Volume 25, Issue 4, April 2013

Inside evaporating twocomponent sessile droplets, a family of the Rayleigh convection exists, driven by salinity gradient formed by evaporation of solvent and solute. In this work, the characteristic of the flow inside an axisymmetric droplet is investigated. A stretched coordinate system is employed to account for the effect of boundary movement. A scaling analysis shows that the flow velocity is proportional to the (salinity) Rayleigh number (Ra s ) at the smallRayleighnumber limit. A numerical analysis for a hemispherical droplet exhibits the flow velocity is proportional to the nondimensional number , at high Rayleigh numbers. A selfsimilar condition is established for the concentration field irrespective of the Rayleigh numbers after a moderate time, and the flow field is invariant with time at this stage. The scaling relation for the high Rayleigh numbers is verified experimentally by using aqueous NaCl droplets.
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Jet meandering by a foil pitching in quiescent fluid
View Description Hide DescriptionThe flow produced by a rigid symmetric NACA0015 airfoil purely pitching at a fixed location in quiescent fluid (the limiting case of infinite Strouhal number) is studied using visualizations and particle image velocimetry. A weak jet is generated whose inclination changes continually with time. This meandering is observed to be random and independent of the initial conditions, over a wide range of pitching parameters.

A pendulum in a flowing soap film
View Description Hide DescriptionWe consider the dynamics of a pendulum made of a rigid ring attached to an elastic filament immersed in a flowing soap film. The system shows an oscillatory instability whose onset is a function of the flow speed, length of the supporting string, the ring mass, and ring radius. We characterize this system and show that there are different regimes where the frequency is dependent or independent of the pendulum length depending on the relative magnitude of the addedmass. Although the system is an infinitedimensional, we can explain many of our results in terms of a one degreeoffreedom system corresponding to a forced pendulum. Indeed, using the vorticity measured via particle imaging velocimetry allows us to make the model quantitative, and a comparison with our experimental results shows we can capture the basic phenomenology of this system.
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 ARTICLES

 Biofluid Mechanics

Performance of a wing with nonuniform flexibility in hovering flight
View Description Hide DescriptionThe deformability of insect wings is associated with the embedded skeleton (venation). In this paper, the aerodynamic performance of wings with nonuniform flexibility is computationally investigated. By using a twodimensional rendition, the underlying veins are modeled as springs, and the membrane is modeled as a flexible plate. The focus is on the effects of the detailed distribution of vein flexibility upon the performance of such a wing in the generation of lift force. Specifically, we are interested in finding the importance of leading edge strengthening. Towards this end, the aerodynamic performances of three wings, a rigid wing, a flexible wing with identical veins, and a flexible wing with strengthened leading edge, are studied and compared against each other. It is shown that the flexible wing with leading edge strengthening is capable of producing significantly higher lift force without consuming more energy. This is found to be related to the stabilizing and cambering effects at the leading edge, which enhances the leading edge vortices. In addition, in contrast to the other two wings, which show sensitivity to kinematic parameters, the wing with strengthened leading edge perform well over a wide range of parameters.

