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Jul 2012

Volume 24, Issue 7, Articles (07xxxx)

Issue Cover Spotlight Figure

Phys. Fluids 24, 074107 (2012); http://dx.doi.org/10.1063/1.4733396 (21 pages)

P. Ramaprabhu, Guy Dimonte, P. Woodward, C. Fryer, G. Rockefeller, K. Muthuraman, P.-H. Lin, and J. Jayaraj
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back to top Micro- and Nanofluid Mechanics

Liquid flow retardation in nanospaces due to electroviscosity: Electrical double layer overlap, hydrodynamic slippage, and ambient atmospheric CO2 dissolution

Chih-Chang Chang, Ruey-Jen Yang, Moran Wang, Jiun-Jih Miau, and Vadim Lebiga

Phys. Fluids 24, 072001 (2012); http://dx.doi.org/10.1063/1.4732547 (23 pages) | Cited 1 time

Online Publication Date: 10 July 2012

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A theoretical investigation is performed into the electroviscous-induced retardation of liquid flows through finitely long nanochannels or nanotubes with large wells at either end. Given the assumption of equilibrium conditions between the ionic solution in the wells and that within the nanochannel or nanotube, an exact solution is derived for the overlapped electrical double layer (EDL) for the case where the concentrations of the positive and negative ions in the wells may be unequal. The ion concentrations in the wells are determined by the conditions of global electroneutrality and mass conservation. It is shown that the overlapped EDL model proposed by Baldessari and Santiago [J. Colloid Interface Sci. 325, 526 (2008)10.1016/j.jcis.2008.06.007] is in fact the same as the “thick EDL model” (i.e., the traditional Poisson-Boltzmann model) when the positive and negative ion concentrations in the large enough wells are both equal to the bulk concentration of the salt solution. Utilizing the proposed overlapped EDL analytical model, an investigation is performed to evaluate the effects of hydrodynamic slippage on the flow retardation caused by electroviscosity in nanochannels or nanotubes. Furthermore, exact and approximate solutions are derived for the electroviscosity in ion-selective nanochannels and nanotubes. It is shown that in the absence of slip, the maximum electroviscosity in nanochannels and nanotubes containing a unipolar solution of simple monovalent counter-ions occurs at surface charge densities of h|σ| = 0.32 nm × C/m2 and a|σ| ≈ 0.4 nm × C/m2, respectively. In addition, it is shown that the electroviscosity in a nanotube is smaller than that in a nanochannel. For example, given a LiCl solution, the maximum electroviscosites in a non-slip nanochannel and non-slip nanotube are ηa/η ≈ 1.6 and 1.47, respectively. For both nanospaces, the electroviscosity is greatly increased when the liquid slip effect is taken into account. Significantly, under slip conditions, the electroviscosity in the nanotube is greater than that in the nanochannel. Finally, an investigation is performed into the effects of ambient atmospheric CO2 dissolution on the electroviscosities of salt/buffer solution and deionized (DI) water in silica nanochannels. The results show that the electroviscosity of CO2-saturated DI water (pH = 5.6) can be reasonably neglected in silica nanochannels with a height of less than 100 nm.
Show PACS
47.61.Fg Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)
47.65.Gx Electrorheological fluids
47.45.Gx Slip flows and accommodation
back to top Interfacial Flows

Reduced equations of motion of the interface of dielectric liquids in vertical electric and gravitational fields

Evgeny A. Kochurin and Nikolay M. Zubarev

Phys. Fluids 24, 072101 (2012); http://dx.doi.org/10.1063/1.4733395 (17 pages)

Online Publication Date: 9 July 2012

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The dynamics of the interface between two dielectric fluids in the presence of vertical electric and gravitational fields is studied theoretically. It is shown that, in the particular case where the rate of change of the electric field is proportional to the effective gravitational acceleration, a special flow regime can be realized for which the velocity and electric potentials are linearly dependent functions. This means that there exists a frame of reference in which liquids move along the electric field lines. We derive and analyze the corresponding reduced equations of motion of a liquid-liquid interface. For small density ratio, they turn into the equations describing the Laplacian growth. In the case of two spatial dimensions, we show that these equations determine the asymptotic behavior of the system. For arbitrary density ratios, the Laplacian growth equations adequately describe the initial (weakly nonlinear) stage of the interface instability development. The integrability of these equations makes it possible to investigate the evolution of nonlinear waves at the boundary and, in particular, to demonstrate the tendency to the formation of singularities (cusps).
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47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
77.84.Nh Liquids, emulsions, and suspensions; liquid crystals
47.35.Bb Gravity waves
47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.11.-j Computational methods in fluid dynamics

Buckling instability of squeezed droplets

Gwynn J. Elfring and Eric Lauga

Phys. Fluids 24, 072102 (2012); http://dx.doi.org/10.1063/1.4731795 (15 pages) | Cited 1 time

