Phys. Fluids (1994-Present) - Physics of Fluids

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Transient swelling, spreading, and drug delivery by a dissolved anti-HIV microbicide-bearing film

Savas Tasoglu, Lisa C. Rohan, David F. Katz, and Andrew J. Szeri

Phys. Fluids 25, 031901 (2013); http://dx.doi.org/10.1063/1.4793598 (16 pages) | Cited 1 time

Online Publication Date: 4 March 2013

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There is a widespread agreement that more effective drug delivery vehicles with more alternatives, as well as better active pharmaceutical ingredients (APIs), must be developed to improve the efficacy of microbicide products. For instance, in tropical regions, films are more appropriate than gels due to better stability of drugs at extremes of moisture and temperature. Here, we apply fundamental fluid mechanical and physicochemical transport theory to help better understand how successful microbicide API delivery depends upon properties of a film and the human reproductive tract environment. Several critical components of successful drug delivery are addressed. Among these are: elastohydrodynamic flow of a dissolved non-Newtonian film; mass transfer due to inhomogeneous dilution of the film by vaginal fluid contacting it along a moving boundary (the locally deforming vaginal epithelial surface); and drug absorption by the epithelium. Local rheological properties of the film are dependent on local volume fraction of the vaginal fluid. We evaluated this experimentally, delineating the way that constitutive parameters of a shear-thinning dissolved film are modified by dilution. To develop the mathematical model, we integrate the Reynolds lubrication equation with a mass conservation equation to model diluting fluid movement across the moving vaginal epithelial surface and into the film. This is a complex physicochemical phenomenon that is not well understood. We explore time- and space-varying boundary flux model based upon osmotic gradients. Results show that the model produces fluxes that are comparable to experimental data. Further experimental characterization of the vaginal wall is required for a more precise set of parameters and a more sophisticated theoretical treatment of epithelium.

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47.63.mh	Transport processes and drug delivery
87.17.Rt	Cell adhesion and cell mechanics
87.85.gf	Fluid mechanics and rheology
47.50.Cd	Modeling
47.57.Qk	Rheological aspects

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Two- and three-dimensional modeling and optimization applied to the design of a fast hydrodynamic focusing microfluidic mixer for protein folding

Benjamin Ivorra, Juana L. Redondo, Juan G. Santiago, Pilar M. Ortigosa, and Angel M. Ramos

Phys. Fluids 25, 032001 (2013); http://dx.doi.org/10.1063/1.4793612 (17 pages)

Online Publication Date: 6 March 2013

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We present a design of a microfluidic mixer based on hydrodynamic focusing which is used to initiate the folding process (i.e., changes of the molecular structure) of a protein. The folding process is initiated by diluting (from 90% to 30%) the local denaturant concentration (initially 6 M GdCl solution) in a short time interval we refer to as mixing time. Our objective is to optimize this mixer by choosing suitable shape and flow conditions in order to minimize this mixing time. To this end, we first introduce a numerical model that enables computation of the mixing time of a mixer. This model is based on a finite element method approximation of the incompressible Navier-Stokes equations coupled with the convective diffusion equation. To reduce the computational time, this model is implemented in both full three-dimensional (3D) and simplified two-dimensional (2D) versions; and we analyze the ability of the 2D model to approximate the mixing time predicted by the 3D model. We found that the 2D model approximates the mixing time predicted by the 3D model with a mean error of about 15%, which is considered reasonable. Then, we define a mixer optimization problem considering the 2D model and solve it using a hybrid global optimization algorithm. In particular, we consider geometrical variables and injection velocities as optimization parameters. We achieve a design with a predicted mixing time of 0.10 μs, approximately one order of magnitude faster than previous mixer designs. This improvement can be in part explained by the new mixer geometry including an angle of π/5 radians at the channel intersection and injections velocities of 5.2 m s⁻¹ and 0.038 m s⁻¹ for the side and central inlet channels, respectively. Finally, we verify the robustness of the optimized result by performing a sensitivity analysis of its parameters considering the 3D model. During this study, the optimized mixer was demonstrated to be robust by exhibiting mixing time variations of the same order than the parameter ones. Thus, the obtained 2D design can be considered optimal also for the 3D model.

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47.85.Np	Fluidics
47.27.te	Turbulent convective heat transfer
47.27.E-	Turbulence simulation and modeling
47.61.Ne	Micromixing
47.61.Fg	Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)
07.10.Cm	Micromechanical devices and systems

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The physics of aerobreakup. III. Viscoelastic liquids

T. G. Theofanous, V. V. Mitkin, and C. L. Ng

Phys. Fluids 25, 032101 (2013); http://dx.doi.org/10.1063/1.4792712 (28 pages)

