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Dec 2006

Volume 18, Issue 12, Articles (12xxxx)

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Report of the Symposium on Interactions for Dispersed Systems in Newtonian and Viscoelastic Fluids, Guanajuato, Mexico, 2006

Morton M. Denn, Eckart H. Meiburg, Jeffrey F. Morris, Eric S. G. Shaqfeh, and Todd M. Squires

Phys. Fluids 18, 121501 (2006); http://dx.doi.org/10.1063/1.2396902 (9 pages) | Cited 1 time

Online Publication Date: 8 December 2006

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This report summarizes the issues discussed during a Symposium of the International Union of Theoretical and Applied Mechanics, entitled “Interactions for Dispersed Systems in Newtonian and Viscoelastic Fluids,” which was held in March 2006 in Guanajuato, Mexico.
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47.57.Gc Granular flow
47.57.ef Sedimentation and migration
47.55.D- Drops and bubbles
47.50.-d Non-Newtonian fluid flows
47.61.Fg Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)
47.85.Np Fluidics

Clusters of particles falling in a viscous fluid with periodic boundary conditions

M. L. Ekiel-Jeżewska and B. U. Felderhof

Phys. Fluids 18, 121502 (2006); http://dx.doi.org/10.1063/1.2396910 (2 pages) | Cited 13 times

Online Publication Date: 8 December 2006

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Exemplary dynamics of three point particles falling under gravity in Stokes flow with periodic boundary conditions is presented in a movie. Stable and unstable solutions of the equations of Stokesian dynamics are explicitly shown for two initial configurations: equilateral triangles with side lengths close to a critical size.
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47.55.Kf Particle-laden flows
47.57.ef Sedimentation and migration
47.35.Bb Gravity waves

The effect of stratification on the wave number selection in the instability of sedimenting spheroids

David Saintillan, Eric S. G. Shaqfeh, and Eric Darve

Phys. Fluids 18, 121503 (2006); http://dx.doi.org/10.1063/1.2396913 (13 pages) | Cited 13 times

Online Publication Date: 8 December 2006

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It is well known that a dilute suspension of spheroids sedimenting under gravity at low Reynolds number is unstable to density fluctuations as a result of hydrodynamic interactions [ D. L. Koch and E. S. G. Shaqfeh, J. Fluid Mech. 209, 521 (1989) ]. Using a linear stability analysis, it is shown that a vertical density gradient in such a suspension can lead to a wave number selection by damping fluctuations at long wavelengths. A scaling for the most unstable wavelength, or characteristic size of the density fluctuations, is obtained in terms of the background stratification and volume fraction, and is compared to results from numerical simulations in stratified particulate suspensions using methods that we have developed previously. In initially homogeneous suspensions, simulations show a continuous decay of the size of the density fluctuations over time, which we demonstrate can be attributed to the development of stratification inside the suspension.
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47.55.Hd Stratified flows
47.20.-k Flow instabilities
47.55.Kf Particle-laden flows
47.57.ef Sedimentation and migration
47.35.Bb Gravity waves
02.60.Cb Numerical simulation; solution of equations

Dynamics of bidisperse suspensions under Stokes flows: Linear shear flow and sedimentation

Micheline Abbas, Eric Climent, Olivier Simonin, and Martin R. Maxey

Phys. Fluids 18, 121504 (2006); http://dx.doi.org/10.1063/1.2396916 (20 pages) | Cited 17 times

