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Feb 2013

Volume 25, Issue 2, Articles (02xxxx)

Issue Cover Spotlight Figure

Phys. Fluids 25, 025102 (2013); http://dx.doi.org/10.1063/1.4790640 (31 pages)

T. A. Casey, J. Sakakibara, and S. T. Thoroddsen
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back to top Biofluid Mechanics

Stability of passive locomotion in inviscid wakes

Babak G. Oskouei and Eva Kanso

Phys. Fluids 25, 021901 (2013); http://dx.doi.org/10.1063/1.4789901 (12 pages)

Online Publication Date: 8 February 2013

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We consider the passive locomotion of rigid bodies in inviscid point-vortex wakes. This work is motivated by a common belief that live and inanimate objects may extract energy from unsteady flows for locomotory advantages. Studies on energy extraction from unsteady flows focus primarily on energy efficiency. Besides efficiency, a fundamental aspect of energy extraction for locomotion purposes is stability of motion. Here, we propose idealized wake models using periodically generated point vortices to emulate shedding of vortices from an un-modeled moving or stationary object. We assess the stability of these point-vortex wakes and find that they are stable for a range of periods, unlike the von Kármán street model which is mainly unstable. We then investigate the dynamics of a rigid body submerged in such wakes. In particular, we calculate periodic trajectories where the rigid body “swims” passively against the flow by extracting energy from the ambient vortices. All the periodic trajectories we find are unstable. The largest instabilities reported are for elliptic bodies where rotational effects play a role in destabilizing their motion. Within the context of this model, we conclude that passive locomotion of rigid bodies in inviscid wakes is unstable. Questions as to whether passive stability can be achieved when accounting for fluid viscosity and body elasticity remain open.
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47.20.Cq Inviscid instability
47.27.wb Turbulent wakes
47.32.cd Vortex stability and breakdown
47.11.-j Computational methods in fluid dynamics
FREE

Aerodynamic forces and vortical structures in flapping butterfly's forward flight

Naoto Yokoyama, Kei Senda, Makoto Iima, and Norio Hirai

Phys. Fluids 25, 021902 (2013); http://dx.doi.org/10.1063/1.4790882 (24 pages)

Online Publication Date: 21 February 2013

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Forward flights of a bilaterally symmetrically flapping butterfly modeled as a four-link rigid-body system consisting of a thorax, an abdomen, and left and right wings are numerically simulated. The joint motions of the butterflies are adopted from experimental observations. Three kinds of the simulations, distinguished by ways to determine the position and attitude of the thorax, are carried out: a tethered simulation, a prescribed simulation, and free-flight simulations. The upward and streamwise forces as well as the wake structures in the tethered simulation, where the thorax of the butterfly is fixed, reasonably agree with those in the corresponding tethered experiment. In the prescribed simulation, where the thoracic trajectories as well as the joint angles are given by those observed in a free-flight experiment, it is confirmed that the butterfly can produce enough forces to achieve the flapping flights. Moreover, coherent vortical structures in the wake and those on the wings are identified. The generation of the aerodynamic forces due to the vortical structures are also clarified. In the free-flight simulation, where only the joint angles are given as periodic functions of time, it is found that the free flight is longitudinally unstable because the butterfly cannot maintain the attitude in a proper range. Focusing on the abdominal mass, which largely varies owing to feeding and metabolizing, we have shown that the abdominal motion plays an important role in periodic flights. The necessity of control of the thoracic attitude for periodic flights and maneuverability is also discussed.
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47.85.Gj Aerodynamics
87.19.rj Contraction
02.60.Cb Numerical simulation; solution of equations
47.32.-y Vortex dynamics; rotating fluids
back to top Micro- and Nanofluid Mechanics

Sample dispersion in isotachophoresis with Poiseuille counterflow

Somnath Bhattacharyya, Partha P. Gopmandal, Tobias Baier, and Steffen Hardt

Phys. Fluids 25, 022001 (2013); http://dx.doi.org/10.1063/1.4789967 (15 pages)

Online Publication Date: 8 February 2013

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A particular mode of isotachophoresis (ITP) employs a pressure-driven flow opposite to the sample electromigration direction in order to anchor a sample zone at a specific position along a channel or capillary. We investigate this situation using a two-dimensional finite-volume model based on the Nernst-Planck equation. The imposed Poiseuille flow profile leads to a significant dispersion of the sample zone. This effect is detrimental for the resolution in analytical applications of ITP. We investigate the impact of convective dispersion, characterized by the area-averaged width of a sample zone, for various values of the sample Péclet-number, as well as the relative mobilities of the sample and the adjacent electrolytes. A one-dimensional model for the area-averaged concentrations based on a Taylor-Aris-type effective axial diffusivity is shown to yield good agreement with the finite-volume calculations. This justifies the use of such simple models and opens the door for the rapid simulation of ITP protocols with Poiseuille counterflow.
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47.60.Dx Flows in ducts and channels
02.60.Cb Numerical simulation; solution of equations
47.11.Df Finite volume methods
47.55.nb Capillary and thermocapillary flows
82.45.-h Electrochemistry and electrophoresis

