Volume 20, Issue 2, February 2008

A new tensor statistic, the dispersedphase structure dimensionality , is defined to describe the preferred orientation of clusters of discrete bodies. The evolution of is calculated via direct numerical simulations of passive, Stokesian particles driven by initially isotropic, decaying magnetohydrodynamicturbulence. Results are presented for five magnetic field strengths as characterized by magnetic interaction parameters, , in the range 0–50. Four field strengths are studied at a grid resolution of . The strongest field strength is also studied at resolution. In each case, the externally applied magnetic field was spatially uniform and followed a step function in time. Particles with initially uniform distributions were tracked through hydrodynamicturbulence for up to 2800 particle response times before the step change in the magnetic field. In the lower resolution simulation, the particle response time, , matched the Kolmogorov time scale at the magnetic field application time . The higherresolution simulation tracked ten sets of particles with spanning four decades bracketing the Kolmogorov time scale and the Joule time. The results demonstrate that distinguishes between uniformly distributed particles, those organized into randomly oriented clusters, and those organized into twodimensional sheets everywhere tangent to the magnetic field lines. Lumley triangles are used to demonstrate that the degree of structural anisotropy depends on , , and the time span over which the magnetic field is applied.
 ARTICLES

 Interfacial Flows

Determination of the pseudopotential gradient in multiphase lattice Boltzmann models
View Description Hide DescriptionUsing the multiphase lattice Boltzmann method of Shan and Chen [Phys. Rev. E47, 1815 (1993)], the intermolecular force is calculated from the gradient of a pseudopotential. The pseudopotential is in quadratic relation with the equation of state of the fluid model. This fact motivated some researchers [P. Yuan and L. Schaefer, Phys. Fluids18, 042101 (2006); R. S. Qin, Phys. Rev E73, 066703 (2006)] to introduce new forms for the pseudopotential and to model fluids with some desired equation of state. Using such models the determination of the pseudopotential and its gradient is often ambiguous and lead to numerical instabilities as we demonstrate in this paper. We propose a simple method to solve this problem.

Asymptotic analysis of the selective dip coating of powerlaw fluids
View Description Hide DescriptionThe dip coating of a chemically micropatterned surface bearing alternating wetting and nonwetting vertical strips is analyzed for a nonNewtonian powerlaw fluid. Asymptotic matching is used to determine the thickness of liquid films deposited on the strips at small capillary and Bond numbers. The chemical patterning that confines the fluid laterally induces a significant transverse curvature of the freesurface. The streamwise variation in this transverse curvature along the strip provides an additional contribution to the capillary pressure gradient that is not present for uniform surfaces. Consequently, the difference in the thickness of the deposited liquid film relative to a Newtonian fluid is significantly less than for homogeneous plates or fibers.

A simple model to describe the lateral oscillations of axisymmetric liquid bridges
View Description Hide DescriptionThe axisymmetric dynamics of an isothermal liquid bridge has been analyzed frequently over the past years. The studies have considered different phenomena such as free oscillations, forced vibrations, gjitter effects, extensional deformation, and the breakup process, among others. Works considering the nonaxisymmetric dynamical behavior of a liquid bridge have been far less common, probably due to the further difficulties associated with its threedimensional nature. Based on simple physical arguments, a model is proposed in this paper to describe the linear lateral oscillations of an axisymmetric viscousliquid bridge. The accuracy of the model is established from comparison with the Navier–Stokes equations for zero Capillary number and with experimental measurements for viscousliquid bridges. Good agreement is found in both cases for frequencies smaller than or of the order of the first resonance frequency. Potential applications of the model are discussed.