Online Publication Date: 8 December 2006

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Sedimenting and sheared bidisperse homogeneous suspensions of non-Brownian particles are investigated by numerical simulations in the limit of vanishing small Reynolds number and negligible inertia of the particles. The numerical approach is based on the solution of the three-dimensional Stokes equations forced by the presence of the dispersed phase. Multibody hydrodynamic interactions are achieved by a low order multipole expansion of the velocity perturbation. The accuracy of the model is validated on analytic solutions of generic flow configurations involving a pair of particles. The first part of the paper aims at investigating the dynamics of monodisperse and bidisperse suspensions embedded in a linear shear flow. The macroscopic transport properties due to hydrodynamic and nonhydrodynamic interactions (short range repulsion force) show good agreement with previous theoretical and experimental works on homogeneous monodisperse particles. Increasing the volumetric concentration of the suspension leads to an enhancement of particle fluctuations and self-diffusion. The velocity fluctuation tensor scales linearly up to 15% concentration. Multibody interactions weaken the correlation of velocity fluctuations and lead to a diffusion-like motion of the particles. Probability density functions show a clear transition from Gaussian to exponential tails while the concentration decreases. The behavior of bidisperse suspensions is more complicated, since the respective amount of small and large particles modifies the overall response of the flow. Our simulations show that, for a given concentration of both species, when the size ratio λ varies from 1 to 2.5, the fluctuation level of the small particles is strongly enhanced. A similar trend is observed on the evolution of the shear induced self-diffusion coefficient. Thus, for a fixed λ and total concentration, increasing the respective volume fraction of large particles can double the velocity fluctuation of small particles. In the second part of the paper, the sedimentation of a single test particle embedded in a suspension of monodisperse particles allows the determination of basic hydrodynamic interactions involved in a bidisperse suspension. Good agreement is achieved when comparing the mean settling velocity and fluctuation levels of the test sphere with experiments. Two distinct behaviors are observed depending on the physical properties of the particle. The Lagrangian velocity autocorrelation function has a negative region when the test particle has a settling velocity twice as large as the reference velocity of the surrounding suspension. The test particle settles with a zig-zag vertical trajectory while a strong reduction of horizontal dispersion occurs. Then, several configurations of bidisperse settling suspensions are investigated. Mean velocity depends on the concentration of both species, density ratio and size ratio. Results are compared with theoretical predictions at low concentration and empirical correlations when the assumption of a dilute regime is no longer valid. For particular configurations, a segregation instability sets in. Columnar patterns tend to collect particles of the same species and eventually a complete separation of the suspension is observed. The instability threshold is compared with experiments in the case of suspensions of buoyant and heavy spheres. The basic features are well reproduced by the simulation model.
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47.57.ef Sedimentation and migration
47.55.Kf Particle-laden flows
47.57.eb Diffusion and aggregation
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.54.Bd Theoretical aspects
47.85.Dh Hydrodynamics, hydraulics, hydrostatics

Interaction of cavitation bubbles on a wall

Nicolas Bremond, Manish Arora, Stephan M. Dammer, and Detlef Lohse

Phys. Fluids 18, 121505 (2006); http://dx.doi.org/10.1063/1.2396922 (10 pages) | Cited 23 times

Online Publication Date: 8 December 2006

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We report experimental and numerical investigations on the dynamics of the cavitation of bubbles on a solid surface and the interaction between them with the help of controlled cavitation nuclei: hemispherical bubbles are nucleated from hydrophobic microcavities that act as gas traps when the substrate is immersed in water. The expansion of these nuclei is triggered by an impulsive lowering of the liquid pressure. The patterning of the substrate allows us to control the number of bubbles and the distance between them. Each hemispherical bubble experiences the effect of its mirror image. Correspondingly, an isolated hemispherical bubble together with its mirror image behaves like a free spherical bubble, i.e., its dynamics is well described by the Rayleigh-Plesset equation. We employ the setup to study the dynamics of two and more bubbles in a row at controlled and fixed distances from each other. For weak interaction, namely when the maximum size of the bubbles is smaller than the bubble distance, the dynamics of the system is well captured by an extended Rayleigh-Plesset equation, where mutual pressure coupling through sound emission is included. Bubble pairs last longer than an isolated bubble as neighboring bubbles modify the surrounding pressure and screen each other. For strong interaction, obtained by increasing the tensile stress or decreasing the bubble distance, the bubbles eventually flatten and form a liquid film between each other which can rupture, leading to coalescence. The film thinning is inertia dominated. A potential flow boundary integral simulation captures the overall shape evolution of the bubbles, including the formation of jets horizontal to the wall. These horizontal jets are caused by symmetry breaking due to the neighboring bubbles.
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47.55.dp Cavitation and boiling
47.11.-j Computational methods in fluid dynamics

Dynamics of particle-particle collisions in a viscous liquid

F.-L. Yang and M. L. Hunt

Phys. Fluids 18, 121506 (2006); http://dx.doi.org/10.1063/1.2396925 (11 pages) | Cited 7 times

Online Publication Date: 8 December 2006

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When two solid spheres collide in a liquid, the dynamic collision process is slowed by viscous dissipation and the increased pressure in the interparticle gap as compared with dry collisions. This paper investigates liquid-immersed head-on and oblique collisions, which complements previously investigated particle-on-wall immersed collisions. By defining the normal from the line of centers at contact, the experimental findings support the decomposition of an oblique collision into its normal and tangential components of motion. The normal relative particle motion is characterized by an effective coefficient of restitution and a binary Stokes number with a correlation that follows the particle-wall results. The tangential motion is described by a collision model using a normal coefficient of restitution and a friction coefficient that are modified for the liquid effects.
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47.55.-t Multiphase and stratified flows

