Volume 27, Issue 5, May 2015
Index of content:

We report results on rotating stratified turbulence in the absence of forcing and with largescale isotropic initial conditions using direct numerical simulations computed on grids of up to 4096^{3} points. The Reynolds and Froude numbers are, respectively, equal to Re = 5.4 × 10^{4} and Fr = 0.0242. The ratio of the BruntVäisälä to the inertial wave frequency, N/f, is taken to be equal to 4.95, a choice appropriate to model the dynamics of the southern abyssal ocean at mid latitudes. This gives a global buoyancy Reynolds number RB = ReFr ^{2} ≈ 32, a value sufficient for some isotropy to be recovered in the small scales beyond the Ozmidov scale, but still moderate enough that the intermediate scales where waves are prevalent are well resolved. We concentrate on the largescale dynamics, for which we find a spectrum compatible with the BolgianoObukhov scaling. This scaling is also found for geostrophically balanced initial conditions on a run at a lower resolution and hence lower RB ≈ 4. Furthermore, we confirm that the Froude number based on a typical vertical length scale is of order unity, with strong gradients in the vertical. Two characteristic scales emerge from this computation and are identified from sharp variations in the spectral distribution of either total energy or helicity. A spectral break is also observed at a scale at which the partition of energy between the kinetic and potential modes changes abruptly, and beyond which a Kolmogorovlike spectrum recovers. Large slanted layers are ubiquitous in the flow, in the velocity and temperature fields, with local overturning events indicated by small local Richardson numbers and strong localized vortex tangles . Finally, a small largescale enhancement of energy directly attributable to the effect of rotation is also observed.
 LETTERS


Particle dispersion in sheared suspensions: Crucial role of solidsolid contacts
View Description Hide DescriptionWe performed high resolution measurements of the dynamics of nonBrownian and neutrally buoyant particles subjected to a periodic shear flow under low Reynolds number conditions. By changing the particle roughness and showing that it significantly affects the particle motion, we provide direct evidence that particle solidsolid contacts occur in viscous suspensions and strongly influence the particle dynamics. An accurate prediction of the particle trajectories is obtained with a minimal model that solely includes normal lubrication interactions and a frictionless contact force.

Heat transport by coherent RayleighBénard convection
View Description Hide DescriptionSteady but generally unstable solutions of the 2D Boussinesq equations are obtained for noslip boundary conditions and Prandtl number 7. The primary solution that bifurcates from the conduction state at Rayleigh number Ra ≈ 1708 has been calculated up to Ra ≈ 5.10^{6} and its Nusselt number is Nu ∼ 0.143 Ra ^{0.28} with a delicate spiral structure in the temperature field. Another solution that maximizes Nu over the horizontal wavenumber has been calculated up to Ra = 10^{9} and scales as Nu ∼ 0.115 Ra ^{0.31} for 10^{7} < Ra ≤ 10^{9}, quite similar to 3D turbulent data that show Nu ∼ 0.105 Ra ^{0.31} in that range. The optimum solution is a simple yet multiscale coherent solution whose horizontal wavenumber scales as 0.133 Ra ^{0.217}. That solution is unstable to larger scale perturbations and in particular to mean shear flows, yet it appears to be relevant as a backbone for turbulent solutions, possibly setting the scale, strength, and spacing of elemental plumes.

Negative vortices: The formation of vortex rings with reversed rotation in viscoelastic liquids
View Description Hide DescriptionThe formation process of vortex rings in a viscoelastic liquid is studied experimentally considering a pistoncylinder arrangement. Initially, a vortex ring begins to form as fluid is injected from the cylinder into the tank in a manner similar to that observed for Newtonian liquids. For later times, when the piston ceases its motion, the flow changes dramatically. A secondary vortex with reversed spinning direction appears and grows to be as large in size as the original one. The formation process is studied by contrasting the evolution with that obtained for Newtonian liquids with equivalent Reynolds numbers and stroke ratios. We argue that the reversing flow, or negative vortex, results from the combined action of shear and extension rates produced during the vortex formation, in a process similar to that observed behind ascending bubbles and falling spheres in viscoelastic media.

