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Dec 2012

Volume 24, Issue 12, Articles (12xxxx)

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Phys. Fluids 24, 122103 (2012); http://dx.doi.org/10.1063/1.4771605 (18 pages)

Tristan Gilet and John W. M. Bush
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Germano identity-based subgrid-scale modeling: A brief survey of variations on a fertile theme

Charles Meneveau

Phys. Fluids 24, 121301 (2012); http://dx.doi.org/10.1063/1.4772062 (14 pages) | Cited 1 time

Online Publication Date: 27 December 2012

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It has now been over 20 years since the introduction of the Germano identity. Mostly, the identity has been applied to closures for the subgrid-scale 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.
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47.27.ep Large-eddy simulations
47.10.ad Navier-Stokes equations
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Biomimetic flow control based on morphological features of living creatures

Haecheon Choi, Hyungmin Park, Woong Sagong, and Sang-im Lee

Phys. Fluids 24, 121302 (2012); http://dx.doi.org/10.1063/1.4772063 (20 pages)

Online Publication Date: 27 December 2012

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Despite the long history of biomimetics (or biomimetic engineering), a scientific discipline of implementing nature-inspired 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 skin friction. Several examples of successful biomimetic flow 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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47.85.lb Drag reduction
47.85.Gj Aerodynamics
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Infrared imagery of streak formation in a breaking wave

Robert A. Handler, Ivan Savelyev, and Michael Lindsey

Phys. Fluids 24, 121701 (2012); http://dx.doi.org/10.1063/1.4769459 (7 pages) | Cited 1 time

Online Publication Date: 5 December 2012

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High resolution infrared imagery of breaking waves in a wave-tank free of wind shear or current reveals the production of a “streaky,” quasi-periodic thermal pattern produced during the breaking process. The streaks, or elongated patterns of warm and cold fluid, are found to form only when surface turbulence is present before wave breaking occurs. This suggests that wave-turbulence 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 pre-existing vertical vorticity by the Stokes drift generated at or near the breaking wave crests, thereby generating a coherent system of counter-rotating 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.
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47.80.Jk Flow visualization and imaging
47.27.N- Wall-bounded shear flow turbulence
47.32.Ef Rotating and swirling flows
47.35.De Shear waves
47.35.Jk Wave breaking
47.54.De Experimental aspects
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Vorticity alignment of rigid fibers in an oscillatory shear flow: Role of confinement

Braden Snook, Elisabeth Guazzelli, and Jason E. Butler

Phys. Fluids 24, 121702 (2012); http://dx.doi.org/10.1063/1.4770141 (7 pages)

Online Publication Date: 11 December 2012

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Rigid fibers suspended in a viscous, Newtonian fluid at high concentrations can be aligned in the direction perpendicular to the flow-gradient plane (vorticity direction) by applying an oscillatory shear flow. A simple model, which considers only excluded volume and self-mobilities, 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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47.32.cb Vortex interactions
47.11.-j Computational methods in fluid dynamics
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.27.N- Wall-bounded shear flow turbulence
47.55.Kf Particle-laden flows
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back to top Biofluid Mechanics

Numerical study of pulsatile channel flows undergoing transition triggered by a modelled stenosis

Md. Mamun Molla, Bing-Chen Wang, and David C. S. Kuhn

Phys. Fluids 24, 121901 (2012); http://dx.doi.org/10.1063/1.4771604 (25 pages) | Cited 1 time

Online Publication Date: 20 December 2012

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In this research, we numerically investigate the physics of pulsatile flows confined within a 3-dimensional channel with a modelled stenosis formed eccentrically on the upper wall using the method of large-eddy simulation (LES). An advanced dynamic nonlinear subgrid-scale 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 in-house 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 subgrid-scale 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 laminar-turbulent-laminar patterns in the streamwise direction. Correspondingly, the slope of the energy spectra deviates significantly from the well-known −5/3 law for the inertial subrange to reflect the transition in the flow patterns.
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47.63.-b Biological fluid dynamics
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.60.Dx Flows in ducts and channels
47.15.Fe Stability of laminar flows
47.20.-k Flow instabilities
47.54.Bd Theoretical aspects