Frequency dependence and frequency control of microbubble streaming flows

Cheng Wang, Bhargav Rallabandi, and Sascha Hilgenfeldt

Phys. Fluids 25, 022002 (2013); http://dx.doi.org/10.1063/1.4790803 (16 pages)

Online Publication Date: 13 February 2013

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Steady streaming from oscillating microbubbles is a powerful actuating mechanism in microfluidics, enjoying increased use due to its simplicity of manufacture, ease of integration, low heat generation, and unprecedented control over the flow field and particle transport. As the streaming flow patterns are caused by oscillations of microbubbles in contact with walls of the set-up, an understanding of the bubble dynamics is crucial. Here we experimentally characterize the oscillation modes and the frequency response spectrum of such cylindrical bubbles, driven by a pressure variation resulting from ultrasound in the range of 1 kHz ≲f≲ 100 kHz. We find that (i) the appearance of 2D streaming flow patterns is governed by the relative amplitudes of bubble azimuthal surface modes (normalized by the volume response), (ii) distinct, robust resonance patterns occur independent of details of the set-up, and (iii) the position and width of the resonance peaks can be understood using an asymptotic theory approach. This theory describes, for the first time, the shape oscillations of a pinned cylindrical bubble at a wall and gives insight into necessary mode couplings that shape the response spectrum. Having thus correlated relative mode strengths and observed flow patterns, we demonstrate that the performance of a bubble micromixer can be optimized by making use of such flow variations when modulating the driving frequency.
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47.55.dd Bubble dynamics
47.55.dr Interactions with surfaces
47.61.Fg Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)
47.61.Ne Micromixing
47.60.Dx Flows in ducts and channels
47.54.De Experimental aspects
FREE

Nanodrop impact on solid surfaces

Joel Koplik and Rui Zhang

Phys. Fluids 25, 022003 (2013); http://dx.doi.org/10.1063/1.4790807 (12 pages)

Online Publication Date: 15 February 2013

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The impact of nanometer sized drops on solid surfaces is studied using molecular dynamics simulations. Equilibrated floating drops consisting of short chains of Lennard-Jones liquids with adjustable volatility are directed normally onto an atomistic solid surface where they are observed to bounce, stick, splash, or disintegrate, depending on the initial velocity and the nature of the materials involved. Drops impacting at low velocity bounce from non-wetting surfaces but stick and subsequently spread slowly on wetting surfaces. Higher velocity impacts produce an prompt splash followed by disintegration of the drop, while at still higher velocity, drops disintegrate immediately. The disintegration can be understood as either a loss of coherence of the liquid or as the result of a local temperature exceeding the liquid-vapor coexistence value. In contrast to macroscopic drops, the presence of vapor outside the drop does not effect the behavior in any significant way. Nonetheless, the transition between the splashing and bouncing/sticking regimes occurs at Reynolds and Weber numbers similar to those found for larger drops.
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47.55.dr Interactions with surfaces
61.20.Ja Computer simulation of liquid structure
68.08.Bc Wetting
47.10.-g General theory in fluid dynamics
47.11.Mn Molecular dynamics methods
47.55.db Drop and bubble formation
back to top Interfacial Flows

Thin film flow down a porous substrate in the presence of an insoluble surfactant: Stability analysis

Anjalaiah, R. Usha, and S. Millet

Phys. Fluids 25, 022101 (2013); http://dx.doi.org/10.1063/1.4789459 (26 pages)

Online Publication Date: 1 February 2013

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The stability of a gravity-driven film flow on a porous inclined substrate is considered, when the film is contaminated by an insoluble surfactant, in the frame work of Orr-Sommerfeld analysis. The classical long-wave asymptotic expansion for small wave numbers reveals the occurrence of two modes, the Yih mode and the Marangoni mode for a clean/a contaminated film over a porous substrate and this is confirmed by the numerical solution of the Orr-Sommerfeld system using the spectral-Tau collocation method. The results show that the Marangoni mode is always stable and dominates the Yih mode for small Reynolds numbers; as the Reynolds number increases, the growth rate of the Yih mode increases, until, an exchange of stability occurs, and after that the Yih mode dominates. The role of the surfactant is to increase the critical Reynolds number, indicating its stabilizing effect. The growth rate increases with an increase in permeability, in the region where the Yih mode dominates the Marangoni mode. Also, the growth rate is more for a film (both clean and contaminated) over a thicker porous layer than over a thinner one. From the neutral stability maps, it is observed that the critical Reynolds number decreases with an increase in permeability in the case of a thicker porous layer, both for a clean and a contaminated film over it. Further, the range of unstable wave number increases with an increase in the thickness of the porous layer. The film flow system is more unstable for a film over a thicker porous layer than over a thinner one. However, for small wave numbers, it is possible to find the range of values of the parameters characterizing the porous medium for which the film flow can be stabilized for both a clean film/a contaminated film as compared to such a film over an impermeable substrate; further, it is possible to enhance the instability of such a film flow system outside of this stability window, for appropriate choices of the porous substrate characteristics.
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47.20.Dr Surface-tension-driven instability
47.35.-i Hydrodynamic waves
47.56.+r Flows through porous media
68.03.Cd Surface tension and related phenomena
68.15.+e Liquid thin films

