Volume 16, Issue 2, February 2004
 LETTERS


On the inverse Magnus effect in free molecular flow
View Description Hide DescriptionA Newtoninspired particle interaction model is introduced to compute the sideways force on spinning projectiles translating through a rarefied gas. The simple model reproduces the inverse Magnus force on a sphere reported by Borg, Söderholm and Essén [Phys. Fluids 15, 736 (2003)] using probability theory. Further analyses given for cylinders and parallelepipeds of rectangular and regular polygon section point to a universal law for this class of geometric shapes: when the inverse Magnus force is steady, it is proportional to onehalf the mass M of gas displaced by the body.

Freesurface entrainment into a rimming flow containing surfactants
View Description Hide DescriptionWe study experimentally the freesurface entrainment of tubes into a steady rimming flow formed inside a partially filled horizontally rotating cylinder. The liquid consists of a glycerin–water mixture containing surfactants (fatty acids). The phenomenon does not occur without the surfactants and the details are sensitive to their concentration. The entrainment of numerous closely spaced air tubes and/or surfactant columns can start intermittently along a twodimensional stagnation line, but is usually associated with the appearance of an axially periodic vortex structure, the socalled shark teeth, which fixes the spanwise location of these tubes. The number of tubes is governed by the threedimensional shape of the free surface, reducing from more than 10 to only two in each trough, as the rotation rate is increased. The tubes vary in diameter from 10–30 μm and can extend hundreds of diameters into the liquid layer before breaking up into a continuous stream of bubbles and/or drops. The tubes are driven through the stagnation line by the strong viscous shear and are stretched in the downstream direction. The entrainment starts when the Capillary number
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 ARTICLES


Nonequilibrium moleculardynamics simulation of net evaporation and net condensation, and evaluation of the gaskinetic boundary condition at the interphase
View Description Hide DescriptionAlgorithms for simulating steady net evaporation and net condensation with molecular dynamics are presented. The evaporation and condensation coefficients are calculated, showing that they are not equal outside equilibrium. The distribution function at the interphase boundary is evaluated. There is a drift away from the interphase in the distribution function for the evaporated molecules and a drift velocity towards the interphase for the reflected molecules, both for net evaporation and for net condensation.

Computational analysis of the deformability of leukocytes modeled with viscous and elastic structural components
View Description Hide DescriptionThe objective of this work is to systematically include nonNewtonian effects in a previous Newtonian model of the leukocyte and to study the effects thereof on leukocyte rheology. The standard Newtoniandrop model of the cell is enhanced in three respects: (1) The cortical layer is treated as an elasticmembrane with a nonlinear stress–strain curve to simulate unfolding of the excess surface area of the membrane. (2) A powerlaw shear thinning fluid is used for the cytoplasm. (3) A threelayer or compound cellmodel is used, which is comprised of the membrane cortex, cytoplasm and nucleus. Combinations of these aspects are also investigated. The governing equations for this multifluid system are solved in the Stokes limit. The immersed boundary technique is used to simulate the interaction of the elasticmembrane with the flow field. Results indicate that each of these additional elements in the leukocyte model yield significant deviations from the Newtonian deformation and recovery behavior of the leukocyte. However, the added modeling sophistication does not appear to be sufficient to fully capture all the distinctive responses of the leukocytes under a wide variety of deformation and recovery protocols. It is shown that although a comprehensive model for the leukocyte remains elusive, the threelayer leukocyte model with cortical elasticity is a promising candidate.

Effect of system size on particlephase stress and microstructure formation
View Description Hide DescriptionIn this paper, we investigate the effect of particle number, or system size, on threedimensional (3D) particle dynamic simulation results. Specifically, we simulate conditions with varying e (coefficient of restitution) and φ (solids volume fraction), containing particle numbers ranging from 250 to 300 000. Various algorithmic improvements are implemented in the simulation to efficiently handle these large numbers of particles. We observe, for the first time for 3D simulations, particlephase microstructure formation at high coefficients of restitution. Furthermore, we show the onset of the particlephase microstructure formation at various threshold system sizes, depending on the value of e and φ, and relate it to an increase in particlephase stress. Visual observations are used to conduct a preliminary investigation of the nature of the microstructure formation. Multiple welldefined bands are observed for simulations of at least 100 000 particles.