Collapse and growth of cavity regions in granular media due to viscous flow

Osamu Sano and Yusaku Nagata

Phys. Fluids 18, 121507 (2006); http://dx.doi.org/10.1063/1.2396931 (10 pages) | Cited 3 times

Online Publication Date: 8 December 2006

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Experimental studies of viscous flow are made on the effect of macroscopic cavity regions in an otherwise homogeneous granular material. The presence of such cavity regions enhances local velocity, which can accelerate the collapse of their boundaries. At the same time, the mobilized regions grow toward the upstream direction. In a continuation of our previous paper [ Kaneko and Sano, Phys. Fluids 17, 033102 (2005) ], we focus our attention on the latter processes in this paper. For a certain configuration of two interacting cavities, mobilized regions spread faster and in larger scale, which is likely to play an important role in the network formation of a water channel and the onset of a landslide. A numerical simulation based on the two-fluid model is also performed, and is compared with our experimental results.
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47.57.Gc Granular flow
47.11.-j Computational methods in fluid dynamics

Selection of the ripple length on a granular bed sheared by a liquid flow

François Charru

Phys. Fluids 18, 121508 (2006); http://dx.doi.org/10.1063/1.2397005 (9 pages) | Cited 25 times

Online Publication Date: 8 December 2006

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The stability of a granular bed sheared by a liquid flow is investigated using an erosion-deposition model for the moving grains. Extending to arbitrary wave number a previous long wave analysis [ F. Charru and E. J. Hinch, J. Fluid Mech. 550, 111 (2006) ], this study shows that short waves are stabilized by a crest-erosion mechanism that is absent when the local particle flux is assumed to be in equilibrium with the local bed shear stress. The cutoff length associated with this mechanism scales on a deposition length of the particles. This characteristic length is similar, although of a different physical nature, to the inertial length involved in relaxation models of dune dynamics under the wind. Two stabilizing mechanisms cooperate for the most amplified wave number: the new crest-erosion mechanism and the gravity force parallel to the local slope of the inclined bed. The predictions of this model are compared to observations, showing better agreement than previous stability analyses, which strongly underpredict the observed lengths.
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92.40.Gc Erosion and sedimentation; sediment transport
47.10.-g General theory in fluid dynamics

On velocity profiles and stresses in sheared and vibrated granular systems under variable gravity

Oleh Baran and Lou Kondic

Phys. Fluids 18, 121509 (2006); http://dx.doi.org/10.1063/1.2397007 (9 pages) | Cited 5 times

Online Publication Date: 8 December 2006

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We employ discrete element three-dimensional simulations that include realistic modeling of physical system boundaries to determine the influence of gravity on velocity profiles and stresses for frictional inelastic particles that are confined in an angular Couette cell, and sheared by a rotated upper wall. In addition to Earth gravity, we consider other gravitational fields, in particular those of the Moon and Mars. The computational techniques are based on hard-sphere simulations of polydisperse particles at relatively high volume fraction (50–55%). We find that the presence of gravity induces significant changes of the velocity profiles and stresses. One important nondimensional parameter in the problem is shown to be IΩ = mathd/math, where math is the imposed shear rate, Pg is the weight of the system per unit area due to gravity, and ρs is the solid density. We also consider systems that are vibrated in addition to being sheared, since vibrations are one of several important methods for agitating (e.g., fluidizing and/or unjamming) granular systems. We find that the introduction of nondimensional acceleration Γ = a(2πf)2/g, where a,f,g are the amplitude and frequency of oscillations, and the acceleration of gravity, explains novel features that develop in these complex granular systems.
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47.57.Gc Granular flow
47.11.-j Computational methods in fluid dynamics
45.70.Mg Granular flow: mixing, segregation and stratification

A study of velocity discontinuity for single air bubbles rising in an associative polymer

E. Soto, C. Goujon, R. Zenit, and O. Manero

Phys. Fluids 18, 121510 (2006); http://dx.doi.org/10.1063/1.2397011 (12 pages) | Cited 8 times