Online Publication Date: 16 July 2012

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Motivated by recent experiments, we consider theoretically the compression of droplets pinned at the bottom on a surface of finite area. We show that if the droplet is sufficiently compressed at the top by a surface, it will always develop a shape instability at a critical compression. When the top surface is flat, the shape instability occurs precisely when the apparent contact angle of the droplet at the pinned surface is π, regardless of the contact angle of the upper surface, reminiscent of a past work on liquid bridges and sessile droplets as first observed by Plateau. After the critical compression, the droplet transitions from a symmetric to an asymmetric shape. The force required to deform the droplet peaks at the critical point then progressively decreases the indicative of catastrophic buckling. We characterize the transition in droplet shape using illustrative examples in two dimensions followed by perturbative analysis as well as numerical simulation in three dimensions. When the upper surface is not flat, the simple apparent contact angle criterion no longer holds, and a detailed stability analysis is carried out to predict the critical compression.
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47.55.dk Surfactant effects
47.20.Dr Surface-tension-driven instability
68.03.Cd Surface tension and related phenomena
64.70.fh Boiling and bubble dynamics
47.11.-j Computational methods in fluid dynamics
02.60.-x Numerical approximation and analysis

Stability of a viscous pinching thread

Jens Eggers

Phys. Fluids 24, 072103 (2012); http://dx.doi.org/10.1063/1.4732545 (11 pages)

Online Publication Date: 16 July 2012

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We consider the dynamics of a fluid thread near pinch-off, in the limit that inertial effects can be neglected. There exists an infinite hierarchy of similarity solutions corresponding to pinch-off. Only one of the similarity solutions (the “ground state”) is stable, all other solutions are linearly unstable to perturbations, and thus cannot be observed. Eigenvalues and eigenfunctions are calculated analytically.
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47.20.-k Flow instabilities
47.53.+n Fractals in fluid dynamics
02.10.Ud Linear algebra
47.11.-j Computational methods in fluid dynamics

Theory of the forced wetting transition

Tak Shing Chan, Jacco H. Snoeijer, and Jens Eggers

Phys. Fluids 24, 072104 (2012); http://dx.doi.org/10.1063/1.4736531 (10 pages) | Cited 3 times

Online Publication Date: 17 July 2012

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We consider a solid plate being withdrawn from a bath of liquid which it does not wet. At low speeds, the meniscus rises below a moving contact line, leaving the rest of the plate dry. At a critical speed of withdrawal, this solution bifurcates into another branch via a saddle-node bifurcation: two branches exist below the critical speed, the lower branch is stable, the upper branch is unstable. The upper branch eventually leads to a solution corresponding to film deposition. We add the local analysis of the upper branch of the bifurcation to a previous analysis of the lower branch. We thus provide a complete description of the dynamical wetting transition in terms of matched asymptotic expansions.
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47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
47.55.nd Spreading films
68.08.Bc Wetting
47.15.gm Thin film flows

Thermocapillary effects on steadily evaporating contact line: A perturbative local analysis

Adel M. Benselama, Souad Harmand, and Khellil Sefiane

Phys. Fluids 24, 072105 (2012); http://dx.doi.org/10.1063/1.4732151 (38 pages) | Cited 1 time

Online Publication Date: 20 July 2012

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The evaporation process taking place close to the three-phase contact line is considered and studied theoretically using a linear stability analysis approach. A domain perturbation method, taking into consideration thermocapillary effects and surface forces, is used to develop the higher-order solution in terms of series expansion about lubrication condition. A closed-form solution is found for the film thickness, the pressure jump across the liquid-vapor interface and the evaporative flux in the vicinity of the contact line. The key novelty in this work is considering thermocapillary instability for very thin films (∼10 nm) accounting for surface forces. For (quasi-) flat-very-thin films, the analysis shows no instability, which is consistent with general knowledge in this field. However, for films extending from a meniscus, as encountered in wetting configurations, it is found that the competition between London–van der Waals, capillary, and thermocapillary forces leads to contact line instability and behavior revealed for the first time. According to the sign of the Marangoni number, the instability can enhance (if positive) or reduce (if negative) the evaporation rate by widening out or narrowing, respectively, the contact region and, in both cases, significantly modifies the vortical structure of the flow. If the Marangoni number is positive, the film interface close to the contact line can exhibit corrugations. The occurrence of these latter is discriminated, in addition to the Marangoni number, by the value of three operating parameters, namely the film aspect ratio, the ratio of the film diffusive thermal resistance to evaporative heat transfer resistance, and the ratio of capillary pressure to disjoining pressure. By modifying the physical and operating parameters, it is also shown that the system can be optimized in order to suppress these corrugations.
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47.55.nb Capillary and thermocapillary flows
47.55.nd Spreading films
47.55.pf Marangoni convection
68.03.Cd Surface tension and related phenomena
68.08.Bc Wetting
47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
back to top Viscous and Non-Newtonian Flows

Insights into symmetric and asymmetric vortex mergers using the core growth model

Fangxu Jing, Eva Kanso, and Paul K. Newton

Phys. Fluids 24, 073101 (2012); http://dx.doi.org/10.1063/1.4730344 (17 pages)