Biased swimming cells do not disperse in pipes as tracers: A population model based on microscale behaviour

R. N. Bearon, M. A. Bees, and O. A. Croze

Phys. Fluids 24, 121902 (2012); http://dx.doi.org/10.1063/1.4772189 (20 pages)

Online Publication Date: 27 December 2012

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There is much current interest in modelling suspensions of algae and other micro-organisms for biotechnological exploitation, and many bioreactors are of tubular design. Using generalized Taylor dispersion theory, we develop a population-level swimming-advection-diffusion model for suspensions of micro-organisms 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 diffusion tensor 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 swimming-advection-diffusion 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.
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47.85.-g Applied fluid mechanics
47.60.Dx Flows in ducts and channels
47.11.Fg Finite element methods
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.57.E- Suspensions
47.63.Gd Swimming microorganisms
back to top Micro- and Nanofluid Mechanics

Capillary droplets on Leidenfrost micro-ratchets

Álvaro G. Marín, Daniel Arnaldo del Cerro, Gertwillem R. B. E. Römer, B. Pathiraj, Albertus Huis in 't Veld, and Detlef Lohse

Phys. Fluids 24, 122001 (2012); http://dx.doi.org/10.1063/1.4768813 (10 pages)

Online Publication Date: 6 December 2012

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Leidenfrost 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 micron-sized 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 micro-ratchets. 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)10.1209/0295-5075/96/58001] to capillary droplets and find good agreement with our measurements.
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47.55.nb Capillary and thermocapillary flows
47.80.Jk Flow visualization and imaging
66.20.Gd Diffusive momentum transport
47.55.dr Interactions with surfaces

Ferrofluid pipe flow under the influence of the magnetic field of a cylindrical coil

P. K. Papadopoulos, P. Vafeas, and P. M. Hatzikonstantinou

Phys. Fluids 24, 122002 (2012); http://dx.doi.org/10.1063/1.4769177 (13 pages)

Online Publication Date: 7 December 2012

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Ferrofluid pipe flow under the effect of a co-linear, 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 magnetization equation and assess its validity when used for non-uniform 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 non-uniform magnetic fields.
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47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.60.Dx Flows in ducts and channels
02.60.-x Numerical approximation and analysis
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Bubble-driven inertial micropump

Erik D. Torniainen, Alexander N. Govyadinov, David P. Markel, and Pavel E. Kornilovitch

Phys. Fluids 24, 122003 (2012); http://dx.doi.org/10.1063/1.4769755 (18 pages) | Cited 1 time

Online Publication Date: 11 December 2012

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The fundamental action of the bubble-driven 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 non-axial. In the axial regime, the drive bubble either remains inside the channel, or continues to grow axially when it reaches the reservoir. In the non-axial 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 cross-section, but in the non-axial regime it is not. From numerical modeling, it is determined that the net flow is maximal when the axial regime crosses over to the non-axial regime. To elucidate the basic physical principles of the pump, a phenomenological one-dimensional model is developed and solved. A linear array of micropumps has been built using silicon-SU8 fabrication technology that is used to manufacture thermal inkjet printheads. Semi-continuous pumping across a 2 mm-wide channel has been demonstrated experimentally. Measured net flow with respect to viscosity variation is in excellent agreement with simulation results.
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47.55.dd Bubble dynamics
47.61.Fg Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)
68.03.Cd Surface tension and related phenomena
47.60.Dx Flows in ducts and channels
02.60.Cb Numerical simulation; solution of equations
07.10.Cm Micromechanical devices and systems
back to top Interfacial Flows

Oscillations of a gas pocket on a liquid-covered solid surface

Hanneke Gelderblom, Aaldert G. Zijlstra, Leen van Wijngaarden, and Andrea Prosperetti