Online Publication Date: 8 December 2006

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The motion of air bubbles in aqueous solutions of a hydrophobic alkali-swellable associative polymer is studied in this work. The associative nature of these polymer systems dictates their rheological properties: for moderate values of the shear rate, the formation of structure can lead to a shear-thickening behavior and to the appearance of first normal stress difference. For larger shear rates, the polymer associations can be broken, leading to shear thinning. In general, these fluids show a Newtonian behavior for small values of the shear rate, but behave as viscoelastic liquids for large shear rates. Experimental results show the appearance of a critical bubble volume at which a discontinuity in the relation velocity-volume occurs; however, the velocity increase found in this case is not as large as that previously reported for the case of shear-thinning viscoelastic fluids. The discontinuity is associated with a significant change of the bubble shape: before the critical volume, the bubbles are convex spheroids, while past the critical volume a sharp cusped end appears. The appearance of the tail is also associated with the appearance of an inflection point (change of curvature) on the bubble surface. Moreover, since the rheology of the liquids is measured it was found that the discontinuity, and hence the change of shape, occurs when the elastic nature of the liquid first manifests itself (appearance of a first normal stress difference). A comparison of the measured velocities for small bubbles with predictions from a Stokes-Hadamard law shows a discrepancy. The Newtonian viscosity measured in a viscometric flow was smaller than that determined from a falling-ball arrangement. Considering the viscosity measured under this nonviscometric flow, the comparison between theory and experiments was very good for bubbles having volumes lower than the critical one. Moreover, due to the importance of the elasticity, and due to the change of the shape of the bubble, a dimensionless number formed as the ratio of elastic to surface tension forces clearly defines the change of the behavior for the bubbles rising in these fluids. Finally, a photographic study of the peculiar shapes of the bubble tails, tip-, and edge-streaming phenomena is presented. To our knowledge, experiments in this class of fluids have not been reported to date.
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47.57.Ng Polymers and polymer solutions
47.57.Qk Rheological aspects
47.55.dd Bubble dynamics
47.50.Ef Measurements
83.50.Ax Steady shear flows, viscometric flow
83.60.Fg Shear rate dependent viscosity

Entrapped air bubbles in piezo-driven inkjet printing: Their effect on the droplet velocity

Jos de Jong, Roger Jeurissen, Huub Borel, Marc van den Berg, Herman Wijshoff, Hans Reinten, Michel Versluis, Andrea Prosperetti, and Detlef Lohse

Phys. Fluids 18, 121511 (2006); http://dx.doi.org/10.1063/1.2397015 (7 pages) | Cited 14 times

Online Publication Date: 8 December 2006

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Air bubbles entrapped in the ink channel are a major problem in piezo-driven inkjet printing. They grow by rectified diffusion and eventually counteract the pressure buildup at the nozzle, leading to a breakdown of the jetting process. Experimental results on the droplet velocity udrop as a function of the equilibrium radius R0 of the entrained bubble are presented. Surprisingly, udrop(R0) shows a pronounced maximum around R0 = 17 μm before it sharply drops to zero around R0 = 19 μm. A simple one-dimensional model is introduced to describe this counterintuitive behavior which turns out to be a resonance effect of the entrained bubble.
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47.55.dd Bubble dynamics
47.55.db Drop and bubble formation
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.85.-g Applied fluid mechanics

Microscale tipstreaming in a microfluidic flow focusing device

Shelley L. Anna and Hans C. Mayer

Phys. Fluids 18, 121512 (2006); http://dx.doi.org/10.1063/1.2397023 (13 pages) | Cited 78 times

Online Publication Date: 8 December 2006

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A microfluidic flow-focusing device is used to explore the use of surfactant-mediated tipstreaming to synthesize micrometer-scale and smaller droplets. By controlling the surfactant bulk concentration of a soluble nonionic surfactant in the neighborhood of the critical micelle concentration, along with the capillary number and the ratio of the internal and external flow rates, we observe several distinct modes of droplet breakup. For the most part, droplet breakup in microfluidic devices results in highly monodisperse droplets in the range of tens of micrometers in size. However, we observe a new mode of breakup called “thread formation” that resembles tipstreaming and yields tiny droplets in the range of a few micrometers in size or smaller. In this work, we characterize the growth of the thread and its maximum length as a function of flow variables and surfactant content, and we also characterize the period of droplet breakup as a function of these variables. Our results suggest possible methods for controlling the process. Using a simple flow visualization experiment as the basis, we report on preliminary efforts to model the thread formation process.
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47.85.Np Fluidics
47.61.Fg Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)
47.55.db Drop and bubble formation
47.55.df Breakup and coalescence
47.55.dk Surfactant effects
47.55.nb Capillary and thermocapillary flows
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Stabilization of a suspension of sedimenting rods by induced-charge electrophoresis

David Saintillan, Eric S. G. Shaqfeh, and Eric Darve

Phys. Fluids 18, 121701 (2006); http://dx.doi.org/10.1063/1.2404948 (4 pages) | Cited 15 times

Online Publication Date: 14 December 2006

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We use numerical simulations to investigate the dynamics in suspensions of ideally polarizable rods sedimenting under gravity in a vertical electric field. While such suspensions are unstable to concentration fluctuations when no field is applied, we show that the induced-charge electrophoresis that results from the application of the field provides control over the concentration instability by causing particle alignment in the field direction. A phase diagram is obtained for the occurrence of the instability in terms of field strength and volume fraction. In stable suspensions velocity hindrance is shown to occur, and results for the hindered settling function are presented.
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47.57.ef Sedimentation and migration
47.57.jd Electrokinetic effects
47.55.Kf Particle-laden flows
47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.35.Bb Gravity waves
47.85.Np Fluidics