Online Publication Date: 5 July 2012

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We revisit the two vortex merger problem (symmetric and asymmetric) for the Navier-Stokes equations using the core growth model for vorticity evolution coupled with the passive particle field and an appropriately chosen time-dependent rotating reference frame. Using the combined tools of analyzing the topology of the streamline patterns along with the careful tracking of passive fields, we highlight the key features of the stages of evolution of vortex merger, pinpointing deficiencies in the low-dimensional model with respect to similar experimental/numerical studies. The model, however, reveals a far richer and delicate sequence of topological bifurcations than has previously been discussed in the literature for this problem, and, at the same time, points the way towards a method of improving the model.
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47.32.C- Vortex dynamics
47.11.-j Computational methods in fluid dynamics
47.10.ad Navier-Stokes equations
02.30.Jr Partial differential equations

Thermally excited vortical flow in a thin bidirectionally oriented nematic cell

A. V. Zakharov and A. A. Vakulenko

Phys. Fluids 24, 073102 (2012); http://dx.doi.org/10.1063/1.4732784 (14 pages)

Online Publication Date: 9 July 2012

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The theoretical description of the reorientational dynamics in a thin bidirectionally aligned liquid crystal cell (BALC), where the nematic sample is confined by two horizontal and two lateral surfaces, under the influence of a temperature gradient ∇T is presented. We have carried out a numerical study of the system of hydrodynamic equations including director reorientation, fluid flow  v, and the temperature redistribution across the BALC cell under the influence of ∇T, when the sample is heated both from below and from above. Calculations show that, due to interaction between the gradient of the director field ∇math and ∇T, the BALC sample settles down to a stationary bi-vortical flow regime. As for a nematogenic material, we have considered the BALC cell to be occupied by 4 − n − pentyl − 4′ − cyanobiphenyl, and investigated the effect of both ∇math and ∇T on the magnitude and direction of  v, for a number of hydrodynamic regimes.
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42.79.Kr Display devices, liquid-crystal devices
47.32.-y Vortex dynamics; rotating fluids
47.57.Lj Flows of liquid crystals

The effects of hydrodynamic interaction and inertia in determining the high-frequency dynamic modulus of a viscoelastic fluid with two-point passive microrheology

Andrés Córdoba, Jay D. Schieber, and Tsutomu Indei

Phys. Fluids 24, 073103 (2012); http://dx.doi.org/10.1063/1.4734388 (19 pages) | Cited 2 times

Online Publication Date: 16 July 2012

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In two-point passive microrheology, a modification of the original one-point technique, introduced by Crocker et al. [Phys. Rev. Lett. 85, 888 (2000)]10.1103/PhysRevLett.85.888, the cross-correlations of two micron-sized beads embedded in a viscoelastic fluid are used to estimate the dynamic modulus of a material. The two-point technique allows for the sampling of larger length scales, which means that it can be used in materials with a coarser microstructure. An optimal separation between the beads exists at which the desired length and time scales are sampled while keeping a desired signal-to-noise-ratio in the cross-correlations. A large separation can reduce the effect of higher order reflections, but will increase the effects of medium inertia and reduce the signal-to-noise-ratio. The modeling formalisms commonly used to relate two-bead cross-correlations to G*(ω) neglect inertia effects and underestimate the effect of reflections. A simple dimensional analysis for a model viscoelastic fluid suggests that there exists a very narrow window of bead separation and frequency range where these effects can be neglected. Therefore, we consider both generalized data analysis and generalized Brownian dynamics (BD) simulations to examine the magnitude of these effects. Our proposed analysis relies on the recent analytic results of Ardekani and Rangel [Phys. Fluids 18, 103306 (2006)]10.1063/1.2363351 for a purely viscous fluid, which are generalized to linear viscoelastic fluids. Implementation requires approximations to estimate Laplace transforms efficiently. These approximations are then used to create generalized BD simulation algorithms. The data analysis formalism presented in this work can expand the region of separation between the beads and frequencies at which rheological properties can be accurately measured using two-point passive microrheology. Moreover, the additional physics introduced in the data analysis formalisms do not add additional significant computational costs.
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47.50.-d Non-Newtonian fluid flows
47.55.-t Multiphase and stratified flows
83.10.Mj Molecular dynamics, Brownian dynamics
02.30.Uu Integral transforms
02.60.Gf Algorithms for functional approximation
47.11.-j Computational methods in fluid dynamics

Squeeze flow of a Carreau fluid during sphere impact

J. Uddin, J. O. Marston, and S. T. Thoroddsen

Phys. Fluids 24, 073104 (2012); http://dx.doi.org/10.1063/1.4736742 (17 pages) | Cited 1 time

Online Publication Date: 19 July 2012

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We present results from a combined numerical and experimental investigation into the squeeze flow induced when a solid sphere impacts onto a thin, ultra-viscous film of non-Newtonian fluid. We examine both the sphere motion through the liquid as well as the fluid flow field in the region directly beneath the sphere during approach to a solid plate. In the experiments we use silicone oil as the model fluid, which is well-described by the Carreau model. We use high-speed imaging and particle tracking to achieve flow visualisation within the film itself and derive the corresponding velocity fields. We show that the radial velocity either diverges as the gap between the sphere and the wall diminishes (Ztip → 0) or that it reaches a maximum value and then decays rapidly to zero as the sphere comes to rest at a non-zero distance (Ztip = Zmin) away from the wall. The horizontal shear rate is calculated and is responsible for significant viscosity reduction during the approach of the sphere. Our model of this flow, based on lubrication theory, is solved numerically and compared to experimental trials. We show that our model is able to correctly describe the physical features of the flow observed in the experiments.
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47.50.Cd Modeling
47.50.Ef Measurements
47.80.Jk Flow visualization and imaging
47.85.mf Lubrication flows
02.60.Cb Numerical simulation; solution of equations

