Volume 23, Issue 8, August 2011

The influence of solid walls on the Lagrangian statistics of statistically stationary twodimensional turbulence is investigated by comparing the flow in a circular wallbounded and in an unbounded periodic domain. A Fourier pseudospectral method is used, which is combined in the wall bounded case with a volume penalization technique to impose noslip conditions. A particular emphasis is put on the acceleration of fluid particles. It is investigated to what extent the impact of the boundaries influences the shape of the probability density functions of Lagrangian velocity increments. It is shown that the influence of walls is not confined to a small nearwall region but alters the statistics in the entire flow domain. This can be explained by the vorticity generation in the turbulent boundary layer which destabilizes and leads to the formation of vortices that subsequently detach and travel into the bulk flow. The enstrophy level is thus increased with respect to the one in the unbounded periodic domain.
 LETTERS


Imbibition of concentrated suspensions in capillaries
View Description Hide DescriptionWe observe the imbibition of concentrated suspensions of rigid spherical particles into capillary tubes. We find that while the meniscus position advances according to the square root of time, the prefactor of this “diffusive” scaling is smaller than that predicted by an adhoc extension of classical imbibition using an effective viscosity for the imbibing fluid. The reduction in the prefactor is traced to the presence of axial variations in particle volume fraction, which arise as a result of shearinduced migration of particles across streamlines. In addition, we develop a model that accounts for the effect of both radial and axial variations in particle volume fraction on the movement of the imbibition front which partially accounts for the main experimental observations.

Extensibility enables locomotion under isotropic drag
View Description Hide DescriptionAnisotropicviscous drag is usually believed to be a requirement for the low Reynolds numberlocomotion of slender bodies such as flagella and cilia. Here, we show that locomotion under isotropic drag is possible for extensible slender bodies. After general considerations, a tworing swimmer and a model dinoflagellate flagellum are studied analytically to illustrate how extensibility can be exploited for selfpropulsion without drag anisotropy. This new degree of freedom could be useful for some complex swimmer geometries and locomotion in complex fluid environments where drag anisotropy is weak or even absent.

Turbulent boundary layer flow subject to streamwise oscillation of spanwise wallvelocity
View Description Hide DescriptionDirect numerical simulations have been performed to study the effect of a stationary distribution of spanwise wallvelocity that oscillates in the streamwise direction on a turbulent boundary layer. For the first time, a spatially developing flow with this type of forcing is studied. The part of the boundary layer which flows over the alternating wallvelocity section is greatly affected with a drag reduction close to 50% which exhibits an oscillatory distribution with a wavenumber which is twice that of the imposed wallvelocity. The maximum in drag reduction occurs where the wall velocity is at its maximum (or minimum) and the minimum occurs where the wall velocity is zero. Comparisons of the mean spanwise velocity profiles with the analytical solution to the laminar NavierStokes equations show very good agreement. The streamwise velocity profile indicates a thickening of the viscous sublayer when scaled with the local friction velocity and an upward shifting of the logarithmic region when scaled with the reference (unmanipulated) friction velocity. An estimation of the idealized power consumption shows that—with the present wall forcing magnitude—more energy is required for the spatial oscillation than what is saved by drag reduction.
 Top

 ARTICLES

 Biofluid Mechanics

Stokesian peristaltic pumping in a threedimensional tube with a phaseshifted asymmetry
View Description Hide DescriptionMany physiological flows are driven by waves of muscular contractions passed along a tubular structure. This peristaltic pumping plays a role in ovum transport in the oviduct and in rapid sperm transport through the uterus. As such, flow due to peristalsis has been a central theme in classical biological fluid dynamics. Analytical approaches and numerical methods have been used to study flow in twodimensional channels and threedimensional tubes. In two dimensions, the effect of asymmetry due to a phase shift between the channel walls has been examined. However, in three dimensions, peristalsis in a nonaxisymmetric tube has received little attention. Here, we present a computational model of peristaltic pumping of a viscous fluid in three dimensions based upon the method of regularized Stokeslets. In particular, we study the flow structure and mean flow in a threedimensional tube whose asymmetry is governed by a single phaseshift parameter. We view this as a threedimensional analog of the phaseshifted twodimensional channel. We find that the maximum mean flow rate is achieved for the parameter that results in an axisymmetric tube. We also validate this approach by comparing our computational results with classical longwavelength theory for the threedimensional axisymmetric tube. This computational framework is easily implemented and may be adapted to more comprehensive physiological models where the kinematics of the tube walls are not specified a priori, but emerge due to the coupling of its passive elastic properties, force generating mechanisms, and the surrounding viscous fluid.
 Micro and Nanofluid Mechanics

