Volume 22, Issue 6, June 2010

The singlepoint active nonlinear microrheology of a colloidalsuspension is measured using laser tweezers in the limit that the diameter of the probe particle approaches the diameter of the bath suspension particles. The microviscosity thins as the probe velocity (and corresponding microrheological Péclet number) increases. This thinning behavior correlates with the development of a nonequilibrium suspension microstructure surrounding the probe particle, in which a boundary layer forms on the upstream face of the probe and a wake depleted of bath particles trails the probe. The magnitude of the microviscosities and the thinning behavior are in good agreement with Brownian dynamics simulations reported by Carpen and Brady [J. Rheol.49, 1483 (2005)]. The microviscosity increment collapses onto a single curve for all volume fractions when scaled by the contact distribution of bath particles around the probe. Scaling the microviscosity increment yields values lower than the dilute theory; furthermore, it plateaus at significantly higher Péclet numbers. The latter effect is corrected by rescaling the Péclet number with the suspension collective diffusion coefficient in place of the bath particle selfdiffusivity. The magnitude of the microviscosity increment suggests the theory overestimates the frequency of bathprobe collisions. The presence and role of hydrodynamic interactions and the effect of the soft repulsive potential are discussed.
 LETTERS


Viscous tilting and production of vorticity in homogeneous turbulence
View Description Hide DescriptionViscous depletion of vorticity is an essential and well known property of turbulent flows, balancing, in the mean, the net vorticity production associated with the vortex stretching mechanism. In this letter, we, however, demonstrate that viscouseffects are not restricted to a mere destruction process, but play a more complex role in vorticitydynamics that is as important as vortex stretching. Based on the results from three dimensional particle tracking velocimetry experiments and direct numerical simulation of homogeneous and quasiisotropic turbulence, we show that the viscous term in the vorticity equation can also locally induce production of vorticity and changes of the orientation of the vorticity vector (viscous tilting).

Dissipationenergy flux correlations as evidence for the Lagrangian energy cascade in turbulence
View Description Hide DescriptionWe study the spatial and temporal evolution of kinetic energy flux at different scales using direct numerical simulations of isotropic turbulence. The correlation coefficients at different times, between the molecular energy dissipation and local energy fluxes across inertialrange scales, are computed in both Eulerian and Lagrangian frames. The Eulerian correlation coefficients are found to decay monotonically backward in time. However, the Lagrangiancorrelation coefficients peak after a certain time delay. The peak time delay is found to be proportional to the local eddy turnover time (it scales with wave number according to ), consistent with Kolmogorov’s theory. Conditional sampling is used to isolate effects of strong rotation. The results presented provide strong evidence of the Lagrangian nature of turbulentenergy cascade.

Experimental and numerical study of weak shock wave transmissions through minitubes
View Description Hide DescriptionThe aim of this letter is to present an original experimental technique to study weak shock wave in a minitube. Thus, we designed an apparatus that can be connected to any classical shock tube in order to characterize high speed flows induced by the shock wave transmission in minitubes. We proposed appropriated measurements based on high speed strioscopy coupled with pressure sensors. Two minitube diameters are considered: and . We realized preliminary experimental and numerical campaigns with an incident shock waveMach number at . The generation of a microshock wave was observable in the two minitubes. For the smallest minitube, we found an attenuation of the strength of the shock wave with a decrease of 1.8% of the Mach number.

Taylor’s (1935) dissipation surrogate reinterpreted
View Description Hide DescriptionNew results from direct numerical simulation of decaying isotropic turbulence show that Taylor’s expression for the viscous dissipation rate is more appropriately interpreted as a surrogate for the inertial energy flux. As a consequence, the well known dependence of the Taylor prefactor on Reynolds number can be understood as corresponding to the onset of an inertial range.

Pulling bubbles from a bath
View Description Hide DescriptionDeposition of bubbles on a wall withdrawn from a liquid bath is a phenomenon observed in many everyday situations—the foam lacing left behind in an emptied glass of beer, for instance. It is also of importance to the many industrial processes where uniformity of coating is desirable. We report work on an idealized version of this situation, the dragout of a single bubble in Landau–Levich–Derjaguin flow. We find that a welldefined critical wall speed exists, separating the two regimes of bubble persistence at the meniscus and bubble deposition on the moving wall. Experiments show that this transition occurs at . A similar result is obtained theoretically by balancing viscous stresses and gravity.
 Top

 ARTICLES

 Biofluid Mechanics

Flexible sheets falling in an inviscid fluid
View Description Hide DescriptionWe use inviscid simulations to study falling flexible sheets in the twoparameter space of sheet density and bending rigidity. The basic behavior is a repeated series of accelerations to a critical speed at which the sheet flexes and rapidly decelerates, shedding large vortices. The maximum and average speeds of the sheet are closely related to the critical flutter speed. The sheet trajectories also show persistent circling, quasiperiodic flapping, and more complex repeated patterns. For small bending rigidity, the motion becomes less regular. At intermediate bending rigidity, trajectories show a welldefined falling angle relative to the vertical. For larger sheet density and bending rigidity, the overall motion is more horizontal.

