Volume 24, Issue 1, January 2012

We simulate the crossflow migration of rigid particles such as platelets in a red blood cell (RBC) suspension using the Stokes flowboundary integralequation method. Two types of flow environments are investigated: a suspension undergoing a bulk shear motion and a suspension flowing in a microchannel or duct. In a cellularsuspension undergoing bulk shear deformation, the crossflow migration of particles is diffusional. The velocity fluctuations in the suspension, which are the root cause of particle migration, are analyzed in detail, including their magnitude, the autocorrelation of Lagrangian tracer points and particles, and the associated integral time scales. The orientation and morphology of red blood cells vary with the shear rate, and these in turn cause the dimensionless particle diffusivity to vary nonmonotonically with the flow capillary number. By simulating RBCs and platelets flowing in a microchannel of 34 μm height, we demonstrate that the velocity fluctuations in the core cellularflow region cause the platelets to migrate diffusively in the wall normal direction. A mean lateral velocity of particles, which is most significant near the edge of the cellfree layer, further expels them toward the wall, leading to their excess concentration in the cellfree layer. The calculated shearinduced particle diffusivity in the cellladen region is in qualitative agreement with the experimental measurements of micronsized beads in a cylindrical tube of a comparable diameter. In a smaller duct of 10 × 15 μm cross section, the volume exclusion becomes the dominant mechanism for particle margination, which occurs at a much shorter time scale than the migration in the bigger channel.
 ANNOUNCEMENTS


Announcement: The 2011 François Naftali Frenkiel Award for Fluid Mechanics
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Announcement: New Format for Physics of Fluids
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Referee Acknowledgment for 2011
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 AWARD AND INVITED PAPERS


Developed quantum turbulence and its decay^{a)}
View Description Hide DescriptionThis article is primarily a review of our knowledge of the correspondence between classical and quantum turbulence, though it is interspersed with a few new interpretations. This review is deemed timely because recent work in quantum turbulence promises to provide a better understanding of aspects of classical turbulence, though the two fields of turbulence have similarities as well as differences. We pay a particular attention to the conceptually simplest case of zero temperature limit where quantum turbulence consists of a tangle of quantized vortex line and represents a simple prototype of turbulence. At finite temperature, we anchor ourselves at the level of twofluid description of the superfluid state—consisting of a normal viscousfluid and a frictionless superfluid—and review much of the available knowledge on quantum turbulence in liquid helium (both He II and ^{3}HeB). We consider counterflows in which the normal and superfluid components flow against each other, as well as coflows in which the direction of the two fluids is the same. We discuss experimental methods, phenomenological results as well as key theoretical concepts.
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 LETTERS


The onset of oblique vortex shedding behind a heated circular cylinder in laminar wake regime
View Description Hide DescriptionOblique vortex shedding (OVS) behind a heated circular cylinder in air was experimentally investigated. Similar to that in the parallel vortex shedding (PVS), the results show that the nondimensionalized shedding frequency, Strouhal number, decreases under the influence of cylinder heating for oblique shedding mode. Although the onset Reynolds number of OVS increases with the cylinder temperature, the onset effective Reynolds number remains 63.3 ± 1.3 regardless of the cylinder heating. A general StrouhalReynoldsnumber relationship for OVS has been found based on the effective temperature concept in the present study. The ratio of the critical Reynolds numbers for the onsets of OVS and PVS is found to be an invariant with value of 4/3 for both isothermal and nonisothermal cases despite different length/diameter ratios and end conditions.

Gridpoint requirements for large eddy simulation: Chapman’s estimates revisited
View Description Hide DescriptionResolution requirements for large eddy simulation(LES), estimated by Chapman [AIAA J. 17, 1293 (1979)], are modified using accurate formulae for high Reynolds number boundary layer flow. The new estimates indicate that the number of grid points (N) required for wallmodeled LES is proportional to , but a wallresolving LES requires , where is the flatplate length in the streamwise direction. On the other hand, direct numerical simulation, resolving the Kolmogorov length scale, requires .

Direct simulation Monte Carlo method for an arbitrary intermolecular potential
View Description Hide DescriptionA scheme to implement an arbitrary intermolecular potential into the direct simulation Monte Carlo method is proposed. To illustrate the scheme, two benchmark problems are solved employing the LennardJones potential. Since the computational effort of the new scheme is comparable with that of the hard sphere model of molecules, it can completely substitute the widely used models such as variable hard spheres and variable soft spheres.