Selfsimilar impulsive capillary waves on a ligament
View Description Hide DescriptionWe study the shorttime dynamics of a liquid ligament, held between two solid cylinders, when one is impulsively accelerated along its axis. A set of onedimensional equations in the slenderslope approximation is used to describe the dynamics, including surface tension and viscous effects. An exact selfsimilar solution to the linearized equations is successfully compared to experiments made with millimetric ligaments. Another nonlinear selfsimilar solution of the full set of equations is found numerically. Both the linear and nonlinear solutions show that the axial depth at which the liquid is affected by the motion of the cylinder scales like , a consequence of the imposed radial uniformity of the axial velocity at the cylinder surface, and differs from t ^{2/3} known to prevail in surfacetensiondriven flows. The nonlinear solution presents the peculiar feature that there exists a maximum driving velocity U ^{⋆} above which the solution disappears, a phenomenon probably related to the depinning of the contact line observed in experiments for large pulling velocities.

 ARTICLES

 Biofluid Mechanics

Protein mediated membrane adhesion
View Description Hide DescriptionAdhesion in the context of mechanical attachment, signaling, and movement in cellular dynamics is mediated by the kinetic interactions between membraneembedded proteins in an aqueous environment. Here, we present a minimal theoretical framework for the dynamics of membrane adhesion that accounts for the kinetics of protein binding, the elastic deformation of the membrane, and the hydrodynamics of squeeze flow in the membrane gap. We analyze the resulting equations using scaling estimates to characterize the spatiotemporal features of the adhesive patterning and corroborate them using numerical simulations. In addition to characterizing aspects of cellular dynamics, our results might also be applicable to a range of phenomena in physical chemistry and materials science where flow, deformation, and kinetics are coupled to each other in slender geometries.
 Micro and Nanofluid Mechanics

Thermal transport in laminar flow over superhydrophobic surfaces, utilizing an effective medium approach
View Description Hide DescriptionAn analytical methodology to characterizing the effects of heat transport in internal laminar flows over ridged patterns, mimicking superhydrophobic surfaces, is indicated. The finite slip velocity on such surfaces and the thermal conductivity characteristics of the constituent material are both shown to modify the convective heat transport in the fluid. We use an effective medium approach to model the lowered thermal conductivity caused by the presence of air in the ridge interstices. The proposed analytical solutions for fully developed flow were verified through comparison with numerical simulations for a periodically ridged geometry in laminar flow. While the convective heat transport and the Nusselt Number (Nu) increase due to the modified fluid velocity profile on superhydrophobic surfaces, the decrease in the thermal conductivity of the substrate may play a larger role in determining the overall heat transfer in the channel.

Constitutive models for linear compressible viscoelastic flows of simple liquids at nanometer length scales
View Description Hide DescriptionSimple bulk liquids such as water are commonly assumed to be Newtonian. While this assumption holds widely, the fluidstructure interaction of mechanical devices at nanometer scales can probe the intrinsic molecular relaxation processes in a surrounding liquid. This was recently demonstrated through measurement of the high frequency (20 GHz) linear mechanical vibrations of bipyramidal nanoparticles in simple liquids [Pelton et al., “Viscoelastic flows in simple liquids generated by vibrating nanostructures,” Phys. Rev. Lett. 111, 244502 (2013)]. In this article, we review and critically assess the available constitutive equations for compressible viscoelastic flows in their linear limits—such models are required for analysis of the abovementioned measurements. We show that previous models, with the exception of a very recent proposal, do not reproduce the required response at high frequency. We explain the physical origin of this recent model and show that it recovers all required features of a linear viscoelastic flow. This constitutive equation thus provides a rigorous foundation for the analysis of vibrating nanostructures in simple liquids. The utility of this model is demonstrated by solving the fluidstructure interaction of two common problems: (1) a sphere executing radial oscillations in liquid, which depends strongly on the liquid compressibility and (2) the extensional mode vibration of bipyramidal nanoparticles in liquid, where the effects of liquid compressibility are negligible. This highlights the importance of shear and compressional relaxation processes, as a function of flow geometry, and the impact of the shear and bulk viscosities on nanometer scale flows.

Atomicscale thermocapillary flow in focused ion beam milling
View Description Hide DescriptionFocused ion beams provide a means of nanometerscale manufacturing and material processing, which is used for applications such as forming nanometerscale pores in thin films for DNA sequencing. We investigate such a configuration with Ga^{+} bombardment of a Si thinfilm target using molecular dynamics simulation. For a range of ion intensities in a realistic configuration, a recirculating melt region develops, which is seen to flow with a symmetrical pattern, counter to how it would flow were it driven by the ion momentum flux. Such flow is potentially important for the shape and composition of the formed structures. Relevant stress scales and estimated physical properties of silicon under these extreme conditions support the importance thermocapillary effects. A flow model with Marangoni forcing, based upon the temperature gradient and geometry from the atomistic simulation, indeed reproduces the flow and thus could be used to anticipate such flows and their influence in applications.