Satellite generation during bubble coalescence
View Description Hide DescriptionWe experimentally study the formation of a satellitebubble, during the coalescence of two larger bubbles. The daughter bubble is generated by capillary waves which propagate from the growing neck, connecting the two bubbles and focus on the opposite apex. As the successive waves converge on the top, their amplitude grows until a small daughter bubble is pinched off. The mechanism is robust over a large range of parameters. We have observed it in water for bubble diameters from down to . For equally sized parent bubbles, the size of the daughter bubble is times that of the mother bubble, but the daughter size also depends weakly on the approach velocity of the two initial bubbles. The effects of viscosity is to dampen the capillary waves, preventing the pinchoff for Ohnesorge number , which is significantly smaller than the critical value observed for the coalescence cascade of a drop. The relative size of the parent bubbles has a large influence on the pinchoff, suppressing it when the size difference is too large. Linear wavetheory can reproduce the overall wave phenomenon and the amplitude evolution of the capillary waves, with the dominant mode number .

Thin Newtonian film flow down a porous inclined plane: Stability analysis
View Description Hide DescriptionThe flow of a thin Newtonian fluid layer on a porous inclined plane is considered. Applying the longwave theory, a nonlinear evolution equation for the thickness of the film is obtained. It is assumed that the flow through the porous medium is governed by Darcy’s law. The critical conditions for the onset of instability of a fluid layer flowing down an inclined porous wall, when the characteristic length scale of the pore space is much smaller than the depth of the fluid layer above, are obtained. The results of the linear stability analysis reveal that the filmflow system on a porous inclined plane is more unstable than that on a rigid inclined plane and that increasing the permeability of the porous medium enhances the destabilizing effect. A weakly nonlinear stability analysis by the method of multiple scales shows that there is a range of wave numbers with a supercritical bifurcation, and a range of larger wave numbers with a subcritical bifurcation.Numerical solution of the evolution equation in a periodic domain indicates the existence of permanent finiteamplitude waves of different kinds in the supercritical stable region. The longtime waveforms are either timeindependent waves of permanent form that propagate or timedependent modes that oscillate slightly in the amplitude. The presence of the porous substrate promotes this oscillatory behavior. The results show that the shape and amplitude of the waves are influenced by the permeability of the porous medium.
 Viscous and NonNewtonian Flows

Chaotic mixing in microfluidic devices driven by oscillatory cross flow
View Description Hide DescriptionThe kinematics of oscillatory cross flow has been studied numerically as a means for generating chaotic mixing in microfluidic devices for both confined and continuous throughput flow configurations. The flow is analyzed using numerical simulation of the unsteady Navier–Stokes equations combined with tracking of single and multispecies passive tracer particles. Two characteristics of chaotic flow are demonstrated: the stretching and folding of material lines leading to particle dispersion and a positive “effective” Lyapunov exponent. The primary mechanism for the generation of chaotic flow is a periodic combination of stretching (which occurs via shear in the channels) and rotation (which occurs via the timing of the oscillations), making these systems effective tendrilwhorl type flows. First, the case of confined mixing is studied. It is shown that chaotic flow is generated in a crosscell device when sinusoidally driven, outofphase, perpendicular fluid streams intersect in the flow domain. Calculations indicate that the flow becomes chaotic in the center region starting at a Strouhal number on the order of 1. A degree of mixing based on a relative mixing entropy as high as 91% is obtained. Approximately 10–15 sinusoidal cycles are needed in order to effectively mix different groups of passive tracer particles. In the second phase of the analysis, the cross flowmixing mechanism is utilized in a continuous operation by combining a throughput channel flow with an oscillatory cross flow in a configuration called the starcell geometry. It is shown that the oscillatory flow remains chaotic even in combination with the throughput flow, and a degree of mixing in the 80%–90% range is obtained for the range of parameters studied here.

Cavitation in anisotropic fluids
View Description Hide DescriptionSustained cavitation in the lubrication layer between a rotating heavy sphere and a nearby wall in a Newtonian fluid is an essential aspect of the motion. Here we extend these findings to the case of anisotropic materials using both shearthinning and viscoelastic fluids. As in the case of Newtonian fluids, cavitation is observed but new interesting features emerge. These include the formation of long fingers that can either be steady or dynamic with apparent irregular interactions.

