Volume 21, Issue 8, August 2009

A spherical bead deposited on a smooth tilted dry plane wall rolls down the slope under the uniform acceleration of gravity. We describe an analogous experiment conducted using a plane wall that is coated with a thin layer (of order ) of a viscousliquid. The steady motion of the sphere under gravity involves a combination of rotation and sliding. We examine the dependence of the experimentally observed steady translational and rotational speeds on the physical parameters in the system. In particular, the interplay between viscous forces and interfacial forces leads to nontrivial exponents for the scaling of the speeds with the characteristics of the sphere and the viscousliquid. The overhang situation, in which the sphere rolls down the underside of an inclined lubricated plane, is also examined. In this case, the steady motion is still observed for a certain range of angles and bead sizes; that is, the sphere does not always detach from the surface. The adhesive force arises dynamically from the motion of the sphere and can exceed classical quasistatic capillary forces. Such a force should also play a role in other problems of lubrication mechanics such as humid granular flows.
 LETTERS


Motion of a vortex ring in a simple shear flow
View Description Hide DescriptionThe motion and deformation of a vortex ring in a linear or simple shear flow have been simulated numerically by using the lattice Boltzmann method with multiple relaxation times. The study is motivated by a recent experiment [T. T. Lim, K. B. Lua, and K. Thet, Phys. Fluids20, 051701 (2008)], which shows that a vortex ring propagating in a uniform cross flow does not experience Kutta lift and undergo tilting and deformation. The focus of the present study is to examine the effect of a simple shear in a cross flow on the motion of a vortex ring. Numerical approach is adopted here because a truly simple shear flow is difficult to generate experimentally. Our computation shows that a vortex ring tilts and deforms in a simple shear flow, and the tilting can be attributed to the modification of the vorticity distribution of the vortex ring as a result of the entrainment of background vorticity by the vortex core. It is further shown that although the shear in the flow has the tendency to elongate the vortex ring, the tilting angle of the ring increases with the shear ratio.

The behavior of subgridscale models near the turbulent/nonturbulent interface in jets
View Description Hide DescriptionThe behavior of subgridscale models near the turbulent/nonturbulent interface in jets is analyzed by using direct numerical simulation and largeeddy simulation(LES). The subgrid scales of motion near this region are far from equilibrium and contain an important fraction of the total kinetic energy. The Smagorinsky constant needs to be corrected near the jet edge and the method used to obtain the dynamic Smagorinsky constant is not able to cope with the intermittent nature of this region. A priori tests and LES show that near the jet edge the Smagorinsky model is superior both to the dynamic Smagorinsky and to the gradient models.

Coupled flutter of parallel plates
View Description Hide DescriptionExperimental visualizations of the coupled flutter of an assembly of two, three, and four flexible parallel cantilevered plates immersed in an axial uniform flow are presented. Depending on the flowvelocity, on the interplate distance, and on the plate length, different coupled modes are observed. Selected modes and the associated thresholds and frequencies are compared with the results of a linear stability analysis.

Turbulenceinduced secondary motion in a buoyancydriven flow in a circular pipe
View Description Hide DescriptionWe analyze the results of a direct numerical simulation of the turbulentbuoyancydriven flow that sets in after two miscible fluids of slightly different densities have been initially superimposed in an unstable configuration in an inclined circular pipe closed at both ends. In the central region located midway between the end walls, where the flow is fully developed, the resulting mean flow is found to exhibit nonzero secondary velocity components in the tube cross section. We present a detailed analysis of the generation mechanism of this secondary flow which turns out to be due to the combined effect of the lateral wall and the shearinduced anisotropy between the transverse components of the turbulent velocity fluctuations.