Propulsion efficiency of bodies appended with multiple flapping fins: When more is less
View Description Hide DescriptionUnderwater animals propel themselves by flapping their pectoral and caudal fins in a narrow range of frequencies, given by Strouhal number St, to produce transitional vortex jets (St is generally expressed nondimensionally as the product of flapping frequency and stroke (arc) length divided by forward speed). The organized nature of the selection of St and of the vortex jet is thought to maximize hydrodynamic efficiency, although the exact mechanism is not known. Our recent StuartLandau equation models, which have selfregulation properties, indicate that the fin and its jet vortices couple. Temporal maps of forces in single isolated fins show a bimodal behavior in certain ranges of the transitional Reynolds number; this behavior bears resemblance to neural bifurcation properties that owe their origin to the selfregulation mechanism. In view of our theoretical and biorobotic evidence of selfregulation in single flapping fins, we explore if this property is altered in a finappended body, the goal being to understand how the narrow selection of St, selfregulation, and maximization of hydrodynamic efficiency are related. Swimming vehicles of 1m scale have been built where a rigid cylindrical body is appended with six flapping fins, three at each end. The fins are rigid, have a rounded leading edge and a laminar section (NACA 0012), and are hinged at one end. The planform is an abstracted version of the penguin wing; it has low aspect ratio and a chord Reynolds number that varies in the transitional range from 10 000 to 60 000. The fin geometry, Reynolds number range, and the nonflexible nature of the main body are in common with those in penguins, and the length and displacement volume are similar to those of sharks. The maximum hydrodynamic efficiency of the finappended body (0.40) is lower than that of the single fin (0.57), but is close to that of a fish using several fins. The propulsion density (kW/m3 of displacement volume) of the finappended cylinder is similar to that of a cruising shark. If we allow comparison of electrical versus thermal measurements, the total efficiency of the finappended body is similar to that of the damselfly and dragonfly, which are also based on vortex propulsion. The fin force fluctuations are modeled by a van der Pol oscillator. Measured phase maps of force fluctuation versus its time derivative correlate with the Strouhal numbers. Until stabilization, the maximum hydrodynamic efficiency of the finappended body increases with fin Reynolds number in a staircase pattern whose boundaries correlate with similar transitional subregimes in single fins, including the bimodal subregimes, thereby relating efficiency with the selfregulating jet vortex oscillators. At low Reynolds numbers, the peak of hydrodynamic efficiency remains flat over a wide range of St, becoming steeper at higher Reynolds numbers with the maximum occurring at lower values of St. The modeling shows that for selfregulation, future biorobotic design should focus on the reduction of structural damping and on a finbody assembly that has reciprocal energetic interaction with the shed vortex.
 Micro and Nanofluid Mechanics

Evaporationinduced saline Rayleigh convection inside a colloidal droplet
View Description Hide DescriptionInside evaporating twocomponent sessile droplets, a family of the Rayleigh convection exists, driven by salinity gradient formed by evaporation of solvent and solute. In this work, the characteristic of the flow inside an axisymmetric droplet is investigated. A stretched coordinate system is employed to account for the effect of boundary movement. A scaling analysis shows that the flow velocity is proportional to the (salinity) Rayleigh number (Ra s ) at the smallRayleighnumber limit. A numerical analysis for a hemispherical droplet exhibits the flow velocity is proportional to the nondimensional number , at high Rayleigh numbers. A selfsimilar condition is established for the concentration field irrespective of the Rayleigh numbers after a moderate time, and the flow field is invariant with time at this stage. The scaling relation for the high Rayleigh numbers is verified experimentally by using aqueous NaCl droplets.

Effect of electroosmotic flow on energy conversion on superhydrophobic surfaces
View Description Hide DescriptionIt has been suggested that superhydrophobic surfaces, due to the presence of a noshear zone, can greatly enhance transport of surface charges, leading to a considerable increase in the streaming potential. This could find potential use in microenergy harvesting devices. In this paper, we show using analytical and numerical methods, that when a streaming potential is generated in such superhydrophobic geometries, the reverse electroosmotic flow and hence current generated by this, is significant. A decrease in streaming potential compared to what was earlier predicted is expected. We also show that, due to the electroosmotic streamingcurrent, a saturation in both the power extracted and efficiency of energy conversion is achieved in such systems for large values of the free surface charge densities. Nevertheless, under realistic conditions, such microstructured devices with superhydrophobic surfaces have the potential to even reach energy conversion efficiencies only achieved in nanostructured devices so far.
 Interfacial Flows

Onedimensional wavepropelled bouncing drop on an oscillating liquid bath
View Description Hide DescriptionWe investigate the wavepropelled phenomena of the drop on the oscillating flat surface and on the Faraday wave. With the quasionedimensional setup, we observe the deformations of the oscillating oil surface and the gliding drop on the oil surface. The “glider” drop is found reaching the largest speed while system is driving at 65 Hz, which is consistent with the resonance of the drop and the oscillating surface. The distorted surface wave with different slopes is suspected of being responsible for the acceleration of the traveling drop. Furthermore, for drop traveling on the Faraday wave, the traveling speed is affected by the wavelength and the amplitude of the wave. The drops are found being trapped or slowed down around the nodes of the Faraday wave where the slopes are alternatively changed. The traveling speed of the drop is found decreasing linearly with the increase of the wave amplitude.