The phase-locked mean impulse response of a turbulent channel flow

Paolo Luchini, Maurizio Quadrio, and Simone Zuccher

Phys. Fluids 18, 121702 (2006); http://dx.doi.org/10.1063/1.2409729 (4 pages) | Cited 1 time

Online Publication Date: 14 December 2006

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We describe the first DNS-based measurement of the complete mean response of a turbulent channel flow to small external disturbances. Space-time impulsive perturbations are applied at one channel wall, and the linear response describes their mean effect on the flow field as a function of spatial and temporal separations. The turbulent response is shown to differ from the response of a laminar flow with the turbulent mean velocity profile as the base flow.
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47.27.nd Channel flow
47.27.nb Boundary layer turbulence
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.27.ek Direct numerical simulations
02.60.Cb Numerical simulation; solution of equations

Large-scale dynamics in two-dimensional Euler and surface quasigeostrophic flows

Chuong V. Tran and David G. Dritschel

Phys. Fluids 18, 121703 (2006); http://dx.doi.org/10.1063/1.2424496 (3 pages) | Cited 3 times

Online Publication Date: 19 December 2006

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The large-scale dynamics in classical two-dimensional Euler and surface quasigeostrophic flows are studied by examining the evolution of the mean-square stream function 〈ψ2〉 and of the Fourier mode math(k,t) for small wave number k = ∣k∣. Upper bounds for 〈ψ2〉 and ∣math(k,t)∣2 are derived. The growth of 〈ψ2〉 is at most quadratic in time t and nearly quadratic in time for surface quasigeostrophic and Euler flows, respectively. At the modal level, it is found that ∣math(k,t)∣2 ≤ ck2t2 and ∣math(k,t)∣2 ≤ c′t2, where c and c′ are constant, for the surface quasigeostrophic and Euler cases, respectively. These bounds imply a steep energy spectrum at small k respectively, k5 and k3. The latter is consistent with previous statistical predictions and numerical results.
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47.32.cb Vortex interactions
47.32.Ef Rotating and swirling flows
47.55.Hd Stratified flows
47.10.Fg Dynamical systems methods
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back to top Interfacial Flows

Wave impact loads: The role of the flip-through

C. Lugni, M. Brocchini, and O. M. Faltinsen

Phys. Fluids 18, 122101 (2006); http://dx.doi.org/10.1063/1.2399077 (17 pages) | Cited 16 times

Online Publication Date: 6 December 2006

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The impact of waves upon a vertical, rigid wall during sloshing is analyzed with specific focus on the modes that lead to the generation of a flip-through [ M. J. Cooker and D. H. Peregrine, “A model for breaking wave impact pressures,” in Proceedings of the 22nd International Conference on Coastal Engineering (ASCE, Delft, 1990), Vol. 2, pp. 1473–1486 ]. Experimental data, based on a time-resolved particle image velocimetry technique and on a novel free-surface tracking method [ M. Miozzi, “Particle image velocimetry using feature tracking and Delaunay tessellation,” in Proceedings of the 12th International Symposium on Applications of Laser Techniques to Fluid Mechanics (2004) ], are used to characterize the details of the flip-through dynamics while wave loads are computed by integrating the experimental pressure distributions. Three different flip-through modes are observed and studied in dependence on the amount and modes of air trapping. No air entrapment characterizes a “mode (a) flip-through,” engulfment of a single, well-formed air bubble is typical of a “mode (b)” event, while the generation of a fine-scale air-water mixing occurs for a “mode (c)” event. Upward accelerations of the flip-through jet exceeding 1500 g have been measured and the generation/collapse process of a small air cavity is described in conjunction with the available pressure time histories. Predictions of the vertical pressure distributions made with the pressure-impulse model of Cooker and Peregrine [ M. J. Cooker and D. H. Peregrine, “Pressure-impulse theory for liquid impact problems,” J. Fluid Mech. 297, 193 (1995) ] show good agreement with the experimental data.
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47.35.Lf Wave-structure interactions
47.80.Jk Flow visualization and imaging
47.55.db Drop and bubble formation
47.55.df Breakup and coalescence
47.51.+a Mixing
47.85.Dh Hydrodynamics, hydraulics, hydrostatics
back to top Viscous and Non-Newtonian Flows