Resonant pumping in a multilayer impedance pump
View Description Hide DescriptionThis paper introduces the concept of multilayer impedance pump, a novel pumping mechanism inspired by the embryonic heart structure. The pump is a composite twolayer fluidfilled elastic tube featuring a thick gelatinous internal. Pumping is based on the impedance pumping mechanism. In an impedance pump, elastic waves are generated upon external periodic compressions of the elastic tube. These waves propagate along the tube’s walls, reflect at the tube’s extremities, and drive the flow in a preferential direction. The originality in the multilayer impedance pump design relies on the use of the thick internal gelatinous layer to amplify the elastic waves responsible for the pumping. As a consequence, only small excitations are needed to produce significant flow. This fully coupled fluidstructure interaction problem is solved for the flow and the structure using the finite element method over a relevant range of frequencies of excitation. Results show that the multilayer impedance pump is a complex system that exhibits a resonant response. Flow output and inner wall motion are maximal when the pump is actuated at the resonant frequency. The wave interaction mechanism present in an impedance pump is described here in details for the case of a multilayer impedance pump. Using energy balance for the passive portion of the elastic tube, we show that the elastic tube itself works as a pump and that at resonance maximum energy transmission between the elastic tube and the fluid occurs. Finally, the pump is especially suitable for many biomedical applications.

Viscous gravity currents inside confining channels and fractures
View Description Hide DescriptionUnidirectional flows of long, thin, Newtonian, viscous gravity currents inside either horizontal or inclined channels are studied theoretically and experimentally. Effects due to temporal variations in the input rate at a point source and spatial variations in the channel shape are considered, with surface tension effects neglected. The current evolves with a selfsimilar structure at large times when the total volume of fluid scales with time like and the spreading in the lateral direction is constrained by a rigid boundary of height , where the length scale of the channel size varies with distance along the flow like and , and are prescribed constants. The extent of the flow scales like , where the constant depends linearly on and is determined in terms of , , and . Amongst channels that remain uniform along the flow, a Vshaped channel gives rise to either a fastest or slowest propagation rate of the current depending on whether or , respectively, while the value of is the same for all when , with either or for horizontal or inclined flows, respectively. The position of a current inside either an extremely narrow or nearly flat Vshaped channel that gently widens along the flow is also studied and shown to be proportional to a power of time. We determine that the spreading is constrained mainly by volume conservation for the case inside wide channels and by frictional drag at the rigid boundaries for inside narrow fractures.
 Particulate, Multiphase, and Granular Flows

Effect of packing fraction on granular jetting from solid sphere entry into aerated and fluidized beds
View Description Hide DescriptionWhen a solid sphere impacts on a granular bed, a highspeed vertical jet can arise following the collapse of the cavity that is formed by the penetration of the sphere into the bed. The jet then becomes unstable and breaks into discrete clusters due to density inhomogeneities. In this study, the jetting process was observed using highspeed photography and determined to be a function not only of impact velocity and particle size, but also of the packing fraction in the bed during the impact. Experiments were performed for two different bed diameters, two bed heights, and two impact velocities. Under certain conditions, below a threshold packing fraction, the jet is seen to divide into two distinct parts: a thin upper section followed by a thick base. Geometrical constraints are also shown to be critical in determining the dynamics of the jet.

Spreading fronts in sedimentation of dilute suspension of spheres
View Description Hide DescriptionThe thickness of the diffuse front between a sedimenting dilute suspension and the clear fluid above grows linearly in time due to polydispersity in the size of the particles and due to a hydrodynamic effect in which randomly heavy clusters fall out of the front leaving it depleted. Experiments and simplified pointparticle numerical simulations agree that these two effects are not simply linearly additive.
 Laminar Flows

A simple method for deducing properties of laminar wall jets in uniform pressure fields, with undetermined farfield conditions
View Description Hide DescriptionA simple method is proposed in order to draw various information concerning boundary layers that develop axisymmetrically on a flat plate, when the outer pressure field is uniform, and when the farfield conditions, perpendicularly to the plate, are unknown. It is shown that if, at an arbitrary radial coordinate , one measures both the value of the maximum radial velocity (i.e., ) and the height (i.e., ) where the radial velocity reaches its maximum value, one can build a nondimensional number, which we shall call . This number is an invariant in this study. It also allows us to calculate several parameters, such as, for instance, the local shear rate on the plate or the power laws for the radial velocity decrease and the boundary layer thickness increase, according to the downstream distance, corresponding here to the radial coordinate .