An analogy of Taylor’s instability criterion in Couette and rotatingmagneticfielddriven flows
View Description Hide DescriptionThe classical stability solution of Taylor for the Couette flow between a rotating inner cylinder and a stationary outer cylinder is used to model the “critical magnetic Taylor number,” , in a flow of a liquid metal driven by a rotating magnetic field (RMF) in a cylindrical cavity characterized by the parameter height/radius. (The magnetic Taylor number is defined as , where , and are the electrical conductivity, kinematic viscosity, and density of the liquid; and are the magnetic field frequency and induction; is the radius of the cavity; the cr superscript means “critical”) In typical conditions, the RMF flow develops a solidbodyrotating core analogous to the inner rotating cylinder, embedded in a layer in which the swirl decays to zero at the outer wall. Using smallEkmannumber approximations for the core and gap flow, the analogy yields an insightful expression for . In particular, the model indicates that depends strongly on the parameter H. Comparisons of the present theoretical results with available realistic data show a good qualitative agreement and plausible quantitative agreement. The model was improved by an empirical adjustment of a coefficient and can be used as simple approximate prediction tool for in a quite wide range of cylindrical cavity configurations.

Amplification factors in shockturbulence interactions: Effect of shock thickness
View Description Hide DescriptionAmplification factors of streamwise velocity are investigated in canonical shockturbulence interactions. The ratio of laminar shock thickness to the Kolmogorov length scale is suggested as the appropriate parameter to understand data from simulations and experiments. The different regimes of the interaction suggested in the literature can also be understood in terms of this parameter.
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 ARTICLES

 Biofluid Mechanics

A twosphere model for bacteria swimming near solid surfaces
View Description Hide DescriptionWe present a simple model for bacteria like Escherichia coli swimming near solid surfaces. It consists of two spheres of different radii connected by a dragless rod. The effect of the flagella is taken into account by imposing a force on the tail sphere and opposite torques exerted by the rod over the spheres. The hydrodynamic forces and torques on the spheres are computed by considering separately the interaction of a single sphere with the surface and with the flow produced by the other sphere. Numerically, we solve the linear system which contains the geometrical constraints and the forcefree and torquefree conditions. The dynamics of this swimmer near a solid boundary is very rich, showing three different behaviors depending on the initial conditions: (1) swimming in circles in contact with the wall, (2) swimming in circles at a finite distance from the wall, and (3) swimming away from it. Furthermore, the order of magnitude of the radius of curvature for the circular motion is in the range m, close to values observed experimentally.

Shearinduced particle migration and margination in a cellular suspension
View Description Hide DescriptionWe simulate the crossflow migration of rigid particles such as platelets in a red blood cell (RBC) suspension using the Stokes flowboundary integralequation method. Two types of flow environments are investigated: a suspension undergoing a bulk shear motion and a suspension flowing in a microchannel or duct. In a cellularsuspension undergoing bulk shear deformation, the crossflow migration of particles is diffusional. The velocity fluctuations in the suspension, which are the root cause of particle migration, are analyzed in detail, including their magnitude, the autocorrelation of Lagrangian tracer points and particles, and the associated integral time scales. The orientation and morphology of red blood cells vary with the shear rate, and these in turn cause the dimensionless particle diffusivity to vary nonmonotonically with the flow capillary number. By simulating RBCs and platelets flowing in a microchannel of 34 μm height, we demonstrate that the velocity fluctuations in the core cellularflow region cause the platelets to migrate diffusively in the wall normal direction. A mean lateral velocity of particles, which is most significant near the edge of the cellfree layer, further expels them toward the wall, leading to their excess concentration in the cellfree layer. The calculated shearinduced particle diffusivity in the cellladen region is in qualitative agreement with the experimental measurements of micronsized beads in a cylindrical tube of a comparable diameter. In a smaller duct of 10 × 15 μm cross section, the volume exclusion becomes the dominant mechanism for particle margination, which occurs at a much shorter time scale than the migration in the bigger channel.
 Micro and Nanofluid Mechanics

Scaling laws for slippage on superhydrophobic fractal surfaces
View Description Hide DescriptionWe study the slippage on hierarchical fractalsuperhydrophobicsurfaces and find an unexpected rich behavior for hydrodynamicfriction on these surfaces. We develop a scaling law approach for the effective slip length, which is validated by numerical resolution of the hydrodynamic equations. Our results demonstrate that slippage does strongly depend on the fractal dimension and is found to be always smaller on fractalsurfaces as compared with surfaces with regular patterns. This shows that in contrast to naive expectations, the value of effective contact angle is not sufficient to infer the amount of slippage on a fractalsurface: depending on the underlying geometry of the roughness, strongly superhydrophobicsurfaces may, in some cases, be fully inefficient in terms of drag reduction. Finally, our scaling analysis can be directly extended to the study of heat transfer at fractalsurfaces, in order to estimate the Kapitsa surface resistance on patternedsurfaces, as well as to the question of trapping of diffusing particles by patchy hierarchical surfaces, in the context of chemoreception.

