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Volume 11, Issue 4, April 1999
 ARTICLES


Screening mechanisms in sedimentation
View Description Hide DescriptionThis paper considers a mixture of sedimenting particles at low Reynolds numbers and volume fractions. Simple theoretical arguments have long suggested that for a random suspension of particles in an infinite system, the fluctuations in the velocity about the mean should diverge with system size. On the other hand, experiments have shown no such divergence. The primary goal of this paper is to examine the effect of side walls on the predicted divergence in fluctuations, through theory, scaling arguments, and numerical simulations. Side walls lead to important modifications of the standard arguments. A scaling argument (based on wall effects) is presented to rationalize recent experiments by Segré et al. [Phys. Rev. Lett. 79, 2574 (1997)]. The paper also briefly discusses the role of inertia in screening fluctuations in infinite systems when the particle Reynolds number is very low, and also the coupling between the velocity fluctuations and the mean sedimenting velocity. A physical argument suggests that in some circumstances the fluctuations give a leading order correction to the mean sedimenting velocity as a function of volume fraction.

Dynamics of nonBrownian rodlike particles in a nonuniform elongational flow
View Description Hide DescriptionThis paper deals with the orientation of nonBrownian rodlike particles in a nonuniform elongational flow at lowReynolds number. Experimentally, an elongational flow is created by introducing a small circular orifice into a cylindrical channel. The flow field is studied using a tracer anemometry technique. On the axis of symmetry, the deformation field is that of a pure elongation with a nonuniform elongation rate. It is well described by the analytical solution obtained for an infinite contraction ratio. This flow is used to study the dynamics of nonBrownian rodlike particles subject to nonuniform elongation. The orientation dynamics of a particle depends on the history of the deformation that it has experienced. The effects of small perturbations existing in the vicinity of the orifice are greatly amplified downstream. Consequently, particle motion does not exhibit the symmetry with respect to the orifice which is expected at lowReynolds number.

Radial displacement of a fluid annulus in a rotating Hele–Shaw cell
View Description Hide DescriptionThe radial displacement of a fluid annulus in a rotating circular Hele–Shaw cell has been investigated experimentally. It has been found that the flow depends sensitively on the wetting conditions at the outer interface. Displacements in a prewet cell are well described by Darcy’s law in a wide range of experimental parameters, with little influence of capillary effects. In a dry cell, however, a more careful analysis of the interfacemotion is required; the interplay between a gradual loss of fluid at the inner interface, and the dependence of capillary forces at the outer interface on interfacial velocity and dynamic contact angle, result in a constant velocity for the interfaces. The experimental results in this case correlate in the form of an empirical scaling relation between the capillary number Ca and a dimensionless group, related to the ratio of centrifugal to capillary forces, which spans about three orders of magnitude in both quantities. Finally, the relative thickness of the coating film left by the inner interface, is obtained as a function of Ca.

The rear meniscus of a long bubble steadily displacing a Newtonian liquid in a capillary tube
View Description Hide DescriptionIn this work the interfacial shapes and the flow occurring at the trailing meniscus of a long bubble is numerically analyzed. The technique employed solves the complete set of governing equations simultaneously. The numerical results reported complete previous descriptions of the creeping flow regime; the influence of the inertia forces on the free surface shapes, interfacial undulations, and flowpatterns is also analyzed.

Hydrodynamics and stability of a deformable body moving in the proximity of interfaces
View Description Hide DescriptionThe motion of a deformable body embedded in an inviscid irrotational nonuniform ambient flow field in the proximity of interfaces is treated here using a newly developed Hamiltonian formalism. The corresponding dynamic equations governing the motion of the body are derived and their integrability is investigated. We find that the presence of boundaries results in an additional chaotization of a body’s motion. Based on the derived Hamiltonian formalism the Liapunov stability of the motion of a body translating parallel or towards a remote flat wall is also considered using the EnergyCasimir approach. The appropriate stability criteria are derived. Finally some applications for bubble dynamics concerning an influence of a periodical deformation of a bubble on its motion is presented.