Spreading of a ferrofluid core in threestream micromixer channels
View Description Hide DescriptionSpreading of a water based ferrofluid core, cladded by a diamagnetic fluid, in threestream micromixer channels was studied. This spreading, induced by an external magnetic field, is known as magnetofluidic spreading (MFS). MFS is useful for various novel applications where control of fluidfluid interface is desired, such as micromixers or microchemical reactors. However, fundamental aspects of MFS are still unclear, and a model without correction factors is lacking. Hence, in this work, both experimental and numerical analyses were undertaken to study MFS. We show that MFS increased for higher applied magnetic fields, slower flow speed of both fluids, smaller flow rate of ferrofluid relative to cladding, and higher initial magnetic particle concentration. Spreading, mainly due to connective diffusion, was observed mostly near the channel walls. Our multiphysics model, which combines magnetic and fluidic analyses, showed, for the first time, excellent agreement between theory and experiment. These results can be useful for labonachip devices.

Quantifying transport within a twocell microdroplet induced by circular and sharp channel bends
View Description Hide DescriptionA passive method for obtaining good mixing within microdroplets is to introduce curves in the boundaries of the microchannels in which they flow. This article develops a method which quantifies the role of piecewise circular or straight channel boundaries on the transport within a twocell microdroplet. Transport between the two cells is quantified as an easily computable timevarying flux, which quantifies how lobes intrude from one cell to the other as the droplet traverses the channel. The computation requires neither numerically solving unsteady boundary value problems nor performing trajectory integration, thereby providing an efficient new method for investigating the role of channel geometry on intradroplet transport.

Why are fluid densities so low in carbon nanotubes?
View Description Hide DescriptionThe equilibrium density of fluids under nanoconfinement can differ substantially from their bulk density. Using a meanfield approach to describe the energetic landscape near the carbon nanotube (CNT) wall, we obtain analytical results describing the lengthscales associated with the layering observed at the interface of a LennardJones fluid and a CNT. We also show that this approach can be extended to describe the multiplering structure observed in larger CNTs. When combined with molecular simulation results for the fluid density in the first two rings, this approach allows us to derive a closedform prediction for the overall equilibrium fluid density as a function of CNT radius that is in excellent agreement with molecular dynamics simulations. We also show how aspects of this theory can be extended to describe some features of water confinement within CNTs and find good agreement with results from the literature.

Estimation of viscous dissipation in nanodroplet impact and spreading
View Description Hide DescriptionThe developments in nanocoating and nanospray technology have resulted in the increasing importance of the impact of micro/nanoscale liquid droplets on solid surface. In this paper, the impact of a nanodroplet on a flat solid surface is examined using molecular dynamics simulations. The impact velocity ranges from 58 m/s to 1044 m/s, in accordance with the Weber number ranging from 0.62 to 200.02 and the Reynolds number ranging from 0.89 to 16.14. The obtained maximum spreading factors are compared with previous models in the literature. The predicted results from the previous models largely deviate from our simulation results, with mean relative errors up to 58.12%. The estimated viscous dissipation is refined to present a modified theoretical model, which reduces the mean relative error to 15.12% in predicting the maximum spreading factor for cases of nanodroplet impact.
 Interfacial Flows

A rivulet of a powerlaw fluid with constant contact angle draining down a slowly varying substrate
View Description Hide DescriptionLocally unidirectional steady gravitydriven flow of a thin rivulet of a powerlaw fluid with prescribed volume flux down a locally planar substrate is considered. First, the solution for unidirectional flow of a uniform rivulet down a planar substrate is obtained, and then it is used to obtain the solution for a slowly varying rivulet with prescribed constant (nonzero) contact angle down a slowly varying substrate, specifically flow in the azimuthal direction around the outside of a large horizontal circular cylinder. The solution is shown to depend strongly on the value of the powerlaw index of the fluid. For example, a rivulet of strongly shearthinning fluid “selfchannels” its flow down a narrow central channel between two “levées” of slowly moving fluid that form at its sides, and in the central channel there is a “pluglike” flow except in a boundary layer near the substrate. On the other hand, in a rivulet of a strongly shearthickening fluid the velocity profile is linear except in a boundary layer near the free surface. Another notable qualitative departure from Newtonian behaviour is that, whereas the mass of a rivulet of a Newtonian or a shearthinning fluid is theoretically infinite, the mass of a rivulet of a shearthickening fluid is finite.