Online Publication Date: 5 March 2013

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We extend the work of Theofanous and Li [Phys. Fluids 20, 052103 (2008)10.1063/1.2907989] on aerobreakup physics of water-like, low viscosity liquid drops, and of Theofanous et al. [Phys. Fluids 24, 022104 (2012)10.1063/1.3680867] for Newtonian liquids of any viscosity, to polymer-thickened liquids over wide ranges of viscoelasticity. The scope includes the full range of aerodynamics from near incompressible to supersonic flows and visualizations are recorded with μs/μm resolutions. The key physics of Rayleigh-Taylor piercing (RTP, first criticality) and of Shear-Induced Entrainment (SIE, second criticality) are verified and quantified on the same scaling approach as in our previous work, but with modifications due to the shear-thinning and elastic nature of these liquids. The same holds for the onset of surface waves by Kelvin-Helmholtz instability, which is a key attribute of the second criticality. However, in the present case, even at conditions well-past the first criticality, there is no breakup (particulation) to be found; instead the apparently unstable (extensively stretched into sheets) drops rebound elastically to reconstitute an integral mass. Such a resistance to breakup is found also past the second criticality, now with extensive filament formation that maintain a significant degree of cohesiveness, until the gas-dynamic pressure is high enough to cause filament ruptures. Thereby we define the onset of a third criticality peculiar to viscoelastic liquids—SIER, for SIE with ruptures. Past this criticality the extent of particulation increases and the characteristic dimension of fragments generated decreases in a more or less continuous fashion with increasing dynamic pressure. We outline a rheology-based scaling approach for these elasticity-modulated phenomena and suggest a path to similitude (with polymer and solvent variations) in terms of a critical rupture stress that can be measured independently. The advanced stages of breakup and resulting particle clouds are observed and a clear definition and quantification of breakup time is offered.

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47.50.Gj	Instabilities
47.55.df	Breakup and coalescence
47.40.Ki	Supersonic and hypersonic flows
47.20.Ma	Interfacial instabilities (e.g., Rayleigh-Taylor)
47.35.-i	Hydrodynamic waves

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On the levitation force in horizontal core-annular flow with a large viscosity ratio and small density ratio

G. Ooms, M. J. B. M. Pourquie, and J. C. Beerens

Phys. Fluids 25, 032102 (2013); http://dx.doi.org/10.1063/1.4793701 (16 pages)

Online Publication Date: 5 March 2013

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A numerical study has been made of horizontal core-annular flow: the flow of a high-viscosity liquid core surrounded by a low-viscosity liquid annular layer through a horizontal pipe. Special attention is paid to the question how the buoyancy force on the core, caused by a density difference between the core and the annular layer, is counterbalanced. The volume-of-fluid method is used to calculate the velocities and pressures in the two liquids. At the start of the calculation the core is in a concentric position. Thereafter the core starts to rise under the influence of buoyancy until it reaches an eccentric equilibrium position where the buoyancy force is counterbalanced by hydrodynamic forces generated by the movement of a wave at the core-annular interface with respect to the pipe wall. At high Reynolds number of the flow in the annular layer core levitation is due to inertial forces, whereas at low Reynolds number viscous (lubrication) forces are responsible for levitation. We carried out two types of calculation. In the first we assume the interface to be smooth (without wave) at the start of the calculation and study how the wave develops during the rising period of the core. In the second a wave is already present at the start of the calculation.

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47.55.-t	Multiphase and stratified flows
47.60.Dx	Flows in ducts and channels
66.20.-d	Viscosity of liquids; diffusive momentum transport
47.11.-j	Computational methods in fluid dynamics
47.35.-i	Hydrodynamic waves
02.60.-x	Numerical approximation and analysis

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Viscous instability of a sheared liquid-gas interface: Dependence on fluid properties and basic velocity profile

Thomas Otto, Maurice Rossi, and Thomas Boeck

Phys. Fluids 25, 032103 (2013); http://dx.doi.org/10.1063/1.4792311 (37 pages)

Online Publication Date: 7 March 2013

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In the framework of linear stability theory, we analyze how a liquid-gas mixing layer is affected by several parameters: viscosity ratio, density ratio, and several length scales. These scales reflect the presence of a velocity defect induced by the wake behind the splitter plate and the presence of boundary layers which develop ahead of the plate trailing edge. Incorporating such effects, we compute the various temporal and spatial instability modes and identify their driving instability mechanism based on their Reynolds number dependence, spatial structure, and energy budget. It is examined how the velocity defect modifies the temporal and the spatial stability properties. In addition, the transition from convective to absolute instability occurs at lower velocity contrast between gas and liquid free streams when a defect is present. This transition is also promoted by surface tension. Compared to inviscid stability computations, our spatial stability analysis displays a better agreement with measured growth rates obtained in two recent air-water experiments.

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47.55.Ca	Gas/liquid flows
66.20.Cy	Theory and modeling of viscosity and rheological properties, including computer simulation
47.51.+a	Mixing
47.20.Ft	Instability of shear flows (e.g., Kelvin-Helmholtz)
47.20.Ib	Instability of boundary layers; separation
68.03.Cd	Surface tension and related phenomena

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Air flow in a collapsing cavity

Ivo R. Peters, Stephan Gekle, Detlef Lohse, and Devaraj van der Meer

Phys. Fluids 25, 032104 (2013); http://dx.doi.org/10.1063/1.4794125 (14 pages)

Online Publication Date: 13 March 2013

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We experimentally study the airflow in a collapsing cavity created by the impact of a circular disc on a water surface. We measure the air velocity in the collapsing neck in two ways: Directly, by means of employing particle image velocimetry of smoke injected into the cavity and indirectly, by determining the time rate of change of the volume of the cavity at pinch-off and deducing the air flow in the neck under the assumption that the air is incompressible. We compare our experiments to boundary integral simulations and show that close to the moment of pinch-off, compressibility of the air starts to play a crucial role in the behavior of the cavity. Finally, we measure how the air flow rate at pinch-off depends on the Froude number and explain the observed dependence using a theoretical model of the cavity collapse.