A boundary element model of the transport of a semiinfinite bubble through a microvessel bifurcation
View Description Hide DescriptionMotivated by a developmental gas embolotherapy technique for selective occlusion of blood flow to tumors, we examined the transport of a pressuredriven semiinfinite bubble through a liquidfilled bifurcating channel. Homogeneity of bubble splitting as the bubble passes through a vessel bifurcation affects the degree to which the vascular network near the tumor can be uniformly occluded. The homogeneity of bubble splitting was found to increase with bubble driving pressure and to decrease with increased bifurcation angle. Viscous losses at the bifurcation were observed to affect the bubble speed significantly. The potential for oscillating bubble interfaces to induce flow recirculation and impart high stresses on the vessel endothelium was also observed.
 Micro and Nanofluid Mechanics

Gasflow animation by unsteady heating in a microchannel
View Description Hide DescriptionWe study the flowfield generated in a onedimensional wallbounded gas layer due to an arbitrary smallamplitude time variation in the temperature of its boundaries. Using the Fourier transform technique, analytical results are obtained for the slipflow/Navier–Stokes limit. These results are complemented by lowvariance simulations of the Boltzmann equation, which are useful for establishing the limits of the slipflow description, as well as for bridging the gap between the slipflow analysis and previously developed freemolecular analytical predictions. Results are presented for both periodic (sinusoidal) and nonperiodic (stepjump) heating profiles. Our slipflow solution is used to elucidate a singular limit reported in the literature for oscillatory heating of a dynamically incompressible fluid.

Absolute to convective instability transition in charged liquid jets
View Description Hide DescriptionWe show that the presence of electric charge at the interface of a capillary liquid jet plays a secondary role concerning the onset of an absolute or a convective instability in common operational conditions for conejet electrosprays, compared to other factors such as the convective velocity, jet diameter, surface tension , density , or viscosity. Thus, in most situations, the critical convective velocity (or its related dimensionless number, the critical Weber number ) at the threshold between the dripping and the jetting regimes depends mainly on the viscosity of the fluid, scaled as a Reynolds number Re, and not so importantly on the electric forces at the interface of the jet. Accordingly, for any liquid, the classical curve of Leib and Goldstein [Phys. Fluids29, 952 (1986)] for versus Re is accurate enough to explore the parametrical conditions where a steady conejet mode is to be expected, linked to the convectively unstable nature of the issued jet. However, at the limit of low Reynolds numbers, the stability behavior becomes strongly sensitive to the electrical conductivity of the liquid. Thus, a parametrical region where a charged capillary jet becomes strongly stabilized by the viscous damping against the destabilizing surface electrical forces is described in detail in this work. The “unconditional jetting” limit previously described for a capillary jet surrounded by a coflowing liquid [A. M. GañánCalvo, Phys. Rev. E78, 026304 (2008)] is here recovered in the absence of a coflowing fluid when “frozen” surface charges are present.

Active microrheology of a colloidal suspension in the direct collision limit
View Description Hide DescriptionThe singlepoint active nonlinear microrheology of a colloidalsuspension is measured using laser tweezers in the limit that the diameter of the probe particle approaches the diameter of the bath suspension particles. The microviscosity thins as the probe velocity (and corresponding microrheological Péclet number) increases. This thinning behavior correlates with the development of a nonequilibrium suspension microstructure surrounding the probe particle, in which a boundary layer forms on the upstream face of the probe and a wake depleted of bath particles trails the probe. The magnitude of the microviscosities and the thinning behavior are in good agreement with Brownian dynamics simulations reported by Carpen and Brady [J. Rheol.49, 1483 (2005)]. The microviscosity increment collapses onto a single curve for all volume fractions when scaled by the contact distribution of bath particles around the probe. Scaling the microviscosity increment yields values lower than the dilute theory; furthermore, it plateaus at significantly higher Péclet numbers. The latter effect is corrected by rescaling the Péclet number with the suspension collective diffusion coefficient in place of the bath particle selfdiffusivity. The magnitude of the microviscosity increment suggests the theory overestimates the frequency of bathprobe collisions. The presence and role of hydrodynamic interactions and the effect of the soft repulsive potential are discussed.