Lattice Boltzmann simulations of a single nbutanol drop rising in water
View Description Hide DescriptionThe motion of an nbutanol drop in water under the influence of gravity was numerically studied using a diffuse interface free energy lattice Boltzmann method. A pure twoliquid system without mass transfer between the phases was considered. A range of drop diameters of 1.0–4.0 mm covered the flow conditions. Most calculations were carried out in a moving reference frame. This allowed studying of longterm drop behavior in a relatively small computational domain. The capability of the method to capture the drop shape especially in the oscillating regime was demonstrated. For each drop diameter the evolution of the drop velocity in time, the terminal rise velocity and drop's shape were determined. The results were compared to experimental and numerical results and to semiempirical correlations. The deviation of the simulated terminal velocity from other results is within 5% for smaller drops and up to 20% for large oscillating drops. It was shown that beyond the onset of shape oscillations the binary system converges towards a constant capillary number of 0.056.

Hydrodynamic force measurements under precisely controlled conditions: Correlation of slip parameters with the mean free path
View Description Hide DescriptionA customized atomic force microscope has been utilized in dynamic mode to measure hydrodynamic forces between a sphere and a flat plate, both coated with gold. In order to study the influence of the mean free path on slippage without systematic errors due to varying surface properties, all data have been acquired at precisely the same spot on the plate. Local accommodation coefficients and slip lengths have been extracted from experimental data for He, Ne, Ar, Kr, as well as N2, CO2, and C2H6, at Knudsen numbers between 3 × 10−4 and 3. We found that slippage is effectively suppressed if the mean free path of the fluid is lower than the roughness amplitude on the surface, while we could not observe a clear correlation between the accommodation coefficient and the molecular mass.

Coalescence of armored interface under impact
View Description Hide DescriptionArmored interfaces refer to fluid interfaces on which a compact monolayer of particles is adsorbed. In this paper, we probe their robustness under impact. For such an investigation, the impact of a drop (covered or not by particles) on a flat armored interface is considered. Two regimes are observed: small drops impacting at low velocities do not coalesce, while bigger drops falling at higher velocities lead to coalescence. The coalescence which occurs when the impacting drop has just reached its maximum extension directly results from the formation of bare regions within the armor. We therefore propose a geometric criterion to describe this transition. This simple modeling is able to capture the dependence of the measured velocity threshold with particle size and drop diameter. The additional robustness experienced by double armors (both drop and puddle covered) results in an increase of the measured velocity threshold, which is quantitatively predicted.

A progressive correction to the circular hydraulic jump scaling
View Description Hide DescriptionThis document presents theoretical and numerical results of the circular hydraulic jump derived from the inertial lubrication theory[N. O. Rojas, M. Argentina, E. Cerda, and E. Tirapegui, Phys. Rev. Lett.104, 187801–1187801–4 (Year: 2010)]10.1103/PhysRevLett.104.187801. In particular, a correction for the hydraulic jump scaling is obtained. The results depend on subcritical depth, density, and surface tension, in agreement with experimental data at low Reynolds numbers[T. Bohr, C. Ellegaard, A. E. Hansen, and A. Haaning, Physica B228, 1–10 (Year: 1996)10.1016/S09214526(96)003730; S. H. Hansen, S. Horluck, D. Zauner, P. Dimon, C. Ellegaard, and S. C. Creagh, Phys. Rev. E55, 7048–7061 (Year: 1997)]10.1103/PhysRevE.55.7048.
 Viscous and NonNewtonian Flows

Viscous cavities
View Description Hide DescriptionWe study experimentally the impact of solid spheres in a viscous liquid at moderate Reynolds numbers (Re ∼ 5–100). We first determine the drag force by following the slowdown dynamics of projectiles. We then focus on the shape of the free surface: such impacts generate cavities, whose original shape is described and modeled.

