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

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The limits of Navier-Stokes theory and kinetic extensions for describing small-scale gaseous hydrodynamics

Nicolas G. Hadjiconstantinou

Phys. Fluids 18, 111301 (2006); http://dx.doi.org/10.1063/1.2393436 (19 pages) | Cited 15 times

Online Publication Date: 27 November 2006

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This paper reviews basic results and recent developments in the field of small-scale gaseous hydrodynamics which has received significant attention in connection with small-scale science and technology. We focus on the modeling challenges arising from the breakdown of the Navier-Stokes description, observed when characteristic lengthscales become of the order of, or smaller than, the molecular mean free path. We discuss both theoretical results and numerical methods development. Examples of the former include the limit of applicability of the Navier-Stokes constitutive laws, the concept of second-order slip and the appropriate form of such a model, and how to reconcile experimental measurements of slipping flows with theory. We also review a number of recently developed theoretical descriptions of canonical nanoscale flows of engineering interest. On the simulation front, we review recent progress in characterizing the accuracy of the prevalent Boltzmann simulation method known as direct simulation Monte Carlo. We also present recent variance reduction ideas which address the prohibitive cost associated with the statistical sampling of macroscopic properties in low-speed flows.

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47.10.ad	Navier-Stokes equations
47.11.-j	Computational methods in fluid dynamics
47.45.Gx	Slip flows and accommodation
01.30.Rr	Surveys and tutorial papers; resource letters

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Flow dynamics and forces associated with a cylinder rolling along a wall

Bronwyn Stewart, Kerry Hourigan, Mark Thompson, and Thomas Leweke

Phys. Fluids 18, 111701 (2006); http://dx.doi.org/10.1063/1.2375062 (4 pages) | Cited 6 times

Online Publication Date: 1 November 2006

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The wake flow structures and the drag force for a cylinder rolling along a wall without slipping were calculated for the Reynolds number range 20<Re<200, covering the two-dimensional shedding regime. Time-dependent numerical computations show the wake undergoes a steady to periodic shedding transition between 85<Re<90. The Strouhal number varies only weakly at higher Reynolds number, and is a factor of 3–4 lower than for an isolated rotating or nonrotating body. Also, within this shedding regime, the wake is characterized by counter-rotating vortex pairs, which propagate away from the wall via mutual induction. These pairs are formed as compact vortex structures from the top separating shear layer induce secondary vorticity at the wall, which is pulled up from the boundary to form the semidiscrete flow structures. Over both the steady and unsteady regimes, the (time-mean) recirculation length and drag are quantified.

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47.32.cb	Vortex interactions
47.32.Ef	Rotating and swirling flows
47.15.Tr	Laminar wakes
47.15.Fe	Stability of laminar flows
47.15.St	Free shear layers
47.15.Cb	Laminar boundary layers

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Decomposition of a two-layer thin liquid film flowing under the action of Marangoni stresses

A. A. Nepomnyashchy and I. B. Simanovskii

Phys. Fluids 18, 112101 (2006); http://dx.doi.org/10.1063/1.2387866 (11 pages) | Cited 15 times

Online Publication Date: 6 November 2006

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The decomposition of a laterally heated two-layer film caused by intermolecular forces is considered. Long-wave nonlinear equations, which incorporate thermocapillary flows and the influence of the van der Waals forces, are derived. The main stages of the three-dimensional evolution of films are presented. The influence of the thermocapillary flow on the morphology and the evolution of unstable two-layer films is investigated. It is shown that the film instability leads typically to formation of droplets driven by the thermocapillary flow. Anisotropic coalescence of droplets and formation of rivulets are observed.