Multiscale modeling of particle in suspension with smoothed dissipative particle dynamics
View Description Hide DescriptionWe apply smoothed dissipative particle dynamics (SDPD) [Español and Revenga, Phys. Rev. E 67, 026705 (2003)] to model solid particles in suspension. SDPD is a thermodynamically consistent version of smoothed particle hydrodynamics (SPH) and can be interpreted as a multiscale particle framework linking the macroscopic SPH to the mesoscopic dissipative particle dynamics (DPD) method. Rigid structures of arbitrary shape embedded in the fluid are modeled by frozen particles on which artificial velocities are assigned in order to satisfy exactly the noslip boundary condition on the solidliquid interface. The dynamics of the rigid structures is decoupled from the solvent by solving extra equations for the rigid body translational/angular velocities derived from the total drag/torque exerted by the surrounding liquid. The correct scaling of the SDPD thermal fluctuations with the fluidparticle size allows us to describe the behavior of the particle suspension on spatial scales ranging continuously from the diffusiondominated regime typical of submicronsized objects towards the nonBrownian regime characterizing macrocontinuum flow conditions. Extensive tests of the method are performed for the case of two/three dimensional bulk particlesystem both in Brownian/nonBrownian environment showing numerical convergence and excellent agreement with analytical theories. Finally, to illustrate the ability of the model to couple with external boundary geometries, the effect of confinement on the diffusional properties of a single sphere within a microchannel is considered, and the dependence of the diffusion coefficient on the wallseparation distance is evaluated and compared with available analytical results.

Numerical demonstration of the reciprocity among elemental relaxation and drivenflow problems for a rarefied gas in a channel
View Description Hide DescriptionRelaxations from a uniform mass/heat flow and flows driven by an external force/temperaturegradient for a rarefied gas between two parallel plates are studied on the basis of the kinetic theory of gases. By numerical computations of the linearized Bhatnagar–Gross–Krook model of the Boltzmann equation, it is demonstrated that the reciprocity among these elemental flows derived from a general reciprocity theory for timedependent problems [S. Takata, J. Stat. Phys. 140, 985 (2010)] holds at any time and any Knudsen numbers. Moreover, a propagation of the discontinuity of the velocity distribution function (VDF) in the relaxation problems and that of the derivative discontinuity of the VDF in the drivenflow problems are demonstrated. Their relation is also clarified.

Dipolophoresis of dielectric spheroids under asymmetric fields
View Description Hide DescriptionNonspherical particles are common in colloidal science. Spheroidal shapes are particularly convenient for the analysis of the pertinent electrostatic and hydrodynamic problems and are thus widely used to model the manipulation of biological cells as well as deformed drops and bubbles. We study the rotary motion of a dielectric spheroidal microparticle which is freely suspended in an unbounded electrolyte solution in the presence of a uniform applied electric field, assuming a thin Debye layer. For the common case of a uniform distribution of the native surfacecharge density, the rotary motion of the particle is generated by the contributions of the inducedcharge electroosmotic (ICEO) slip and the dielectrophoresis associated with the distribution of the Maxwell stress, respectively. Series solutions are obtained by using spheroidal (prolate or oblate) coordinates. Explicit results are presented for the angular velocity of particles spanning the entire spectrum from rodlike to disklike shapes. These results demonstrate the nonmonotonic variation of the angular speed with the eccentricity of particle shape and the singularity of the multiple limits corresponding to conducting (ideally polarizable) particles of extreme eccentricity (e ≈ 1). The nonmonotonic variation of the angular speed with the particle dielectric permittivity is related to the inducedcharge contribution. We apply these results to describe the motion of particles subject to a uniform field rotating in the plane. For a sufficiently slow rotation rate, prolate particles eventually become “locked” to the external field with their stationary relative orientation in the plane of rotation being determined by the particle eccentricity and dielectric constant. This effect may be of potential use in the manipulation of polydisperse suspensions of dielectric nonspherical particles. Oblate spheroids invariably approach a uniform orientation with their symmetry axes directed normal to the externalfield plane of rotation.