Buckling of a thin, viscous film in an axisymmetric geometry
View Description Hide DescriptionBy adapting the Föpplvon Kàrmàn equation, which describes the deformation of a thin elastic membrane, we present an analysis of the buckling pattern of a thin, very viscous fluid layer subject to shear in an axisymmetric geometry. A linear stability analysis yields a differential eigenvalue problem, whose solution, obtained using spectral techniques, yields the most unstable azimuthal wavenumber, m ⋆. Contrary to the discussion of Slim et al. [J. Fluid Mech.694, 5–28 (Year: 2012)]10.1017/jfm.2011.437, it is argued that the axisymmetric problem shares the same degeneracy as its rectilinear counterpart, i.e., at the onset of instability, m ⋆ is indefinitely large. Away from this point, however, a comparison with analogue experimental results is both possible and generally favorable. In this vein, we describe the laboratory apparatus used to make new measurements of m ⋆, the phase speed and the wave amplitude; note that no prediction concerning the latter two quantities can be made using the present theory. Experiments reveal a limited range of angular velocities wherein waves of either small or large amplitude may be excited. Transition from one to the other regime does not appear to be associated with a notable change in m ⋆.

On the weak viscous effect of the reflection and transmission over an arbitrary topography
View Description Hide DescriptionIn this article, monochromatic viscous waves propagating over an arbitrary topography are studied, specifically the effect of bottom sliding coefficient and molecular viscosity. In the theoretical formulation, the perturbation approximation is directly applied to the NavierStokes equation and boundary conditions which are specified to correspond to realistic situations. Furthermore, the arbitrary topography is approximated using successive shelves separated by abrupt steps. On each shelf, the solution is represented in terms of reflection and transmission of monochromatic waves. Matching kinematic and dynamic conditions are implemented to interpret the solutions. The formulation of our modified planewave approximation can be analytically reduced to the traditional formulation by Lamb [Hydrodynamics, 6th ed. (Cambridge University Press, Cambridge, Year: 1937)] when the bottom sliding coefficient and molecular viscosity are neglected. Next, the wave transformations over three different trenches are simulated. The results indicate that wave reflection and transmission are certainly affected by molecular viscosity especially in shallow or intermediate fluid depths. In addition, numerical results are in good agreement with existing theoretical results and laboratory experiments without considering bottom sliding coefficient and molecular viscosity.

Thermocapillary drift on a spherical drop in a viscous fluid
View Description Hide DescriptionThe problem of nonisothermal fluid flow in and around a liquid drop has been studied. The temperature of the fluid is assumed to be nonconstant, steady and hence is governed by the Laplace's equation. The thermal and hydrodynamic problems have been solved under nonisothermal boundary conditions assuming Stokes equations for the flow inside and outside the drop. The drag and torque on the droplet in the form of Faxen's laws are presented. The use of the drag formula has been demonstrated by few particular cases. Some important asymptotic limiting cases have been discussed.

Viscoelastic Poiseuille flows with total normal stress dependent, nonlinear Navier slip at the wall
View Description Hide DescriptionThe effect of slip at the wall in steady, isothermal, incompressible Poiseuille flows in channel/slits and circular tubes of viscoelastic fluids is investigated analytically. The nonlinear Navier law at the wall, for the dependence on the shear stress, along with an exponential dependence of the slip coefficient on the total normal stress is assumed. The viscoelasticity of the fluid is taken into account by employing the OldroydB constitutive model. The flow problems are solved using a regular perturbation scheme in terms of the dimensionless exponential decay parameter of the slip coefficient, ɛ. The sequence of partial differential equations resulting from the perturbation procedure is solved analytically up to third order. As a consequence of the nonlinearity of the slip model, a twodimensional, continuously developing, flow field arises. Spectral analysis on the solution shows that the velocity and pressure profiles are fully resolved even for high values of ɛ, which indicates that the perturbation series up to third order approximates the full solution very well. The effects of the dimensionless slip coefficient, isotropic pressure, and deviatoric part of the total normal stress in the slip model, as well as the other parameters and dimensionless numbers in the flow are presented and discussed. Average quantities, in the cross section of the channel/slit or tube, with emphasis given on the pressure drop and the skin friction factor, are also offered.