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47.40.-x	Compressible flows; shock waves
47.55.-t	Multiphase and stratified flows
47.55.dp	Cavitation and boiling
47.80.Cb	Velocity measurements
47.80.Jk	Flow visualization and imaging

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Liquid film drag out in the presence of molecular forces

I. Schmidhalter, R. L. Cerro, M. D. Giavedoni, and F. A. Saita

Phys. Fluids 25, 032105 (2013); http://dx.doi.org/10.1063/1.4794972 (13 pages)

Online Publication Date: 18 March 2013

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From a practical as well as a conceptual point of view, one of the most interesting problems of physicochemical hydrodynamics is the drag out of a liquid film by a moving solid out of a pool of liquid. The basic problem, sometimes denoted the Landau-Levich problem [L. Landau and B. Levich, “Dragging of a liquid by a moving plate,” Acta Physicochim. USSR 17, 42–54 (1942)], involves an interesting blend of capillary and viscous forces plus a matching of the static solution for capillary rise with a numerical solution of the film evolution equation, neglecting gravity, on the downstream region of the flow field. The original solution describes experimental data for a wide range of Capillary numbers but fails to match results for large and very small Capillary numbers. Molecular level forces are introduced to create an augmented version of the film evolution equation to show the effect of van der Waals forces at the lower range of Capillary numbers. A closed form solution for static capillary rise, including molecular forces, was matched with a numerical solution of the augmented film evolution equation in the dynamic meniscus region. Molecular forces do not sensibly modify the static capillary rise region, since film thicknesses are larger than the range of influence of van der Waals forces, but are determinant in shaping the downstream dynamic meniscus of the very thin liquid films. As expected, a quantitatively different level of disjoining pressure for different values of molecular constants remains in the very thin liquid film far downstream. Computational results for a wide range of Capillary numbers and Hamaker constants show a clear transition towards a region where the film thickness becomes independent of the coating speed.

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68.15.+e	Liquid thin films
47.55.nb	Capillary and thermocapillary flows
02.60.Cb	Numerical simulation; solution of equations
47.11.-j	Computational methods in fluid dynamics
66.20.Cy	Theory and modeling of viscosity and rheological properties, including computer simulation

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Electrorotation of a viscous droplet in a uniform direct current electric field

Hui He, Paul F. Salipante, and Petia M. Vlahovska

Phys. Fluids 25, 032106 (2013); http://dx.doi.org/10.1063/1.4795021 (14 pages)

Online Publication Date: 20 March 2013

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We present a small-deformation theory which explains the experimentally observed nonaxisymmetric droplet deformation and orientation in a uniform DC electric field. The model shows that above a threshold electric field a rotational flow is induced about the droplet. As a result, drop shape becomes a general ellipsoid with major axis obliquely oriented to the applied field direction. The theory is in excellent agreement with the experimental data for high viscosity drops.

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47.65.-d	Magnetohydrodynamics and electrohydrodynamics
47.32.Ef	Rotating and swirling flows
47.55.D-	Drops and bubbles

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Transition from Newtonian to non-Newtonian surface shear viscosity of phospholipid monolayers

A. H. Sadoughi, J. M. Lopez, and A. H. Hirsa

Phys. Fluids 25, 032107 (2013); http://dx.doi.org/10.1063/1.4795448 (10 pages)

Online Publication Date: 20 March 2013

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The surface shear viscosity of DPPC (dipalmitoylphosphatidylcholine) monolayers on the air/water interface was determined over a wide range of surface concentrations in an annular channel. DPPC is studied widely because it is ubiquitous in biological systems. Brewster angle microscopy (BAM) was found to be capable of measuring the monolayer velocity field, even in the absence of co-existing phase domains. Interfacial velocimetry via cross correlations of BAM images provides accurate and non-invasive measurements, useful for both macro and microrheology. The measured velocity profiles are compared with computed profiles obtained over a range of surface shear conditions using the Boussinesq-Scriven surface model, from which the surface shear viscosity was determined. For monolayers in the liquid expanded (LE) and liquid expanded/liquid condensed (LE/LC) co-existing phases, we observe Newtonian behavior. We also show how the flow departs from the Newtonian regime for monolayers with larger surface concentration, corresponding to LC phase transition to solid phase.