 ARTICLES

 Biofluid Mechanics

Linear stability analysis of gyrotactic plumes
View Description Hide DescriptionBioconvection occurs as the result of the collective behavior of many microorganisms swimming in a fluid and is realized as patterns similar to those of thermal convection, which occur when a layer of fluid is heated from below. We consider the phenomenon of pattern formation due to gyrotaxis, an orientation mechanism which results from the balance of gravitational and viscous torques acting on bottomheavy microorganisms. Using the continuum model of Pedley et al. [“The growth of bioconvection patterns in a uniform suspension of gyrotactic microorganisms,” J. Fluid Mech.195, 223 (1988)], the linear stability of a gyrotactic plume (descending line of concentrated microorganisms) is investigated. Linear stability analysis predicts that a plume is always unstable to both the varicose and meandering modes. The growth rates of these instability modes and their dependence on parameter values are investigated. Comparisons are made with the experimental and numerical results.

Approximate behavior of arbitrarily unsteady laminar flow in long, straight, flexible tubes
View Description Hide DescriptionAnalytical solutions have been obtained for laminar flows in long, straight tubes with linearly elastic walls that undergo arbitrary spatial/temporal unsteadiness from a known initial state. These initialboundary value solutions express quantities such as the momentary wall deflection, flow rate, and wall shear stress as functionals of the pressure field’s history under the assumptions that unsteady effects propagate as longwavelength disturbances at a constant wave speed and produce changes in the wall shear stress that are significantly less than in the pressure. These solutions are particularly useful for analysis of pulsatile periodic and aperiodic flows that come to rest before restarting, for which existing continuously unsteady analytical solutions do not apply. When the arbitrary unsteadiness is given the particular form of a sinusoidally varying pressure field that starts from rest at time zero, the longtime behavior of these approximate solutions is in excellent agreement with existing analytical solutions for continuously unsteady flow at all but low values of the Womersley frequency parameter.
 Micro and Nanofluid Mechanics

Extending the Navier–Stokes solutions to transition regime in twodimensional micro and nanochannel flows using information preservation scheme
View Description Hide DescriptionThe kinetictheorybased numerical schemes, such as direct simulation Monte Carlo (DSMC) and information preservation (IP), can be readily used to solve transition flow regimes. However, their high computational cost still promotes the researchers to extend the Navier–Stokes (NS) equations beyond the slip flow and to the transition regime applications. Evidently, a suitable extension would accurately predict both the local velocity profiles and the mass flow rate magnitude as well as the streamwise pressure distribution. The secondorder slip velocity model derived from kinetic theory can provide relatively accurate velocity profiles up to a Knudsen (Kn) number of around 0.5; however, its mass flow rate accuracy decreases as Knudsen number approaches the upper bound. One remedy is to consider the rarefaction effects in calculating the NS viscosity coefficient. In this work, we use the shear stress distribution derived from our IP simulations, extend an analytical expression for the viscosity coefficient, impose it in the NS equations, and evaluate it via solving the transition regime. Using the new viscosity coefficient, we also derive an analytical expression for the mass flow rate, which provides accurate solutions for and even beyond in micro and nanochannel flows. We also show that the obtained streamwise pressure distribution agrees well with that of the DSMCIP in this range. The current study is concerned with low speed diatomic gas flow through twodimensional micro and nanochannels.
 Interfacial Flows

Stability of gravitycapillary waves generated by a moving pressure disturbance in water of finite depth
View Description Hide DescriptionIn previous work, we investigated twodimensional steady gravitycapillary waves generated by a localized pressure distribution moving with a constant speed in water of finite depth . Localized solitary waves can only exist in subcritical flows where the Froude number , and were found using a combination of numerical simulations of the fully nonlinear inviscid, irrotational equations, and analytically from a weakly nonlinear longwave model, the steady forced Korteweg–de Vries equation. The solution branches depended on three parameters, the Froude number, , the Bond number, , and the magnitude and sign of the pressure distribution, . In this paper, we examine the twodimensional stability of these waves using numerical simulations of the fully nonlinear unsteady equations. The results are favorably compared to analogous numerical solutions of the unsteady forced Korteweg–de Vries equation. We find that for , the smallamplitude steady depression wave is stable whereas the largeamplitude steady depression wave is unstable. The depression wave with a dimple at its crest, which occurs only when is unstable, but the smallamplitude elevation wave with is stable.