Direct numerical simulation of binary off-center collisions of shear thinning droplets at high Weber numbers

C. Focke and D. Bothe

Phys. Fluids 24, 073105 (2012); http://dx.doi.org/10.1063/1.4737582 (18 pages) | Cited 1 time

Online Publication Date: 25 July 2012

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Binary droplet collisions, a prototype elementary subprocess inside sprays, are investigated by direct numerical simulations (DNS) based on an extended volume of fluid method. We focus on shear-thinning droplet collisions. In order to capture the dynamics of droplet collisions with different outcomes, we account for off-center collisions at high Weber numbers. Such collision conditions lead to the formation of extremely thin fluid lamellae. It turns out that these thin lamellae determine the smallest length scales which must be resolved in a DNS. A stabilization algorithm is presented which prevents the lamellae from rupturing. It is validated by comparison with experimental data and applied for a droplet collision study of shear-thinning liquids. The results show that, independent of the off-set of the colliding droplets, a collision of Newtonian liquid droplets with appropriately chosen viscosity can reproduce the collision dynamics of the shear-thinning liquid droplets. This includes temporal evolution of shapes and energy.
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47.55.dr Interactions with surfaces
66.20.Cy Theory and modeling of viscosity and rheological properties, including computer simulation
02.60.-x Numerical approximation and analysis
47.11.-j Computational methods in fluid dynamics
47.20.-k Flow instabilities
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
back to top Particulate, Multiphase, and Granular Flows

Mitigation of preferential concentration of small inertial particles in stationary isotropic turbulence using electrical and gravitational body forces

Aditya U. Karnik and John S. Shrimpton

Phys. Fluids 24, 073301 (2012); http://dx.doi.org/10.1063/1.4732540 (16 pages)

Online Publication Date: 16 July 2012

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Particles with a certain range of Stokes numbers preferentially concentrate due to action of turbulent motion and body forces such as gravity are known to influence this process. The effect of electric charge, residing on particles, upon the phenomenon of preferential concentration is investigated. We use direct numerical simulations of one-way coupled stationary isotropic turbulence over a range of particle Stokes numbers, fluid Taylor Reynolds numbers, and electrical and gravitational particle body force magnitudes, the latter characterized by non-dimensional settling velocities, vc* and vg*, respectively. In contrast to the gravitational body force, the electrical analogue, acting on an electrically charged particle, is generated by an electric field, which is in turn a function of the degree of preferential concentration. Thus, the electrical body force is created by, and mitigates, preferential concentration. In the absence of gravity, it is estimated that vc* ≈ 1.0 is sufficient to homogenise a preferentially concentrated particle distribution. It is seen that charging drastically reduces the radial distribution function values at Kolmogorov scale separations, which gravitational force does not. This implies that charging the particles is an efficient means to destroy small clusters of particles. On incorporating the gravitational force, the amount of charge required to homogenise the particle distribution is reduced. It is estimated that vc* ≈ 0.6 is sufficient to homogenise particle distribution at vg* = 2.0. This estimation is corroborated by several different indicators of preferential concentration, and the results also agree reasonably well with corresponding experiments reported in literature. Calculations also suggest that sprays generated by practical charge injection atomizers would benefit from this electrical dispersion effect.
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47.27.De Coherent structures
47.27.ek Direct numerical simulations
47.27.Gs Isotropic turbulence; homogeneous turbulence
47.55.Kf Particle-laden flows

Concentration instability of sedimenting spheres in a second-order fluid

Ramanathan Vishnampet and David Saintillan

Phys. Fluids 24, 073302 (2012); http://dx.doi.org/10.1063/1.4733700 (17 pages)

Online Publication Date: 18 July 2012

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The slow sedimentation of a dilute suspension of spherical particles in a second-order fluid is investigated using theory and numerical simulations. We first analyze the motion of a single isolated spherical particle sedimenting under gravity when placed in a linear flow field. In the limit of weak viscoelasticity (low Deborah number), the velocity of the particle is calculated, and the nonlinear coupling of the settling motion with the local flow field is shown to result in a lateral drift in a direction perpendicular to gravity. By the same effect, the mean flow driven by weak horizontal density fluctuations in a large-scale suspension of hydrodynamically interacting particles will also result in a horizontal drift, which has the effect of reinforcing the fluctuations as we demonstrate using a linear stability analysis. Based on this mechanism, an initially homogeneous suspension is expected to develop concentration fluctuations, a prediction supported by previous experiments on sedimentation in polymeric liquids. We further confirm this prediction using large-scale weakly nonlinear numerical simulations based on a point-particle model. Concentration fluctuations are indeed found to grow in the simulations, and are shown to result in an enhancement of the mean settling speed and velocity fluctuations compared to the Newtonian case.
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47.20.Gv Viscous and viscoelastic instabilities
47.55.Kf Particle-laden flows
02.60.Cb Numerical simulation; solution of equations
82.70.Kj Emulsions and suspensions
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
47.50.Gj Instabilities