Ferrofluid flow in the annular gap of a multipole rotating magnetic field
View Description Hide DescriptionA solution is obtained for the ferrohydrodynamic problem of ferrofluidflow in the annular gap between two coaxial cylinders under the influence of the magnetic field generated by a multipole stator winding. The solution is applicable to small values of the applied magnetic field amplitude, takes into account the spatial harmonics produced by the multipole stator winding, and includes the effect of spin viscosity. The special case for which the internal diameter goes to zero, corresponding to the cylindrical “spinup flow” geometry, is also obtained. Results show that for zero spin viscosity, no flow is predicted for any number of poles in the winding. In the case of nonzero spin viscosity, for a twopole stator winding (m = 1) the solution predicts counterrotating flow with respect to the magnetic field close to the inner cylinder and corotating flow with respect to the magnetic field near the outer cylinder, in agreement with previously reported experimental observations. For stator windings with larger number of poles , the solution predicts corotation of fluid and field in the annular gap. Using a fourpole stator winding , experimental measurements show that a ferrofluid corotates with the magnetic field in both the cylindrical and annular cases, with qualitative agreement between the theory with nonzero spin viscosity and the experiments. Nonidealities in the stator winding distribution, e.g., due to slot effects, are considered through linear superposition of higher order harmonics, again predicting zero flow in the absence of spin viscosity and counterrotating flow with respect to the magnetic field close to the inner cylinder wall only for the case where the fundamental harmonic is dominant.

Selfsimilar analysis of fluid flow and heatmass transfer of nanofluids in boundary layer
View Description Hide DescriptionProcesses of heat, momentum, and concentration transport in a boundary layer of a nanofluid near a flat wall were studied. The study was performed by means of numerical analysis of boundary layer equations in a selfsimilar form. Selfsimilar forms of these equations were obtained based on symmetry properties (Lie groups). In doing so, dependence of physical properties (viscosity, thermal conductivity, and diffusion coefficient) on concentration of nanofluids and temperature were taken into account. Effects of concentration of the nanoparticles on velocity and temperature profiles, as well as on the relative Nusselt numbers and skinfriction coefficients, were elucidated.

An integral perturbation model of flow and momentum transport in rotating microchannels with smooth or microstructured wall surfaces
View Description Hide DescriptionThis paper summarizes the development of an integral perturbation solution of the equations governing flow momentum transport and energy conversion in microchannels between disks of multipledisk drag turbines such as Tesla turbines. Analysis of this type of flow problem is a key element in optimal design of Tesla dragtype turbines for geothermal or solar alternative energy technologies. In multipledisk turbines, high speed flow enters tangentially at the outer radius of cylindrical microchannels formed by closely spaced parallel disks, spiraling through the channel to an exhaust at a small radius, or at the center of the disk. Previous investigations have generally developed models based on simplifying idealizations of the flow in these circumstances. Here, beginning with the momentum and continuity equations for incompressible and steady flow in cylindrical coordinates, an integral solution scheme is developed that leads to a dimensionless perturbation series solution that retains the full complement of momentum and viscous effects to consistent levels of approximation in the series solution. This more rigorous approach indicates all dimensionless parameters that affect flow and transport and allows a direct assessment of the relative importance of viscous, pressure, and momentum effects in different directions in the flow. The resulting lowestorder equations are solved explicitly and higher order terms in the series solutions are determined numerically. Enhancement of rotor drag in this type of turbine enhances energy conversion efficiency. We also developed a modified version of the integral perturbation analysis that incorporates the effects of enhanced drag due to surface microstructuring. Results of the model analysis for smooth disk walls are shown to agree well with experimental performance data for a prototype Tesla turbine and predictions of performance models developed in earlier investigations. Model predictions indicate that enhancement of disk drag by strategic microstructuring of the disk surfaces can significantly increase turbine efficiency. Exploratory calculations with the model indicate that turbine efficiencies exceeding 75% can be achieved by designing for optimal ranges of the governing dimensionless parameters.

Combined influence of streaming potential and substrate compliance on load capacity of a planar slider bearing
View Description Hide DescriptionIn the present study, we investigate the combined interplay of streaming potential and substrate compliance with sliding dynamics on the load carrying capacity of a planar slider bearing. We relax previously utilized simplifying assumptions to model the electrokinetic effects and demonstrate that the streaming potential may augment the load carrying capacity of the bearing to a considerable extent. Interestingly, we also reveal that the electrokinetically augmented load carrying capacity exhibits strong dependencies on a combination of the compliance and the sliding dynamics, which have, hitherto, not been extensively explored. This rich interplay reveals certain parametric regimes of interest, which are significant from the viewpoint of practical design considerations.