Stratified thinfilm flow in a rheometer
View Description Hide DescriptionWhen two immiscible layered fluids are present in a rheometer, interfacial distortions driven by the centripetal pressure gradient can modify torque measurements and induce dewetting. In particular, we examine the steadystate interface shape of a thin film coating a stationary substrate beneath a second immiscible fluid that is driven by a rotating parallelplate or cone. An asymptotic analysis of the interfacial distortion for the parallelplate flow is compared with numerical solutions for both the parallelplate and cone and plate configurations. We develop asymptotic criteria for dewetting of the thin film as a function of fluid and flow properties, and show that significant interfacial distortion and dewetting can occur due to secondary flow effects even at low Reynolds numbers. The distortion of the interface can result in increased or decreased torque measurements depending on the viscosity and density ratios between the two fluid layers. We relate these effects to recent experimental studies on liquidinfused rough media and discuss the stabilizing effect of surface microstructure.
 Viscous and NonNewtonian Flows

Twodimensional liftup problem for a rigid porous bed
View Description Hide DescriptionThe present study analytically reinvestigates the twodimensional liftup problem for a rigid porous bed that was studied by Mei, Yeung, and Liu [“Lifting of a large object from a porous seabed,” J. Fluid Mech. 152, 203 (1985)]. Mei, Yeung, and Liu proposed a model that treats the bed as a rigid porous medium and performed relevant experiments. In their model, they assumed the gap flow comes from the periphery of the gap, and there is a shear layer in the porous medium; the flow in the gap is described by adhesion approximation [D. J. Acheson, Elementary Fluid Dynamics (Clarendon, Oxford, 1990), pp. 243245.] and the pore flow by Darcy’s law, and the slipflow condition proposed by Beavers and Joseph [“Boundary conditions at a naturally permeable wall,” J. Fluid Mech. 30, 197 (1967)] is applied to the bed interface. In this problem, however, the gap flow initially mainly comes from the porous bed, and the shear layer may not exist. Although later the shear effect becomes important, the empirical slipflow condition might not physically respond to the shear effect, and the existence of the vertical velocity affects the situation so greatly that the slipflow condition might not be appropriate. In contrast, the present study proposes a more general model for the problem, applying Stokes flow to the gap, the Brinkman equation to the porous medium, and Song and Huang’s [“Laminar poroelastic media flow,” J. Eng. Mech. 126, 358 (2000)] complete interfacial conditions to the bed interface. The exact solution to the problem is found and fits Mei’s experiments well. The breakout phenomenon is examined for different soil beds, mechanics that cannot be illustrated by Mei’s model are revealed, and the theoretical breakout times obtained using Mei’s model and our model are compared. The results show that the proposed model is more compatible with physics and provides results that are more precise.

Tailoring wall permeabilities for enhanced filtration
View Description Hide DescriptionThe buildup of contaminants at the wall of crossflow membrane filtration systems can be detrimental to the operation of such systems because of, amongst other things, the osmotic backflow it may induce. In this paper, we propose a strategy to avoid the negative effects of backflow due to osmosis by using 2D channels bounded by walls with a combination of permeable and impermeable segments. We show that preventing flow through the final portion of the channel can increase the efficiency of filtration and we determine the optimal fraction occupied by the permeable wall that maximizes efficiency. Our analysis uses a combination of numerical techniques and asymptotic analysis in the limit of low wall permeabilities. Finally, we consider how the energy cost of filtration depends on the Péclet number and show that the energy cost per unit of filtered water may be minimized by appropriately choosing both the Péclet number and the permeableregion fraction.