Kinetic-theory-based model of dense granular flows down inclined planes

Cheng-Hsien Lee and Ching-Jer Huang

Phys. Fluids 24, 073303 (2012); http://dx.doi.org/10.1063/1.4736738 (18 pages)

Online Publication Date: 18 July 2012

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This work extends a continuum model of sheared granular material comprising two-dimensional disks [C. H. Lee and C. J. Huang, Phys. Fluids 22, 043307 (2010)10.1063/1.3400203] to elucidate the dynamics of three-dimensional spheres. The proposed model is applied to investigate dense granular flows down an inclined plane. In the model, stress has a static component and a kinetic component. The constitutive model for shear stress reduces to the Bagnold model when the diffusion of granular temperature is small. The predicted rheological characteristics are identical to those observed in the preceding experiments and numerical simulations, validating the present model. The predicted rheological characteristics reveal that dense granular flows down an inclined plane are characterized by three special angles that determine the phase diagram. The predicted thick granular flow on an inclined plane exhibits the Bagnold velocity profile and a uniform volume fraction throughout its depth. The governing equation of granular temperature is simplified and solved analytically. The proposed shear granular flow model is also solved completely using the finite volume method. The predicted velocity and volume fraction agree very well with previous discretely simulated results. This work also proposes an equation for determining the characteristic length of dense granular flows and shows that its static component is close to the stopping height.
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47.57.Gc Granular flow
47.57.Qk Rheological aspects
02.60.Cb Numerical simulation; solution of equations
47.11.Df Finite volume methods

Metal particle nucleation in laminar jets

Jun Liu and Sean C. Garrick

Phys. Fluids 24, 073304 (2012); http://dx.doi.org/10.1063/1.4737002 (10 pages) | Cited 1 time

Online Publication Date: 23 July 2012

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Gas to particle conversion in the form of nucleation within various flow systems plays a significant role in a variety of industrial and natural processes. Recently developed surface tension models offer increased accuracy in the modeling of metal particle nucleation. These models facilitate the probing of the effects of fluid, scalar, and thermal transport on nucleation in an accurate manner. In this work we investigate the formation of metal nanoparticles in laminar flows. The flows consist of metal vapor diluted in argon issuing into a cooler argon stream. The fluid, thermal, and chemical fields are obtained by solving the Navier Stokes, enthalpy, and mass-fraction transport equations while nucleation is simulated via a homogeneous nucleation model with size-dependent surface tension. This approach is attractive in that it promises to be more accurate than the classical nucleation theory (CNT) while maintaining much of its simplicity when coupling with fluid dynamics. The results show that the size-dependent surface tension nucleation model is more accurate than CNT and agrees well with physical data. Physically, the sensitivity of the saturation ratio to changes in temperature is shown to be greater than its sensitivity to mass fraction, highlighting the significance of differential molecular transport of energy and mass and the significance of non-unity Lewis numbers. More significantly, the size-dependent surface tension approach suggests that certain metals may have a maximum nucleation rate and further cooling—a strategy employed to increase particle nucleation rates—will actually decrease particle nucleation.
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47.15.Uv Laminar jets
47.55.Kf Particle-laden flows
68.03.Cd Surface tension and related phenomena
47.10.ad Navier-Stokes equations

Anisotropy in pair dispersion of inertial particles in turbulent channel flow

Enrico Pitton, Cristian Marchioli, Valentina Lavezzo, Alfredo Soldati, and Federico Toschi

Phys. Fluids 24, 073305 (2012); http://dx.doi.org/10.1063/1.4737655 (25 pages) | Cited 1 time

Online Publication Date: 27 July 2012

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The rate at which two particles separate in turbulent flows is of central importance to predict the inhomogeneities of particle spatial distribution and to characterize mixing. Pair separation is analyzed for the specific case of small, inertial particles in turbulent channel flow to examine the role of mean shear and small-scale turbulent velocity fluctuations. To this aim an Eulerian-Lagrangian approach based on pseudo-spectral direct numerical simulation (DNS) of fully developed gas-solid flow at shear Reynolds number Reτ = 150 is used. Pair separation statistics have been computed for particles with different inertia (and for inertialess tracers) released from different regions of the channel. Results confirm that shear-induced effects predominate when the pair separation distance becomes comparable to the largest scale of the flow. Results also reveal the fundamental role played by particles-turbulence interaction at the small scales in triggering separation during the initial stages of pair dispersion. These findings are discussed examining Lagrangian observables, including the mean square separation, which provide prima facie evidence that pair dispersion in non-homogeneous anisotropic turbulence has a superdiffusive nature and may generate non-Gaussian number density distributions of both particles and tracers. These features appear to persist even when the effects of shear dispersion are filtered out, and exhibit strong dependency on particle inertia. Application of present results is discussed in the context of modelling approaches for particle dispersion in wall-bounded turbulent flows.
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47.27.nb Boundary layer turbulence
47.27.nd Channel flow
47.32.Ff Separated flows
47.51.+a Mixing
47.60.Dx Flows in ducts and channels
47.27.ek Direct numerical simulations
back to top Laminar Flows