Bicomponent Newtonian filaments
View Description Hide DescriptionA model is introduced which captures the mechanical behavior of slender bicomponent filaments. The model is deduced from the threedimensional free surfaceboundary value problem through integration over the filament cross section, and applied to core and sheath fluids which are Newtonian with a bonded interface. Through examples simulating filament manufacturing processes, we investigate different regimes of bicomponent filament behavior, examining the interplay of core and sheath viscosities and densities, and surface and interfacial tensions (which are found to have special importance). We focus on features which are special to bicomponent filaments, namely the traction at the core/sheath interface, the partition of the axial force in the filament between core and sheath, and dependence on sheathtocore ratios of material properties.

An analysis of flow, temperature, and chemical composition distortion in gas sampling through an orifice during chemical vapor deposition
View Description Hide DescriptionMeasurement of the chemical composition of gases sampled through a small hole in the substrate can be a useful diagnostic for investigations of the chemistry of chemical vapor deposition(CVD) processes. Ideally, one would measure the composition of the gas at the growth surface. However, the flow disturbance due to sampling causes the conditions at the mouth of the orifice to be different from those at the growth surface. Unless the orifice diameter is sufficiently small, relative to the thickness of chemical and thermal boundary layers above the growth surface, the sampled composition will differ from the composition at the growth surface. In this work, we present results of twodimensional simulations of the flow,heat transfer, and chemical reactions in an axisymmetric stagnation point flow with gas sampling through a small orifice in the substrate on the symmetry axis of the flow field. Detailed results are given for atmosphericpressure radiofrequency plasma CVD of diamond, corresponding to experiments performed in our laboratory. We also present more general results, approximate analytical representations of the flow field, and scaling rules for the size of the disturbance due to the sampling orifice.

Stability of oscillatory twophase Couette flow: Theory and experiment
View Description Hide DescriptionThe interfacialinstability due to viscosity stratification is studied experimentally in a closed Couette geometry. A vertical interface is formed between two concentric cylinders with densitymatched fluids of unequal viscosity. The outer cylinder is rotated with a timeharmonic motion, causing spatially periodic disturbances of the interface. The wavelengths and growth rates predicted by linear theory agree well with experimental results. Application of Fjo/rtoft’s inflection point theorem shows the neutral stability curves to be consistent with an internal instability occurring in the less viscous phase. Because the standard Floquet theory yields only timeaveraged growth rates, the instantaneous behavior of the system is examined numerically. This reveals the flow to be unstable to a disturbance which has a maximum that oscillates between the interface and a location within the less viscous fluid. Surprisingly, it is found that interfacialwave amplification originates with the internal disturbance, and is not directly caused by interfacial shear. This unsteady instability may explain the growth of waves in “transient” process flows, e.g., fluids encountering changing flow geometry. It is also demonstrated that in the long wave limit the problem of steadyplusoscillatory plate motion is simply additive. This implies that it is possible to use oscillations to stabilize steady waves over a limited range of parameter values, but only when the less viscous phase is adjacent to the moving boundary.

Dry arches within flowing films
View Description Hide DescriptionWhen a liquid filmflows down an inclined nonwettable surface, dewetting can be triggered at low flow rate. After a transient, stationary dry patches edged with a liquid rim form. From experimental investigations, we deduce that their shape arises in a large flow range from a balance between the rim weight and surface tension. A simple model based on this assumption provides an analytical expression for the arch shape, in excellent agreement with experiments. The patch size scales as capillary length, capillary velocity, Γ flow rate per unit length). Above a critical flow rate, of order dry patches cannot be stationary and are swept away, leaving a fully wet surface. Both the typical size and the critical flow rate depend nontrivially on the contact angle and on the solid surface inclination.