Axisymmetric creeping motion of particles towards a circular orifice or disk
View Description Hide DescriptionWall effect on the hydrodynamic interaction among particles is important for their transport in many applications such as filtration. We investigate an axisymmetric creeping flow caused by one or two spherical particles migrating towards a circular orifice or disk. A boundary integral/element method is used to solve for the flow field and calculate the drag force. A crucial advantage of this approach is its capability of tackling a problem with more than one particle in the close vicinity of a solid wall. In the absence of a second particle, our results for the particle drag force agree more favorably with asymptotic behaviors than those from a superposition/collocation method. For cases with two particles driven by a constant external force, a relative motion between them arises from the hydrodynamic friction of the solid wall, leading to a decrease in the evolved separation distance or even occurrence of coagulation.
 Particulate, Multiphase, and Granular Flows

Grad's moment method for a granular fluid at moderate densities: NavierStokes transport coefficients
View Description Hide DescriptionThe NavierStokes transport coefficients of a granular dense fluid of smooth inelastic hard disks or spheres are explicitly determined by solving the inelastic Enskog equation by means of Grad's moment method. The transport coefficients are explicitly determined as functions of the (constant) coefficient of restitution and the solid volume fraction. In addition, the cooling rate is also calculated to first order in the spatial gradients. The calculations are performed for an arbitrary number of dimensions. The results are not limited to small dissipation and are expected to apply at moderate densities. It is found that the expressions of the NavierStokes transport coefficients and the cooling rate agree with those previously obtained from the ChapmanEnskog method by using the leading terms in a Sonine polynomial expansion. This shows the equivalence between both methods for granular fluids in the NavierStokes approximation. A comparison with previous results derived from Grad's moment method for inelastic disks and spheres is also carried out.

Diffusion transport coefficients for granular binary mixtures at low density: Thermal diffusion segregation
View Description Hide DescriptionThe mass flux of a lowdensity granular binary mixture obtained previously by solving the Boltzmann equation by means of the ChapmanEnskog method is considered further. As in the elastic case, the associated transport coefficients D, D p , and D′ are given in terms of the solutions of a set of coupled linear integral equations which are approximately solved by considering the first and second Sonine approximations. The diffusion coefficients are explicitly obtained as functions of the coefficients of restitution and the parameters of the mixture (masses, diameters, and concentration) and their expressions hold for an arbitrary number of dimensions. In order to check the accuracy of the second Sonine correction for highly inelastic collisions, the Boltzmann equation is also numerically solved by means of the direct simulation Monte Carlo (DSMC) method to determine the mutual diffusion coefficient D in some special situations (selfdiffusion problem and tracer limit). The comparison with DSMC results reveals that the second Sonine approximation to D improves the predictions made from the first Sonine approximation. We also study the granular segregation driven by a unidirectional thermal gradient. The segregation criterion is obtained from the socalled thermal diffusion factor Λ, which measures the amount of segregation parallel to the temperature gradient. The factor Λ is determined here by considering the secondorder Sonine forms of the diffusion coefficients and its dependence on the coefficients of restitution is widely analyzed across the parameter space of the system. The results obtained in this paper extend previous works carried out in the tracer limit (vanishing mole fraction of one of the species) by some of the authors of the present paper.

Power spectral distributions of pseudoturbulent bubbly flows
View Description Hide DescriptionAn experimental study was carried out to determinate the power spectral density (PSD) of monodispersed bubbly flows in a vertical channel using flying hotfilm anemometry. To improve bubble detection, optical fibers were installed in close proximity to the anemometer sensing element; in this way, the collisions of bubbles with the probe can be detected and removed from the signal. Measurements were performed with gas fractions up to 6%. The PSD distributions were found to decay with a power of −3, in agreement with previous studies, but for a much wider range of Reynolds and Weber numbers. Our measurements indicate that the power decay does not depend strongly on the nature of hydrodynamic interactions among bubbles.