The Richtmyer–Meshkov instability in magnetohydrodynamics
View Description Hide DescriptionIn ideal magnetohydrodynamics(MHD), the Richtmyer–Meshkov instability can be suppressed by the presence of a magnetic field. The interface still undergoes some growth, but this is bounded for a finite magnetic field. A model for this flow has been developed by considering the stability of an impulsively accelerated, sinusoidally perturbed density interface in the presence of a magnetic field that is parallel to the acceleration. This was accomplished by analytically solving the linearized initial value problem in the framework of ideal incompressible MHD. To assess the performance of the model, its predictions are compared to results obtained from numerical simulation of impulse driven linearized, shock driven linearized, and nonlinear compressible MHD for a variety of cases. It is shown that the analytical linear model collapses the data from the simulations well. The predicted interface behavior well approximates that seen in compressible linearized simulations when the shock strength, magnetic field strength, and perturbation amplitude are small. For such cases, the agreement with interface behavior that occurs in nonlinear simulations is also reasonable. The effects of increasing shock strength, magnetic field strength, and perturbation amplitude on both the flow and the performance of the model are investigated. This results in a detailed exposition of the features and behavior of the MHD Richtmyer–Meshkov flow. For strong shocks, large initial perturbation amplitudes, and strong magnetic fields, the linear model may give a rough estimate of the interface behavior, but it is not quantitatively accurate. In all cases examined the accuracy of the model is quantified and the flow physics underlying any discrepancies is examined.

Rolling stones: The motion of a sphere down an inclined plane coated with a thin liquid film
View Description Hide DescriptionA spherical bead deposited on a smooth tilted dry plane wall rolls down the slope under the uniform acceleration of gravity. We describe an analogous experiment conducted using a plane wall that is coated with a thin layer (of order ) of a viscousliquid. The steady motion of the sphere under gravity involves a combination of rotation and sliding. We examine the dependence of the experimentally observed steady translational and rotational speeds on the physical parameters in the system. In particular, the interplay between viscous forces and interfacial forces leads to nontrivial exponents for the scaling of the speeds with the characteristics of the sphere and the viscousliquid. The overhang situation, in which the sphere rolls down the underside of an inclined lubricated plane, is also examined. In this case, the steady motion is still observed for a certain range of angles and bead sizes; that is, the sphere does not always detach from the surface. The adhesive force arises dynamically from the motion of the sphere and can exceed classical quasistatic capillary forces. Such a force should also play a role in other problems of lubrication mechanics such as humid granular flows.

Separation of sheet flow on the surface of a circular cylinder
View Description Hide DescriptionThe shape of a spout of a pot is very important for the liquid to flow smoothly from the pot. This is known as the “teapot effect.” Separation of flow must take place at the tip of the spout. Separation of sheet flow on the surface of a circular cylinder may provide an explanation as to why pot spouts have such a unique shape. As can be easily observed by a simple experiment, separation of sheet flow from the surface of a circular cylinder is a very interesting phenomenon beyond intuition. In the nonviscous case, the flow released at the top of the surface may proceed completely around the surface and come back to the flow start point without separation. In the present paper, effects of gravity and viscosity on sheet flow are theoretically explained and the theory is verified by experiments. The results of the theoretical model proposed in the present study were very similar to the experimental measurements. In the present study, the effects of viscosity on sheet flow on a circular cylinder, the location of flow separation, and other associated responses were investigated.

On the breakup of fluid rivulets
View Description Hide DescriptionWe study the stability of rivulets on horizontal substrates. The implemented model includes the effects of capillarity, fluidsolid interaction, and gravity if appropriate, within the framework of the lubrication approximation. We find that the results compare favorably with those in literature, in the regime where previous analyses are valid. By isolating the effect of van der Waals interactions for nanoscale rivulets, and of gravity for macrosize rivulets, we are able to analyze the influence of these forces on the stability. We discuss in detail the scaling of the emerging wavelengths (distance between drops formed after the breakup process) with the rivulet crosssectional area. Perhaps surprisingly, we uncover close connection between this scaling and the one for the breakup of a freespace fluid jet (Rayleigh–Plateau instability). Finally, we consider rivulets of finite length and find that the finite size effects are considerably different from the ones obtained previously for semiinfinite fluid films.
 Viscous and NonNewtonian Flows

