Volume 24, Issue 12, December 2012

We present the results of an experimental investigation of fluid drops impacting an inclined rigid surface covered with a thin layer of high viscosity fluid. We deduce the conditions under which droplet bouncing, splitting, and merger arise. Particular attention is given to rationalizing the observed contact time and coefficients of restitution, the latter of which require a detailed consideration of the drop energetics.
 AWARD AND INVITED PAPERS


Germano identitybased subgridscale modeling: A brief survey of variations on a fertile theme
View Description Hide DescriptionIt has now been over 20 years since the introduction of the Germano identity. Mostly, the identity has been applied to closures for the subgridscale fluxes required in large eddy simulations in the bulk of turbulent flows. However, the basic ideas underlying the Germano identity can be applied in various other contexts. In recent years a number of such generalizations have been developed, and several of these are surveyed in this paper. The survey is based on an interpretation of the Germano identity stating that the sum of resolved and modeled contributions to basic quantities of intrinsic physical interest must be independent of filter scale. The focus of this survey is on the conceptual bases of the various generalizations and their common features, as a way of pointing to possible further extensions.

Biomimetic flow control based on morphological features of living creatures^{a)}
View Description Hide DescriptionDespite the long history of biomimetics (or biomimetic engineering), a scientific discipline of implementing natureinspired ideas to engineering systems for their performance enhancement, successful developments have been made only recently, especially in the field of flow control. In the present paper, we discuss flow controls based on the biomimetic approach, paying special attention to surface morphology of living creatures, to develop novel concepts or devices for drag reduction and aerodynamic performance enhancement. We consider two types of flow control devices: (1) devices attached or added to wing surfaces for high aerodynamic performance and (2) smart surfaces for low skinfriction. Several examples of successful biomimeticflow controls are presented and discussed in this paper. Further issues like the difference in the operating environments (e.g., the Reynolds number) between the biological and engineering systems are discussed. Finally, guidelines for effective integration of engineering and biology are suggested.
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 LETTERS


Infrared imagery of streak formation in a breaking wave
View Description Hide DescriptionHigh resolution infrared imagery of breaking waves in a wavetank free of wind shear or current reveals the production of a “streaky,” quasiperiodic thermal pattern produced during the breaking process. The streaks, or elongated patterns of warm and cold fluid, are found to form only when surfaceturbulence is present before wave breaking occurs. This suggests that waveturbulence interaction is one mechanism that can lead to streak formation in breaking wave systems. More specifically, the streaky structures observed in these experiments may be caused by an intense, rapid tilting, and stretching of preexisting vertical vorticity by the Stokes drift generated at or near the breaking wave crests, thereby generating a coherent system of counterrotating vortices. We attempt to relate our observations to the recent theory of Teixeira and Belcher [J. Fluid Mech.458, 229–267 (2002)10.1017/S0022112002007838]. Some properties of the streaks, such as the dependence of their lifetimes and spanwise scale on wave amplitude, are presented.

Vorticity alignment of rigid fibers in an oscillatory shear flow: Role of confinement
View Description Hide DescriptionRigid fibers suspended in a viscous, Newtonian fluid at high concentrations can be aligned in the direction perpendicular to the flowgradient plane (vorticity direction) by applying an oscillatory shear flow. A simple model, which considers only excluded volume and selfmobilities, can accurately predict the orientation distributions measured in experiments by Franceschini et al. [“Transverse alignment of fibers in a periodically sheared suspension: An absorbing phase transition with a slowly varying control parameter,” Phys. Rev. Lett.107, 250603 (2011)10.1103/PhysRevLett.107.250603]. Furthermore, simulations reveal that the alignment of the fibers in the vorticity direction depends strongly on the presence of the bounding walls.
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 ARTICLES