Twophase flow pattern transition across micropillars: Size scale effect at the microscale
View Description Hide DescriptionSize scale effect of adiabatic twophase crossflow over micropillars was experimentally investigated, and the mechanisms controlling the formation and transition of the recently discovered bridge flow was examined. A transition criterion, based on the Weber and Euler numbers, for the breakage of the bridges, is provided. The bridges break from the surface when the product of the Weber and Euler numbers is larger than ; otherwise, the bridges cease to exist by coalescing with liquid slugs.
 Instability and Transition

Appearance of target pattern and spiral flames in radial microchannels with air mixtures
View Description Hide DescriptionThis paper presents the experimental evidence of the formation of rotating spiral flames with premixed methaneair mixtures introduced at the center of the two parallel circular quartz plates which are separated by a millimeter scale distance . Both plates are externally heated to create a positive wall temperature gradient in the flow direction to resemble heat recirculation through solid walls, which is a requisite to obtain stabilized combustion in microburners. Contrary to the general perception of a stable premixed flame front at a radial location, a variety of nonstationary flame propagation modes are observed. For lower mixture flow rates and a range of mixture equivalence ratios, a radial flame propagation mode is observed with simultaneous presence of two circular flames at different radial locations. For higher flow rates, a rotating spiral flame propagation mode is observed. In addition to radial and spiral flame propagation modes, random and unsymmetrical flame oscillations are also observed. The rotational rates of the spiral flame fronts were observed to vary from 28 to . A simple analysis is carried out to describe the formation of spiral flames from a steady circular flame.

Asymptotic theory of wallattached convection in a horizontal fluid layer with a vertical magnetic field
View Description Hide DescriptionA horizontal fluid layer heated from below in the presence of a vertical magnetic field is considered. A simple asymptotic analysis is presented which demonstrates that a convection mode attached to the side walls of the layer sets in at Rayleigh numbers much below those required for the onset of convection in the bulk of the layer. The analysis complements an earlier analysis by Houchens et al. [J. Fluid Mech.469, 189 (2002)] which derived expressions for the critical Rayleigh number for the onset of convection in a vertical cylinder with an axial magnetic field in the cases of two aspect ratios.

Evaluation of mean energy fluxes in thermoacoustic oscillations of a gas in a tube
View Description Hide DescriptionIn a previous paper [N. Sugimoto and M. Yoshida, Phys. Fluids19, 074101 (2007)], the marginal condition for the onset of thermoacoustic oscillations of a gas in a tube subjected to the parabolic temperature distribution was derived in the framework of the linear and firstorder theory in the boundarylayer thickness. This paper examines the marginal oscillations from a viewpoint of mean energy fluxes averaged over one period of oscillations, aiming at understanding an action of the boundary layer under finite temperature gradient. Using the nonlinear energy equation, formulas for the acoustic energy flux and the convective heat flux (entropy flux times temperature) are derived in the mainflow region and in the boundary layer within the lowest, quadratic order in the pressure amplitude. These fluxes may be evaluated in terms of the linearized solutions and their axial distributions are displayed graphically. The boundary layer occupying nearly half of the side wall near the open end plays an active role to pump energy into the acoustic mainflow region, whereas the other half plays a passive role to dissipate energy. The acoustic energy flux in the mainflow region flows toward the closed end, while the flux in the boundary layer flows down the gradient of the pressure amplitude and toward the open end. The convective heat flux flows only in the boundary layer and directed down the temperature gradient. In the vicinity of the closed end, however, this heat flux flows against the temperature gradient. The heat flux through the side wall comes mostly into the boundary layer but goes out of it near the closed end. Such an Eulerian picture of the flow field is examined from a Lagrangian viewpoint in terms of thermodynamic relations for a gas particle fixed. While the particle in the mainflow region is subjected to the adiabatic change to yield no net power per one period of oscillations, the one in the boundary layer is subjected to a thermodynamic cycle of a prime mover or a heat pump, depending on whether the value of the product of the gradients of the logarithmic temperature and pressure amplitude is beyond a certain value. Discussions are also focused on the mechanisms to maintain the marginal state of oscillations and the efficiency as heat engines.

