amplitudes is lost by the formation of the singularity, and the amplitudes of high wavenumbers exhibit an algebraic decay, while in the inviscid vortex sheet, the algebraic decay of the Fourier amplitudes is valid from fairly small wavenumbers. The algebraic decay rate of the viscous vortex sheet is approximately −2.5, independent of viscosity, which is the same rate as the asymptotic analysis of the inviscid sheet. Results for evolutions of the regularized vortex sheets show that the roll-up is weakened by viscosity, and the regularization parameter has more significant effects on the fine-structure of the core than does viscosity.
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47.32.-y Vortex dynamics; rotating fluids
02.30.Nw Fourier analysis
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