 Biofluid Mechanics

Numerical study of pulsatile channel flows undergoing transition triggered by a modelled stenosis
View Description Hide DescriptionIn this research, we numerically investigate the physics of pulsatile flows confined within a 3dimensional channel with a modelled stenosis formed eccentrically on the upper wall using the method of largeeddy simulation(LES). An advanced dynamic nonlinear subgridscale stress model was utilized to conduct numerical simulations and its predictive performance was examined in comparison with that of the conventional dynamic model. The Womersley number tested in the simulation was fixed at 10.5 and the Reynolds numbers tested were set to 750 and 2000, which are characteristics of human blood flows in large arteries. An inhouse LES code, based on curvilinear Cartesian coordinates, has been developed to conduct the unsteady numerical simulations using three different grid systems. The physical characteristics of the flow field have been studied in terms of the resolved mean velocity, turbulence kinetic energy, viscous wall shear stress, resolved and subgridscale turbulent shear stresses, local kinetic energy fluxes between the filtered and subgrid scales, and turbulence energy spectra along the central streamline of the domain. Triggered by the stenosis, the flow field driven by the pulsatile inlet condition undergoes laminarturbulentlaminar patterns in the streamwise direction. Correspondingly, the slope of the energy spectra deviates significantly from the wellknown −5/3 law for the inertial subrange to reflect the transition in the flow patterns.

Biased swimming cells do not disperse in pipes as tracers: A population model based on microscale behaviour
View Description Hide DescriptionThere is much current interest in modelling suspensions of algae and other microorganisms for biotechnological exploitation, and many bioreactors are of tubular design. Using generalized Taylor dispersion theory, we develop a populationlevel swimmingadvectiondiffusion model for suspensions of microorganisms in a vertical pipe flow. In particular, a combination of gravitational and viscous torques acting on individual cells can affect their swimming behaviour, which is termed gyrotaxis. This typically leads to local cell drift and diffusion in a suspension of cells. In a flow in a pipe, small amounts of radial drift across streamlines can have a major impact on the effective axial drift and diffusion of the cells. We present a Galerkin method to calculate the local mean swimming velocity and diffusiontensor based on local shear for arbitrary flow rates. This method is validated with asymptotic results obtained in the limits of weak and strong shear. We solve the resultant swimmingadvectiondiffusion equation using numerical methods for the case of imposed Poiseuille flow and investigate how the flow modifies the dispersion of active swimmers from that of passive scalars. We establish that generalized Taylor dispersion theory predicts an enhancement of gyrotactic focussing in pipe flow with increasing shear strength, in contrast to earlier models. We also show that biased swimming cells may behave very differently to passive tracers, drifting axially at up to twice the rate and diffusing much less.
 Micro and Nanofluid Mechanics

Capillary droplets on Leidenfrost microratchets
View Description Hide DescriptionLeidenfrost ratchets are structures with the ability of transporting liquid droplets when heated over the critical Leidenfrost temperature. Once this temperature is reached, the droplet levitates over the surface and moves in the direction marked by the slope of the ratchet at terminal velocities around 10 cm/s. Here we provide new experiments with micronsized ratchets, which have been produced with picosecond pulse laser ablation. In the following work, we use a simple method to measure the thrust driving droplets of capillary size over the microratchets. The mechanism responsible for the force acting on the drop on superheated ratchets has been recently under debate. We extend the recently proposed “viscous mechanism” proposed by Dupeux et al. [Europhys. Lett.96, 58001 (2011)10.1209/02955075/96/58001] to capillary droplets and find good agreement with our measurements.

Ferrofluid pipe flow under the influence of the magnetic field of a cylindrical coil
View Description Hide DescriptionFerrofluid pipe flow under the effect of a colinear, finite length cylindrical coil is examined numerically. The specific flow configuration is chosen as it is encountered in engineering and bioengineering applications such as magnetic drug targeting systems. The objective of the paper is twofold: first, to investigate the accuracy of an analytical solution for the magnetizationequation and assess its validity when used for nonuniform magnetic fields. It is found that it can be very helpful as a means of estimating the magnetization, especially for strong magnetic fields with low gradients; second, to examine the effects of the magnetic field on the flow and study the relevant importance of the magnetic terms of the momentum equation. The parameters that we examine are the strength of the magnetic field and of its gradients, the volumetric concentration of the magnetic particles, and the dimensions (length and diameter) of the coil. It is revealed that the axial pressure drop depends linearly on the volumetric concentration and that the magnetoviscosity effect is negligible in cases of nonuniform magnetic fields.