Inertial effects of the semipassive flapping foil on its energy extraction efficiency
View Description Hide DescriptionThe inertia plays a significant role in the response of a system undergoing flowinduced vibrations, which has been extensively investigated by previous researchers. However, the inertial effects of an energy harvester employing the mechanism of flowinduced vibrations have attracted little attention. This paper concentrates on a semipassive energy extraction system considering its inertial effects. The incompressible NavierStokes equations are solved using a finitevolume based numerical solver with a moving grid technique. A partitioned method is used to couple the fluid and structure motions with the subiteration technique and an Aitken relaxation, which guarantees a strong fluidstructure coupling. In addition, a fictitious mass is added to resolve the numerical instability aroused by low density ratios. First, at a fixed mass ratio of r = 1, we identify an optimal set of parameters, at which a maximum efficiency of η = 34% is achieved. Further studies with r ranging from 0.125 to 100 are performed around the optimal parameters. The results show that for the semipassive flapping energy harvester, the energy harvesting efficiency decreases monotonically with increasing mass ratio. We also notice that the total power extraction stays at a high level with little variation for r < 10; therefore, if we concern more about the amount of power extraction rather than its efficiency, the inertial effects can be neglectable for r < 10. Moreover, since one degree of freedom is released for the semipassive system, it is possible for the system to automatically determine its optimal operational parameters. We note that the optimal phase difference ϕ = 82° has been well determined, which leads to a good timing of vortexfoil interactions. We note two different trends on phase difference for the effects of reduced frequency and mass ratio, respectively. By varying the reduced frequency f ^{∗}, an optimal f ^{∗} is identified, at which the minimum phase difference is achieved. While the relationship between phase difference and mass ratio is monotonic, a maximum phase difference is achieved at the nearly zero mass ratio. Nevertheless, both trends point to the same optimal phase difference, i.e., ϕ = 82° at θ 0 = 75°. Furthermore, the relationship between the leading edge vortex and the phase difference is systematically investigated, accounting for the physical reason of existence of the optimal phase difference.

Vortex dynamics during bladevortex interactions
View Description Hide DescriptionVortex dynamics during parallel bladevortex interactions (BVIs) were investigated in a subsonic wind tunnel using particle image velocimetry (PIV). Vortices were generated by applying a rapid pitchup motion to an airfoil through a pneumatic system, and the subsequent interactions with a downstream, unloaded target airfoil were studied. The bladevortex interactions may be classified into three categories in terms of vortex behavior: close interaction, very close interaction, and collision. For each type of interaction, the vortex trajectory and strength variation were obtained from phaseaveraged PIV data. The PIV results revealed the mechanisms of vortex decay and the effects of several key parameters on vortex dynamics, including separation distance (h/c), Reynolds number, and vortex sense. Generally, BVI has two main stages: interaction between vortex and leading edge (vortexLE interaction) and interaction between vortex and boundary layer (vortexBL interaction). VortexLE interaction, with its small separation distance, is dominated by inviscid decay of vortex strength due to pressure gradients near the leading edge. Therefore, the decay rate is determined by separation distance and vortex strength, but it is relatively insensitive to Reynolds number. VortexLE interaction will become a viscoustype interaction if there is enough separation distance. VortexBL interaction is inherently dominated by viscous effects, so the decay rate is dependent on Reynolds number. Vortex sense also has great impact on vortexBL interaction because it changes the velocity field and shear stress near the surface.
 Particulate, Multiphase, and Granular Flows

Concentrations of inertial particles in the turbulent wake of an immobile sphere
View Description Hide DescriptionDirect numerical simulations are used to study the interaction of a stream of small heavy inertial particles with the laminar and turbulent wakes of an immobile sphere facing an incompressible uniform inflow. Particles that do not collide with the obstacle but move past it are found to form preferential concentrations both in the sphere boundary layer and in its wake. In the laminar case, the upstream diverging flow pattern is responsible for particle clustering on a cylinder that extends far downstream the sphere. The interior of this surface contains no particles and can be seen as a shadow of the large obstacle. Such concentration profiles are also present in the case of turbulent wakes but show a finite extension. The sphere shadow is followed by a region around the axis of symmetry where the concentration is higher than the average. It originates from a resonant centrifugal expulsion of particles from shed vortices. The consequence of this concentration mechanism on monodisperse interparticle collisions is also briefly discussed. They are enhanced by both the increased concentration and the presence of large velocity differences between particles in the wake.

A computational study of droplet evaporation with fuel vapor jet ejection induced by localized heat sources
View Description Hide DescriptionDroplet evaporation by a localized heat source under microgravity conditions was numerically investigated in an attempt to understand the mechanism of the fuel vapor jet ejection, which was observed experimentally during the flame spread through a droplet array. An EulerianLagrangian method was implemented with a temperaturedependent surface tension model and a local phase change model in order to effectively capture the interfacial dynamics between liquid droplet and surrounding air. It was found that the surface tension gradient caused by the temperature variation within the droplet creates a thermocapillary effect, known as the Marangoni effect, creating an internal flow circulation and outer shear flow which drives the fuel vapor into a tail jet. A parametric study demonstrated that the Marangoni effect is indeed significant at realistic droplet combustion conditions, resulting in a higher evaporation constant. A modified Marangoni number was derived in order to represent the surface force characteristics. The results at different pressure conditions indicated that the nonmonotonic response of the evaporation rate to pressure may also be attributed to the Marangoni effect.