Shape of a large drop on a rough hydrophobic surface

Joonsik Park, Jaebum Park, Hyuneui Lim, and Ho-Young Kim

Phys. Fluids 25, 022102 (2013); http://dx.doi.org/10.1063/1.4789494 (13 pages)

Online Publication Date: 1 February 2013

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Large drops on solid surfaces tend to flatten due to gravitational effect. Their shapes can be predicted by solving the Young-Laplace equation when their apparent contact angles are precisely given. However, for large drops sitting on rough surfaces, the apparent contact angles are often unavailable a priori and hard to define. Here we develop a model to predict the shape of a given volume of large drop placed on a rough hydrophobic surface using an overlapping geometry of double spheroids and the free energy minimization principle. The drop shape depends on the wetting state, thus our model can be used not only to predict the shape of a drop but also to infer the wetting state of a large drop through the comparison of theory and experiment. The experimental measurements of the shape of large water drops on various micropillar arrays agree well with the model predictions. Our theoretical model is particularly useful in predicting and controlling shapes of large drops on surfaces artificially patterned in microscopic scales, which are frequently used in microfluidics and lab-on-a-chip technology.
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47.55.dr Interactions with surfaces
47.85.L- Flow control
68.03.Cd Surface tension and related phenomena
68.08.Bc Wetting
47.54.Bd Theoretical aspects

Longitudinal instability of a liquid rim

Gilou Agbaglah, Christophe Josserand, and Stéphane Zaleski

Phys. Fluids 25, 022103 (2013); http://dx.doi.org/10.1063/1.4789971 (15 pages)

Online Publication Date: 4 February 2013

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We study the transverse instability of a retracting liquid rim using a long wavelength approximation model and full numerical simulations. We observe that the instability of the rim is driven both by the Rayleigh-Taylor mechanism because of the initial rim acceleration, and by the Rayleigh-Plateau one. The coupling between the rim and the sheet stabilizes the rim at long wavelength. Full numerical simulations are in good agreement with the model and the subsequent break-up of droplets is observed in the numerical simulations when the instability is strong enough.
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47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.55.df Breakup and coalescence
02.60.Cb Numerical simulation; solution of equations
02.60.Gf Algorithms for functional approximation
47.11.-j Computational methods in fluid dynamics

The effect of viscoelasticity on the dynamics of gas bubbles near free surfaces

S. J. Lind and T. N. Phillips

Phys. Fluids 25, 022104 (2013); http://dx.doi.org/10.1063/1.4790512 (32 pages)

Online Publication Date: 15 February 2013

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The dynamics of bubbles immersed in a viscoelastic fluid directly beneath an initially plane free surface is modelled using the boundary integral method. The model predicts a range of dynamics that is dependent on the Deborah number, the Reynolds number and the proximity of the bubble to the free surface. The motion of the free surface jet caused by the collapse of a bubble in a viscoelastic fluid can be significantly retarded compared with the Newtonian case. The axial jet predicted in many instances in the Newtonian case is not observed when the inertial forces are sufficiently small. In this case an annular jet forms that can penetrate the bubble. At high Deborah numbers, there is a return to Newtonian-like dynamics since the effects of viscosity are abated by elasticity to such an extent that inertia is the prevailing influence on bubble dynamics.
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47.50.Cd Modeling
47.55.dd Bubble dynamics
51.20.+d Viscosity, diffusion, and thermal conductivity
02.60.Nm Integral and integrodifferential equations

Film drainage of viscous liquid on top of bare bubble: Influence of the Bond number

Helena Kočárková, Florence Rouyer, and Franck Pigeonneau

Phys. Fluids 25, 022105 (2013); http://dx.doi.org/10.1063/1.4792310 (14 pages)

Online Publication Date: 25 February 2013

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We present experimental results of film drainage on top of gas bubbles pushed by gravity towards the free surface of highly viscous Newtonian liquid with a uniform interface tension. The temporal evolution of the thickness of the film between a single bubble and the air/liquid interface is investigated via interference method. Experiments under various physical conditions (range of viscosities and surface tension of the liquid, and bubble sizes) evidence the influence of the deformation of the thin film on the thinning rate and confirm the slow down of film drainage with Bond number as previously reported by numerical work of Pigeonneau and Sellier [Phys. Fluids 23, 092102 (2011)]10.1063/1.3629815. Considering the liquid flow in the cap squeezed by buoyancy force of the bubble, we provide an approximation of thinning rate as a function of Bond number that agrees with experimental and numerical data. Qualitatively, the smaller the area of the thin film compare to the surface of the bubble, the faster the drainage.
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47.55.dd Bubble dynamics
68.03.Cd Surface tension and related phenomena
68.15.+e Liquid thin films
66.20.-d Viscosity of liquids; diffusive momentum transport
47.55.Ca Gas/liquid flows
back to top Viscous and Non-Newtonian Flows