Optimizing mixing in liddriven flow designs through predictions from Eulerian indicators
View Description Hide DescriptionIn this paper, we further develop the notion of Eulerian indicators (EIs) for predicting Lagrangianmixing behavior. We employ a twodimensional “blinking” Stokes flow as a model for mixing in a threedimensional, spatially periodic channel flow. Each blinking flow alternates two distinct velocity fields that were calculated using a liddriven cavity model. A new EI termed mobility is introduced to measure how effectively the blinking velocity fields transport fluid throughout the domain. We also calculate the transversality for these flows, which is an EI measuring how much the velocity direction at each point in the domain changes when the velocity fields blink. For the studied flows, we show that although individually the mobility and transversality do not correlate well with mixing as measured by the decay of the variance of concentration, the product of mobility and transversality does correlate well with the decay of the variance of concentration and predicts which combinations of velocity fields will produce the most effective mixing.
 Interfacial Flows

Droplet formation in microfluidic crossjunctions
View Description Hide DescriptionUsing a lattice Boltzmann multiphase model, threedimensional numerical simulations have been performed to understand dropletformation in microfluidic crossjunctions at low capillary numbers. Flow regimes, consequence of interaction between two immiscible fluids, are found to be dependent on the capillary number and flow rates of the continuous and dispersed phases. A regime map is created to describe the transition from dropletsformation at a crossjunction (DCJ), downstream of crossjunction to stable parallel flows. The influence of flow rate ratio, capillary number, and channel geometry is then systematically studied in the squeezingpressuredominated DCJ regime. The plug length is found to exhibit a linear dependence on the flow rate ratio and obey powerlaw behavior on the capillary number. The channel geometry plays an important role in droplet breakup process. A scaling model is proposed to predict the plug length in the DCJ regime with the fitting constants depending on the geometrical parameters.

The effect of surface shear viscosity on the damping of oscillations in millimetric liquid bridges
View Description Hide DescriptionThe damping rate of the small free oscillations in a noncylindrical, axisymmetric liquid bridge between two circular disks is calculated and compared with some previous experimental measurements using hexadecane in a millimetric liquid bridge. Current theories, accounting for viscous damping in both the boundary layers attached to the disks and the bulk, underestimated the measured damping by a O(1) quantity; and no improvement resulted from calculations based on the full NavierStokes equations. These discrepancies are essentially eliminated in this paper considering the effect of the surface shear viscosity (whose value results from empirical fitness), which could be due to the presence of a contaminating monolayer. Some consequences are extracted in connection with surface wave damping in microfluidic devices.

Thermocapillary instabilities in liquid bridges revisited
View Description Hide DescriptionThe study of convective thermocapillary instabilities in liquid bridges [J. J. Xu and S. H. Davis, Phys. Fluids 27(5), 1102 (1984)] is revisited. A new branch of neutral mode m = 1 is found. The previously reported results are confirmed in the range of low Prandtl numbers. It is shown that for large Prandtl numbers, the flow becomes unstable at much smaller values of the Marangoni number than it was reported previously. The calculations are performed for adiabatic and heat conductivefree surface. In both cases, the critical mode is m = 1. The previously reported change of critical mode from m = 1 to m = 0 with increasing the Prandtl number is not confirmed. The corrected results provide a better agreement with the experimental data.
 Viscous and NonNewtonian Flows

Perturbation solution for the viscoelastic 3D flow around a rigid sphere subject to simple shear
View Description Hide DescriptionWe study the steady, threedimensional creeping, and viscoelasticflow around a freely rotating rigid sphere subject to simple shear flow imposed at infinity. The viscoelasticity of the ambient fluid is modeled using the secondorderfluid model, the Upper Convected Maxwell, the exponential affine PhanThienTanner, and the Giesekus constitutive equations. A spherical coordinate system with origin at the center of the sphere is used to describe the flow field. The solution of the governing equations is expanded as a series for small values of the Deborah number. The resulting sequence of differential equations is solved analytically up to second order and numerically up to fourth order in Deborah number by employing fully spectral representations for all the primary variables. In particular, Chebyshev polynomials are used in the radial coordinate and the double Fourier series in the longitudinal and latitudinal coordinates. The numerical results up to secondorder agree within machine accuracy with the available analytical solutions clearly indicating the correctness and accuracy of the numerical method developed here. Analytical expressions for the angular velocity of the rigid sphere up to fourth order, which show the slowdown of the rotation of the sphere with respect to the Newtonian creeping case, are also derived. For small Deborah numbers, these expressions, along with those presented in a recent letter [Housiadas and Tanner, Phys. Fluids 23, 051702 (2011)] are in agreement with the few available experimental data and numerical results.