Phys. Fluids 24, 122101 (2012); http://dx.doi.org/10.1063/1.4769179 (15 pages)

Online Publication Date: 6 December 2012

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The 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 semi-analytical 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.
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47.55.dr Interactions with surfaces
47.11.-j Computational methods in fluid dynamics
47.35.-i Hydrodynamic waves
68.03.Cd Surface tension and related phenomena
02.60.Gf Algorithms for functional approximation
47.60.-i Flow phenomena in quasi-one-dimensional systems

Capillary effects on floating cylindrical particles

Harish N. Dixit and G. M. Homsy

Phys. Fluids 24, 122102 (2012); http://dx.doi.org/10.1063/1.4769758 (19 pages)

Online Publication Date: 7 December 2012

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In this study, we develop a systematic perturbation procedure in the small parameter, B1/2, 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.
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47.55.nb Capillary and thermocapillary flows
47.55.nd Spreading films
68.08.Bc Wetting
02.60.Gf Algorithms for functional approximation
47.11.-j Computational methods in fluid dynamics
47.55.Kf Particle-laden flows

Droplets bouncing on a wet, inclined surface

Tristan Gilet and John W. M. Bush

Phys. Fluids 24, 122103 (2012); http://dx.doi.org/10.1063/1.4771605 (18 pages) | Cited 1 time

Online Publication Date: 13 December 2012

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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.
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47.55.dr Interactions with surfaces
47.80.Jk Flow visualization and imaging

Stability characteristics of solutocapillary Marangoni motion in evaporating thin films

Stefania K. Serpetsi and Stergios G. Yiantsios

Phys. Fluids 24, 122104 (2012); http://dx.doi.org/10.1063/1.4771903 (22 pages) | Cited 1 time

Online Publication Date: 19 December 2012

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The 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. E 6, 421 (2001)10.1007/s10189-001-8055-3] when the surface tension increases with increasing concentration of a non-volatile 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 well-known 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 long-wave oscillatory behavior leading to fast leveling of film thickness disturbances and subsequent reversal, as explained by Overdiep [Prog. Org. Coat. 14, 159 (1986)10.1016/0033-0655(86)80010-3]. 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 long-wave 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 short-wave patterns and small roughness or long-wave patterns and significant roughness, depending on whether surface tension of the solvents increases or decreases by the polymer solutes.
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47.20.Dr Surface-tension-driven instability
47.54.Bd Theoretical aspects
47.55.nb Capillary and thermocapillary flows
47.55.pf Marangoni convection
47.85.md Polymer processing flows
68.03.Cd Surface tension and related phenomena

Coalescence of liquid drops: Different models versus experiment

J. E. Sprittles and Y. D. Shikhmurzaev

Phys. Fluids 24, 122105 (2012); http://dx.doi.org/10.1063/1.4773067 (27 pages)

Online Publication Date: 27 December 2012

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The 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 theory-guided experiments are suggested that would help to further elucidate the details of the coalescence phenomenon. As a by-product 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.
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47.55.df Breakup and coalescence
47.55.nb Capillary and thermocapillary flows
47.55.nk Liquid bridges
02.60.Cb Numerical simulation; solution of equations
47.11.-j Computational methods in fluid dynamics
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Rebound and jet formation of a fluid-filled sphere

Taylor W. Killian, Robert A. Klaus, and Tadd T. Truscott

Phys. Fluids 24, 122106 (2012); http://dx.doi.org/10.1063/1.4771985 (17 pages)

Online Publication Date: 27 December 2012

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This 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.
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47.80.Jk Flow visualization and imaging
47.60.-i Flow phenomena in quasi-one-dimensional systems
back to top Viscous and Non-Newtonian Flows
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Falling plumes of point particles in viscous fluid

Andrew Crosby and John R. Lister

Phys. Fluids 24, 123101 (2012); http://dx.doi.org/10.1063/1.4769125 (21 pages)