Bubbledriven inertial micropump
View Description Hide DescriptionThe fundamental action of the bubbledriven inertial micropump is investigated. The pump has no moving parts and consists of a thermal resistor placed asymmetrically within a straight channel connecting two reservoirs. Using numerical simulations, the net flow is studied as a function of channel geometry, resistor location, vapor bubble strength, fluid viscosity, and surface tension. Two major regimes of behavior are identified: axial and nonaxial. In the axial regime, the drive bubble either remains inside the channel, or continues to grow axially when it reaches the reservoir. In the nonaxial regime, the bubble grows out of the channel and in all three dimensions while inside the reservoir. The net flow in the axial regime is parabolic with respect to the hydraulic diameter of the channel crosssection, but in the nonaxial regime it is not. From numerical modeling, it is determined that the net flow is maximal when the axial regime crosses over to the nonaxial regime. To elucidate the basic physical principles of the pump, a phenomenological onedimensional model is developed and solved. A linear array of micropumps has been built using siliconSU8 fabrication technology that is used to manufacture thermal inkjet printheads. Semicontinuous pumping across a 2 mmwide channel has been demonstrated experimentally. Measured net flow with respect to viscosity variation is in excellent agreement with simulation results.
 Interfacial Flows

Oscillations of a gas pocket on a liquidcovered solid surface
View Description Hide DescriptionThe dynamic response of a gas bubble entrapped in a cavity on the surface of a submerged solid subject to an acoustic field is investigated in the linear approximation. We derive semianalytical expressions for the resonance frequency, damping, and interface shape of the bubble. For the liquid phase, we consider two limit cases: potential flow and unsteady Stokes flow. The oscillation frequency and interface shape are found to depend on two dimensionless parameters: the ratio of the gas stiffness to the surface tension stiffness, and the Ohnesorge number, representing the relative importance of viscous forces. We perform a parametric study and show, among others, that an increase in the gas pressure or a decrease in the surface tension leads to an increase in the resonance frequency until an asymptotic value is reached.

Capillary effects on floating cylindrical particles
View Description Hide DescriptionIn this study, we develop a systematic perturbation procedure in the small parameter, B ^{1/2}, where B is the Bond number, to study capillary effects on small cylindrical particles at interfaces. Such a framework allows us to address many problems involving particles on flat and curved interfaces. In particular, we address four specific problems: (i) capillary attraction between cylinders on flat interface, in which we recover the classical approximate result of Nicolson [“The interaction between floating particles,” Proc. Cambridge Philos. Soc.45, 288–295 (1949)10.1017/S0305004100024841], thus putting it on a rational basis; (ii) capillary attraction and aggregation for an infinite array of cylinders arranged on a periodic lattice, where we show that the resulting Gibbs elasticity obtained for an array can be significantly larger than the two cylinder case; (iii) capillary force on a cylinder floating on an arbitrary curved interface, where we show that in the absence of gravity, the cylinder experiences a lateral force which is proportional to the gradient of curvature; and (iv) capillary attraction between two cylinders floating on an arbitrary curved interface. The present perturbation procedure does not require any restrictions on the nature of curvature of the background interface and can be extended to other geometries.

Droplets bouncing on a wet, inclined surface
View Description Hide DescriptionWe present the results of an experimental investigation of fluid drops impacting an inclined rigid surface covered with a thin layer of high viscosity fluid. We deduce the conditions under which droplet bouncing, splitting, and merger arise. Particular attention is given to rationalizing the observed contact time and coefficients of restitution, the latter of which require a detailed consideration of the drop energetics.

Stability characteristics of solutocapillary Marangoni motion in evaporating thin films
View Description Hide DescriptionThe characteristics of solutocapillary Marangoni instability in evaporating thin films are analyzed by linear stability analysis and direct numerical simulations. As predicted by de Gennes [Eur. Phys. J. E6, 421 (2001)10.1007/s1018900180553] when the surface tension increases with increasing concentration of a nonvolatile solute the Marangoni stresses can sustain motion in the film and lead to the development of cellular patterns with small interfacial deformation, similar to the wellknown hexagons of the thermally driven Marangoni motion. The critical Marangoni number is found to be proportional to the inverse square root of a dimensionless evaporation rate. There exists an additional mode of instability analogous to the deformational mode of thermocapillary instability. This mode is due to the coordinated action of capillary pressure and Marangoni stresses and is manifested as a longwave oscillatory behavior leading to fast leveling of film thickness disturbances and subsequent reversal, as explained by Overdiep [Prog. Org. Coat.14, 159 (1986)10.1016/00330655(86)800103]. This type of instability appears over a range of wavenumbers determined by the evaporation parameter and the capillary number and is likely to be observed at relatively small Marangoni numbers because otherwise it is overwhelmed by the cellular mode. Systems where the surface tension decreases with increasing solute concentration are not immune to instabilities either but there exists a longwave deformational mode leading to monotonic growth of thickness disturbances. The above characteristics of evaporating film behavior are supported by experimental observations in the literature, where thin films of dried polymer solutions are found to have shortwave patterns and small roughness or longwave patterns and significant roughness, depending on whether surface tension of the solvents increases or decreases by the polymer solutes.

