Volume 25, Issue 5, May 2013

In this study, numerical experiments are carried out to control the vortex shedding of a circular cylinder by utilizing an oscillating foil. The thin foil of elliptic shape undergoes prescribed harmonic oscillations in the streamwise direction in the near wake region. This simplified model is intended to study how wake dynamics are modified via localized wake disturbance, and then to stabilize the global wake instability. The results show that, at proper gap spacing, the oscillating foil can completely suppress the wake unsteadiness and recover the recirculating bubble type flow. The global instability suppression is then established on the imposition of local symmetry into the reversed flow behind the cylinder. It is revealed that the dynamic interaction between the main shears layer and oscillatory boundary layers is responsible for the wake stabilization mechanism. In addition, the kinematic/dynamic parameters related to foil motions and flow properties are widely discussed to reveal their effects on the performance of wake stabilization and drag reduction.
 ARTICLES

 Biofluid Mechanics

Force and torque on a cylinder rotating in a narrow gap at low Reynolds number: Scaling and lubrication analyses
View Description Hide DescriptionThe hydrodynamic forces and torques on a rotating cylinder in a narrow channel are investigated in this paper using lubrication analysis and scaling analysis. To explore the effect of the shape of the gap, three different geometries are considered. The force and torque expressions from lubrication analysis agree well with numerical solutions when the gap between cylinder and wall is small. The solutions from scaling analysis can be applied over a broader range, but only if the scaling coefficients are properly deduced from numerical solution or lubrication analysis. Selfsimilarity in the solutions is discussed as well.

The near wake of a freely flying European starling
View Description Hide DescriptionThe wake of a freely flying European starling (Sturnus vulgaris) has been measured using high speed, timeresolved, particle image velocimetry, simultaneously with high speed cameras which imaged the bird. These have been used to generate vector maps that can be associated with the bird's location and wing configuration in the wind tunnel. Time series of measurements have been expressed as composite wake plots which depict segments of the wing beat cycle for various spanwise locations in the wake. Measurements indicate that downwash is not produced during the upstroke, suggesting that the upstroke does not generate lift. As well, the wake velocities imply the presence of streamwise vortical structures, in addition to tip vortices. These two characteristics indicate similarities between the wake of a bird and the wake of a bat, which may be general features of the wakes of flapping wings.
 Micro and Nanofluid Mechanics

Regularized 13 moment equations for hard sphere molecules: Linear bulk equations
View Description Hide DescriptionThe regularized 13 moment equations of rarefied gas dynamics are derived for a monatomic hard sphere gas in the linear regime. The equations are based on an extended Gradtype moment system, which is systematically reduced by means of the Order of Magnitude Method [H. Struchtrup, “Stable transport equations for rarefied gases at high orders in the Knudsen number,” Phys. Fluids16(11), 3921–3934 (Year: 2004)]10.1063/1.1782751. ChapmanEnskog expansion of the final equations yields the linear Burnett and superBurnett equations. While the Burnett coefficients agree with literature values, this seems to be the first time that superBurnett coefficients are computed for a hard sphere gas. As a first test of the equations the dispersion and damping of sound waves is considered.

Shearrate dependent effective thermal conductivity of H_{2}O+SiO_{2} nanofluids
View Description Hide DescriptionEffective thermal conductivity (ETC) of waterbased silicon dioxide nanofluids in shear flow fields (flow shear rate range was 0–820 1/s) was measured using a rotating Couette apparatus. The results show that the ETC of the nanofluids in shear flow fields is significantly higher than that in static states. For the flow shear rates lower than a critical value (infiniteshear rate), the ETC asymptotically increases with increasing the flow shear rate; for the flow shear rates higher than the critical value, the ETC displays a plateau value (infiniteshear thermal conductivity). The increase of the ETC with shear rate is more obvious as increase the nanoparticle diameter and the nanoparticle volume fraction. For 16 different measured nanofluids, the infiniteshear rates vary from 445.0 to 712.1 1/s, while the infiniteshear thermal conductivities increase by 9%–17% comparing with the zeroshear thermal conductivities. The conventional ETC prediction correlation proposed for the suspensions containing microsized particles is not suitable for the nanofluids qualitatively and quantitatively. Finally, an exponential correlation is proposed based on our measured data to predict the ETC of nanofluids considering the effects of flow shear rate, nanoparticle diameter, and nanoparticle volume fraction.