The role of boundary conditions in a simple model of incipient vortex breakdown
View Description Hide DescriptionWe consider incipient vortex breakdown and describe how infinitesimal perturbations may destabilize a columnar swirling jet. The framework is axisymmetric and inviscid following Wang and Rusak’s [J. Fluid Mech. 340, 177 (1997)] analysis. The goal of the present study is to relate the local properties of swirling flows in infinite pipes to their global stability properties in pipes of finite length. A spatial linear stability analysis is pursued which gives a complementary point of view to the subcritical/supercritical concept introduced by Benjamin [J. Fluid Mech. 14, 593 (1962)]. In contrast to supercritical flows which exhibit two neutral spatial branches traveling downstream and two counterpropagating evanescent spatial branches, subcritical flows exhibit a frequency range where all spatial branches are neutral, three of which travel downstream and one upstream. By using global energy budget arguments and monitoring how the upstream wave is reflected into the downstream waves and conversely, the inlet and outlet conditions are shown to drive the instability in the limit of long but finite pipes. Various inlet and outlet conditions are proposed that stabilize or destabilize the flow, depending on their ability to supply energy. The analysis demonstrates therefore that the global instability accounting for incipient vortex breakdown in Wang and Rusak’s model may arise from the combination of a locally neutral flow and suitable inlet and outlet conditions.

The effects of thin and ultrathin liquid films on dynamic wetting
View Description Hide DescriptionWe examine the effects of thick (micron scale) fluid films and thin molecular scale (10–100 Å) films on the hydrodynamics near advancing contact lines by measuring the liquid–vapor interface shape of a meniscus and comparing the measurements to three models. Using flow visualization, we directly observe the fluid flow field near the moving contact line and give a qualitative description of the stagnation point and dividing streamline emanating from the contact line region. For thick films, when the capillary number satisfies (where d is the film thickness and a is the macroscopic length scale of the system), the liquid–vapor interface is bent only slightly by the viscous flow and the effective dynamic contact angle is close to zero. As Ca approaches a modulated wedgelike region appears at some distance from the film and expands both away from and toward the film as Ca increases. The dynamic contact angle approaches the classic power law behavior as this region expands. For molecularly thin films, the liquid–vapor interface shape within microns of the moving contact line is correctly described by theoretical models based purely on hydrodynamics and without disjoining pressure effects.

A loss of memory in stratified momentum wakes
View Description Hide DescriptionIn this paper we compare the wakes of various bluff bodies in a stratified fluid at moderately high Froude numbers and Reynolds numbers (Re≈5000). The size and amplitude of the longlasting wakes clearly depend on the shape of the bluff body, the wake width being small for a streamlined object and large for an object with sharp edges. However, the wake width can be collapsed when it is normalized by an effective diameter based on the drag force, often called the momentum thickness. General laws for the wake width, the velocity defect, and the Strouhal number are thus deduced and fit the data well. Finally, the crossfluctuations of the velocity and the turbulent kinetic energy are analyzed. Their amplitudes and widths are proportional to those of the mean profile. Thus, the wake remembers only the momentum flux given by the bluff body to the fluid and not any other aspects of its geometry.

Spray characterization during vibrationinduced drop atomization
View Description Hide DescriptionVibrationinduced drop atomization is a process of rapid droplet ejection from a larger liquid drop. This occurs when a liquid drop resting on a thin diaphragm is vibrated under the appropriate forcing conditions using an attached piezoelectric actuator. The resulting spray of small droplets is characterized in this work using highspeed imaging and particletracking techniques. The results show that the average spatial and velocity distributions of the spray droplets are fairly axisymmetric during all stages of the atomization. The mean diameter of the droplets depends on the forcing frequency to the −2/3 power. The ejection velocity of the spray droplets depends on both the magnitude and the rate of change of the forcing amplitude. Thus, controlling the characteristics of the forcing signal may lead to strategies for controlling the spray process in specific applications.

Rarefaction effects on shear driven oscillatory gas flows: A direct simulation Monte Carlo study in the entire Knudsen regime
View Description Hide DescriptionA complete mathematical description of oscillatory Couette flows within the framework of kinetic theory is not available in the literature. Motivated by this and their vast engineering applications, we present a parametric study of timeperiodic oscillatory Couette flows using the unsteady direct simulation Monte Carlo (DSMC) method. Computations are performed as a function of the Knudsen (Kn) and Stokes (β) numbers, in the entire Knudsen regime and a wide range of Stokes numbers The DSMC results are validated using a recently developed semianalytical/empirical model that is applicable for quasisteady flows in the entire Knudsen regime, and for any Stokes number flow in the slip flow regime In addition, we derived an analytical solution of the linearized collisionless Boltzmann equation for oscillatory Couette flows, and utilized this to validate the DSMC results in the freemolecular flow regime. Dynamic response of the flow, including the velocity profiles, phase angle, wave speed, shear stress, and the penetration depth for high Stokes number flows are presented. Increasing the Stokes number at fixed Kn, we observed formation of “bounded Stokes layers,” as expected. However, increasing the Knudsen number at fixed β results in “bounded rarefaction layers,” where the penetration depth continuously decreases with increasing the Kn. Interplay between the rarefaction and unsteadiness contributes to this interesting flow physics, and also introduces a new characteristic length scale to the problem.