Variational derivation of secondorder slip coefficients on the basis of the Boltzmann equation for hardsphere molecules
View Description Hide DescriptionThe objective of the present paper is to provide an analytic expression for the first and secondorder velocity slip coefficients. Therefore, gas flow rates in microchannels have been rigorously evaluated in the nearcontinuum limit by means of a variational technique which applies to the integrodifferential form of the Boltzmann equation based on the true linearized collision operator. The diffusespecular reflection condition of Maxwell’s type has been considered in order to take into account the influence of the accommodation coefficient on the slip parameters. The polynomial form of the Knudsen number obtained for the Poiseuille mass flow rate and the values of the velocity slip coefficients, found on the basis of our variational solution of the linearized Boltzmann equation for hardsphere molecules, are analyzed in the frame of potential applications of classical continuum numerical tools in simulations of microscale flows.
 Interfacial Flows

Drop dynamics after impact on a solid wall: Theory and simulations
View Description Hide DescriptionWe study the impact of a fluid drop onto a planar solid surface at high speed so that at impact, kinetic energy dominates over surface energy and inertia dominates over viscous effects. As the drop spreads, it deforms into a thin film, whose thickness is limited by the growth of a viscous boundary layer near the solid wall. Owing to surface tension, the edge of the film retracts relative to the flow in the film and fluid collects into a toroidal rim bounding the film. Using mass and momentum conservation, we construct a model for the radius of the deposit as a function of time. At each stage, we perform detailed comparisons between theory and numerical simulations of the Navier–Stokes equation.

A numerical study of thermocapillary migration of a small liquid droplet on a horizontal solid surface
View Description Hide DescriptionIn the present study, the transient thermocapillary migration of a small liquiddroplet on a horizontal solid surface is numerically investigated. The droplet has a large static contact angle and a high aspect ratio of the maximum height of the droplet to its footprint. The Navier–Stokes and energy equations for both the droplet and surrounding air are solved through the finite element method. The evolution of the isotherms, the flow fields and the contact angle hysteresis are presented. Two asymmetric thermocapillary vortices appear inside the droplet. The variation of the size of the thermocapillary vortex during the migration process causes the speed of the droplet to first increase significantly, and then decrease gradually to approach a constant value. The higher imposed temperature gradient causes the droplet velocity to reach its maximal value earlier and have a higher final speed. If the static contact angle of the droplet is less than (or higher) than 90°, the droplet speed is lower (or higher) since the net thermocapillary momentum in the horizontal direction is diminished (or enhanced) by the presence of capillary force. The present results for the migration velocity and the contact angle hysteresis for a squalane droplet are also in good agreement with the previous experimental results.
 Particulate, Multiphase, and Granular Flows

Dispersion and temperature statistics of inertial particles in isotropic turbulence
View Description Hide DescriptionThe dispersion and temperature distribution of inertial particles are important in many turbulent, multiphase flow problems. In order to understand these better, direct numerical simulations (DNSs) are performed for inertial particles in a fluid with a constant temperature gradient and whose motion is either statistically stationary or decaying, isotropic turbulence. It is found that, for long times, the dispersion of inertial particles is the greatest when the Stokes number, , is of order 1, where and are, respectively, the particle response time and the flow Kolmogorov time scale. A similar result is found for the long time behavior of the time rate of change of the meansquare particle temperature fluctuations,. To understand the DNS results better, an evolution equation for , along with the short and long time limits, is derived analytically from the thermal energy equation for inertial particles.

Investigation and modeling of bubblebubble interaction effect in homogeneous bubbly flows
View Description Hide DescriptionThe effect of bubblebubble interaction in homogeneous bubblyflow is investigated by direct numerical simulation and a bubbly mixture model for bubbly shock flows at void fraction 0.4%–13%. It is found that the bubblebubble interaction effect is significant at void fraction higher than O(1)% and decreases the amplitude and wavelength of the macroscale oscillations in the dispersive shock structure. For the modeling of bubblebubble interaction effect, the locally volume averaged Rayleigh–Plesset (LVARP) equation, which is an extended version of the original Rayleigh–Plesset equation, is proposed in the present study. The results of bubbly mixture model using LVARP agree well with the direct simulation results for bubbly shock flows at void fraction up to 13%. The bubblebubble interaction in nonuniform bubblyflows is also investigated in bubblyflows with randomized initial bubble positions. It is found that the LVARP model predicts the ensemble averaged behavior with reasonable accuracy.
 Laminar Flows

Counterflow driven by swirl decay
View Description Hide DescriptionThe global meridional circulation of a viscous fluid, caused by swirl decay in a cylindrical container, is studied. To this end, a new solution to the Navier–Stokes equations is obtained, and simple experiments are performed to verify the predictions of the theory. The swirl decay mechanism explains elongated counterflows in hydrocyclones and vortex tubes sometimes extending over a hundred diameters.