Rayleigh-Bénard convection for viscoplastic fluids

Mohamed Darbouli, Christel Métivier, Jean-Michel Piau, Albert Magnin, and Ahmed Abdelali

Phys. Fluids 25, 023101 (2013); http://dx.doi.org/10.1063/1.4790521 (15 pages)

Online Publication Date: 8 February 2013

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The influence of rheological and interfacial properties of yield stress fluids is investigated on the onset of the Rayleigh-Bénard convection. Different Carbopol® (B.F. Goodrich) gels are used in a circular cell for Rayleigh-Bénard experimental setup. The influence of the boundary conditions is also investigated by controlling either slip or no-slip conditions. The onset of thermoconvection is shown by measuring temperature differences and also by using shadowgraph flow visualization. Experimental results show that convection occurs in the range of our experiments. Considering Carbopol gels as elasto-plastic materials with a yield stress τy, a generalized Rayleigh number is obtained: Rag = Y−1, with Y the yield number, which represents the balance between the yield stress of the gel and the buoyancy effects. The results show that the Rayleigh number is proportional to d, the height of the setup, and that the control parameter is the yield number at the onset of convection. Critical values of Y−1 have been determined for slip conditions 1/YcS ≈ 40 as well as for no-slip conditions 1/YcNS ≈ 80. It highlights that the change in surface conditions affect significantly the critical conditions.
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83.60.La Viscoplasticity; yield stress
47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.45.Gx Slip flows and accommodation
47.55.pb Thermal convection
47.57.-s Complex fluids and colloidal systems
47.80.Jk Flow visualization and imaging
back to top Particulate, Multiphase, and Granular Flows

Longitudinal and transverse disturbances in unbounded, gas-fluidized beds

K. Mandich and R. J. Cattolica

Phys. Fluids 25, 023301 (2013); http://dx.doi.org/10.1063/1.4789498 (18 pages)

Online Publication Date: 6 February 2013

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A temporal linear stability analysis is performed on the continuum-averaged equations of motion for the fluid and dispersed particle phases which describe a uniform, boundless fluidized bed. The present analysis considers disturbances ranging from purely transverse to purely longitudinal, with respect to the flow direction of the base-state fluid velocity. It is found that disturbances over the entire horizontal-vertical wavenumber spectrum may be unstable, although the dominant disturbance is either the classically recognized longitudinal disturbance travelling in the vertical direction or a non-oscillating, purely transverse disturbance. The nature of the preferred mode depends upon the dimensionless parameters of the system. For all parameter cases the growth constants of the two modes remain within an order of magnitude of each other, thereby highlighting the importance of both modes in stability considerations of this system. Dispersion relations for each of the separated horizontal and vertical modes are derived and long-wavelength analyses are performed on the corresponding relations. It is shown that the unstable transverse mode shares similar mechanisms with the longitudinal mode, and that the dominant stabilizing mechanism for each mode is the same for closely-packed beds.
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47.55.Lm Fluidized beds
47.20.-k Flow instabilities
47.55.Kf Particle-laden flows

Unconfined slumping of a granular mass on a slope

Fukashi Maeno, Andrew J. Hogg, R. Stephen J. Sparks, and Gary P. Matson

Phys. Fluids 25, 023302 (2013); http://dx.doi.org/10.1063/1.4792707 (22 pages)

Online Publication Date: 25 February 2013

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This study investigates the gravitationally driven dynamics of dense granular materials, released from rest and allowed to flow down a slope until they stop moving. Laboratory experiments were performed in which a measured volume of material was released from rest in a cylindrical tube and spread across an unconfined rigid plane inclined at angles less than the angle of repose. Upon release, the particles initially spread outward radially. However, up-slope motion is rapidly suppressed while down-slope motion is promoted, which leads to an approximately ellipsoidally shaped deposit once the flow has been fully arrested. The flows were modeled under the shallow layer approximation and integrated numerically to capture the motion from initiation to final arrest. In modeling, two types of Coulomb-type friction models were employed. One had a constant friction coefficient, and another had a friction coefficient that depends upon the dimensionless inertial number of the motion. When the initial aspect ratio of a granular mass is small and the slope angle is low (<5°), the model with a constant friction coefficient can capture the shape of the deposit. However, when the slope angle is increased, the friction model that is dependent on inertial number becomes more important. For granular columns of initially high aspect ratios, the shallow water model fails to reproduce some aspects of the experimental observations. Finally, the dependence of the shape and depth of the deposit upon dimensionless parameters that characterize the system is examined under the constant friction coefficient model, demonstrating that the deduced scaling arguments are borne out by the numerical simulations and laboratory data.
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47.57.Gc Granular flow
45.70.Mg Granular flow: mixing, segregation and stratification
47.60.Dx Flows in ducts and channels
47.11.-j Computational methods in fluid dynamics
02.60.Cb Numerical simulation; solution of equations
47.10.-g General theory in fluid dynamics
back to top Laminar Flows