Combined effect of volume and gravity on the threedimensional flow instability in noncylindrical floating zones heated by an equatorial ring
View Description Hide DescriptionThe present paper strongly extends a previous analysis dealing with the investigation of the threedimensional Marangoni flow instability in cylindrical floating zones (straight liquid column of fullzone extent) of a low Prandtl liquid laterally heated by a ring positioned around the equatorial plane and under microgravity conditions. The new study gives insights into the combined influence of volume and gravitational effects. The deformation of the free melt–gas interface due to the gravity field is taken into account. Parallel supercalculus is used to reduce the otherwise prohibitive computational time. The prominent features of the threedimensional field are largely dependent on geometrical parameters. The results (full zone) are heretofore unseen and show that the interplay between the upper half and lower half of the liquid domain is an essential factor for the correct description of the phenomena under investigation. They are contrasted with the case of the half zone for which a rich variety of interesting and worthy contributions is available in literature.

Flow over yawed circular cylinders: Wall pressure spectra and flow regimes
View Description Hide DescriptionThe fluctuating wall pressure on a circular cylinder in cross flow has been investigated experimentally in a water tunnel to examine the effect of yaw angle on the spectral characteristics of the wall pressure field and to provide insight into the periodic and turbulent structures of the flow. Wall pressure was measured at five azimuthal positions around the periphery of the cylinder for seven yaw angles from α=90° (normal flow) to α=0° (axial flow) at three subcritical Reynolds numbers As the yaw angle is varied from α=90° to 0°, large systematic and nonmonotonic variations in both the narrowband (periodic vortex shedding) and broadband (turbulent) spectral levels occur. The results provide additional insight into the structural characteristics of the yawed cylinder flow regimes over that which has been identified previously through measurements of mean wall forces and flow field characteristics. Significant Reynolds numbereffects were also observed over the range of the measurements, particularly at small yaw angles, that may indicate fundamental shifts in the structure of the wake or underlying regime transition mechanisms. Possible effects due to vortexinduced cylinder vibrations are not entirely clear but predominantly confined to the larger yaw angles. Simultaneous wall pressure, cylinder vibration, radiated acoustic pressure, and wake velocity measurements are required to appropriately isolate the various potential contributions to the wall pressure field and thus provide a clearer understanding of the underlying boundary layer separation, transitional wake, and fluidstructural coupling mechanisms.

Oscillatory Marangoni convection in binary mixtures in square and nearly square containers
View Description Hide DescriptionThreedimensional simulations of oscillatory convection in binary mixtures driven by the Marangoni effect have been performed. The upper surface of the fluid is heated by a constant heat flux while the bottom is maintained at a constant temperature. Surface deflection is ignored. Oscillations are the result of concentrationinduced changes in the surface tension due to the presence of an anomalous Soret effect. In domains with a square horizontal cross section and aspect ratio Γ=1.5 these take the form of either a standing wave with left–right reflection symmetry or a discrete rotating wave, depending on the separation ratio and the Schmidt number. Standing oscillations with reflection symmetry in a diagonal are unstable. When the cross section is slightly rectangular only the former bifurcate from the conduction state, and the transition to stable rotating waves with increasing Marangoni number proceeds via a sequence of secondary local and global bifurcations. The results are interpreted in terms of predictions from equivariant bifurcation theory.

On selfsimilarity of detonation diffraction
View Description Hide DescriptionWe consider diffraction of a detonation into an unconfined region of explosive. One might expect detonation flow to be selfsimilar, as in inert shock diffraction, when the reaction zone length is short compared to a geometric flow scale. One might expect that at very early time after the detonation has turned the corner, the region of explosive along the wall behaves according to the selfsimilar expansion for an inert flow, or as a selfsimilar Taylor blast wave of fixed strength. We use direct numerical simulations and study dynamic transients in selfsimilar coordinates to explore these hypotheses. We consider stateinsensitive and statesensitive reaction rate laws that mimic condensed explosives. We find through an analysis of shock arrival times, that the cylindrical detonation is useful in describing the dynamics of the expansion region in a twodimensional detonation diffraction event. Therefore, we believe that detailed study of cylindrical (or spherical) detonations can be used to develop simplified or analytic models of detonation diffraction.