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47.55.nd	Spreading films
47.55.Hd	Stratified flows
47.55.pf	Marangoni convection
47.55.nb	Capillary and thermocapillary flows
47.20.Ma	Interfacial instabilities (e.g., Rayleigh-Taylor)
47.55.db	Drop and bubble formation

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Influence of the flow field in curtain coating onto a prewet substrate

J. O. Marston, M. J. H. Simmons, S. P. Decent, and S. P. Kirk

Phys. Fluids 18, 112102 (2006); http://dx.doi.org/10.1063/1.2378562 (10 pages) | Cited 6 times

Online Publication Date: 9 November 2006

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The onset of air entrainment for curtain coating onto a surface prewetted with the coating fluid was studied. The substrate used was a polished, scraped steel wheel and coating was performed over ranges of dimensionless parameters observed in commercial coating processes (Reynolds number, 0.14<Re = ρQ/μ<33.02; Capillary number, 0.19<Ca = μU/σ<25.07). The substrate velocity for the onset of air entrainment was obtained as a function of the curtain flow rate per unit width of curtain (1<Q<9 cm² s⁻¹), fluid dynamic viscosity (0.0326<μ<0.878 Pa s), curtain height (0.035<h<0.095 m), and thickness of the prewet film (1×10⁻⁷<c<3×10⁻⁵ m). A remarkable and strong dependence of the onset of air entrainment on curtain flow rate was observed (hydrodynamic assist) and the general features of the hydrodynamics were very similar to those observed for previous works onto dry substrates. However, the presence of the prewet film led to higher maximum substrate velocities at the onset of air entrainment than observed for dry substrates. For high liquid viscosities, the air entrainment curve bifurcates; under these conditions, the maximum substrate velocity is no longer inversely proportional to the fluid viscosity and stable coating is possible at higher substrate velocities than would be predicted by conventional theory. This “intense assist” exhibits a complex relationship with the prewet film thickness. The results presented in this paper demonstrate that hydrodynamic assist is not exclusive to wetting, but is a generic phenomenon of fluid flows.

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47.85.mb	Coating flows
47.55.nm	Curtains/sheets
47.55.Hd	Stratified flows
47.55.nb	Capillary and thermocapillary flows
47.15.gm	Thin film flows
47.55.nd	Spreading films

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Dynamics of an interface with adsorption layer between two fluids

B. U. Felderhof

Phys. Fluids 18, 112103 (2006); http://dx.doi.org/10.1063/1.2372460 (10 pages) | Cited 1 time

Online Publication Date: 10 November 2006

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The dynamics of a flat interface with adsorption layer between two viscous fluids is studied on the basis of the linearized Navier-Stokes equations. The dispersion equation for interfacial waves involves surface tension and elasticity moduli of the interface, besides gravitational acceleration. The displacement of the interface due to a force density applied at the interface is characterized by a susceptibility tensor. Wave excitation due to a monochromatic plane wave source or a monochromatic line source located at some distance from the interface is discussed.

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47.35.Bb	Gravity waves
47.35.Pq	Capillary waves
47.55.nb	Capillary and thermocapillary flows
47.10.ad	Navier-Stokes equations
68.03.Fg	Evaporation and condensation of liquids
68.03.Cd	Surface tension and related phenomena

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The evaluation of the far-field integral in the Green’s function representation for steady Oseen flow

Nina Fishwick and Edmund Chadwick

Phys. Fluids 18, 113101 (2006); http://dx.doi.org/10.1063/1.2388248 (5 pages) | Cited 1 time

Online Publication Date: 7 November 2006

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Consider the Green’s function representation of an exterior problem in steady Oseen flow. The far-field integral in the formulation is shown to be zero.

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47.20.Cq	Inviscid instability
47.32.cb	Vortex interactions
47.27.wb	Turbulent wakes
47.10.ad	Navier-Stokes equations
47.85.Gj	Aerodynamics
02.30.Rz	Integral equations

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Tuning gastropod locomotion: Modeling the influence of mucus rheology on the cost of crawling

Eric Lauga and A. E. Hosoi

Phys. Fluids 18, 113102 (2006); http://dx.doi.org/10.1063/1.2382591 (9 pages) | Cited 9 times

Online Publication Date: 22 November 2006

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Common gastropods such as snails crawl on a solid substrate by propagating muscular waves of shear stress on a viscoelastic mucus. Producing the mucus accounts for the largest component in the gastropod’s energy budget, more than 20 times the amount of mechanical work used in crawling. Using a simple mechanical model, we show that the shear-thinning properties of the mucus favor a decrease in the amount of mucus necessary for crawling, thereby decreasing the overall energetic cost of locomotion.