Unsteady separated stagnation-point flow of an incompressible viscous fluid on the surface of a moving porous plate

S. Dholey and A. S. Gupta

Phys. Fluids 25, 023601 (2013); http://dx.doi.org/10.1063/1.4788713 (18 pages)

Online Publication Date: 6 February 2013

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Using group-theoretic method, an analysis is presented for a similarity solution of boundary layer equations which represents an unsteady two-dimensional separated stagnation-point (USSP) flow of an incompressible fluid over a porous plate moving in its own plane with speed u0(t). It is observed that the solution to the governing nonlinear ordinary differential equation for the USSP flow admits of two solutions (in contrast with the corresponding steady flow where the solution is unique): one is the attached flow solution (AFS) and the other is the reverse flow solution (RFS). A novel result of the analysis is that in the case of stationary plate (u0(t) = 0), after a certain value of the magnitude of the blowing d (<0) at the plate, only the AFS exists and the solution becomes unique. For a stationary plate (u0(t) = 0), the USSP flow is found to be separated for all values of d in both the cases of AFS and RFS. It is also observed that when u0(t) = 0, in the RFS flow with wall suction d (>0), there are two stagnation-points in the flow but in the presence of blowing d (<0), there is only one stagnation-point in the flow which moves further and further up with increase in |d|. Suction is shown to increase the wall shear stress while blowing has an opposite effect. Streamlines for an USSP flow when u0(t) ≠ 0 are also plotted. It is found that in this case, the USSP flow is not in general separated.
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47.20.Ib Instability of boundary layers; separation
47.32.Ff Separated flows
47.56.+r Flows through porous media
02.20.-a Group theory
02.30.Hq Ordinary differential equations
47.15.Cb Laminar boundary layers

Deformation of vortex patches by boundaries

A. Crosby, E. R. Johnson, and P. J. Morrison

Phys. Fluids 25, 023602 (2013); http://dx.doi.org/10.1063/1.4790809 (19 pages)

Online Publication Date: 13 February 2013

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The deformation of two-dimensional vortex patches in the vicinity of fluid boundaries is investigated. The presence of a boundary causes an initially circular patch of uniform vorticity to deform. Sufficiently far away from the boundary, the deformed shape is well approximated by an ellipse. This leading order elliptical deformation is investigated via the elliptic moment model of Melander, Zabusky, and Styczek [J. Fluid Mech. 167, 95 (1986)10.1017/S0022112086002744]. When the boundary is straight, the centre of the elliptic patch remains at a constant distance from the boundary, and the motion is integrable. Furthermore, since the straining flow acting on the patch is constant in time, the problem is that of an elliptic vortex patch in constant strain, which was analysed by Kida [J. Phys. Soc. Jpn. 50, 3517 (1981)10.1143/JPSJ.50.3517]. For more complicated boundary shapes, such as a square corner, the motion is no longer integrable. Instead, there is an adiabatic invariant for the motion. This adiabatic invariant arises due to the separation in times scales between the relatively rapid time scale associated with the rotation of the patch and the slower time scale associated with the self-advection of the patch along the boundary. The interaction of a vortex patch with a circular island is also considered. Without a background flow, the conservation of angular impulse implies that the motion is again integrable. The addition of an irrotational flow past the island can drive the patch towards the boundary, leading to the possibility of large deformations and breakup.
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47.32.Ef Rotating and swirling flows
47.32.Ff Separated flows
47.54.Bd Theoretical aspects
47.55.Hd Stratified flows
47.10.-g General theory in fluid dynamics
47.32.C- Vortex dynamics

Numerical simulation of vortex-induced vibration of a square cylinder at a low Reynolds number

Ming Zhao, Liang Cheng, and Tongming Zhou

Phys. Fluids 25, 023603 (2013); http://dx.doi.org/10.1063/1.4792351 (25 pages)