Effects of curvature on rarefied gas flows between rotating concentric cylinders
View Description Hide DescriptionThe gas flow between two concentric rotating cylinders is considered in order to investigate nonequilibrium effects associated with the Knudsen layers over curved surfaces. We investigate the nonlinear flow physics in the nearwall regions using a new powerlaw (PL) wallscaling approach. This PL model incorporates Knudsen layer effects in nearwall regions by taking into account the boundary limiting effects on the molecular free paths. We also report new direct simulation Monte Carlo results covering a wide range of Knudsen numbers and accommodation coefficients, and for various outertoinner cylinder radius ratios. Our simulation data are compared with both the classical slip flow theory and the PL model, and we find that nonequilibrium effects are not only dependent on Knudsen number and accommodation coefficient but are also significantly affected by the surface curvature. The relative merits and limitations of both theoretical models are explored with respect to rarefaction and curvature effects. The PL model is able to capture some of the nonlinear trends associated with Knudsen layers up to the early transition flow regime. The present study also illuminates the limitations of classical slip flow theory even in the early slip flow regime for higher curvature test cases, although the model does exhibit good agreement throughout the slip flow regime for lower curvature cases. Torque and velocity profile comparisons also convey that a good prediction of integral flow properties does not necessarily guarantee the accuracy of the theoretical model used, and it is important to demonstrate that field variables are also predicted satisfactorily.

Weakly nonlinear electrophoresis of a highly charged colloidal particle
View Description Hide DescriptionAt large zeta potentials, surface conduction becomes appreciable in thindoublelayer electrokinetic transport. In the linear weakfield regime, where this effect is quantified by the Dukhin number, it is manifested in nonSmoluchowski electrophoretic mobilities. In this paper we go beyond linear response, employing the recently derived macroscale model of Schnitzer and Yariv [“Macroscale description of electrokinetic flows at large zeta potentials: Nonlinear surface conduction,” Phys. Rev. E86, 021503 (Year: 2012)10.1103/PhysRevE.86.021503] as the infrastructure for a weakly nonlinear analysis of sphericalparticle electrophoresis. A straightforward perturbation in the field strength is frustrated by the failure to satisfy the farfield conditions, representing a nonuniformity of the weakfield approximation at large distances away from the particle, where salt advection becomes comparable to diffusion. This is remedied using innerouter asymptotic expansions in the spirit of Acrivos and Taylor [“Heat and mass transfer from single spheres in Stokes flow,” Phys. Fluids5, 387 (Year: 1962)10.1063/1.1706630], with the inner region representing the particle neighborhood and the outer region corresponding to distances scaling inversely with the field magnitude. This singular scheme furnishes an asymptotic correction to the electrophoretic velocity, proportional to the applied field cubed, which embodies a host of nonlinear mechanisms unfamiliar from linear electrokinetic theories. These include the effect of induced zetapotential inhomogeneity, animated by concentration polarization, on electroosmosis and diffusoosmosis; bulk advection of salt; nonuniform bulk conductivity; Coulomb body forces acting on bulk volumetric charge; and the nonzero electrostatic force exerted upon the otherwise screened particlelayer system. A numerical solution of the macroscale model validates our weakly nonlinear analysis.
 Interfacial Flows

Viscous coalescence of droplets: A lattice Boltzmann study
View Description Hide DescriptionThe coalescence of two resting liquid droplets in a saturated vapor phase is investigated by Lattice Boltzmann simulations in two and three dimensions. We find that, in the viscous regime, the bridge radius obeys a t 1/2scaling law in time with the characteristic time scale given by the viscous time. Our results differ significantly from the predictions of existing analytical theories of viscous coalescence as well as from experimental observations. While the underlying reason for these deviations is presently unknown, a simple scaling argument is given that describes our results well.

A mapping method for distributive mixing with diffusion: Interplay between chaos and diffusion in timeperiodic sine flow
View Description Hide DescriptionWe present an accurate and efficient computational method for solving the advectiondiffusion equation in timeperiodic chaotic flows. The method uses operator splitting, which allows the advection and diffusion steps to be treated independently. Taking advantage of flow periodicity, the advection step is solved using a mapping method, and diffusion is “added” discretely after each iteration of the advection map. This approach results in the construction of a composite mapping matrix over an entire period of the chaotic advectiondiffusion process and provides a natural framework for the analysis of mixing. To test the approach, we consider twodimensional timeperiodic sine flow. By comparing the numerical solutions obtained by our method to reference solutions, we find qualitative agreement for large time steps (structure of concentration profile) and quantitative agreement for small time steps (low error). Further, we study the interplay between mixing through chaotic advection and mixing through diffusion leading to an analytical model for the evolution of the intensity of segregation with time. Additionally, we demonstrate that our operator splitting mapping approach can be readily extended to three dimensions.