Direct simulation Monte Carlobased expressions for the gas mass flow rate and pressure profile in a microscale tube
View Description Hide DescriptionThe direct simulation Monte Carlo (DSMC) method of Bird is used to develop simple closedform expressions for the mass flow rate and the pressure profile for the steady isothermal flow of an ideal gas through a microscale tube connecting two infinite reservoirs at different pressures but at the temperature of the tube wall. Gas molecules reflect from the tube wall according to the Maxwell model (a linear combination of specular and diffuse reflections at the wall temperature) with a unity or subunity value of the accommodation coefficient (the probability that molecules reflect diffusely from the wall). The DSMCbased expressions have four parameters. Two parameters are specified so that the mass flow rate reduces to the known expression in the freemolecular regime. One parameter was previously determined by comparison to DSMC simulations in the slip regime. The remaining parameter is determined by comparison to DSMC simulations for pressures spanning the transition regime with several values of the accommodation coefficient. The expressions for the mass flow rate and the pressure profile agree well with the DSMC simulations (rms and maximum differences of 2% and 5% for all cases examined), with other more complicated expressions and with recent experiments involving microscale tubes and channels for all flow regimes.
 Interfacial Flows

Transient reduction of the drag coefficient of charged droplets via the convective reversal of stagnant caps
View Description Hide DescriptionDroplets are frequently observed to move as if they were solid rather than liquid, i.e., with no slip at the liquidliquid interface. This behavior is usually explained in terms of the socalled “stagnant cap” model, in which surfactants accumulate at the trailing edge of the droplet, immobilizing the surface and increasing the observed drag coefficient. Here, we show that the drag coefficient for chargeddroplets is temporarily reduced by reversing the direction of an electric driving force. Using high speed video, we simultaneously track the velocity and relative interfacial velocity of individual aqueous droplets moving electrophoretically through oil. The observed velocity behavior is highly sensitive to the concentration of surfactant. For sufficiently low or sufficiently high concentration, upon reversal of the electric field the droplet rapidly accelerates in the opposite direction but then decelerates, concurrent with a transient rearrangement of tracer particles on the dropletsurface. In contrast, droplets with intermediate surfactant concentrations exhibit neither deceleration nor significant tracer particle rearrangement. We interpret the observations in terms of convectively dominated rearrangement of the stagnant cap, and we discuss the implications for precise electrophoretic control of dropletmotion in labonachip devices and industrial electrocoalescers.

Stability and breakup of confined threads
View Description Hide DescriptionA boundaryintegral method for periodic arrays of drops, threads or sheets between parallel walls is presented. The Green’s functions take the form of a farfield HeleShaw description, which is used to generate periodic Green’s functions for the parallelwall configuration. The method is applied to study the effect of confinement on the breakup of threads. A comparison is made with classical Tomotika’s theory and growth rates parallel and perpendicular to the walls are determined as a function of confinement ratio. Contrary to existing belief, we find that confined threads are not stable, but that the time for breakup increases with confinement and viscosity ratio, at least for threads whose diameter is smaller than the wallspacing. We also show the inphase and outofphase breakup for an array of threads, as well as the stabilizing effect of shear flow.
 Particulate, Multiphase, and Granular Flows

Particulate mixing in a turbulent serpentine duct
View Description Hide DescriptionDirect numerical simulations of particles in a serpentine duct were conducted at bulk flow Stokes numbers between 0.125 and 6. The geometrical curvature causes particles to depart direction from the mean flow. Above a Stokes number of about unity, a reflection layer forms along the outer curve of the bend. Reflectional mixing creates regions of nearly uniform particle mean velocity and kinetic energy. Particles leave the inner bend in a plume that separates from the inner wall at low Stokes number. At higher Stokes number, the plume splits in two, adding an upper part consisting of ballistic particles, that do not follow the geometrical curvature. When the Stokes number is low, the instantaneous 3D distribution of particles visualizes wall streaks. But at higher Stokes number, particles disperse out of the reflection layer and form large scale puffs in the central portion of the duct.

Rheological measurements of large particles in high shear rate flows
View Description Hide DescriptionThis paper presents experimental measurements of the rheological behavior of liquidsolid mixtures at moderate Stokes and Reynolds numbers. The experiments were performed in a coaxial rheometer that was designed to minimize the effects of secondary flows. By changing the shear rate, particle size, and liquid viscosity, the Reynolds numbers based on shear rate and particle diameter ranged from 20 to 800 (Stokes numbers from 3 to 90), which is higher than examined in earlier rheometric studies. Prior studies have suggested that as the shear rate is increased, particleparticle collisions also increase resulting in a shear stress that depends nonlinearly on the shear rate. However, over the range of conditions that were examined in this study, the shear stress showed a linear dependence on the shear rate. Hence, the effective relative viscosity is independent of the Reynolds and Stokes numbers and a nonlinear function of the solid fraction. The present work also includes a series of roughwall experiments that show the relative effective viscosity is also independent of the shear rate and larger than in the smooth wall experiments. In addition, measurements were made of the nearwall particle velocities, which demonstrate the presence of slip at the wall for the smoothwalled experiments. The depletion layer thickness, a region next to the walls where the solid fraction decreases, was calculated based on these measurements. The relative effective viscosities in the current work are larger than found in lowReynolds number suspension studies but are comparable with a few granular suspension studies from which the relative effective viscosities can be inferred.