Online Publication Date: 27 February 2013

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Vortex-induced vibrations (VIV) of a square cylinder at a Reynolds number of 100 and a low mass ratio of 3 are studied numerically by solving the Navier-Stokes equations using the finite element method. The equation of motion of the square cylinder is solved to simulate the vibration and the Arbitrary Lagrangian Eulerian scheme is employed to model the interaction between the vibrating cylinder and the fluid flow. The numerical model is validated against the published results of flow past a stationary square cylinder and the results of VIV of a circular cylinder at low Reynolds numbers. The effect of flow approaching angle (α) on the response of the square cylinder is investigated. It is found that α affects not only the vibration amplitude but also the lock-in regime. Among the three values of α (α = 0°, 45°, and 22.5°) that are studied, the smallest vibration amplitude and the narrowest lock-in regime occur at α = 0°. It is discovered that the vibration locks in with the natural frequency in two regimes of reduced velocity for α = 22.5°. Single loop vibration trajectories are observed in the lock-in regime at α = 22.5° and 45°, which is distinctively different from VIV of a circular cylinder. As a result, the vibration frequency in the in-line direction is the same as that in the cross-flow direction.
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47.32.-y Vortex dynamics; rotating fluids
47.15.ki Inviscid flows with vorticity
47.11.Fg Finite element methods
02.70.Dh Finite-element and Galerkin methods
47.10.ad Navier-Stokes equations
back to top Instability and Transition

Dissolution-driven convection in a Hele–Shaw cell

Anja C. Slim, M. M. Bandi, Joel C. Miller, and L. Mahadevan

Phys. Fluids 25, 024101 (2013); http://dx.doi.org/10.1063/1.4790511 (20 pages)

Online Publication Date: 15 February 2013

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Motivated by convection in the context of geological carbon-dioxide (CO2) storage, we present an experimental study of dissolution-driven convection in a Hele–Shaw cell for Rayleigh numbers R in the range 100<R<1700. We use potassium permanganate (KMnO4) in water as an analog for CO2 in brine and infer concentration profiles at high spatial and temporal resolution and accuracy from transmitted light intensity. We describe behavior from first contact up to 65% average saturation and measure several global quantities including dissolution flux, average concentration, amplitude of perturbations away from pure one-dimensional diffusion, and horizontally averaged concentration profiles. We show that the flow evolves successively through distinct regimes starting with a simple one-dimensional diffusional profile. This is followed by linear growth in which fingers are initiated and grow quasi-exponentially, independently of one-another. Once the fingers are well-established, a flux-growth regime begins as fresh fluid is brought to the interface and contaminated fluid removed, with the flux growing to a local maximum. During this regime, fingers still propagate independently. However, beyond the flux maximum, fingers begin to interact and zip together from the root down in a merging regime. Several generations of merging occur before only persistent primary fingers remain. Beyond this, the reinitiation regime begins with new fingers created between primary existing ones before merging into them. Through appropriate scaling, we show that the regimes are universal and independent of layer thickness (equivalently R) until the fingers hit the bottom. At this time, progression through these regimes is interrupted and the flow transitions to a saturating regime. In this final regime, the flux gradually decays in a manner well described by a Howard-style phenomenological model.
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89.60.-k Environmental studies
91.67.-y Geochemistry
44.25.+f Natural convection
51.20.+d Viscosity, diffusion, and thermal conductivity

Study of instabilities and quasi-two-dimensional turbulence in volumetrically heated magnetohydrodynamic flows in a vertical rectangular duct

N. Vetcha, S. Smolentsev, M. Abdou, and R. Moreau

Phys. Fluids 25, 024102 (2013); http://dx.doi.org/10.1063/1.4791605 (24 pages)

Online Publication Date: 15 February 2013

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We consider magnetohydrodynamic (MHD) rectangular duct flows with volumetric heating. The flows are upward, subject to a strong transverse magnetic field perpendicular to the temperature gradient, such that the flow dynamics is quasi-two-dimensional. The internal volumetric heating imitates conditions of a blanket of a fusion power reactor, where a buoyancy-driven flow is imposed on the forced flow. Studies of this mixed-convection flow include analysis for the basic flow, linear stability analysis and Direct Numerical Simulation (DNS)-type computations. The parameter range covers the Hartmann number (Ha) up to 500, the Reynolds number (Re) from 1000 to 10 000, and the Grashof number (Gr) from 105 to 5 × 108. The linear stability analysis predicts two primary instability modes: (i) bulk instability associated with the inflection point in the velocity profile near the “hot” wall and (ii) side-wall boundary layer instability. A mixed instability mode is also possible. An equation for the critical Hartmann number has been obtained as a function of Re and Gr. Effects of Ha, Re, and Gr on turbulent flows are addressed via nonlinear computations that demonstrate two characteristic turbulence regimes. In the “weak” turbulence regime, the induced vortices are localized near the inflection point of the basic velocity profile, while the boundary layer at the wall parallel to the magnetic field is slightly disturbed. In the “strong” turbulence regime, the bulk vortices interact with the boundary layer causing its destabilization and formation of secondary vortices that may travel across the flow, even reaching the opposite wall. In this regime, the key phenomena are vortex-wall and various vortex-vortex interactions. Flow and magnetic field effects on heat transfer are also analyzed.
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47.20.Ib Instability of boundary layers; separation
47.27.nb Boundary layer turbulence
47.27.nf Flows in pipes and nozzles
47.32.cd Vortex stability and breakdown
47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.60.Dx Flows in ducts and channels