Pearl and mushroom instability patterns in two miscible fluids' core annular flows
View Description Hide DescriptionWe report on experiments with two miscible fluids of equal density but different viscosities. The fluids were injected cocurrently and concentrically into a cylindrical pipe. The resulting base state is an axisymmetric parallel flow. The ratio of the two fluid flow rates determines the relative amount of the fluids, thus the radius of the inner core fluid. Depending on this radius and the total flow rate, two different and unstable axisymmetric patterns, denoted by mushrooms and pearls, were observed. We delineate the diagram of occurrence of the two patterns as a function of the various parameters.

On the inviscid neutral curve of rotating Poiseuille pipe flow
View Description Hide DescriptionThis paper concerns linear instabilities of incompressible flow along a rotating pipe when the disturbances are inviscid. The inviscid spectrum comprises an infinite number of eigenmodes, and significant complications arise from (i) switching in the identity of the most unstable mode and (ii) the existence of distinguished parameter limits in which some or all of the modes acquire special scalings. Nevertheless, we show that in one sense all the instabilities form a single ordered family, which we term a centermode family, by applying an asymptotic theory recently developed for the trailing line vortexflow. We give complete computed neutral curves (stability boundaries) over a wide range of Rossby numbers, as well as contour plots of maximum growth rate. We find that the numerical calculations are in good agreement with the asymptotic theory and correctly recover previous results, including the limits of very large and very small Rossby number. There is some disagreement, however, with published results on the neutral curve at finite Rossby number. We show that this disagreement results from the intricate nature of the spectrum, which possesses two different types of neutral mode with two distinguished scalings.

Kelvin waves with helical Beltrami flow structure
View Description Hide DescriptionIn this work we show that when an inviscid axisymmetric Rankine flow experiences a soft expansion, rotating Kelvin waves can be excited. Downstream of the region where the expansion occurs (the transition region) the resulting flow can be expressed as the addition of a Rankine and a Beltrami flow. The Beltrami constant is determined from the Rankine upstream flow, and the helix pitch of the mode results from the boundary conditions downstream. Finally, a discussion of the process leading to oscillatory flow and a conjecture about the topological background that sustains the Beltrami flow structure are offered.

Streak interactions and breakdown in boundary layer flows
View Description Hide DescriptionThe objective of this paper is to show that the interaction of streamwise velocity streaks of finite length can lead to turbulentbreakdown in the flatplate boundary layer flow. The work is motivated by previous numerical and experimental studies of transitional flows where the highfrequency oscillations leading to turbulence are seen to form in the region of strongest shear induced by streaks in relative motion. Therefore, a model for the interaction of steady and unsteady (i.e., slowly moving in the spanwise direction) spanwise periodic streaks is proposed. The interaction of two subsequent streaks is investigated for varying collision parameters. In particular, the relative spanwise position and angle are considered. The results show that the interaction is able to produce both a symmetric and asymmetric breakdown without the need for additional random noise from the main stream. Velocity structures characteristic of both scenarios are analyzed. Hairpin and vortices are found in the case of symmetric collision between a lowspeed region and an incoming highspeed streak, when a region of strong wallnormal shear is induced. Alternatively, when the incoming highmomentum fluid is misaligned with the lowspeed streak in front, single quasistreamwise vortices are identified. Despite the different symmetry at the breakdown, the detrimental interaction involves for both cases the tail of a lowspeed region and the head of a highspeed streak. Further, the breakdown appears in both scenarios as an instability of threedimensional shear layers formed between the two streaks. The streak interaction scenario is suggested to be of relevance for turbulence production in wallbounded flows.