Experimental and numerical study of RayleighBénard convection affected by a rotating magnetic field
View Description Hide DescriptionIn the present paper we experimentally study the effects of a rotating magnetic field (RMF) on the fluid flow in an electrically conducting melt (Gallium), kept in a cylindrical container heated from below (RayleighBénard configuration). The experimental data are compared to results obtained from threedimensional, timedependent numerical calculations. The paper presents the influence of the magnetic inductionB, the frequency of the RMF Ω, and the temperature difference between the hot bottom and cold top of the melt on heat transport and fluid flow, respectively. The results can be summarized in terms of the parameter which is defined as the ratio of magnetic Taylor number to Grashof number It is shown that for largescale regular thermal waves exist, which travel azimuthally in the same direction as the rotation direction of the RMF. These thermal waves are connected with largescale temperature fluctuations (amplitude 6%–10% of ). The amplitude decreases with increasing whereas the mean frequency increases from 0.001 Hz up to 0.1 Hz for For temperature fluctuations with amplitudes smaller than 1%–2% of and frequencies greater than 0.1 Hz are observed. These oscillations can be attributed to Taylor vortices generated at the vertical cylinder walls. The regions of the different oscillation modes within the parameter space are shown in a stability diagram.

A numerical revisit of backwardfacing step flow problem
View Description Hide DescriptionIn the present study we take a fresh look at a laminar flow evolving into a larger channel through a step configured in a backwardfacing format. We conduct steady threedimensional Navier–Stokes flow analysis in the channel using the step geometry and flow conditions reported by Armaly et al. This allows a direct comparison with the results of physical experiments, thus serving to validate the numerical results computed in the range of 100⩽Re⩽1000. Results show that there is generally excellent agreement between the present results and the experimental data for Re=100 and 389. Fair agreement for Re=1000 is also achieved, except in the streamwise range of The main difference stems from the fact that the roof eddy is not extended toward the midspan in the channel with a span width 35 times of the height of the upstream channel. In the present study we also reveal that the flow at the plane of symmetry develops into a twodimensionallike profile only when the channel width is increased up to 100 times of the upstream step height for the case with Re=800. The present computational results allow the topological features of the flow to be identified using critical point theory. The insight thus gained is useful in revealing a mechanism for the development of an endwallinduced threedimensional vortical flow with increasing Reynolds number.

Variational methods and nonlinear quasigeostrophic waves
View Description Hide DescriptionIn this paper, we discuss zonally periodic steady quasigeostrophic waves in a plane channel, by using variational methods. A class of steady quasigeostrophic waves are determined by the potential vorticity field profile, g(⋅), which is a function of the stream function. We show that zonally periodic steady quasigeostrophic waves exist when the bottom topography and the potential vorticity field are bounded. We also show that these waves are unique if, in addition, the potential vorticity field profile is increasing and passes through the origin. Finally, we demonstrate that the zonal periodic wave in the case with is nonlinearly stable in the sense of Liapunov, under a boundedness condition for the potential vorticity field, or equivalently, under suitable conditions on the bottom topography, β parameter, and zonal period T.

An anelastic, scaleseparated model for mixing, with application to atmospheric transport phenomena
View Description Hide DescriptionWe present and analyze a simplified, scaleseparated, anelastic fluid model which is designed to assess the influence of weak compressibility in the diffusive transport of a passive scalar. Our model incorporates a slowly varying, density induced, anisotropy into a fixed, rapidly varying (small scale) fluid flow. This anisotropy is physically motivated through the anelastic mass balance which retains vertical density variations occurring over the atmospheric scale height (∼8 km). Consequently, these steady flows are nonsolenoidal over large scales and approximately incompressible on small scales. We apply homogenization methods to calculate the large scale, effective mixing experienced by a passive scalar diffusing in the presence of this small scale flow. Over large scales, the evolution of the scalar field is governed by an effective, variable coefficient, anelastic mixing equation. The variable coefficients entering this equation are shown to depend nontrivially upon both the large scale anisotropy as well as the structure of the small scale fluid flow. We establish that anelastic effects produce anisotropic mixing properties not shared by the analogous incompressible closure. Specifically, the mixing equation possesses exact nontrivial bounded steady states, whereas the incompressible regime has only constant (i.e., spatially homogeneous) steady states. Furthermore, the anelastic mixing equation is shown numerically to possess local regions of trapped (Fig. 3) and focused (Figs. 6 and 7) contaminants, behavior not possible in the analogous incompressible model. These results imply that anelastic effects, which occur naturally in the atmosphere, provide mechanisms which locally reduce mixing and generate inhomogeneities in large scale concentration fields.