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47.50.Ef	Measurements
47.80.Cb	Velocity measurements
83.60.Fg	Shear rate dependent viscosity
83.85.Jn	Viscosity measurements
47.60.Dx	Flows in ducts and channels
66.20.Ej	Studies of viscosity and rheological properties of specific liquids

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Reshaping and capturing Leidenfrost drops with a magnet

Keyvan Piroird, Baptiste Darbois Texier, Christophe Clanet, and David Quéré

Phys. Fluids 25, 032108 (2013); http://dx.doi.org/10.1063/1.4796133 (10 pages)

Online Publication Date: 26 March 2013

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Liquid oxygen, which is paramagnetic, also undergoes Leidenfrost effect at room temperature. In this article, we first study the deformation of oxygen drops in a magnetic field and show that it can be described via an effective capillary length, which includes the magnetic force. In a second part, we describe how these ultra-mobile drops passing above a magnet significantly slow down and can even be trapped. The critical velocity below which a drop is captured is determined from the deformation induced by the field.

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47.55.dm	Thermocapillary effects
62.10.+s	Mechanical properties of liquids
75.20.Ck	Nonmetals
75.50.Mm	Magnetic liquids
47.65.Cb	Magnetic fluids and ferrofluids
47.55.nb	Capillary and thermocapillary flows

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Simulations of insonated contrast agents: Saturation and transient break-up

Kostas Tsigklifis and Nikos A. Pelekasis

Phys. Fluids 25, 032109 (2013); http://dx.doi.org/10.1063/1.4794289 (34 pages)

Online Publication Date: 28 March 2013

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Under insonation contrast agents are known to perform nonlinear pulsations and deform statically, in the form of buckling, or dynamically via parametric mode excitation, and often exhibit jetting and break-up like bubbles without coating. Boundary element simulations are performed in the context of axisymmetry in order to establish the nonlinear evolution of these patterns. The viscoelastic stresses that develop on the coating form the dominant force balance tangentially to the shell-liquid interface, whereas the dynamic overpressure across the shell balances viscoelastic stresses in the normal direction. Strain softening and strain hardening behavior is studied in the presence of shape instabilities for various initial conditions. Simulations recover the pattern of static buckling, subharmonic/harmonic excitation, and dynamic buckling predicted by linear stability. Preferential mode excitation during compression is obtained supercritically for strain softening phospholipid shells while the shell regains its sphericity at expansion. It is a result of energy transfer between the emerging unstable modes and the radial mode, eventually leading to saturated oscillations of shape modes accompanied by asymmetric radial pulsations in favor of compression. Strain softening shells are more prone to sustain saturated pulsations due to the mechanical behavior of the shell. As the sound amplitude increases and before the onset of dynamic buckling, both types of shells exhibit transient break-up via unbalanced growth of a number of unstable shape modes. The effect of pre-stress in lowering the amplitude threshold for shape mode excitation is captured numerically and compared against the predictions of linear stability analysis. The amplitude interval for which sustained shape oscillations are obtained is extended, in the presence of pre-stress, by switching from a strain softening constitutive law to a strain hardening one once the shell curvature increases beyond a certain level. This type of mechanical behavior models the formation of lipid bilayer structures on the shell beyond a certain level of bending, as a result of a lipid monolayer folding transition. In this context a compression only type behavior is obtained in the simulations, which is accompanied by preferential shape deformation during compression at relatively small sound amplitudes in a manner that bears significance on the interpretation of available experimental observations exhibiting similar dynamic behavior.

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47.55.dd	Bubble dynamics
62.10.+s	Mechanical properties of liquids
02.60.Lj	Ordinary and partial differential equations; boundary value problems
43.25.Yw	Nonlinear acoustics of bubbly liquids
43.35.Mr	Acoustics of viscoelastic materials
47.11.Hj	Boundary element methods

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Internal solitary wave transformation over a bottom step: Loss of energy

Tatiana Talipova, Katherina Terletska, Vladimir Maderich, Igor Brovchenko, Kyung Tae Jung, Efim Pelinovsky, and Roger Grimshaw

Phys. Fluids 25, 032110 (2013); http://dx.doi.org/10.1063/1.4797455 (14 pages)

Online Publication Date: 29 March 2013

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In this paper, we extend the numerical study of Maderich et al. [“Interaction of a large amplitude interfacial solitary wave of depression with a bottom step,” Phys. Fluids 22, 076602 (2010)10.1063/1.3455984] on the interaction of an interfacial solitary wave with a bottom step, considering (i) the energy loss of solitary waves of both polarities interacting with a bottom step and (ii) features of the transformation of a large-amplitude internal solitary waves at the step. We show that the dependence of energy loss on the step height is not monotonic, but has different maximum positions for different incident wave polarities. The energy loss does not exceed 50% of the energy of an incident wave. The results of our numerical modeling are compared with some recent results from laboratory tank modeling.