Wang’s shrinking cylinder problem with suction near a stagnation point
View Description Hide DescriptionIn this paper, the steady axisymmetric stagnation point flow of a viscous and incompressible fluid over a shrinking circular cylinder with mass transfer (suction) is studied. The flow is induced by a cylinder shrinking with a linear velocity distribution from the stagnation line. The fluid flowsolution is an exact solution of the NavierStokes equation, which is reduced to a nonlinear ordinary differential equation. This equation is solved numerically for some values of the governing parameters that involves a Reynolds numberR, a shrinking parameter λ, and a suction parameter γ. The effects of these governing parameters on the velocity and temperature profiles, skin friction coefficient, Nusselt number, as well as the distributions of the streamlines are investigated. The obtained results for the case of fixed cylinder are compared with those from the open literature and it is shown that they are in excellent agreement. The solutions are nonunique for some values of λ . The streamlines show that the flow structures become complicated due to the shrinking and suction effects.
 Particulate, Multiphase, and Granular Flows

The effect of interstitial fluid viscosity on particle segregation in a slurry rotating drum
View Description Hide DescriptionAlthough the segregation of dry granular surfaceflow has been widely studied, cases where the air is completely replaced by a liquid still remain unexplored. In this study, we report on experiments performed to investigate the phenomena of particle segregation and flowing behavior in a rotating drum with liquids of different viscosities and different filling degrees. The experimental results indicate that the viscosity of the interstitial fluid has a significant effect on the granular flow in the slurrygranular flow. The segregation index and angle of repose are shown to decrease with increased liquid viscosity. When the liquid viscosity is the same, the increase in filling degree causes the segregation index to increase, while the net rate of mixing seems to decrease. A new dimensionless flow variable is used to distinguish the flow regimes. We find that the flow regime changes from rolling regime to cascading regime when the dimensionless flow variable is below a critical value. Furthermore, the change of segregation index occurs during the transition of the granular flow regime.

Roles of particlewall and particleparticle interactions in highly confined suspensions of spherical particles being sheared at low Reynolds numbers
View Description Hide DescriptionThe roles of particlewall and particleparticle interactions are examined for suspensions of spherical particles in a viscous fluid being confined and sheared at low Reynolds numbers by two parallel walls moving with equal but opposite velocities. Both particlewall and particleparticle interactions are shown to decrease the rotational velocity of the spheres, so that in the limit of vanishingly small gaps between the spheres and the walls, the spheres acquire a rotational slip relative to the walls. The presence of the walls also increases the particle stresslet and, therefore, the total viscous dissipation. In the limit of vanishingly small gaps, the increased viscous dissipation in the gaps between pairs of spheres aligned in the flow direction is largely compensated by the reduction in the dissipation in the gaps between the spheres and the walls due to a reduction in the rotational velocity of the spheres. As a result, the effect of shortrange particle interactions on the stresslet is generally insignificant. On the other hand, the channelscale particle interactions in the shear flow induced by the moving walls decrease the particle stresslet, primarily because the fraction of pairs of spheres that are aligned parallel to the flow (the presence of which in a shear flow reduces the stresslet) is relatively higher than in unbounded suspensions. Expressions are also derived for the total stress in dilute random suspensions that account for both the particlewall and the channelscale particleparticle interactions in determining the rotational velocities and stresses. The latter are shown to be consistent with recent numerical [Y. Davit and P. Peyla, Europhys. Lett. 83, 64001 (2008)] and experimental [P. Peyla and C. Verdier, Europhys. Lett. 94, 44001 (2011)] findings according to which, for a range of sphere radius to gap width ratios, the effect of particleparticle interactions is to decrease the total dissipation.