Influence of gravity on nonlinear transport in the planar Couette flow
View Description Hide DescriptionThe effect of gravity on a dilute gas subjected to the steady planar Couette flow with arbitrarily large velocity and temperature gradients is analyzed. The results are obtained from the Bhatnagar–Gross–Krook kinetic model by means of a perturbation expansion in powers of the external field. The reference state corresponds to the pure (nonlinear) Couette flow solution, which retains all the hydrodynamic orders in the shear rate and the thermal gradient. To first order in the gravity field, we explicitly obtain the hydrodynamic profiles and the five relevant nonlinear transport coefficients; the shear viscosity the two viscometric functions and the two nonzero elements, and of the thermal conductivitytensor. The results show that, in general, the influence of gravity on the rheological properties and tend to decrease as the shear rate increases, while this influence is especially important in the case of the thermal conductivity coefficient, which measures the heat flux parallel to the temperature gradient.

Vortex crystals from 2D Euler flow: Experiment and simulation
View Description Hide DescriptionVortexincell simulations that numerically integrate the 2D Euler equations are compared directly to experiments on magnetized electron columns [K. S. Fine, A. C. Cass, W. G. Flynn, and C. F. Driscoll, “Relaxation of 2D turbulence to vortex crystals,” Phys. Rev. Lett. 75, 3277 (1995)], where turbulent flows relax to metastable vortex crystals. A vortex crystal is a lattice of intense small diameter vortices that rotates rigidly in a lower vorticity background. The simulations and experiments relax at the same rates to vortex crystals with similar vorticity distributions. The relaxation is caused by mixing of the background by the intense vortices: the relaxation rate is peaked when the background circulation is 0.2–0.4 times the total circulation. Close quantitative agreement between experiment and simulation provides strong evidence that vortex crystals can be explained without incorporating physics beyond 2D Euler theory, despite small differences between a magnetized electron column and an ideal 2D fluid.

Experiments on the stability of streamwise streaks in plane Poiseuille flow
View Description Hide DescriptionThe development and stability of streamwise streaks are studied in an airflow channel experiment at subcritical Reynolds numbers. The streaks were generated by continuous suction through small slots at the wall. The streak amplitude first grows algebraically, and if the amplitude exceeds a certain threshold secondary instability in the form of travelling waves is observed. These waves give rise to high values in the region of large spanwise mean flow gradient. Measurements with two hotwire probes indicate that velocity fluctuations are 180 out of phase at two neighboring peaks at each side of a low velocity region and implies the existence of a sinuous type instability.Measurements were also made with controlled disturbances where earphones were used to force the secondary instability. Phase averaged data clearly show the oscillation of the low velocity region and also provides the growth rate, phase speed as well as amplitude and phase distributions of the secondary instability. Several of these features suggest that the instability is of inflectional origin. Finally the disturbance breaks down and the flow undergoes transition to turbulence.

Magnetohydrodynamic flow in a rectangular duct in a cusped magnetic field
View Description Hide DescriptionLiquid metalflow in a rectangular duct in a plane cusped magnetic field is considered with the main objective being to investigate the effect of the sidewalls on the flow. At high values of the Hartmann number Ha the velocity profile is characterized by the presence of three jets. One jet is at the symmetry plane, where the transverse component of the magnetic field changes sign, and the magnetic field is parallel to the flow. The other two are at the sidewalls parallel to the field. The overall flow balance is determined by the wall conductance ratios of the sidewalls and the Hartmann walls (these are the walls with a nonzero normal component of the field). If the sidewalls are conducting, the jet at the symmetry plane dominates. If the sidewalls are electrically insulating, the sidewall jets dominate. In the latter case the flow pattern exhibits only a small resemblance to the analogous flow between two parallel plates (no sidewalls), which was investigated before. The pressure drop is higher than in the corresponding flow in a uniform, transverse magnetic field. This means that braking the flow by a cusped field is more effective, and this feature can be used in some applications of magnetohydrodynamics, such as electromagnetic brakes and semiconductorcrystal growth from melts.