Coalescence of liquid drops: Different models versus experiment
View Description Hide DescriptionThe process of coalescence of two identical liquid drops is simulated numerically in the framework of two essentially different mathematical models, and the results are compared with experimental data on the very early stages of the coalescence process reported recently. The first model tested is the “conventional” one, where it is assumed that coalescence as the formation of a single body of fluid occurs by an instant appearance of a liquid bridge smoothly connecting the two drops, and the subsequent process is the evolution of this single body of fluid driven by capillary forces. The second model under investigation considers coalescence as a process where a section of the free surface becomes trapped between the bulk phases as the drops are pressed against each other, and it is the gradual disappearance of this “internal interface” that leads to the formation of a single body of fluid and the conventional model taking over. Using the full numerical solution of the problem in the framework of each of the two models, we show that the recently reported electrical measurements probing the very early stages of the process are better described by the interface formation/disappearance model. New theoryguided experiments are suggested that would help to further elucidate the details of the coalescence phenomenon. As a byproduct of our research, the range of validity of different “scaling laws” advanced as approximate solutions to the problem formulated using the conventional model is established.

Rebound and jet formation of a fluidfilled sphere
View Description Hide DescriptionThis study investigates the impact dynamics of hollow elastic spheres partially filled with fluid. Unlike an empty sphere, the internal fluid mitigates some of the rebound through an impulse driven exchange of energy wherein the fluid forms a jet inside the sphere. Surprisingly, this occurs on the second rebound or when the free surface is initially perturbed. Images gathered through experimentation show that the fluid reacts more quickly to the impact than the sphere, which decouples the two masses (fluid and sphere), imparts energy to the fluid, and removes rebound energy from the sphere. The experimental results are analyzed in terms of acceleration, momentum and an energy method suggesting an optimal fill volume in the neighborhood of 30%. While the characteristics of the fluid (i.e., density, viscosity, etc.) affect the fluid motion (i.e., type and size of jet formation), the rebound characteristics remain similar for a given fluid volume independent of fluid type. Implications of this work are a potential use of similar passive damping systems in sports technology and marine engineering.
 Viscous and NonNewtonian Flows

Falling plumes of point particles in viscous fluid
View Description Hide DescriptionThe growth of radial bulges on the conduit of a falling viscous plume of particles, reported by Pignatel et al. for a finite starting plume [F. Pignatel, M. Nicolas, É. Guazzelli, and D. Saintillan, “Falling jets of particles in viscous fluids,” Phys. Fluids21, 123303 (2009)10.1063/1.3276235], is investigated both numerically and analytically. As a model for the plume conduit, an infinite vertical cylinder of identical nonBrownian point particles falling under gravity in Stokes flow is considered. Numerically, this is implemented with periodic boundary conditions of a large, but finite, period. The quasiperiodic numerical simulations exhibit qualitatively similar behaviour to that previously observed for the finite plume, demonstrating that neither the plume head nor the plume source play a role in the growth of the radial bulges. This growth is instead shown to be due to fluctuations in the average number density of particles along the plume about its mean value n, which leads to an initial growth rate proportional to n ^{−1/2}. The typical length scale of the bulges, which is of the order of 10 plume radii, results from the particle plume responding most strongly to density fluctuations in the axial direction on this scale. Large radial bulges undergo a nonlinear wavebreaking mechanism, which entrains ambient fluid and reduces the magnitude of perturbations on the plume surface. This contributes towards an outwards diffusion of the plume in which the increase in radius, at sufficiently large times, is proportional to t ^{2/3}.