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47.35.Fg	Solitary waves
02.60.Cb	Numerical simulation; solution of equations
47.11.-j	Computational methods in fluid dynamics

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Control and optimization of solute transport in a thin porous tube

I. M. Griffiths, P. D. Howell, and R. J. Shipley

Phys. Fluids 25, 033101 (2013); http://dx.doi.org/10.1063/1.4795545 (18 pages)

Online Publication Date: 26 March 2013

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Predicting the distribution of solutes or particles in flows within porous-walled tubes is essential to inform the design of devices that rely on cross-flow filtration, such as those used in water purification, irrigation devices, field-flow fractionation, and hollow-fibre bioreactors for tissue-engineering applications. Motivated by these applications, a radially averaged model for fluid and solute transport in a tube with thin porous walls is derived by developing the classical ideas of Taylor dispersion. The model includes solute diffusion and advection via both radial and axial flow components, and the advection, diffusion, and uptake coefficients in the averaged equation are explicitly derived. The effect of wall permeability, slip, and pressure differentials upon the dispersive solute behaviour are investigated. The model is used to explore the control of solute transport across the membrane walls via the membrane permeability, and a parametric expression for the permeability required to generate a given solute distribution is derived. The theory is applied to the specific example of a hollow-fibre membrane bioreactor, where a uniform delivery of nutrient across the membrane walls to the extra-capillary space is required to promote spatially uniform cell growth.

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47.85.L-	Flow control
47.60.Dx	Flows in ducts and channels
05.60.-k	Transport processes
46.35.+z	Viscoelasticity, plasticity, viscoplasticity
47.56.+r	Flows through porous media

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Granular suspension avalanches. I. Macro-viscous behavior

Christophe Ancey, Nicolas Andreini, and Gaël Epely-Chauvin

Phys. Fluids 25, 033301 (2013); http://dx.doi.org/10.1063/1.4793719 (21 pages) | Cited 2 times

Online Publication Date: 6 March 2013

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We experimentally studied the flow behavior of a fixed volume of granular suspension, initially contained in a reservoir and released down an inclined flume. Here “granular suspension” refers to a suspension of non-Brownian particles in a viscous fluid. Depending on the solids fraction, density mismatch, and particle size distribution, a wealth of behaviors can be observed. Here we report and interpret results obtained with granular suspensions, which consisted of neutrally buoyant particles with a solids fraction (ϕ = 0.575–0.595) close to the maximum random packing fraction (estimated at ϕ_m = 0.625). The particles had the same refractive index as the fluid, which made it possible to measure the velocity profiles inside the moving bulk and far from the sidewalls. Additional information such as the front position and the flow depth was also recorded. Three regimes were observed. At early times, the flow features were reminiscent of homogeneous Newtonian fluids (e.g., the same dependence of the front position on time). At later times, the free surface became more and more bumpy as fractures developed within the bulk. This fracture process ultimately gave rise to a stick-slip regime, in which the suspension moved intermittently. In this paper, we focus on the first regime referred to as the macro-viscous regime. Although the bulk flow properties looked like those of Newtonian fluids, the internal dynamics were much richer.

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47.57.E-	Suspensions
83.80.Hj	Suspensions, dispersions, pastes, slurries, colloids
83.50.Ha	Flow in channels
47.20.Gv	Viscous and viscoelastic instabilities
47.45.Gx	Slip flows and accommodation
47.60.Dx	Flows in ducts and channels

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Granular suspension avalanches. II. Plastic regime

Nicolas Andreini, Christophe Ancey, and Gaël Epely-Chauvin

Phys. Fluids 25, 033302 (2013); http://dx.doi.org/10.1063/1.4793720 (23 pages) | Cited 2 times

Online Publication Date: 6 March 2013

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We present flume experiments showing plastic behavior for perfectly density-matched suspensions of non-Brownian particles within a Newtonian fluid. In contrast with most earlier experimental investigations (carried out using coaxial cylinder rheometers), we obtained our rheological information by studying thin films of suspension flowing down an inclined flume. Using particles with the same refractive index as the interstitial fluid made it possible to measure the velocity field far from the wall using a laser-optical system. At long times, a stick-slip regime occurred as soon as the fluid pressure dropped sufficiently for the particle pressure to become compressive. Our explanation was that the drop in fluid pressure combined with the surface tension caused the flow to come to rest by significantly increasing flow resistance. However, the reason why the fluid pressure diffused through the pores during the stick phases escaped our understanding of suspension rheology.

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83.80.Hj	Suspensions, dispersions, pastes, slurries, colloids
83.60.La	Viscoplasticity; yield stress
47.57.E-	Suspensions
47.57.Qk	Rheological aspects
83.50.Ha	Flow in channels
47.60.Dx	Flows in ducts and channels

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Decaying versus stationary turbulence in particle-laden isotropic turbulence: Heavy particle statistics modifications

Abouelmagd H. Abdelsamie and Changhoon Lee

Phys. Fluids 25, 033303 (2013); http://dx.doi.org/10.1063/1.4795333 (18 pages)