Influence of miscible viscous fingering of finite slices on an adsorbed solute dynamics
View Description Hide DescriptionViscous fingering (VF) between miscible fluids of different viscosities can affect the dispersion of finite width samples in porous media. We investigate here the influence of such VF due to a difference between the viscosity of the displacing fluid and that of the sample solvent on the spatiotemporal dynamics of the concentration of a passive solute initially dissolved in the injected sample and undergoing adsorption on the porous matrix. Such a three component system is modeled using Darcy’s law for the fluid velocity coupled to massbalance equations for the sample solvent and solute concentrations. Depending on the conditions of adsorption, the spatial distribution of the solute concentration can either be deformed by VF of the sample solvent concentration profiles or disentangle from the fingering zone. In the case of deformation by fingering, a parametric study is performed to analyze the influence of parameters such as the logmobility ratio, the ratio of dispersion coefficients, the sample length, and the adsorption retention parameter on the widening of the solute concentration peak. The results highlight experimental evidences obtained recently in reversedphase liquid chromatography.

Enhancement of transport from drops by steady and modulated electric fields
View Description Hide DescriptionWe consider the problem of transport of heat or mass from circulating droplets that are both settling and subject to an axial electric field. The electric field can be either steady or oscillatory in time and drives an electrohydrodynamic flow, called the Taylor circulation, which augments the Hadamard circulation caused by steady translation. The problem is governed by four dimensionless groups: the Peclet number Pe, the dimensionless amplitudes of both the steady and unsteady electric field, and the dimensionless frequency of the modulation. The convective diffusion equation is solved numerically by an efficient finitedifference scheme that allows a wide range of parameters—in particular, very large Peclet numbers—to be covered. The results are characterized by the asymptotic rate of extraction of heat or mass from the droplet, which is found to be exponential in time. The enhancement factor, defined as the ratio of this rate to that of a stagnant drop, is studied as a function of parameters. For steady drops, we find that transport remains diffusion controlled, but the enhancement factor is significantly higher with the Taylor flow than without. For modulated electric field the enhancement factor is not a simple function of parameters and exhibits spectral “resonant peaks” at particular values of for which the enhancement factor is extremely large. Movies of the simulations are used to study the underlying timeperiodic spatial structures of the concentration field (socalled strange eigenmodes) and the complex time dependence that is responsible for these resonances.

Reduction of the loads on a cylinder undergoing harmonic inline motion
View Description Hide DescriptionWe use the finitedifference computational fluid dynamics method to study in detail the flow field around a circular cylinder in a uniform stream while undergoing inline harmonic motion. For a given motion amplitude, there exists a critical forcing frequency below which the lift and drag can be period, quasiperiodic, or chaotic. Similarly, for a given frequency, there exists a critical amplitude below which the lift and drag can be period, quasiperiodic, or chaotic. Above these critical conditions, the lift and drag are synchronous with the forcing. The lift nearly vanishes and the mean drag drops and saturates at a value that is independent of the driving frequency, whereas the oscillatory drag quadratically depends on it. We relate these features to changes in the wake and the surfacepressure distribution. We examine the influence of the Reynolds number on these critical frequency and amplitude. Second and higherorder spectral analyses show remarkable changes in the linear and quadratic coupling between the lift and drag when synchronization takes place; it destroys the twotoone coupling between them in the cases of no motion and synchronization due to crossflow motion.
 Particulate, Multiphase, and Granular Flows

A numerical investigation of the rheology of sheared fiber suspensions
View Description Hide DescriptionParticlelevel simulations are performed to study the rheology of monodispersed nonBrownian fibers suspended in a Newtonian fluid in shear flow. The effects of fiber aspect ratio, concentration, and interparticle friction on the stress tensor of the suspension in the steady state and on the tendency of fiber agglomeration are investigated. Semiempirical expressions for the steady state apparent shear viscosity and the steady state first and second normal stress difference were obtained for the case of well dispersed suspensions in the nonconcentrated regimes. The simulation predictions of the specific viscosity were in fair agreement with previous experimental investigations.