Cross-stream-line migration in confined flowing polymer solutions: Theory and simulation

Juan P. Hernández-Ortiz, Hongbo Ma, Juan J. de Pablo, and Michael D. Graham

Phys. Fluids 18, 123101 (2006); http://dx.doi.org/10.1063/1.2397571 (12 pages) | Cited 16 times

Online Publication Date: 6 December 2006

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Theory and Brownian dynamics (BD) simulations are used to study cross-stream migration in confined dilute flowing polymer solutions, using bead-spring chain and dumbbell models for the polymer molecules. Different degrees of confinement are explored, from a chain above a single wall to slits whose widths 2h are much bigger than the polymer contour length L and radius of gyration Rg (2h⪢L⪢Rg), much bigger than the radius of gyration but comparable with the contour length (2h ∼ L>Rg), and comparable with the polymer radius of gyration (2h ∼ Rg). The results show that except in the latter case, polymer chains migrate in shear flow away from the confining surfaces due to the hydrodynamic interactions between chains and walls. In contrast, when 2h ∼ Rg, the chain migration in flow is toward the walls. This is a steric effect, caused by extension of the chain in the flow direction and corresponding shrinkage of the chains in the confined direction; here the hydrodynamic effects of each wall cancel one another out. Considering the polymer chain as a Stokeslet-doublet (point-force-dipole) as in a previously developed kinetic theory captures the correct far-field (relative to the walls) behavior. Once a finite-size dipole is used, the theory improves its near-wall predictions. In the regime 2h ∼ L>Rg, the results are significantly affected by the level of discretization of the polymer chain, i.e., number of springs, because the spatial distribution of the forces exerted by the chain on the fluid acts on the scale of the channel geometry.
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47.57.Ng Polymers and polymer solutions
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.11.-j Computational methods in fluid dynamics
05.40.Jc Brownian motion

Small amplitude oscillations of a flexible thin blade in a viscous fluid: Exact analytical solution

Cornelis A. Van Eysden and John E. Sader

Phys. Fluids 18, 123102 (2006); http://dx.doi.org/10.1063/1.2395967 (11 pages) | Cited 13 times

Online Publication Date: 13 December 2006

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The oscillation of a thin blade immersed in a viscous fluid has received considerable attention recently due to its importance in technological applications such as the atomic force microscope and microelectromechanical systems. In this article, we consider the general case of a flexible thin blade executing spatially varying small amplitude oscillations in a viscous fluid. Exact analytical solutions for the three-dimensional flow field and hydrodynamic load are derived for both normal and torsional oscillations of arbitrary wave number. This contrasts previous investigations that focus exclusively on the complementary rigid-blade problem, which is two-dimensional, and rely on computational techniques.
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47.85.Dh Hydrodynamics, hydraulics, hydrostatics
89.20.Kk Engineering

Study of phase transition in homogeneous, rigid extended nematics and magnetic suspensions using an order-reduction method

Guanghua Ji, Qi Wang, Pingwen Zhang, and Hong Zhou

Phys. Fluids 18, 123103 (2006); http://dx.doi.org/10.1063/1.2408484 (17 pages) | Cited 6 times

Online Publication Date: 29 December 2006

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We study the phase transition in rigid extended nematics and magnetic suspensions by solving the Smoluchowski equation for magnetically polarized rigid nematic polymers and suspensions in equilibrium, in which the molecular interaction is modeled by a dipolar and excluded volume potential. The equilibrium solution (or the probability distribution of the molecular distribution) is given by a Boltzmann distribution parametrized by the (first-order) polarity vector and the (second-order) nematic order tensor along with material parameters. We show that the polarity vector coincides with one of the principal axes of the nematic order tensor so that the equilibrium distribution can be reduced to a Boltzmann distribution parametrized by three scalar order parameters, i.e., a polar order parameter and two nematic order parameters, governed by three nonlinear algebraic-integral equations. This reduction in the degree of freedom from 8 (3 in the polarity vector and 5 in the nematic order tensor) to 3 significantly simplifies the solution procedure and allows one to conduct a complete analysis on bifurcation diagrams of the order parameters with respect to the material parameters. The stability of the equilibria is inferred from the second variation of the free energy density.
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47.57.Ng Polymers and polymer solutions
47.57.Lj Flows of liquid crystals
47.65.Cb Magnetic fluids and ferrofluids
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
64.70.M- Transitions in liquid crystals
02.30.Rz Integral equations
back to top Particulate, Multiphase, and Granular Flows

Measurements of the fluid and particle mobilities in strong electric fields

Anil Kumar, Ezinwa Elele, Mike Yeksel, Boris Khusid, Zhiyong Qiu, and Andreas Acrivos