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87.19.rs	Movement
87.19.ru	Locomotion
87.19.rh	Fluid transport and rheology
47.63.-b	Biological fluid dynamics
47.50.Cd	Modeling
47.35.De	Shear waves

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Effect of particle collisions on the expulsion of heavy particles from a vortex core

J. S. Marshall

Phys. Fluids 18, 113301 (2006); http://dx.doi.org/10.1063/1.2370427 (12 pages) | Cited 4 times

Online Publication Date: 1 November 2006

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A computational study has been performed on the effect of particle collisions as heavy particles are expelled from a vortex core. In the absence of collisions, particles collect in a band surrounding the vortex core, where the maximum particle concentration within this band increases indefinitely as the band of particles propagates radially outward. Particle collisions act to regulate the increase in concentration within this band by the enhanced spreading of the particles that occurs through the action of shear-induced migration. The presence of axial flow within the vortex core introduces a drift of the particles within the core toward the low-shear region at the core center, thus resisting the outward particle drift caused by centrifugal force. With increasing axial flow rates, the particles are retained in the vortex core for longer time periods. The role of various parameters on the particle expulsion is evaluated, including particle diameter, restitution coefficient, and initial concentration. The study also examines the effect of collisions on cases with two distinct particle sizes, in which the different outward expulsion rates act to separate particles of different size.

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47.55.Kf	Particle-laden flows
47.32.cb	Vortex interactions
47.85.Np	Fluidics
47.11.Hj	Boundary element methods
02.60.Lj	Ordinary and partial differential equations; boundary value problems

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Comparison of kinetic theory predictions with experimental results for a vibrated three-dimensional granular bed

H. Viswanathan, R. D. Wildman, J. M. Huntley, and T. W. Martin

Phys. Fluids 18, 113302 (2006); http://dx.doi.org/10.1063/1.2353398 (11 pages) | Cited 11 times

Online Publication Date: 15 November 2006

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The three-dimensional conservation equations relating energy and momentum transfer in a vibrated three-dimensional granular bed have been solved numerically by the finite element method. Two closures based on granular kinetic theory were used: one, the standard Fourier law relating heat flux to temperature gradient and the other, including an additional concentration gradient term. Each prediction of the two-dimensional axisymmetric granular temperature and packing fraction fields was compared against a one-dimensional model and three-dimensional experimental results, acquired using the technique of positron emission particle tracking. Both closures resulted in solutions that were in reasonable agreement with the experimental results, but it was found that differences between the predictions of each of the closures were relatively small in comparison to the anisotropy of the experimentally determined temperature distribution.

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47.57.Gc	Granular flow
47.55.Lm	Fluidized beds
47.27.te	Turbulent convective heat transfer
47.45.Ab	Kinetic theory of gases
47.11.Fg	Finite element methods
02.70.Dh	Finite-element and Galerkin methods

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Numerical simulation of biomagnetic fluid downstream an eccentric stenotic orifice

Saud A. Khashan and Yousef Haik

Phys. Fluids 18, 113601 (2006); http://dx.doi.org/10.1063/1.2397578 (10 pages) | Cited 6 times

Online Publication Date: 29 November 2006

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Biomagnetic fluid dynamics is the study of the interaction of biological fluids with an applied steady magnetic field. The composition of the biological fluid is considered nonconducting; however, it has magnetic moment. The magnetic moment of the biological fluid can be enhanced by tagging superparamagnetic particles. Several biomedical applications recently developed utilize the magnetic labeling of cellular components. In this paper, the biomagnetic fluid downstream an eccentric stenotic orifice is considered. An external magnetic field is applied at different locations down stream the stenotic orifice. It is found that based on the location of the magnetic field, the reattachment point downstream the stenotic orifice changes; it is also found that the shear stress will be affected based on the magnetic field location. Major changes in the flow pattern have been also observed based on the magnetic field strength.