Travellingwave similarity solutions for a steadily translating slender dry patch in a thin fluid film
View Description Hide DescriptionA novel family of threedimensional travellingwave similarity solutions describing a steadily translating slender dry patch in an infinitely wide thin fluid film on an inclined planar substrate when surfacetension effects are negligible is obtained, the flow being driven by gravity and/or a prescribed constant shear stress on the free surface of the film. For both driving mechanisms, the dry patch has a parabolic shape (which may be concave up or concave down the substrate), and the film thickness increases monotonically away from the contact lines to its uniform farfield value. The two most practically important cases of purely gravitydriven flow and of purely surfaceshearstressdriven flow are analysed separately.

Spontaneous penetration of a nonwetting drop into an exposed pore
View Description Hide DescriptionWe consider the penetration process of a liquid drop approaching an exposed pore along the axis of symmetry, which is intended to model the penetration of nonwetting drops into a porous medium. Inertia and gravity are neglected at the current stage. In addition to the penetration into a capillary tube in the literature, the drop may spread on the outer surface of the porous medium. Based on the mechanical equilibrium states, we find the critical drop radius, below which the drop penetration is spontaneous. We further identify five penetration regimes based on the drop radius and the static contact angle, all of which are exemplified by phasefield simulations. The free energy as a function of penetration depth reveals only two stable equilibrium states: the drop either enters the pore completely (maximum penetration) or stays at the pore inlet (zero penetration). For a nonpenetrating drop radius, the free energy has a local maximum which constitutes an energy barrier that prevents spontaneous penetration. Finally, we modify the LucasWashburn equation to describe the dynamic process of penetration. Due to the neglect of dissipation from moving contact lines and entry flow, the modified LucasWashburn equation greatly overestimates the penetration rate, especially at the initial stage.

The fastest drop climbing on a wet conical fibre
View Description Hide DescriptionWe use highspeed video imaging to study the capillarydriven motion of a microdroplet along the outside of a prewetted conical fiber. The cones are fabricated on a glasspuller with tip diameters as small as 1 μm, an order of magnitude smaller than in previous studies. The liquid is fed through the hollow fiber accumulating at the fiber tip to form droplets. The droplets are initially attached to the opening as they grow in size before detaching and traveling up the cone. This detachment can produce a transient oscillation of high frequency. The spatial variation of the capillary pressure drives the droplets towards the wider side of the cone. Various liquids were used to change the surface tension by a factor of 3.5 and viscosity by a factor of 1500. Within each droplet size and viscousdissipation regime, the data for climbing speeds collapse on a single curve. Droplets traveling with and against gravity allow us to pinpoint the absolute strength of the driving capillary pressure and viscous stresses and thereby determine the prefactors in the dimensionless relationships. The motions are consistent with earlier results obtained from much larger cones. Translation velocities up to 270 mm/s were observed and overall the velocities follow capillaryviscous scaling, whereas the speed of the fastest droplets is limited by inertia following their emergence at the cone tip.

Rim instability of bursting thin smectic films
View Description Hide DescriptionThe rupture of thin smectic bubbles is studied by means of high speed video imaging. Bubbles of centimeter diameter and film thicknesses in the nanometer range are pierced, and the instabilities of the moving rim around the opening hole are described. Scaling laws describe the relation between film thickness and features of the filamentation process of the rim. A flapping motion of the retracting smectic film is assumed as the origin of the observed filamentation instability. A comparison with similar phenomena in soap bubbles is made. The present experiments extend studies on soap films[H. Lhuissier and E. Villermaux, Phys. Rev. Lett.103, 054501 (Year: 2009)10.1103/PhysRevLett.103.054501] to much thinner, uniform films of thermotropic liquid crystals.