Eulerian indicators under continuously varying conditions

Kevin L. McIlhany and Stephen Wiggins

Phys. Fluids 24, 073601 (2012); http://dx.doi.org/10.1063/1.4732152 (24 pages)

Online Publication Date: 9 July 2012

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In this paper, we extend the notion of Eulerian indicators (EIs) for predicting Lagrangian mixing behavior previously developed for blinking flows to the continuous time setting. We apply the EIs to a study of mixing in a kinematic model of a time-dependent double-gyre with five different time dependencies—sinusoidal, sawtooth, square wave, triangular, and noise (which is constructed so that it is also periodic in time). Each of the five velocity fields is described by two parameters; the strength of the time dependence (ε) and the period (T). Based on a trajectory based quality of mixing diagnostic (Danckwerts’ normalized variance of concentration) we find that noisy time dependence has the largest region of good mixing in the parameter space and triangular time dependence has parameter values corresponding to the most complete and fastest mixing. These Lagrangian based predictions are confirmed by the EIs (product of the transversality and mobility). Although not every feature of the mixing behavior is captured by EIs, we show that they do in general predict the regions in the parameter space under consideration that correspond to good mixing. Moreover, the EIs offer a factor of 100 computational advantage in exploring the parameter space in comparison with the trajectory based mixing diagnostic.
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47.52.+j Chaos in fluid dynamics
05.40.Ca Noise
47.32.Ef Rotating and swirling flows
47.51.+a Mixing

A numerical study of the laminar necklace vortex system and its effect on the wake for a circular cylinder

Gokhan Kirkil and George Constantinescu

Phys. Fluids 24, 073602 (2012); http://dx.doi.org/10.1063/1.4731291 (25 pages) | Cited 1 time

Online Publication Date: 18 July 2012

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Large eddy simulation (LES) is used to investigate the structure of the laminar horseshoe vortex (HV) system and the dynamics of the necklace vortices as they fold around the base of a circular cylinder mounted on the flat bed of an open channel for Reynolds numbers defined with the cylinder diameter, D, smaller than 4460. The study concentrates on the analysis of the structure of the HV system in the periodic breakaway sub-regime, which is characterized by the formation of three main necklace vortices. Over one oscillation cycle of the previously observed breakaway sub-regime, the corner vortex and the primary vortex merge (amalgamate) and a developing vortex separates from the incoming laminar boundary layer (BL) to become the new primary vortex. Results show that while the classical breakaway sub-regime, in which one amalgamation event occurs per oscillation cycle, is present when the nondimensional displacement thickness of the incoming BL at the location of the cylinder is relatively large (δ*/D > 0.1), a new type of breakaway sub-regime is present for low values of δ*/D. This sub-regime, which we call the double-breakaway sub-regime, is characterized by the occurrence of two amalgamation events over one full oscillation cycle. LES results show that when the HV system is in one of the breakaway sub-regimes, the interactions between the highly coherent necklace vortices and the eddies shed inside the separated shear layers (SSLs) are very strong. For the relatively shallow flow conditions considered in this study (H/D ≅ 1, H is the channel depth), at times, the disturbances induced by the legs of the necklace vortices do not allow the SSLs on the two sides of the cylinder to interact in a way that allows the vorticity redistribution mechanism to lead to the formation of a new wake roller. As a result, the shedding of large-scale rollers in the turbulent wake is suppressed for relatively large periods of time. Simulation results show that the wake structure changes randomly between time intervals when large-scale rollers are forming and are convected in the wake (von Karman regime), and time intervals when the rollers do not form. When the wake is in the von Karman regime, the shedding frequency of the rollers is close to that observed for flow past infinitely long cylinders.
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47.27.wb Turbulent wakes
47.32.Ff Separated flows
47.15.Cb Laminar boundary layers
47.27.te Turbulent convective heat transfer
47.27.ep Large-eddy simulations
47.11.-j Computational methods in fluid dynamics

Spectral analysis of mixing in chaotic flows via the mapping matrix formalism: Inclusion of molecular diffusion and quantitative eigenvalue estimate in the purely convective limit

O. Gorodetskyi, M. Giona, and P. D. Anderson

Phys. Fluids 24, 073603 (2012); http://dx.doi.org/10.1063/1.4738598 (34 pages) | Cited 2 times