Crucial flow stabilization and multiple instability branches of gravity-driven films over topography

Thilo Pollak and Nuri Aksel

Phys. Fluids 25, 024103 (2013); http://dx.doi.org/10.1063/1.4790434 (12 pages)

Online Publication Date: 21 February 2013

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In this paper, we present experimental results on the linear instability of gravity-driven viscous films flowing down a strongly undulated incline. To systematically investigate the relation between the eddies which form in the troughs of sufficiently steep undulations and the corresponding stability maps, we vary the liquid's viscosity experimentally. We report on a rich variety of phenomena, which is provoked by the corrugation of the underlying substrate, including: (a) transitions from long-wave to short-wave type instability, (b) a disjoining of the instability branches leading to formation of isles in the stability map, (c) flow destabilization, but also, (d) very strong stabilization of the flow up to a factor of two for arbitrary linear disturbances and even up to a factor of four for linear short-wave disturbances. To our knowledge, this is the first experimental work, which reports on any of these phenomena for gravity-driven liquids flowing down an undulated incline. Since structured substrates turn out to hold an enormous potential for crucial film flow stabilization, we present a first approach for a topography shape, based on the shape of the eddy, which is optimized in terms of flow stability.
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47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.55.nd Spreading films
68.15.+e Liquid thin films
66.20.-d Viscosity of liquids; diffusive momentum transport

The impact of deformable interfaces and Poiseuille flow on the thermocapillary instability of three immiscible phases confined in a channel

Nicolas J. Alvarez and A. Kerem Uguz

Phys. Fluids 25, 024104 (2013); http://dx.doi.org/10.1063/1.4790878 (15 pages)

Online Publication Date: 25 February 2013

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The majority of studies considering thermocapillary convection in multilayer systems assume the interface is rigid (non-deformable) and the fluids are stationary. Motivated by the potential of using thermally generated convection patterns in moving droplets for mixing, this paper re-examines the Marangoni-Bénard instability for a three-layer system with deformable interfaces undergoing Poiseuille flow. Taking into account the deformability of the interface reveals new physics. Linear stability analysis shows that at small wave numbers a deformable interface is of the orders of magnitude less stable than a non-deformable interface. At large wave numbers, both a rigid and a deformable interface have the same stability. Furthermore, a base planar Poiseuille flow affects the linear stability of the system and the type of instability when the interface is allowed to deform. Flow stabilizes an already unstable system and works to destabilize a stable system. Lastly, the dependence of the linear stability of the system on viscosity ratio, depth ratio, and Prandtl number, Pr, experimentally adjustable parameters, is discussed. Whereas Pr has little effect on the stability of the system, we show that a small viscosity ratio and a large depth ratio are advantageous in making the system unstable.
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47.15.Fe Stability of laminar flows
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.55.dm Thermocapillary effects
47.55.Hd Stratified flows
47.55.nb Capillary and thermocapillary flows
47.60.Dx Flows in ducts and channels
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Convectons and secondary snaking in three-dimensional natural doubly diffusive convection

Cédric Beaume, Alain Bergeon, and Edgar Knobloch

Phys. Fluids 25, 024105 (2013); http://dx.doi.org/10.1063/1.4792711 (15 pages)

Online Publication Date: 27 February 2013

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Natural doubly diffusive convection in a three-dimensional vertical enclosure with square cross-section in the horizontal is studied. Convection is driven by imposed temperature and concentration differences between two opposite vertical walls. These are chosen such that a pure conduction state exists. No-flux boundary conditions are imposed on the remaining four walls, with no-slip boundary conditions on all six walls. Numerical continuation is used to compute branches of spatially localized convection. Such states are referred to as convectons. Two branches of three-dimensional convectons with full symmetry bifurcate simultaneously from the conduction state and undergo homoclinic snaking. Secondary bifurcations on the primary snaking branches generate secondary snaking branches of convectons with reduced symmetry. The results are complemented with direct numerical simulations of the three-dimensional equations.
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47.57.eb Diffusion and aggregation
47.27.te Turbulent convective heat transfer
44.25.+f Natural convection
47.11.-j Computational methods in fluid dynamics
47.27.ek Direct numerical simulations
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits

Dielectrophoretic force-driven thermal convection in annular geometry

Harunori N. Yoshikawa, Olivier Crumeyrolle, and Innocent Mutabazi

Phys. Fluids 25, 024106 (2013); http://dx.doi.org/10.1063/1.4792833 (14 pages)