Nonlinear dynamics of longwave Marangoni convection in a binary mixture with the Soret effect
View Description Hide DescriptionWe investigate the nonlinear dynamics of longwave Marangoni convection in a 2D binaryliquid layer heated from below. Free surface deformations and the Soret effect are taken into account. We employ the set of evolution equations derived in earlier work in the case of small Galileo and Lewis numbers and solve it numerically with periodic boundary conditions. We validate our numerical solution by comparison between the results obtained via two different numerical methods, as well as by comparison with the prior analytical results. We study the transitions between the nonlinear regimes emerging at finite supercriticality values and find a rich variety of patterns. In a sufficiently large computational domain, we observe multistability of waves chaotic in time and spatially replicated periodic and quasiperiodic solutions. For sufficiently high values of the Marangoni number, we also observe a breakdown of model equations.

A scaling relation for the capillarypressure driven drainage of thin films
View Description Hide DescriptionHydrodynamic interactions between deformable particles such as drops or vesicles are an integral part of the rheology of emulsions and suspensions. In addition, the drainage of the thin film separating two colliding drops or vesicles is crucial for understanding the dynamics of coalescence or adhesion, which can lead to phase separation. However, despite several decades of study, this phenomenon is still not well understood and existing analytical theories do not agree quantitatively with experimental and numerical results. In this article, new scaling arguments are presented to analyze the drainage process, once the film becomes sufficiently thin. In particular, it is shown that the length over which the pressure varies in the film changes as the film drains, and follows a specific scaling relation. The mass balance in the film is then revisited in light of the new scaling for the pressure gradient. Numerical simulations are conducted to test the new scaling arguments and evaluate the revised mass balance. In the case of vesicles, they exhibit an excellent fit with the new scaling theory. The theory is also found to apply well to drops, but only when the flow inside the drops is determined predominantly by the flow in the thin film rather than by the ambient flow.
 Viscous and NonNewtonian Flows

Nonequilibrium pressure control of the height of a largescale, groundcoupled, rotating fluid column
View Description Hide DescriptionWhen a groundcoupled, rotating fluid column is modeled incorporating nonequilibrium pressure forces in the NavierStokes equations, a new exact solution results. The solution has been obtained in a similar manner to the classical equilibrium solution. Unlike the infiniteheight, classical solution, the nonequilibrium pressure solution yields a groundcoupled rotating fluid column of finite height. A viscous, nonequilibrium Rankine vortex velocity distribution, developed previously, was used to demonstrate how the viscous and nonequilibrium pressure gradient forces, arising in the vicinity of the velocity gradient discontinuity that is present in the classical Rankine vortex model, effectively isolate the rotating central fluid column from the outer potential vortex region. Thus, the nonequilibrium region acts to confine and shield the central, rigidbodylike, rotating fluid core, justifying this examination of how such a rotating fluid column can interact with the ground. The resulting nonequilibrium groundcoupled, rotating fluid column solution was employed to estimate the central column heights of three welldocumented dust devils, and the central column height predictions were consistent with published dust devil height statistics.
 Particulate, Multiphase, and Granular Flows

Magnetic resonance imaging study on near miscible supercritical CO_{2} flooding in porous media
View Description Hide DescriptionCO2 flooding is one of the most popular secondary or tertiary recoveries for oil production. It is also significant for studying the mechanisms of the twophase and multiphase flow in porous media. In this study, an experimental study was carried out by using magnetic resonance imaging technique to examine the detailed effects of pressure and rates on CO2/decane flow in a beadpack porous media. The displacing processes were conducted under various pressures in a region near the minimum miscibility pressure (the system tuned from immiscible to miscible as pressure is increasing in this region) and the temperature of 37.8 °C at several CO2 injection volumetric rates of 0.05, 0.10, and 0.15 ml/min (or linear rates of 3.77, 7.54, and 11.3 ft/day). The evolution of the distribution of decane and the characteristics of the two phase flow were investigated and analyzed by considering the pressure and rate. The area and velocity of the transition zone between the two phases were calculated and analyzed to quantify mixing. The area of transition zone decreased with pressure at near miscible region and a certain injection rate and the velocity of the transition zone was always less than the “volumetric velocity” due to mutual solution and diffusion of the two phases. Therefore, these experimental results give the fundamental understanding of tertiary recovery processes at near miscible condition.