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47.65.Cb	Magnetic fluids and ferrofluids
47.63.Cb	Blood flow in cardiovascular system
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.54.Fj	Chemical and biological applications
87.19.U-	Hemodynamics
87.19.Wx	Pneumodyamics, respiration
87.50.C-	Static and low-frequency electric and magnetic fields effects

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Nonlinear breakup of a coaxial liquid jet in a swirling gas stream

Ashraf A. Ibrahim and Milind A. Jog

Phys. Fluids 18, 114101 (2006); http://dx.doi.org/10.1063/1.2364262 (11 pages) | Cited 1 time

Online Publication Date: 1 November 2006

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Nonlinear asymmetric breakup of a liquid jet exposed to a swirling gas stream is investigated by a perturbation expansion technique with the initial amplitude of the disturbance as the perturbation parameter. The effects of gas-to-liquid axial velocity ratio and gas swirl number on the liquid jet instability and breakup length have been studied. The breakup length predictions show good agreement with the available empirical correlations for liquid jet breakup in still gas as well as jet breakup in a co-flowing gas stream. Earlier linear analyses have predicted that the gas swirl has a stabilizing influence on the jet and that the axisymmetric disturbance is the most unstable disturbance compared to the helical modes. In contrast, experimental studies report that a swirl imparted on the surrounding gas makes the jet unstable, and at high gas swirl the jet disintegrates through an explosive breakup. The present nonlinear temporal analysis correctly captures the destabilizing effect of the gas swirl. With increasing gas swirl number, the helical modes become dominant and the transition to subsequent higher helical mode is achieved with smaller increments in the gas swirl number. The gas swirl number for transition to a highly asymmetric breakup with a high circumferential wave number (n = 5) is found to vary as the inverse of the square root of the gas-to-liquid momentum ratio when the gas-to-liquid momentum ratio is less than 1. The jet breakup length decreases with an increase in the gas-to-liquid axial velocity ratio and the gas swirl number.

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47.27.wg	Turbulent jets
47.32.Ef	Rotating and swirling flows
47.55.Ca	Gas/liquid flows
47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking
47.85.Gj	Aerodynamics

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A finite-volume variational multiscale method coupled with a discrete interpolation filter for large-eddy simulation of isotropic turbulence and fully developed channel flow

P. Sagaut and M. Ciardi

Phys. Fluids 18, 115101 (2006); http://dx.doi.org/10.1063/1.2391133 (15 pages) | Cited 4 times

Online Publication Date: 16 November 2006

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The variational multiscale (VMS) approach proposed by Hughes et al. is applied to the Smagorinsky model and developed within the context of a physical-space unstructured finite-volume solver. A specific explicit filtering procedure is also developed, based on the idea of the discrete interpolation filters, originally proposed by Marsden et al. Tests on decaying isotropic turbulence at infinite Reynolds number and fully developed channel flow at friction Reynolds number Re_τ = 395 are performed, using the dynamic Smagorinsky model for comparison. For the VMS version of the Smagorinsky model, the conservative choice of not adapting the model’s constant is made, giving good indications on the required adjustment directions in both isotropic flows and nonisotropic flows. Promising results are obtained in general by the VMS approach with the two test cases. An overdissipative behavior is observed in the isotropic turbulence test case, which does not have a strong spectral connotation and could probably be cured adjusting the model’s constant. A very good prediction of the levels of unsteadiness is produced by VMS in the channel flow test case, showing the potential of this approach for nonisotropic flows. In both of the test cases the VMS approach gives performances of the same order of accuracy of the dynamic Smagorinsky model used for comparison, being at the same time less computationally expensive.