Online Publication Date: 18 March 2013

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The current paper examines the heavy particle statistics modification by two-way interaction in particle-laden isotropic turbulence in an attempt to interpret their statistics modification using the information of modulated turbulence. Moreover, we clarify the distinctions of this modification between decaying and stationary turbulence as an extension of our previous work [A. H. Abdelsamie and C. Lee, “Decaying versus stationary turbulence in particle-laden isotropic turbulence: Turbulence modulation mechanism,” Phys. Fluids 24, 015106 (2012)10.1063/1.3678332]. Direct Numerical Simulation (DNS) was carried out using 128³ grid points at a Taylor micro-scale Reynolds number of R_λ ∼ 70. The effect of O(10⁶) solid particles with a different Stokes number (St) was implemented as a point-force approximation in the Navier-Stokes equation. Various statistics associated with particle dispersion are investigated, and the auto-correlations models which was provided by Jung et al. [“Behavior of heavy particles in isotropic turbulence,” Phys. Rev. E 77, 016307 (2008)10.1103/PhysRevE.77.016307] are extended in the current paper. DNS results reveal that the two-way coupling interaction enhances the fluid and heavy particle auto-correlation functions and the alignment between their velocity vectors for all Stokes numbers in decaying and stationary turbulence, but for different reasons. The modification mechanisms of particle dispersion statistics in stationary turbulence are different from those in decaying turbulence depending on the Stokes number, particularly for St <1.

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47.55.Kf	Particle-laden flows
02.30.Jr	Partial differential equations
02.30.Mv	Approximations and expansions
47.10.ad	Navier-Stokes equations
47.27.ek	Direct numerical simulations
47.27.Gs	Isotropic turbulence; homogeneous turbulence

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Radial distribution and axial dispersion of suspended particles inside a narrow cylinder due to mildly inertial flow

S. Bhattacharya, D. K. Gurung, and S. Navardi

Phys. Fluids 25, 033304 (2013); http://dx.doi.org/10.1063/1.4791794 (9 pages)

Online Publication Date: 25 March 2013

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The combined effects of radial drift due to flow inertia and diffusion due to Brownian motion significantly modify the radial probability distribution and the axial dispersion of conduit-bound suspended bodies. This interplay depends on the product of Peclet Pe and Reynolds Re numbers so that even apparently non-Brownian systems with high Pe exhibit the changes if Re is small. This article describes the probability distribution and the Taylor dispersion coefficient under such conditions for systems with low vessel-to-particle size-ratios where the effect is especially pronounced, but the flow-simulation is considerably difficult. We also identify the parametric regimes and the physical conditions required to see a substantial manifestation of the effect.

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47.55.Kf	Particle-laden flows
47.57.eb	Diffusion and aggregation
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.11.-j	Computational methods in fluid dynamics

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Laminar flow of two miscible fluids in a simple network

Casey M. Karst, Brian D. Storey, and John B. Geddes

Phys. Fluids 25, 033601 (2013); http://dx.doi.org/10.1063/1.4794726 (17 pages)

Online Publication Date: 11 March 2013

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When a fluid comprised of multiple phases or constituents flows through a network, nonlinear phenomena such as multiple stable equilibrium states and spontaneous oscillations can occur. Such behavior has been observed or predicted in a number of networks including the flow of blood through the microcirculation, the flow of picoliter droplets through microfluidic devices, the flow of magma through lava tubes, and two-phase flow in refrigeration systems. While the existence of nonlinear phenomena in a network with many inter-connections containing fluids with complex rheology may seem unsurprising, this paper demonstrates that even simple networks containing Newtonian fluids in laminar flow can demonstrate multiple equilibria. The paper describes a theoretical and experimental investigation of the laminar flow of two miscible Newtonian fluids of different density and viscosity through a simple network. The fluids stratify due to gravity and remain as nearly distinct phases with some mixing occurring only by diffusion. This fluid system has the advantage that it is easily controlled and modeled, yet contains the key ingredients for network nonlinearities. Experiments and 3D simulations are first used to explore how phases distribute at a single T-junction. Once the phase separation at a single junction is known, a network model is developed which predicts multiple equilibria in the simplest of networks. The existence of multiple stable equilibria is confirmed experimentally and a criterion for existence is developed. The network results are generic and could be applied to or found in different physical systems.

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47.15.Fe	Stability of laminar flows
47.51.+a	Mixing
47.55.-t	Multiphase and stratified flows
47.55.Hd	Stratified flows
64.75.Ef	Mixing
47.10.ad	Navier-Stokes equations

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Inertial particle trapping in viscous streaming

Kwitae Chong, Scott D. Kelly, Stuart Smith, and Jeff D. Eldredge

Phys. Fluids 25, 033602 (2013); http://dx.doi.org/10.1063/1.4795857 (21 pages)

Online Publication Date: 28 March 2013

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The motion of an inertial particle in a viscous streaming flow of Reynolds number order 10 is investigated theoretically and numerically. The streaming flow created by a circular cylinder undergoing rectilinear oscillation with small amplitude is obtained by asymptotic expansion from previous work, and the resulting velocity field is used to integrate the Maxey–Riley equation with the Saffman lift for the motion of an inertial spherical particle immersed in this flow. It is found that inertial particles spiral inward and become trapped inside one of the four streaming cells established by the cylinder oscillation, regardless of the particle size, density and flow Reynolds number. It is shown that the Faxén correction terms divert the particles from the fluid particle trajectories, and once diverted, the Saffman lift force is most responsible for effecting the inward motion and trapping. The speed of this trapping increases with increasing particle size, decreasing particle density, and increasing oscillation Reynolds number. The effects of Reynolds number on the streaming cell topology and the boundaries of particle attraction are also explored. It is found that particles initially outside the streaming cell are repelled by the flow rather than trapped.