Acoustic streaming in simplified liquid rocket engines with transverse mode oscillations
View Description Hide DescriptionThis study considers a simplified model of a liquid rocket engine in which uniform injection is imposed at the faceplate. The corresponding cylindrical chamber has a small lengthtodiameter ratio with respect to solid and hybrid rockets. Given their low chamber aspect ratios, liquid thrust engines are known to experience severe tangential and radial oscillation modes more often than longitudinal ones. In order to model this behavior, tangential and radial waves are superimposed onto a basic meanflow model that consists of a steady, uniform axial velocity throughout the chamber. Using perturbation tools, both potential and viscousflowequations are then linearized in the pressure wave amplitude and solved to the second order. The effects of the headwall Mach number are leveraged as well. While the potential flow analysis does not predict any acoustic streamingeffects, the viscous solution carried out to the second order gives rise to steady secondary flow patterns near the headwall. These axisymmetric, steady contributions to the tangential and radial traveling waves are induced by the convective flow motion through interactions with inertial and viscous forces. We find that suppressing either the convective terms or viscosity at the headwall leads to spurious solutions that are free from streaming. In our problem, streaming is initiated at the headwall, within the boundary layer, and then extends throughout the chamber. We find that nonlinear streaming effects of tangential and radial waves act to alter the outer solution inside a cylinder with headwall injection. As a result of streaming, the radial wavevelocities are intensified in onehalf of the domain and reduced in the opposite half at any instant of time. Similarly, the tangential waves are either enhanced or weakened in two opposing sectors that are at 90° angle to the radial velocity counterparts. The secondorder viscous solution that we obtain clearly displays both an oscillating and a steady flow component. The steady part can be an important contributor to wave steepening, a mechanism that is often observed during the onset of acoustic instability.

Particle image velocimetry measurements of the interaction of synthetic jets with a zeropressure gradient laminar boundary layer
View Description Hide DescriptionAn experimental investigation of the interaction between a synthetic jet actuator and a zeropressure gradient laminar boundary layer is reported. The aim of this study is to quantify the impact of synthetic jet vortical structures; namely, hairpin vortices, stretched vortex rings and tilted vortex rings on a boundary layer, and to assess their relative potential for flow separation control. Streamwise particle imagevelocimetry was employed in a water flume (free stream boundary layer thickness Reynolds number of 500 and boundary layer thicknesstojet orifice diameter ratio of 4) to obtain phase and timeaveraged boundary layer profile information of the impact of synthetic jets near the wall. The potential for flow control was assessed by analyzing near wall fluid mixing, realized by the measure of increase in wall shear stress produced by a passing vortex. Hairpin vortices (produced at a jettofree stream velocity ratio, and dimensionless stroke length, ) and stretched vortex rings (; ) exhibit characteristics akin to a streamwise vortex pair with a common upwash. Conversely, tilted vortex rings (; ) induce a streamwise vortex pair in the near wall region with a common downwash. Wall shear stress measurements show that synthetic jets composed of stretched vortex rings offer the best combination of near wall fluid mixing, persistency, and low rms fluctuations for potential applications of flow separation control.
 Instability and Transition

Effect of thermally induced perturbation in supersonic boundary layers
View Description Hide DescriptionThis paper investigates the mechanism of steady and unsteady thermal perturbation (also denoted as thermal bump) in a Mach 1.5 flat plate boundary layer. A highfidelity upwindbiased thirdorder Roe scheme is used with the compressive van Leer harmonic limiter on a suitably refined mesh. The study consists of two parts. In the first part, the effects of the steady and pulsed thermal bumps are explored. It is shown that the finitespan thermal bumps generate streamwise vortices. With steady heating, the disturbance decays downstream. However, when the thermal bump is pulsed, vortex shedding is observed and the streamwise vortical disturbance grows with downstream distance, consistent with linear stability analysis. The integrated disturbance energy indicates that streamwise kinetic disturbance energy growth dominates over those associated with other two velocity and thermodynamic components. The second part of this paper explores the physical consequences of the nonlinear dynamics between the vortices produced by the pulsed bump and the compressible boundary layer. The resulting threedimensional flow distortion generates hairpin structures which are aligned in the streamwise direction, suggesting that the transition process bears some similarity to Ktype breakdown. The arrangement of these vortices is connected to the lowspeed streaks observed in the evolving boundary layer. The shape factor, velocity, and Reynolds stress profiles suggest that the perturbed flow shows initiation of transition to turbulence, but remains transitional at the end of the plate.

Rayleigh–Taylor instability in dielectric fluids
View Description Hide DescriptionForce on dielectric fluids in the presence of a nonuniform electric field is shown to reduce their specific weights. An appropriately chosen field gradient makes the specific weights of superposed fluids equal and prevents Rayleigh–Taylor instability. We derive the dispersion relation for perturbation at the interface of superposed dielectric fluids, within limits of linear theory, successively for ideal, Newtonian, and those with stratified viscosity. A dimensionless dielectric number is shown to determine the stability of the arrangement.