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47.27.Gs	Isotropic turbulence; homogeneous turbulence
47.27.ep	Large-eddy simulations
47.27.nd	Channel flow
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.11.Df	Finite volume methods
47.11.St	Multi-scale methods

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Characterization of the three-dimensional turbulent boundary layer in a concentric annulus with a rotating inner cylinder

Seo Yoon Jung and Hyung Jin Sung

Phys. Fluids 18, 115102 (2006); http://dx.doi.org/10.1063/1.2391387 (11 pages) | Cited 4 times

Online Publication Date: 20 November 2006

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Direct numerical simulations of fluid flow through a concentric annulus with a rotating inner wall were performed at Re_Dh = 8900. To elucidate the modifications of the near-wall turbulent structure induced by rotation of the inner wall, we compared data obtained at rotation rates of N = 0.0 and 0.429 for a system with a radius ratio (R^*) of 0.5. Conditional quadrant/octant analysis and probability density functions of the velocity fluctuations revealed distinctive features of the three-dimensional turbulent boundary layer (3DTBL) in the concentric annulus with a rotating inner wall. Coherent structures near the inner wall were identified by a λ₂-based eduction scheme to give the detailed information on the activated near-wall turbulent structures. The ensemble-averaging of the educed coherent vortices showed that enhanced ejections near the vortices were primarily responsible for the augmented turbulent structures. The alteration of the turbulent structures was attributed to the centrifugal force arising from rotation of the inner wall. The assumption of Littell and Eaton on the cause of the altered turbulent structures in 3DTBLs was invalid in the present study. Taken together, the present results showed that the 3DTBL in a rotating concentric annulus has features different from those observed in other types of 3DTBL due to the transverse curvature.

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47.27.nb	Boundary layer turbulence
47.27.De	Coherent structures
47.27.ek	Direct numerical simulations
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.32.cb	Vortex interactions
47.32.Ef	Rotating and swirling flows

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Susumu Goto and J. C. Vassilicos

Phys. Fluids 18, 115103 (2006); http://dx.doi.org/10.1063/1.2364263 (10 pages) | Cited 19 times

Online Publication Date: 20 November 2006

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multimedia

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Clustering of inertial particles in fully developed two-dimensional inverse cascading turbulence occurs for all particle relaxation times ranging from an order of magnitude under the smallest eddy turnover time to an order of magnitude above the largest eddy turnover time. Particle voids and clusters are statistically self-similar over a finite range of scales within the inertial range and are explained in terms of coarse-grained vorticity and resonant eddies (for voids) and in terms of zero-acceleration points (for clusters). The clustering of inertial particles reflects the clustering of zero-acceleration points. Essential to both explanations is the sweeping of small eddies by large ones. An important implication is that particle clustering can be explicitly described just in terms of the fluid acceleration field without the need for Lagrangian particle integrations.

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47.53.+n	Fractals in fluid dynamics
47.55.Kf	Particle-laden flows
47.27.Gs	Isotropic turbulence; homogeneous turbulence
47.32.cb	Vortex interactions
47.27.ek	Direct numerical simulations
47.27.De	Coherent structures

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Local and nonlocal advection of a passive scalar

R. K. Scott

Phys. Fluids 18, 116601 (2006); http://dx.doi.org/10.1063/1.2375020 (8 pages) | Cited 8 times

Online Publication Date: 7 November 2006

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Passive and active scalar mixing is examined in a simple one-parameter family of two-dimensional flows based on quasi-geostrophic dynamics, in which the active scalar, the quasi-geostrophic potential vorticity, is confined to a single horizontal surface (so-called surface quasi-geostrophic dynamics) and in which a passive scalar field is also advected by the (horizontal, two-dimensional) velocity field at a finite distance from the surface. At large distances from the surface the flow is determined by the largest horizontal scales, the flow is spectrally nonlocal, and a chaotic advection-type regime dominates. At small distances, z, scaling arguments suggest a transition wavenumber k_c ∼ 1/2z, where the slope of the passive scalar spectrum changes from k^−5/3, determined by local dynamics, to k⁻¹, determined by nonlocal dynamics, analogous to the transition to a k⁻¹ slope in the Batchelor regime in three-dimensional turbulence. Direct numerical simulations reproduce the qualitative aspects of this transition. Other characteristics of the simulated scalar fields, such as the relative dominance of coherent or filamentary structures, are also shown to depend strongly on the degree of locality.