Online Publication Date: 27 February 2013

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The thermal convection driven by the dielectrophoretic force is investigated in annular geometry under microgravity conditions. A radial temperature gradient and a radial alternating electric field are imposed on a dielectric fluid that fills the gap of two concentric infinite-length cylinders. The resulting dielectric force is regarded as thermal buoyancy with a radial effective gravity. This electric gravity varies in space and may change its sign depending on the temperature gradient and the cylinder radius ratio. The linear stability problem is solved by a spectral-collocation method. The critical mode is stationary and non-axisymmetric. The critical Rayleigh number and wavenumbers depend sensitively on the electric gravity and the radius ratio. The mechanism behind the instability is examined from an energetic viewpoint. The instability in wide gap annuli is an exact analogue to the gravity-driven thermal instability.
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47.55.pb Thermal convection
82.45.-h Electrochemistry and electrophoresis
47.60.Dx Flows in ducts and channels
47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
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Mixed-mode instability of a miscible interface due to coupling between Rayleigh-Taylor and double-diffusive convective modes

J. Carballido-Landeira, P. M. J. Trevelyan, C. Almarcha, and A. De Wit

Phys. Fluids 25, 024107 (2013); http://dx.doi.org/10.1063/1.4790192 (10 pages)

Online Publication Date: 28 February 2013

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In a gravitational field, a horizontal interface between two miscible fluids can be buoyantly unstable because of double diffusive effects or because of a Rayleigh-Taylor instability arising when a denser fluid lies on top of a less dense one. We show here both experimentally and theoretically that, besides such classical buoyancy-driven instabilities, a new mixed mode dynamics exists when these two instabilities act cooperatively. This is the case when the upper denser solution contains a solute A, which diffuses sufficiently faster than a solute B initially in the lower layer to yield non-monotonic density profiles after contact of the two solutions. We derive analytically the conditions for existence of this mixed mode in the (R, δ) parameter plane, where R is the buoyancy ratio between the two solutions and δ is the ratio of diffusion coefficient of the solutes. We find an excellent agreement of these theoretical predictions with experiments performed in Hele-Shaw cells and with numerical simulations.
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47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.55.pd Multidiffusive convection
02.60.Cb Numerical simulation; solution of equations
47.11.-j Computational methods in fluid dynamics
47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
back to top Turbulent Flows

Implicit large-eddy simulation of passive scalar mixing in statistically stationary isotropic turbulence

A. J. Wachtor, F. F. Grinstein, C. R. DeVore, J. R. Ristorcelli, and L. G. Margolin

Phys. Fluids 25, 025101 (2013); http://dx.doi.org/10.1063/1.4783924 (19 pages) | Cited 3 times

Online Publication Date: 4 February 2013

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Turbulent mixing of a passive scalar by forced isotropic turbulence with a prescribed mean scalar gradient is studied in the context of implicit large-eddy simulation. The simulation strategy uses a multi-dimensional compressible flux-corrected transport algorithm, with low wavenumber momentum forcing imposed separately for the solenoidal and dilatational velocity components. Effects of grid resolution on the flow and scalar mixing are investigated at turbulent Mach numbers 0.13 and 0.27. Turbulence metrics are used to show that an implicit large-eddy simulation can accurately capture the mixing transition and asymptotic self-similar behaviors predicted by previous theoretical, laboratory, and direct numerical simulation studies, including asymptotically constant scalar variance and increasing velocity-to-scalar Taylor micro-scales ratio as function of effective Reynolds number determined by grid resolution. The results demonstrate the feasibility of predictive under-resolved simulations of high Reynolds number turbulent scalar mixing using implicit large-eddy simulation.
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47.27.Gs Isotropic turbulence; homogeneous turbulence
47.27.wj Turbulent mixing layers
47.40.Dc General subsonic flows
47.11.-j Computational methods in fluid dynamics
47.27.ep Large-eddy simulations
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Scanning tomographic particle image velocimetry applied to a turbulent jet

T. A. Casey, J. Sakakibara, and S. T. Thoroddsen

Phys. Fluids 25, 025102 (2013); http://dx.doi.org/10.1063/1.4790640 (31 pages)

Online Publication Date: 21 February 2013

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multimedia

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We introduce a modified tomographic PIV technique using four high-speed video cameras and a scanning pulsed laser-volume. By rapidly illuminating adjacent subvolumes onto separate video frames, we can resolve a larger total volume of velocity vectors, while retaining good spatial resolution. We demonstrate this technique by performing time-resolved measurements of the turbulent structure of a round jet, using up to 9 adjacent volume slices. In essence this technique resolves more velocity planes in the depth direction by maintaining optimal particle image density and limiting the number of ghost particles. The total measurement volumes contain between 1 ×106 and 3 ×106 velocity vectors calculated from up to 1500 reconstructed depthwise image planes, showing time-resolved evolution of the large-scale vortical structures for a turbulent jet of Re up to 10 000.
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47.80.Jk Flow visualization and imaging
42.62.Eh Metrological applications; optical frequency synthesizers for precision spectroscopy
47.27.wg Turbulent jets
47.32.C- Vortex dynamics
47.80.Cb Velocity measurements
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