Chemical pattern formation driven by a neutralization reaction. I. Mechanism and basic features
View Description Hide DescriptionWe study the chemohydrodynamic pattern formation during interfacial mass transfer accompanied by a neutralization reaction. The system, which is placed in a HeleShaw cell, is a configuration of two immiscible liquid phases in contact along a plane interface. In the upper, organic layer a carboxylic acid is dissolved, the concentration of which is far beyond the equilibrium partition ratio. Interfacial acid transfer initiates the neutralization with an organic base dissolved in the lower, aqueous layer. Focus is on the exploration of a novel instability consisting of a regular cellular structure penetrating into the aqueous bulk solution. By several complementary experimental methods, including shadowgraph visualization with different magnifications, particle imagevelocimetry, differential interferometry, and detailed measurements of relevant material properties, the driving mechanism of the instability is identified. Synthesis of the experimental results suggests that lateral differences in buoyancy are responsible for the convection.

Impaction of a droplet on an orifice plate
View Description Hide DescriptionA novel method of generating secondary droplets using the impaction of a liquiddroplet on an orifice plate is proposed. Here, a numerical simulation of this problem is provided using a one fluid volumeoffluidbased method without considering air in the environment. The impactingdroplet may partly spread on the surface of the plate, and partly penetrate through the orifice. The penetrated part may breakup forming a daughter droplet, as well as smaller satellite droplets. The sizes of the generated droplets are related to the volume of the liquid immediately on top of the orifice upon impact. The outcome of the impaction is discussed based on the sizes of the daughter and satellite droplet formed, their velocities, the breakup time, and the breakup length of the penetrated ligament. The influence of the following parameters on the outcome of the impaction is considered: liquidviscosity,liquid surface tension, initial droplet size and velocity, orifice diameter, and the liquid contact angle. A critical number exists for any given We number, under which droplet generation is impossible. Generally, the size of the generated droplet is weakly influenced by the liquidviscosity, and strongly influenced by the liquid surface tension. The size of the daughter droplet increases with the orifice size and reduces with the liquidviscosity, whereas the size of the satellite droplet increases with the viscosity.

Velocity oscillations in turbulent Rayleigh–Bénard convection
View Description Hide DescriptionA systematic study of velocity oscillations in turbulent thermal convection is carried out in small aspectratio cells filled with water. Local velocity fluctuations and temperaturevelocity crosscorrelation functions are measured over varying Rayleigh numbers and spatial positions across the entire convection cell. These structural measurements reveal how the thermal plumes interact with the bulk fluid in a closed cell and provide an interesting physical picture for the dynamics of the temperature and velocity oscillations in turbulent convection.

Stability of symmetric and asymmetric vortex pairs over slender conical wings and bodies
View Description Hide DescriptionTheoretical analyses are presented for the stability of symmetric and asymmetric vortex pairs over slender conical wings and bodies under small perturbations in an inviscid incompressible flow at high angles of attack and sideslip. The threedimensional problem of a pair of vortices over slender conical wings and bodies is reduced to a problem in two dimensions by using the conical flow assumption and classical slenderbody theory. The stability of symmetric and asymmetric vortex pairs over flatplate delta wings, slender circular cones, and elliptic cones of various thickness ratios are examined. Results are compared with available experimental data.

The rheology of a dilute suspension of Brownian dipolar spheroids in a simple shear flow under the action of an external force
View Description Hide DescriptionThe effect of rotational Brownian motion on the rheology of a dilute suspension of dipolar spheroids in a simple shear flow under the action of an external force field, is investigated through a generalized Langevin equation approach. The force field is assumed to be either constant or periodic. In the case of constant external fields earlier results in the literature are reproduced, while for the case of periodic forcing certain parametric regimes corresponding to weak Brownian diffusion are identified where the rheological parameters evolve chaotically and settle onto a low dimensional attractor. The response of the system to variations in the strengths of the force field and diffusion is also analyzed through numerical experiments. These results correspond to the region of weak Brownian motion where usual methods render the problem intractable.

Slow flow through a brush
View Description Hide DescriptionThis paper reports velocity measurements of slow flow through a model brush. The flow field was created in the annulus between two concentric cylinders, which was filled with a viscous oil. The inner cylinder was stationary and the outer one was installed on a turntable and rotated at a constant speed. A brush was modeled by an array of uniformly spaced rods mounted horizontally onto the inner cylinder. With a generous gap between the rod ends and the outer cylinder, the flow outside the array was circular Couette flow. Three brushes were made and the external shear flow penetrated these because the solid volume fractions were small, namely, 0.025, 0.05, and 0.10. Particle imagevelocimetry was used to study the velocity field in the penetration region, and from these measurements the velocity at the interface, “the slip velocity,” was determined. The slip velocity was found to be close to the value predicted by Brinkman’s equation, and to be higher than velocities found previously for rod arrays in other configurations.