Online Publication Date: 5 December 2012

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The 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. Fluids 21, 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 non-Brownian 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 quasi-periodic 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 wave-breaking 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 t2/3.
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47.55.Kf Particle-laden flows
47.35.Jk Wave breaking
47.35.-i Hydrodynamic waves
47.11.-j Computational methods in fluid dynamics
02.60.Cb Numerical simulation; solution of equations
47.55.Hd Stratified flows

Miscible density-stable displacement flows in inclined tube

K. Alba, S. M. Taghavi, and I. A. Frigaard

Phys. Fluids 24, 123102 (2012); http://dx.doi.org/10.1063/1.4766197 (11 pages) | Cited 2 times

Online Publication Date: 11 December 2012

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We study density-stable laminar miscible displacement flow of two iso-viscous Newtonian fluids in an inclined pipe (diameter math). We present a wide range of novel experimental results. We illustrate the non-monotone relation in displacement efficiency at the density difference moves from positive (density unstable) to negative (density stable), the efficiency being minimal for iso-dense 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 math, 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.
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47.15.Fe Stability of laminar flows
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.60.Dx Flows in ducts and channels
back to top Particulate, Multiphase, and Granular Flows

Shock tube investigation of quasi-steady drag in shock-particle interactions

Justin L. Wagner, Steven J. Beresh, Sean P. Kearney, Brian O. M. Pruett, and Elton K. Wright

Phys. Fluids 24, 123301 (2012); http://dx.doi.org/10.1063/1.4768816 (16 pages)

Online Publication Date: 6 December 2012

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A reassessment of historical drag coefficient data for spherical particles accelerated in shock-induced 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 1-mm 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 quasi-steady phenomenon attributed to increased compressibility rather than true flow unsteadiness.
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47.40.Nm Shock wave interactions and shock effects
47.55.Kf Particle-laden flows
47.60.Dx Flows in ducts and channels
47.40.Ki Supersonic and hypersonic flows

Dynamics of concentric and eccentric compound droplets suspended in extensional flows

Xiaofeng Qu and Yechun Wang

Phys. Fluids 24, 123302 (2012); http://dx.doi.org/10.1063/1.4770294 (21 pages) | Cited 1 time

Online Publication Date: 11 December 2012

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The motion, deformation, and stability of compound droplets in extensional flows are investigated numerically via a three-dimensional 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.
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47.55.D- Drops and bubbles
82.70.Kj Emulsions and suspensions
02.60.Lj Ordinary and partial differential equations; boundary value problems
47.55.nb Capillary and thermocapillary flows
68.03.Cd Surface tension and related phenomena
47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)

Simulations of dilute sedimenting suspensions at finite-particle Reynolds numbers

R. Sungkorn and J. J. Derksen

Phys. Fluids 24, 123303 (2012); http://dx.doi.org/10.1063/1.4770310 (23 pages)

Online Publication Date: 13 December 2012

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An alternative numerical method for suspension flows with application to sedimenting suspensions at finite-particle Reynolds numbers Rep is presented. The method consists of an extended lattice-Boltzmann 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 Rep, there exists a range of domain sizes in which particle velocity fluctuation amplitudes ⟨ΔV∥, ⊥⟩ have a strong domain size dependence, and above which the fluctuation amplitudes become weakly dependent. The size range strongly relates with Rep and the particle volume fraction ϕp. Furthermore, a transition in the fluctuation amplitudes is found at Rep around 0.08. The magnitude and length scale dependence of the fluctuation amplitudes at finite Rep are well represented by introducing new fluctuation amplitude scaling functions C1, (∥, ⊥)(Rep, ϕp) and characteristic length scaling function C2(Rep, ϕp) in the correlation derived by Segre et al. from their experiments at low Rep [“Long-range correlations in sedimentation,” Phys. Rev. Lett. 79, 2574–2577 (1997)10.1103/PhysRevLett.79.2574] in the form 〈ΔV∥,⊥〉 = 〈V∥〉C1,(∥,⊥)(Rep,ϕp)ϕp1/3{1−exp[−L/(C2(Rep,ϕp)rpϕp−1/3)]}.
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47.57.ef Sedimentation and migration
47.55.Kf Particle-laden flows
47.11.Qr Lattice gas
47.11.Df Finite volume methods
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Flipping, scooping, and spinning: Drift of rigid curved nonchiral fibers in simple shear flow