Analytical solution of the problem of the rise of a Taylor bubble
View Description Hide DescriptionIn the classical works of Prandtl and Taylor devoted to the analysis of the problem of the rise of a Taylor bubble in a round tube, a solution of the Laplace equation is used, which contains divergent infinite series. The present paper outlines a method for the correct analysis of the mentioned problem. Using the method of superposition of “elementary flows,” a solution was obtained for flow of an ideal fluid over a body of revolution in a pipe. Satisfying the free surface condition in the vicinity of the stagnation point and using the limiting transition with respect to the main parameter lead to the relation for the rise velocity of a Taylor bubble expressed in terms of the Froude number. In order to validate the method of superposition, it was applied to the problem of the rise of a plane Taylor bubble in a flat gap, which also has an exact analytical solution obtained with the help of the complex variable theory.

Dynamics and rheology of concentrated, finiteReynoldsnumber suspensions in a homogeneous shear flow
View Description Hide DescriptionWe present the lubricationcorrected forcecoupling method for the simulation of concentrated suspensions under finite inertia. Suspension dynamics are investigated as a function of the particlescale Reynolds number and the bulk volume fraction ϕ in a homogeneous linear shear flow, in which is defined from the density ρ f and dynamic viscosity μ of the fluid, particle radius a, and the shear rate as . It is shown that the velocity fluctuations in the velocitygradient and vorticity directions decrease at larger . However, the particle selfdiffusivity is found to be an increasing function of as the motion of the suspended particles develops a longer autocorrelation under finite fluid inertia. It is shown that finiteinertia suspension flows are shearthickening and the particle stresses become highly intermittent as increases. To study the detailed changes in the suspension microstructure and rheology, we introduce a particlestressweighted pairdistribution function. The stressweighted pairdistribution function clearly shows that the increase of the effective viscosity at high is mostly related to the strong normal lubrication interaction in the compressive principal axis of the shear flow.

Momentum transfer in a turbulent, particleladen Couette flow
View Description Hide DescriptionA pointforce model is used to study turbulent momentum transfer in the presence of moderate mass loadings of small (relative to Kolmogorov scales), dense (relative to the carrier phase density) particles. Turbulent Couette flow is simulated via direct numerical simulation, while individual particles are tracked as Lagrangian elements interacting with the carrier phase through a momentum coupling force. This force is computed based on the bulk drag of each particle, computed from its local slip velocity. By inspecting a parameter space consisting of particle Stokes number and mass loading, a general picture of how and under what conditions particles can alter nearwall turbulent flow is developed. In general, it is found that particles which adhere to the requirements for the pointparticle approximation attenuate smallscale turbulence levels, as measured by wallnormal and spanwise velocity fluctuations, and decrease turbulent fluxes. Particles tend to weaken nearwall vortical activity, which in turn, through changes in burst/sweep intensities, weakens the ability of the turbulent carrierphase motion to transfer momentum in the wallnormal direction. Compensating this effect is the oftenignored capacity of the dispersed phase to carry stress, resulting in a total momentum transfer which remains nearly unchanged. The results of this study can be used to interpret physical processes above the ocean surface, where sea spray potentially plays an important role in vertical momentum transfer.

Effects of jet/vortex interaction on contrail formation in supersaturated conditions
View Description Hide DescriptionThe effects of the interaction between a model of aircraft trailing vortex and engine jets on the formation of a contrail in supersaturated ambient air are studied using EulerianLagrangian twophase flows largeeddy simulations. The threedimensional structure of the contrail, the mean flow properties, and the statistical correlations between ice and water vapor are analyzed for different jet and vortex parameters and different soot particle numbers. The interaction is characterized by the entrainment of the jets by the trailing vortex. In the fourengines case, particles exhausting the outboard jets are exposed to local higher supersaturation due to the temperature drop in the lowpressure vortex core region. The soot particle number affects both the structure and the global characteristics of the contrail. The increase in soot loading results in stronger vapor depletion – which leads to larger ice production – and to smaller ice particles for a given amount of vapor exhaust. The fraction of activated particles decreases with soot loading because of the increased competition for the vapor available for condensation. Of particular interest is the interaction between the jet/vortex turbulence and ice microphysics (activation, condensation, particle size distribution, and optical depth). It is found that the characteristic timescales of mixing and condensation can be of the same order in the jet regime. For the present high ambient supersaturation conditions, the competition between the entrainment of humid ambient air and vapor depletion plays an important role in determining the initial growth of the contrail and the spatial and size distributions of ice particles.