Firstorder virial expansion of shorttime diffusion and sedimentation coefficients of permeable particles suspensions
View Description Hide DescriptionFor suspensions of permeable particles, the shorttime translational and rotational selfdiffusion coefficients, and collective diffusion and sedimentation coefficients are evaluated theoretically. An individual particle is modeled as a uniformly permeable sphere of a given permeability, with the internal solvent flow described by the DebyeBuecheBrinkman equation. The particles are assumed to interact nonhydrodynamically by their excluded volumes. The virial expansion of the transport properties in powers of the volume fraction is performed up to the twoparticle level. The firstorder virial coefficients corresponding to twobody hydrodynamic interactions are evaluated with very high accuracy by the series expansion in inverse powers of the interparticle distance. Results are obtained and discussed for a wide range of the ratio, x, of the particle radius to the hydrodynamic screening length inside a permeable sphere. It is shown that for , the virial coefficients of the transport properties are wellapproximated by the hydrodynamic radius (annulus) model developed by us earlier for the effective viscosity of porousparticle suspensions.
 Laminar Flows

On the benefits of hysteresis effects for closedloop separation control using plasma actuation
View Description Hide DescriptionFlow separation control by a nonthermal plasma actuator is considered for a NACA 0015 airfoil at a chord Reynolds number of 1.9 × 10^{5}. Static hysteresis in the lift coefficient is demonstrated for increasing and then decreasing sinusoidal voltage amplitude supplying a typical single dielectric barrier discharge actuator at the leading edge of the model. In addition to these openloop experiments, unsteady surface pressure signals are examined for transient processes involving forced reattachment and natural separation. The results show that strong pressure oscillations in the relatively slow separation process, compared to reattachment, precede the ultimate massive flow separation. To enhance the contrast between the parts of the signal related to the attached flow and those related to the incipient separation, RMS estimate of filtered values of is used to define a flow separation predictor that is implemented in feedback control. Two simple controllers are proposed, one based on a predefined threshold of the unsteady Cp and another that utilizes the flow separation predictor to identify incipient separation. The latter effectively leverages the hysteresis in the poststall regime to reduce the electrical power consumed by the actuator while maintaining continuously attached flow.

Role of streamwise dynamics in spreading and mixing of flows through a rectangular sudden expansion
View Description Hide DescriptionDirect numerical simulations are performed to examine roles of streamwise dynamics in the spreading and mixing of flows in a twostep rectangular sudden expansion channel. The configuration is observed to facilitate higher entrainment by virtue of developed inflow type streamwise dynamics, and the systemgenerated passive forcing provided the necessary impetus for sustainable growth/evolution of the vortices. In addition, with the introduction and proper placement of two tiny rectangular “tabs” over the inlet walls, the downstream growth/dynamics of the vortices could be effectively modified. Through their inflow/outflow type dynamics, the streamwise vortices are found to decisively dictate the transverse jet spreading. The physical process thereby either led to a quick axis switching of the jet, or stopped axis switching altogether. However, the stretching of the azimuthal vortices is found to remain directly linked to the streamwise continuation of jet’s azimuthal curvature variation. A pressure analysis as presented herein, and the simulated nature of dynamics of two azimuthal components of vortices further reveal that the transverse pressure gradient skewing is a dominant source of streamwise vorticity in such flows. With the knowledge of simulated transverse pressure distribution, we formulate here a mechanism which efficiently predicts the inception/dynamics of all the streamwise vortices. Moreover, a novel mathematical foundation in support of the pressure analysis has been outlined here, which ensures further broader universal scope of applicability of our proposed pressure analysis.
 Instability and Transition

Sidewall and thermal boundary condition effects on the evolution of longitudinal rolls in RayleighBénardPoiseuille convection
View Description Hide DescriptionExperimental and numerical studies of steady longitudinal convection rolls that develop in a Poiseuille air flow in a rectangular channel heated from below and cooled from the top are conducted in the range 3500 ≤ Ra ≤ 6000 and 20 ≤ Re ≤ 200. The effect of the lateral vertical walls on the onset and development of the convection cells is investigated by changing the transverse aspect ratio of the channel from 4.7 to 18.4. The influence of the entrance temperature and adiabatic or conductive thermal boundary conditions at the side and top walls of the channel is also investigated. The scenario of the roll formation is described in details. It results in a symmetric pattern in the form of steady longitudinal rolls with an even number of rolls that depends not only on the aspect ratio but possibly on the inlet temperature of the flow. It is shown that the fully developed pattern is determined by the two rolls nearby each vertical side wall that are triggered just at the entrance of the channel due to the presence of velocity boundary layers adjacent to the walls. It is also shown that the heat conduction in the top horizontal wall of the experimental channel must be taken into account in the numerical simulations so that the experimental wavenumber can be properly depicted.