Jianghui Wang, Emilio J. Tozzi, Michael D. Graham, and Daniel J. Klingenberg

Phys. Fluids 24, 123304 (2012); http://dx.doi.org/10.1063/1.4769980 (16 pages)

Online Publication Date: 19 December 2012

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The motion of isolated, rigid, neutrally-buoyant, non-Brownian, curved, nonchiral fibers in simple shear flow of an incompressible Newtonian fluid at low Reynolds number is studied by computer simulation. For some initial orientations, fibers with small curvature drift steadily in the gradient direction without external forces or torques. The average drift velocity and direction depend on the fiber aspect ratio, curvature, and initial orientation. The drift results from the coupling of rotational and translational dynamics, and the combined effects of flipping, scooping, and spinning motions of the fiber.
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47.57.eb Diffusion and aggregation
47.11.-j Computational methods in fluid dynamics
47.15.G- Low-Reynolds-number (creeping) flows
47.15.St Free shear layers
back to top Laminar Flows

Buckling transitions of an elastic filament in a viscous stagnation point flow

Laura Guglielmini, Amit Kushwaha, Eric S. G. Shaqfeh, and Howard A. Stone

Phys. Fluids 24, 123601 (2012); http://dx.doi.org/10.1063/1.4771606 (16 pages) | Cited 1 time

Online Publication Date: 20 December 2012

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The interplay of viscous and elastic stresses is relevant to a number of flow problems involving slender elastic fibers. These range from the swimming of microorganisms to the transport of pulp fibers in processing flow as well as from nanotube and nanocarpet applications to semi-flexible polymer behavior. In some applications, slender fibers are attached to walls where they experience externally applied flows. In this paper, we focus on the model problem of a wall mounted filament in a (compressive) extensional flow and characterize the flow-induced bending and buckling of the fiber. Using a combination of stability analysis and numerical simulations (with the latter based on a discretized beam model), we show that, for a critical value of the ratio between viscous and elastic forces, the filament is susceptible to bending and buckling instabilities at supercritical bifurcation points.
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47.20.Gv Viscous and viscoelastic instabilities
47.11.-j Computational methods in fluid dynamics
47.40.-x Compressible flows; shock waves
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
02.60.Cb Numerical simulation; solution of equations
back to top Instability and Transition

Influence of a simple magnetic bar on buoyancy-driven fingering of traveling autocatalytic reaction fronts

M. Mishra, A. Thess, and A. De Wit

Phys. Fluids 24, 124101 (2012); http://dx.doi.org/10.1063/1.4768722 (13 pages)

Online Publication Date: 6 December 2012

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Magnetic fields have been shown experimentally to modify convective dynamics developing around traveling chemical fronts in presence of unfavorable density gradients. To understand the conditions in which such magnetic fields affect autocatalytic fronts, we study theoretically the influence of a simple magnetic bar on buoyancy-driven density fingering of a chemical front by numerical simulations of a reaction-diffusion-convection system. The model couples Darcy's law for the flow velocity to an evolution equation for the concentration of the autocatalytic product, which affects both the density of the solution and the magnetic force. The solutions of both products and reactants are assumed to be diamagnetic (i.e., negative magnetic susceptibility) and the magnetization is oriented perpendicularly to the plane in which the front travels. We show that, when aligned along the direction of front propagation, the magnetic force is able to suppress or enhance the convective instability depending on the value of the magnetic Rayleigh number of the problem. If the magnetic force is oriented transversely to the front propagation direction, tilted drifting convective patterns are obtained.
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47.65.-d Magnetohydrodynamics and electrohydrodynamics
47.20.Bp Buoyancy-driven instabilities (e.g., Rayleigh-Benard)
47.70.Fw Chemically reactive flows
47.55.P- Buoyancy-driven flows; convection
47.56.+r Flows through porous media
82.40.Ck Pattern formation in reactions with diffusion, flow and heat transfer