Online Publication Date: 31 July 2012

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This paper extends the mapping matrix formalism to include the effects of molecular diffusion in the analysis of mixing processes in chaotic flows. The approach followed is Lagrangian, by considering the stochastic formulation of advection-diffusion processes via the Langevin equation for passive fluid particle motion. In addition, the inclusion of diffusional effects in the mapping matrix formalism permits to frame the spectral properties of mapping matrices in the purely convective limit in a quantitative way. Specifically, the effects of coarse graining can be quantified by means of an effective Péclet number that scales as the second power of the linear lattice size. This simple result is sufficient to predict the scaling exponents characterizing the behavior of the eigenvalue spectrum of the advection-diffusion operator in chaotic flows as a function of the Péclet number, exclusively from purely kinematic data, by varying the grid resolution. Simple but representative model systems and realistic physically realizable flows are considered under a wealth of different kinematic conditions–from the presence of large quasi-periodic islands intertwined by chaotic regions, to almost globally chaotic conditions, to flows possessing “sticky islands”–providing a fairly comprehensive characterization of the different numerical phenomenologies that may occur in the quantitative analysis of mapping matrices, and ultimately of chaotic mixing processes.
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47.52.+j Chaos in fluid dynamics
02.10.Ud Linear algebra
02.50.Ey Stochastic processes
back to top Instability and Transition

Secondary energy growth and turbulence suppression in conducting channel flow with streamwise magnetic field

Shuai Dong, Dmitry Krasnov, and Thomas Boeck

Phys. Fluids 24, 074101 (2012); http://dx.doi.org/10.1063/1.4731293 (20 pages)

Online Publication Date: 2 July 2012

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The effects of a streamwise magnetic field on conducting channel flow are studied by analyzing secondary linear perturbations evolving on streamwise streaks and by direct numerical simulations of relaminarization. By means of an optimal perturbation approach, magnetic damping is found to increase the streamwise wavelength of the most amplified secondary perturbations and to reduce their amplification level. Complete suppression of secondary instability is observed at a critical magnetic interaction parameter that depends on the streak amplitude and on the Reynolds number when the transient evolution of the streaky basic flow is taken into account. Relaminarization in the direct numerical simulation occurs at lower values of the interaction parameter than the critical values from the stability computations for the streak amplitudes considered. The dependence of these threshold values of the interaction parameters on the Reynolds number is fairly similar between simulations and stability analysis. Relaminarization thresholds from the simulations are also in good agreement with experiments on pipe flow with streamwise magnetic field.
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.27.ek Direct numerical simulations
47.27.eb Statistical theories and models
47.27.nf Flows in pipes and nozzles
47.15.Fe Stability of laminar flows
47.60.Dx Flows in ducts and channels

Counterpropagating Rossby waves in confined plane wakes

L. Biancofiore and F. Gallaire

Phys. Fluids 24, 074102 (2012); http://dx.doi.org/10.1063/1.4729617 (13 pages)

Online Publication Date: 3 July 2012

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In the present work, we revisit the temporal and the spatio-temporal stability of confined plane wakes under the perspective of the counterpropagating Rossby waves (CRWs). Within the context of broken line velocity profiles, each vorticity discontinuity can be associated to a counterpropagating Rossby wave. In the case of a wake modeled by a broken line profile, the interaction of two CRWs is shown to originate in a shear instability. Following this description, we first recover the stability results obtained by Juniper [J. Fluid Mech. 590, 163–185 (2007)]10.1017/S0022112007007975 and Biancofiore and Gallaire [Phys. Fluids 23, 034103 (2011)]10.1063/1.3554764 by means of the classical normal mode analysis. In this manner, we propose an explanation of the stabilizing influence of the confinement on the temporal stability properties. The CRW description further allows us to propose a new interpretation of the counterintuitive spatio-temporal destabilization in wake flows at moderate confinement noticed by Juniper [J. Fluid Mech. 565, 171–195 (2006)]10.1017/S0022112006001558: it is well predicted by the mean group velocity of the uncoupled CRWs.
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47.35.De Shear waves
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.27.nf Flows in pipes and nozzles
47.27.wb Turbulent wakes
47.32.C- Vortex dynamics

Direct numerical simulation of Rayleigh-Bénard convection in a cylindrical container of aspect ratio 1 for moderate Prandtl number fluid

You-Rong Li, Yu-Qing Ouyang, Lan Peng, and Shuang-Ying Wu

Phys. Fluids 24, 074103 (2012); http://dx.doi.org/10.1063/1.4731296 (16 pages)

Online Publication Date: 9 July 2012

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A series of three-dimensional numerical simulations were conducted for the Rayleigh-Bénard convection in a cylindrical container with the aspect ratio Γ = 1. The Prandtl number of the fluid is 7 and the Rayleigh number varies from 103 to 105. Results show that the aspect ratio of the cylinder has an important influence on the multiplicity of the steady flow state. The sidewall of the cylinder at Γ = 1 restricts the increase of the number of rolls in the fluid layer. Therefore, only two-roll and single-roll flow patterns are observed at the whole simulation range of the Rayleigh number. During the transition of the Rayleigh-Bénard convection to the unsteady flow, it is found that the unsteady flow pattern and the bifurcation sequence of the oscillation flow are very sensitive to the initial condition.
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47.55.pb Thermal convection
47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.11.-j Computational methods in fluid dynamics

Linear instability of the Darcy–Hadley flow in an inclined porous layer

A. Barletta and D. A. S. Rees

Phys. Fluids 24, 074104 (2012); http://dx.doi.org/10.1063/1.4732781 (22 pages)