Phys. Fluids 18, 123301 (2006); http://dx.doi.org/10.1063/1.2397573 (10 pages) | Cited 2 times

Online Publication Date: 6 December 2006

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We present a method for measuring both the fluid and particle velocities in strong electric fields and carefully analyze the repeatability and reproducibility of the measurements. The experiments were conducted in 50-μm capillaries containing dilute aqueous suspensions of 4-μm polystyrene spheres subjected to dc as well as ac (5−50 Hz) fields of strengths up to 1 and 0.6 kV/cm, respectively. These measurements indicate that the predictions of classical linear theories for electrokinetic phenomena apply well beyond the range of relatively weak electric fields for which these theories were developed. The results of our studies are critical for the quantification of microanalytical systems which make use of electrokinetic phenomena for the transport, control, and manipulation of fluids and particles.
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47.80.-v Instrumentation and measurement methods in fluid dynamics
47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.57.E- Suspensions
47.57.Ng Polymers and polymer solutions
47.55.-t Multiphase and stratified flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.50.Ef Measurements
47.85.Np Fluidics

Experimental study of two-dimensional, monodisperse, frictional-collisional granular flows down an inclined chute

Weitao Bi, Renaud Delannay, Patrick Richard, and Alexandre Valance

Phys. Fluids 18, 123302 (2006); http://dx.doi.org/10.1063/1.2405844 (14 pages) | Cited 4 times

Online Publication Date: 19 December 2006

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In this study, positions, velocities, and rotations of monodisperse disks confined two-dimensionally in a glass-walled chute are measured using a high-speed camera. Steady, fully developed granular flows (SFD) down bumpy inclines are systematically investigated in the frictional-collisional (dense, rapid) regime. Three bottoms with different effective roughness heights and roughness distributions are studied to evaluate the influence of the bottom condition. The granular flows are shallow, having a typical depth of ten disk diameters. In the range of flow rates and inclination angles where SFD flows occur, the mean discharge velocity is approximately proportional to the flow depth. The surface solid fractions slightly decrease from the bottom to the free surface. The streamwise velocity profiles are close to the linear profile at small inclination angles, whereas at large inclination angles, they are best approximated by the Bagnold profile. The mean angular velocity is equal to the half shear rate everywhere in the flow except near the free surface and the bottom. At large inclination angles, relatively deep SFD flows exhibit an S-shaped granular temperature profile, but in the core, the temperature is far from scaling linearly with the square shear rate. The streamwise and crosswise translational temperatures are slightly different from each other, whereas the rotational temperature is only half of the crosswise translational temperature. The rough bottoms have complex influences on the granular flows as revealed by the velocity and temperature profiles.
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47.57.Gc Granular flow
47.32.Ef Rotating and swirling flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.80.Jk Flow visualization and imaging
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)

The effect of inlet conditions on concentrated suspension flows in abrupt expansions

Tracey Moraczewski and Nina C. Shapley

Phys. Fluids 18, 123303 (2006); http://dx.doi.org/10.1063/1.2409619 (4 pages) | Cited 5 times

Online Publication Date: 29 December 2006

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This work explores the influence of inlet conditions on the particle concentration distribution and flow field of a concentrated suspension undergoing steady flow in an abrupt, axisymmetric 1:4 expansion. Specifically, we consider the impact of inlet conditions in the upstream narrow tube on the resulting downstream profiles. Particle concentration and velocity profiles were measured by using nuclear magnetic resonance imaging. Experiments were conducted with two contrasting inlet tube lengths of 10d1 and 128d1, where d1 is the diameter of the narrow inlet tube. In the short inlet case, none of the particle concentration fields were fully developed upon entering the expansion, whereas several of the suspensions had fully developed profiles in the long inlet case. Results indicate that concentration differences between the core and annular regions were greater for the cases with a long inlet tube than in cases with a short inlet tube, likely owing to the higher degree of particle migration occurring in the long inlet tube before entry into the expansion. Also, the lengths of recirculating regions were greater for suspensions in the long inlet than in the short inlet geometry, while both systems followed the same trend of increasing recirculation length with bulk particle volume fraction and correlation with the ratio of tube center to wall concentration values.
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47.57.eb Diffusion and aggregation
47.55.Kf Particle-laden flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.80.Jk Flow visualization and imaging
47.50.Ef Measurements
back to top Instability and Transition

Linear stability of a nonorthogonal axisymmetric stagnation flow on a rotating cylinder

Mustapha Amaouche, Faïçal Nait Bouda, and Hamou Sadat

Phys. Fluids 18, 124101 (2006); http://dx.doi.org/10.1063/1.2403179 (13 pages) | Cited 1 time