Experimental investigation of relaminarizing and transitional channel flows

Daisuke Seki and Masaharu Matsubara

Phys. Fluids 24, 124102 (2012); http://dx.doi.org/10.1063/1.4772065 (23 pages)

Online Publication Date: 20 December 2012

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A hot-wire measurement was conducted in a planar channel flow that originated from a strongly disturbed flow in an entrance channel followed by an expansion channel used to reduce the Reynolds number (Re). From ceasing decrease of the streamwise velocity fluctuation energy and the linear extrapolation of the intermittency factor, the lower marginal Re, which is defined as the minimum Re for partial existence of sustainable turbulence, is estimated around 1400 based on the channel width and the bulk velocity. The upper marginal Re at which the intermittency factor reaches one is about 2600. The flow fields passing a turbulent patch were reconstructed with conditional sampling of the streamwise velocity data based on the time of laminar-turbulence interfaces and the reconstructed flow fields indicate a large-scale flow structure across laminar and turbulent parts. This large structure makes it possible for some regions to be at higher Re than the average, so that turbulence can partly survive. The moderate-scale disturbances larger than the turbulent one appear in the non-turbulent parts of the transitional flow, and in these cases the non-turbulent velocity profile is almost identical to the turbulent one. The large-scale fluctuation is observed even over Re = 2600. This leads to the conclusion that a turbulent channel flow close to the upper marginal Re becomes inhomogeneous.
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47.27.nd Channel flow
47.80.-v Instrumentation and measurement methods in fluid dynamics
47.60.Dx Flows in ducts and channels
02.60.Ed Interpolation; curve fitting
47.15.Fe Stability of laminar flows
47.27.Cn Transition to turbulence

Breakup and coalescence characteristics of a hollow cone swirling spray

Abhishek Saha, Joshua D. Lee, Saptarshi Basu, and Ranganathan Kumar

Phys. Fluids 24, 124103 (2012); http://dx.doi.org/10.1063/1.4773065 (21 pages)

Online Publication Date: 27 December 2012

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This paper deals with an experimental study of the breakup characteristics of water emanating from hollow cone hydraulic injector nozzles induced by pressure-swirling. The experiments were conducted using two nozzles with different orifice diameters 0.3 mm and 0.5 mm and injection pressures (0.3–4 MPa) which correspond to Rep = 7000–26 000. Two types of laser diagnostic techniques were utilized: shadowgraph and phase Doppler particle anemometry for a complete study of the atomization process. Measurements that were made in the spray in both axial and radial directions indicate that both velocity and average droplet diameter profiles are highly dependent on the nozzle characteristics, Weber number and Reynolds number. The spatial variation of diameter and velocity arises principally due to primary breakup of liquid films and subsequent secondary breakup of large droplets due to aerodynamic shear. Downstream of the nozzle, coalescence of droplets due to collision was also found to be significant. Different types of liquid film breakup were considered and found to match well with the theory. Secondary breakup due to shear was also studied theoretically and compared to the experimental data. Coalescence probability at different axial and radial locations was computed to explain the experimental results. The spray is subdivided into three zones: near the nozzle, a zone consisting of film and ligament regime, where primary breakup and some secondary breakup take place; a second zone where the secondary breakup process continues, but weakens, and the centrifugal dispersion becomes dominant; and a third zone away from the spray where coalescence is dominant. Each regime has been analyzed in detail, characterized by timescale and Weber number and validated using experimental data.
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47.55.df Breakup and coalescence
47.57.-s Complex fluids and colloidal systems
47.32.Ef Rotating and swirling flows
47.40.-x Compressible flows; shock waves
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