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47.60.Dx	Flows in ducts and channels
47.11.-j	Computational methods in fluid dynamics

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Three-dimensional flow structure and aerodynamic loading on a revolving wing

Daniel J. Garmann, Miguel R. Visbal, and Paul D. Orkwis

Phys. Fluids 25, 034101 (2013); http://dx.doi.org/10.1063/1.4794753 (27 pages) | Cited 1 time

Online Publication Date: 15 March 2013

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A numerical study is conducted to examine the vortex structure and aerodynamic loading on a revolving wing in quiescent flow. A high-fidelity, implicit large eddy simulation technique is employed to simulate a revolving wing configuration consisting of a single, aspect-ratio-one rectangular plate extended out a distance of half a chord from the rotational axis at a fixed angle relative to the axis. Shortly after the onset of the motion, the rotating wing generates a coherent vortex system along the leading-edge. This vortex system remains attached throughout the motion for the range of Reynolds numbers explored, despite the unsteadiness and vortex breakdown observed at higher Reynolds numbers. The average and instantaneous wing loading also increases with Reynolds number. At a fixed Reynolds number, the attachment of the leading-edge vortex is also shown to be insensitive to the geometric angle of the wing. Additionally, the flow structure and forcing generated by a purely translating wing is investigated and compared with that of the revolving wing. Similar features are present at the inception of the motion, however, the two flows evolve very differently for the remainder of the maneuver. Comparisons of the revolving wing simulations with recent experimental particle image velocimetry (PIV) measurements using a new PIV-like data reduction technique applied to the computational solution show very favorable agreement. The success of the data reduction technique demonstrates the need to compare computations and experiments of differing resolutions using similar data-analysis techniques.

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47.85.Gj	Aerodynamics
02.60.-x	Numerical approximation and analysis
47.11.-j	Computational methods in fluid dynamics
47.32.Ef	Rotating and swirling flows

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Experimental characterization of transition region in rotating-disk boundary layer

M. E. Siddiqui, V. Mukund, J. Scott, and B. Pier

Phys. Fluids 25, 034102 (2013); http://dx.doi.org/10.1063/1.4798435 (10 pages)

Online Publication Date: 29 March 2013

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The three-dimensional boundary layer due to a disk rotating in otherwise still fluid is well known for its sudden transition from a laminar to a turbulent regime, the location of which closely coincides with the onset of local absolute instability. The present experimental investigation focuses on the region around transition and analyses in detail the features that lead from the unperturbed boundary layer to a fully turbulent flow. Mean velocity profiles and high-resolution spectra are obtained by constant-temperature hot-wire anemometry. By carefully analysing these measurements, regions in the flow are identified that correspond to linear, weakly nonlinear, or turbulent dynamics. The frequency that dominates the flow prior to transition is explained in terms of spatial growth rates, derived from the exact linear dispersion relation. In the weakly nonlinear region, up to six clearly identifiable harmonic peaks are found. High-resolution spectra reveal the existence of discrete frequency components that are deemed to correspond to fluctuations stationary with respect to the disk surface. These discrete components are only found in the weakly nonlinear region. By systematically acquiring low- and high-resolution spectra over a range of narrowly spaced radial and axial positions, it is shown that while the transition from laminar to turbulent regimes occurs sharply at some distance from the disk surface, a complex weakly nonlinear region of considerable radial extent continues to prevail close to the disk surface.

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47.27.Cn	Transition to turbulence
47.27.nb	Boundary layer turbulence
47.32.Ef	Rotating and swirling flows
47.80.-v	Instrumentation and measurement methods in fluid dynamics
47.15.Cb	Laminar boundary layers
47.15.Fe	Stability of laminar flows

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Tetrahedron deformation and alignment of perceived vorticity and strain in a turbulent flow

Alain Pumir, Eberhard Bodenschatz, and Haitao Xu

Phys. Fluids 25, 035101 (2013); http://dx.doi.org/10.1063/1.4795547 (21 pages)

Online Publication Date: 26 March 2013

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We describe the structure and dynamics of turbulence by the scale-dependent perceived velocity gradient tensor as supported by following four tracers, i.e., fluid particles, that initially form a regular tetrahedron. We report results from experiments in a von Kármán swirling water flow and from numerical simulations of the incompressible Navier-Stokes equation. We analyze the statistics and the dynamics of the perceived rate of strain tensor and vorticity for initially regular tetrahedron of size r₀ from the dissipative to the integral scale. Just as for the true velocity gradient, at any instant, the perceived vorticity is also preferentially aligned with the intermediate eigenvector of the perceived rate of strain. However, in the perceived rate of strain eigenframe fixed at a given time t = 0, the perceived vorticity evolves in time such as to align with the strongest eigendirection at t = 0. This also applies to the true velocity gradient. The experimental data at the higher Reynolds number suggests the existence of a self-similar regime in the inertial range. In particular, the dynamics of alignment of the perceived vorticity and strain can be rescaled by t₀, the turbulence time scale of the flow when the scale r₀ is in the inertial range. For smaller Reynolds numbers we found the dynamics to be scale dependent.