Online Publication Date: 10 July 2012

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The buoyant flow in a saturated porous layer inclined to the horizontal is studied under the assumption that the plane impermeable boundaries are subject to linear temperature distributions up the layer. The basic solution is stationary and such that the temperature gradient is inclined to the boundary walls. Two parameters govern the thermal boundary conditions: the Rayleigh number, associated with the component of the basic temperature gradient orthogonal to the boundaries, the Hadley-Rayleigh number, associated with the component of the basic temperature gradient parallel to the boundaries. The linear stability of the basic solution with respect to the longitudinal normal modes is studied by employing two different numerical methods: a collocation method of weighted residuals, and a Runge–Kutta solver. Different regimes are considered: the upward–cooling condition, the upward–heating condition, and the buoyancy–balanced condition. The latter regime implies a vanishing velocity distribution and a vertical temperature gradient in the basic state. In the upward–cooling regime, for a fixed Hadley–Rayleigh number, the increasing inclination to the horizontal leads to a destabilising effect. When the inclination exceeds a threshold angle that depends on the Hadley–Rayleigh number, the basic solution becomes unstable for every Rayleigh number. The reverse holds true in the upward–heating regime, where the increasing inclination to the horizontal stabilises the basic flow. The general oblique normal modes are finally considered. It is shown that the longitudinal modes are selected at the onset of convection, except for the case of the Darcy–Bénard limiting case where all the oblique modes are equivalent.
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47.56.+r Flows through porous media
02.60.-x Numerical approximation and analysis
44.30.+v Heat flow in porous media
47.11.Hj Boundary element methods
47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.55.P- Buoyancy-driven flows; convection

Turbulent mixing measurements in the Richtmyer-Meshkov instability

Christopher Weber, Nicholas Haehn, Jason Oakley, David Rothamer, and Riccardo Bonazza

Phys. Fluids 24, 074105 (2012); http://dx.doi.org/10.1063/1.4733447 (22 pages)

Online Publication Date: 12 July 2012

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The Richtmyer-Meshkov instability is experimentally investigated in a vertical shock tube using a new type of broadband initial condition imposed on an interface between a helium-acetone mixture and argon (A = 0.7). The initial condition is created by first setting up a gravitationally stable stagnation plane between the gases and then injecting the same two gases horizontally at the interface to create a shear layer. The perturbations along the shear layer create a statistically repeatable broadband initial condition. The interface is accelerated by a M = 1.6 planar shock wave, and the development of the ensuing turbulent mixing layer is investigated using planar laser induced fluorescence. By the latest experimental time, 2.1 ms after shock acceleration, the layer is shown to be fully turbulent, surpassing both turbulent transition criteria based on the Reynolds number and shear layer scale. Mixing structures are nearly isotropic by the latest time, as seen by the probability density function of gradient angles within the mixing layer. The scalar variance energy spectrum suggests a k−5/3 inertial range by the latest time and an exponential region at higher wavenumbers.
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47.80.-v Instrumentation and measurement methods in fluid dynamics
47.40.Nm Shock wave interactions and shock effects
47.27.nf Flows in pipes and nozzles
47.27.wj Turbulent mixing layers
47.15.Fe Stability of laminar flows
47.40.Ki Supersonic and hypersonic flows

Electric field and van der Waals force induced instabilities in thin viscoelastic bilayers

Dipankar Bandyopadhyay, P. Dinesh Sankar Reddy, and Ashutosh Sharma

Phys. Fluids 24, 074106 (2012); http://dx.doi.org/10.1063/1.4736549 (29 pages)

Online Publication Date: 17 July 2012

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A unified theory is presented for the field-induced spinodal instabilities of thin viscoelastic bilayers composed of the Maxwell fluids or of the soft solids obeying the Kelvin-Voigt model. The analysis includes the different important mechanisms by which a bilayer is rendered unstable: (1) the wetting instability engendered by the excess van der Waals forces in an ultrathin (<100 nm) bilayer (Figure (1a)); (2) the electric field induced instability caused by an external electrostatic field across the bilayer (Figure (1b)); (3) the contact instability caused by the attractive interactions with another surface in the contact proximity of the upper film (Figure (1c)). The key features of the short-, long-, and finite-wavenumber instabilities are compared and contrasted for a host of bilayers having purely viscous, purely elastic, viscoelastic-viscous, and viscoelastic rheological properties. Linear stability analysis shows: (i) controlling mode of instability can shift from one interface to the other, which is accompanied by an abrupt shift in the time and the length scales of the instabilities with the change in the interfacial tensions, relaxation times, and elastic moduli of the films; (ii) purely elastomeric bilayers show a finite wavenumber bifurcation only beyond a critical destabilizing force due to their elastic stiffness; (iii) bilayers with at least one viscous or Maxwell layer show zero elastic-stiffness against the destabilizing influences; (iv) wetting viscoelastic bilayer is unstable only when it is ultrathin and elastically very soft or if one of the layers is purely viscous; (v) Maxwell (elastomer) bilayers show a faster (slower) growth of instability with the increase in relaxation time (elastic modulus).
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47.50.Gj Instabilities
47.55.Hd Stratified flows
47.65.-d Magnetohydrodynamics and electrohydrodynamics
68.03.Cd Surface tension and related phenomena
68.08.Bc Wetting
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
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