Miscible densitystable displacement flows in inclined tube
View Description Hide DescriptionWe study densitystable laminar miscible displacement flow of two isoviscous Newtonian fluids in an inclined pipe (diameter ). We present a wide range of novel experimental results. We illustrate the nonmonotone relation in displacement efficiency at the density difference moves from positive (density unstable) to negative (density stable), the efficiency being minimal for isodense fluids. The density stable configuration has been found to produce highly efficient displacements, with the bulk of the interface moving steadily at the mean velocity. The streamwise length of the stretched interface, or stretch length , is measured over a wide range of parameters. The stretch length increases with the mean flow velocity, increases with inclination β from vertical, decreases with density difference, and increases with viscosity. Our data are well represented by the scaled expression L − tan β = −3680/χ, where χ is the ratio of buoyancy and viscous stresses.
 Particulate, Multiphase, and Granular Flows

Shock tube investigation of quasisteady drag in shockparticle interactions
View Description Hide DescriptionA reassessment of historical drag coefficient data for spherical particles accelerated in shockinduced flows has motivated new shock tube experiments of particle response to the passage of a normal shock wave. Particle drag coefficients were measured by tracking the trajectories of 1mm spheres in the flow induced by incident shocks at Mach numbers 1.68, 1.93, and 2.04. The necessary data accuracy is obtained by accounting for the shock tube wall boundary layer growth and avoiding interactions between multiple particles. Similar to past experiments, the current data clearly show that as the Mach number increases, the drag coefficient increases substantially. This increase significantly exceeds the drag predicted by incompressible standard drag models, but a recently developed compressible drag correlation returns values quite close to the current measurements. Recent theoretical work and low particle accelerations indicate that unsteadiness should not be expected to contribute to the drag increase over the relatively long time scales of the experiments. These observations suggest that elevated particle drag coefficients are a quasisteady phenomenon attributed to increased compressibility rather than true flow unsteadiness.

Dynamics of concentric and eccentric compound droplets suspended in extensional flows
View Description Hide DescriptionThe motion, deformation, and stability of compound droplets in extensional flows are investigated numerically via a threedimensional spectral boundary element method. We examine the droplet stability under the influences of the capillary number, the inner droplet size and the relative magnitude of the surface tension of the two interfaces composing the compound droplet. The influence of viscosity on the droplet deformation is also discussed. We conclude that a compound droplet with a larger inner droplet and/or smaller inner surface tension is less stable and cannot withstand strong flow. For moderate viscosity ratios, a compound droplet with a more viscous “shell” exhibits larger deformation at steady state. In addition, for an eccentric compound droplet, both the inner and outer droplets tend to migrate away from its original location due to the asymmetry of the problem. The initial location of the inner droplet also influences the droplet stability as well as the migration velocity of the compound droplet.

Simulations of dilute sedimenting suspensions at finiteparticle Reynolds numbers
View Description Hide DescriptionAn alternative numerical method for suspension flows with application to sedimenting suspensions at finiteparticle Reynolds numbersRe _{ p } is presented. The method consists of an extended latticeBoltzmann scheme for discretizing the locally averaged conservation equations and a Lagrangian particle tracking model for tracking the trajectories of individual particles. The method is able to capture the main features of the sedimenting suspensions with reasonable computational expenses. Experimental observations from the literature have been correctly reproduced. It is numerically demonstrated that, at finite Re _{ p }, there exists a range of domain sizes in which particle velocityfluctuation amplitudes ⟨ΔV _{∥, ⊥}⟩ have a strong domain size dependence, and above which the fluctuation amplitudes become weakly dependent. The size range strongly relates with Re _{ p } and the particle volume fraction ϕ_{ p }. Furthermore, a transition in the fluctuation amplitudes is found at Re _{ p } around 0.08. The magnitude and length scale dependence of the fluctuation amplitudes at finite Re _{ p } are well represented by introducing new fluctuation amplitude scaling functions C _{1, (∥, ⊥)}(Re _{ p }, ϕ_{ p }) and characteristic length scaling function C _{2}(Re _{ p }, ϕ_{ p }) in the correlation derived by Segre et al. from their experiments at low Re _{ p } [“Longrange correlations in sedimentation,” Phys. Rev. Lett.79, 2574–2577 (1997)10.1103/PhysRevLett.79.2574] in the form .