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47.32.Ef	Rotating and swirling flows
02.10.Ud	Linear algebra
47.10.ad	Navier-Stokes equations
47.11.-j	Computational methods in fluid dynamics
47.27.eb	Statistical theories and models
47.27.ek	Direct numerical simulations

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Effects of Reynolds number on some properties of a turbulent jet from a long square pipe

M. Xu, A. Pollard, J. Mi, F. Secretain, and H. Sadeghi

Phys. Fluids 25, 035102 (2013); http://dx.doi.org/10.1063/1.4797456 (19 pages) | Cited 1 time

Online Publication Date: 28 March 2013

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The flow in the near-to-intermediate field of a jet emanating from a long square pipe is investigated using hot-wire anemometry. The data include distributions of the mean and high order turbulence moments over 8000 < Re < 50 000 along the jet centreline. It is demonstrated that the far-field rates of the mean velocity decay and spread, as well as the asymptotic value of the streamwise turbulent intensity, all decrease as Re increases for Re ≤ 30 000; however, they become approximately Re-independent for Re > 30 000. It follows that the critical Reynolds number should occur at Re_cr = 30 000. Attention is given to the exponents associated with the compensated axial velocity spectra that show that the inertial subrange calculated according to isotropic, homogeneous turbulence emerges at x/D_e = 30 for all Re; however, if the scaling exponent is altered from m = −5/3 to between −1.56 < m < −1.31 the “inertial” range emerges at lower values of Re and the exponent is Re dependent. It is also found that the exponent agrees very well with Mydlarski and Warhaft correlation m = (5/3)(1−3.15R_λ^−2/3), where R_λ is the Taylor Reynolds number, obtained for turbulence decay behind a grid.

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47.27.Gs	Isotropic turbulence; homogeneous turbulence
47.27.nf	Flows in pipes and nozzles
47.27.wg	Turbulent jets
47.60.Dx	Flows in ducts and channels
47.80.-v	Instrumentation and measurement methods in fluid dynamics

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Computational study of detonation wave propagation in narrow channels

Ashwin Chinnayya, Abdellah Hadjadj, and Davy Ngomo

Phys. Fluids 25, 036101 (2013); http://dx.doi.org/10.1063/1.4792708 (22 pages)

Online Publication Date: 7 March 2013

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A numerical study of the propagation of regular detonation waves is conducted in the context of narrow channels undergoing strong wall confinement. To deal with shock waves, chemical reactions, heat and viscous stresses, a high-order Navier-Stokes solver based on Weighted Essentially Non-Oscillatory (WENO) scheme, coupled with the Strang splitting method, is used in the framework of multi-species reacting mixtures. Results show that the wall dissipative effects decrease the speed of the detonation wave compared to the Chapman-Jouguet (CJ) detonation velocity. In addition, the multidimensional results reveal that the development of the thermo-diffusive boundary layers behind the leading shock wave induces an expansion flow, which then determines the contour of the sonic envelope. From the Master Equation and the generalized CJ condition, which are derived and compared to the results of the current simulations, the main energy withdrawals are found to be related to the streamline divergence as well as to the growth of the boundary layer. Moreover, a fraction of the released energy is trapped in the vicinity of the wall and does not contribute to drive the shock front. The influence of the channel height is also investigated. It was found that the transverse instabilities are damped when the channel is scaled down, which results in an increase of the dissipative effects. Finally, the validity of the Fay model is discussed with regard to the channel height and the curvature of the detonation front.

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47.40.Nm

Shock wave interactions and shock effects

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Reflection of an internal gravity wave beam off a horizontal free-slip surface

Qi Zhou and Peter J. Diamessis

Phys. Fluids 25, 036601 (2013); http://dx.doi.org/10.1063/1.4795407 (29 pages)

Online Publication Date: 20 March 2013

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The reflection of a planar finite-amplitude internal gravity wave beam off a free-slip flat horizontal surface is investigated numerically in a uniformly stratified Boussinesq fluid. Nonlinear effects such as mean currents and harmonics are observed in the wave reflection zone. Mean currents form a stationary, vertically oscillatory, layered structure under the free-slip reflecting surface. The vertical wavelength of the mean-flow layers equals half of the vertical wavelength of the reflecting wave. An empirical predictive model for the steady-state mean flow strength, based on the degree of wave nonlinearity and hydrostaticity, is proposed and subsequently compared to the weakly nonlinear theory by Tabaei et al. [J. Fluid Mech. 526, 217–243 (2005)10.1017/S0022112004002769]. Very strong agreement between simulation results and theory is observed for all waves considered, suggesting although weakly nonlinear in its formulation, the Tabaei et al. theory is valid for the full range of finite amplitudes for which a wave remains stable. Both propagating and evanescent superharmonics are observed, and for waves with steepnesses of O(5%), parametric subharmonic instabilities can occur in the later stages of the reflection process. When a subsurface mixed layer is incorporated into the simulations, the mean currents at the middle of the underlying pycnocline are similar in structure and magnitude to their uniformly-stratified counterparts.

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