Drag on random assemblies of spheres in shearthinning and thixotropic liquids
View Description Hide DescriptionThe flow and resulting drag force in suspensions consisting of monodisperse, solid spheres, and nonNewtonian liquids have been studied via direct numerical simulations. The liquids are purely viscous (i.e., nonelastic) with shear thinning and/or thixotropic (timedependent) behavior. The configuration of spheres is static. The interstitial liquid flow is solved by means of the latticeBoltzmann method. Only creeping flow conditions have been considered. Thixotropy enters via a network integrity parameter that relates to the local, apparent viscosity and for which a transport equation has been solved. The results show that the shearthinning character of the liquid manifests itself more pronounced at higher solids volume fractions. Thixotropy tends to increase the drag force due to the decoupling of locations of high deformation rates and low viscosity.

Lateral migration of a small spherical buoyant particle in a wallbounded linear shear flow
View Description Hide DescriptionLateral migration velocities of solid spherical particles suspended in a linear wallbounded shear flow are measured for Reynolds number, (, where is the particle radius, is the local slip velocity between the particle and the fluid, and is the kinematic viscosity of the suspending fluid). The velocity parallel to the wall and the distance between the particle and the wall are measured as a function of time, allowing the lateral migration velocity and the slip velocity of the particle to be determined. The measuredvelocities are compared to the theoretical predictions of McLaughlin [“The lift on a small sphere in wallbounded linear shear flows,” J. Fluid Mech.246, 249 (1993)] and Magnaudet et al. [J. Fluid Mech.476, 115 (2003)] corresponding to the situation where the wall lies in the Oseen region and in the Stokes region of the flow disturbance produced by the particle, respectively. A good agreement is observed in both regimes with the corresponding prediction. The measurements are used to build an empirical fit capable of predicting the migration velocity whatever the distance between the particle and the wall.

Removal of particles from holes in submerged plates with oscillating bubbles
View Description Hide DescriptionThis study is motivated by a common problem in submerged tubes and structures, which is the blockage of the tubes by pollutant particles or debris from the surrounding fluid. To clear the obstruction from the tube, an expanding bubble is used to propel the obstruction away from the tube (the tube is represented as a submerged transparent plate with a hole in our experiments). In some cases the obstruction removal effect is reinforced by the impacting jet of such a collapsing bubble. The bubble is generated via a simple low voltage electric spark discharge circuit. The pressuregenerated by the oscillating bubble effectively pushes the particle away from the tube, thereby successfully clearing the obstruction. Highspeed photography is used to record and analyze the phenomenon. The speed of the particle is found to be around 1 m/s shortly after the collapse of the bubble. Interestingly, there is a clear difference between airbacked plates and waterbacked plates in terms of bubble and particle dynamics. The bubbles in the current study are typically of millimeter size. Since the physics are similar for smaller bubbles, the process can possibly be downsized for other microapplications such as the removal of blood clots in vessels [S. R. Visuri et al., U.S. Patent No. 6428531 (August 6, 2002)].

Experimental study of gravitation effects in the flow of a particleladen thin film on an inclined plane
View Description Hide DescriptionThe flow of viscous, particleladen wettingthin films on an inclined plane is studied experimentally as the particle concentration is increased to the maximum packing limit. The slurry is a nonneutrally buoyant mixture of silicone oil and either solid glass beads or glass bubbles. At low concentrations , the elapsed time versus average front position scales with the exponent predicted by Huppert [Nature (London)300, 427 (1982)]. At higher concentrations, the average front position still scales with the exponent predicted by Huppert on some time interval, but there are observable deviations due to internal motion of the particles. At the larger concentration values and at later times, the departure from Huppert is seen to strongly depend on total slurry volume , inclination angle , density difference, and particle size range.