Online Publication Date: 14 December 2006

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The present analysis deals with the onset of instability in an axisymmetric stagnation flow obliquely impinging on a uniformly rotating circular cylinder. The basic flow is described by an exact solution of the Navier-Stokes equations, discovered by Weidmann and Putkaradze [Eur. J. Mech. B/Fluids 22, 123 (2003) ]. An eigenvalue problem for the linear stability is formulated, regardless of the free stream obliqueness, and then solved numerically by means of a collocation method using Laguerre’s polynomials. It is established that the basic stagnation flow is stable for sufficiently high Reynolds numbers. This is in conformity with the unconditional linear stability of two-dimensional Hiemenz stagnation flow. Instability occurs for Reynolds numbers smaller than some threshold value that increases with the rotation rate of the cylinder. At criticality, the flow undergoes a Hopf bifurcation, leading then to an oscillatory secondary motion.
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47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
47.32.Ef Rotating and swirling flows
47.52.+j Chaos in fluid dynamics
47.10.ad Navier-Stokes equations
47.85.Np Fluidics
02.60.Cb Numerical simulation; solution of equations

Convective instabilities in a rotating vertical Hele-Shaw cell

Keke Zhang, Xinhao Liao, Xiaoya Zhan, and Rixiang Zhu

Phys. Fluids 18, 124102 (2006); http://dx.doi.org/10.1063/1.2404946 (10 pages)

Online Publication Date: 15 December 2006

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Convective instabilities driven by vertical buoyancy in a Boussinesq fluid in a rotating vertical Hele-Shaw cell, a long channel with rectangular cross section of finite height h and small width Γh with Γ≪1, are investigated both analytically and numerically. The problem is characterized by the Taylor number T, the Rayleigh number R, and the aspect ratio Γ. Explicit asymptotic solutions describing convective instabilities are derived for ΓT1/6≪1, where T is assumed to be large compared to unity. Comparison between the asymptotic and fully numerical solutions shows a satisfactory quantitative agreement. It is found that an overall condition for convective instabilities becomes optimal when ΓT1/6 = O(1). Direct three-dimensional simulations for strongly nonlinear convection are also carried out in the regime 0<(R−Rc)/Rc ≤ O(10), where Rc denotes the critical Rayleigh number. As a consequence of both the geometric and dynamic constraints imposed by the narrow channel (geometric) and rapid rotation (dynamic), the nonlinear flow remains temporally stationary and spatially simple and is comprised primarily of vertically long thin convection cells that transport heat all the way from the bottom to the top of the channel.
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47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.55.pb Thermal convection
47.32.Ef Rotating and swirling flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
02.60.Cb Numerical simulation; solution of equations

Influence of Prandtl number on stability of mixed convective flow in a vertical channel filled with a porous medium

P. Bera and A. Khalili

Phys. Fluids 18, 124103 (2006); http://dx.doi.org/10.1063/1.2405321 (10 pages) | Cited 9 times

Online Publication Date: 20 December 2006

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Buoyancy opposed mixed convection is considered in a vertical channel filled with an isotropic, porous medium, in which the motion of an incompressible fluid is induced by external pressure gradients and buoyancy forces. The Brinkman-Wooding-extended Darcy model has been used to study the instability mechanisms of the basic flow and its dependence on the Prandtl number (Pr) of the fluid. The stability analysis indicated that for the same Reynolds number (Re), the fully developed base flow was highly unstable for a fluid with high Pr. For a porous medium with a Darcy number (Da) of 10−6 and Pr ≥ 0.7, two different types of instability, Rayleigh-Taylor (R-T) and buoyant instability, are observed. The R-T instability mode is observed for relatively small values of Re. Further, the results show that for Da = 10−5 and Pr<1, the spectrum of the energy profile is abrupt and sudden, whereas the same is smooth when Da = 10−6. In the case of R-T instability, the critical value of Ra at low Re is given by −2.47/Da. Though the R-T mode of instability is independent of Pr, the range of Re that sustains the R-T mode is a function of Pr. It has been found that enhancement of Pr reduces the Re range mentioned above. In contrast to the case of a purely viscous fluid, where the effect of Pr is not significant, in isotropic porous media Pr plays a significant role in characterizing the flow stability. The instability characteristics of zero temperature flux perturbation (BC-I) and zero heat flux perturbation (BC-II) on the boundaries differ significantly in the case of the R-T stability mode. However, both conditions lead to similar results for buoyant stability, except at small values of Re.
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47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.55.pb Thermal convection
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.56.+r Flows through porous media
47.85.Np Fluidics
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