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47.32.cb	Vortex interactions
47.51.+a	Mixing
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.52.+j	Chaos in fluid dynamics
47.27.De	Coherent structures
47.27.ek	Direct numerical simulations

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Magnetohydrodynamic activity inside a sphere

Pablo D. Mininni and David C. Montgomery

Phys. Fluids 18, 116602 (2006); http://dx.doi.org/10.1063/1.2393438 (13 pages) | Cited 9 times

Online Publication Date: 30 November 2006

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We present a computational method to solve the magnetohydrodynamic equations in spherical geometry. The technique is fully nonlinear and wholly spectral, and uses an expansion basis that is adapted to the geometry: Chandrasekhar-Kendall vector eigenfunctions of the curl. The resulting lower spatial resolution is somewhat offset by being able to build all the boundary conditions into each of the orthogonal expansion functions and by the disappearance of any difficulties caused by singularities at the center of the sphere. The results reported here are for mechanically and magnetically isolated spheres, although different boundary conditions could be studied by adapting the same method. The intent is to be able to study the nonlinear dynamical evolution of those aspects that are peculiar to the spherical geometry at only moderate Reynolds numbers. The code is parallelized, and will preserve to high accuracy the ideal magnetohydrodynamic invariants of the system (global energy, magnetic helicity, cross helicity). Examples of results for selective decay and mechanically driven dynamo simulations are discussed. In the dynamo cases, spontaneous flips of the dipole orientation are observed.

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47.65.-d	Magnetohydrodynamics and electrohydrodynamics
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.52.+j	Chaos in fluid dynamics
47.11.Kb	Spectral methods
95.30.Qd	Magnetohydrodynamics and plasmas
05.45.-a	Nonlinear dynamics and chaos

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Effects of conical lids on vortex breakdown in an enclosed cylindrical chamber

Peng Yu, Thong See Lee, Yan Zeng, and Hong Tong Low

Phys. Fluids 18, 117101 (2006); http://dx.doi.org/10.1063/1.2387107 (9 pages) | Cited 7 times

Online Publication Date: 3 November 2006

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The effects of the conical lids on vortex breakdown have been investigated numerically. The boundaries for the onset of vortex breakdown are plotted in terms of the Reynolds number, the aspect ratio H₁/R, where H₁ is the height of the side wall, and the height ratio H₂/H₁, where H₂ is the height of the axis. The concave-cone lid (H₂/H₁>1) delays or even completely suppresses vortex breakdown, while the convex-cone lid (H₂/H₁<1) precipitates the onset of vortex breakdown. The attached bubbles were found in the chamber with the convex-cone lid at a smaller height ratio. The critical aspect ratio, below which vortex breakdown cannot occur, decreases with the increase of the height ratio. The results indicate that a conical lid can enlarge the vortex breakdown boundaries and this might be of practical interest when using this device for mixing. The results also suggest that the actual shape of the lid has an influence on suppressing or intensifying vortex breakdown.

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47.32.cd	Vortex stability and breakdown
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.55.dd	Bubble dynamics
47.85.Gj	Aerodynamics
02.60.Cb	Numerical simulation; solution of equations

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Fluid enhancement of particle transport in nanochannels

Zhigang Li and German Drazer

Phys. Fluids 18, 117102 (2006); http://dx.doi.org/10.1063/1.2372715 (7 pages) | Cited 6 times

Online Publication Date: 6 November 2006

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We investigate the effect that fluid density has on the mobility of a spherical nanoparticle moving through a cylindrical nanochannel. The solid nanoparticle, the channel wall, and the fluid are described at the molecular level, and we use molecular dynamics simulations to study their behavior. We consider densities ranging from a few fluid molecules to a relatively dense fluid inside the channel. The inhomogeneous distribution of the fluid molecules inside the channel results in the competition of two effects as the fluid density is increased. The fluid molecules adsorb on the channel surface, and thus reduce the friction with the wall and enhance the mobility of the particle. On the other hand, the addition of fluid molecules increases the viscous drag on the particle and thus reduces its mobility. The outcome of these competing effects depends on the strength of the interaction between the atoms in the particle and those in the wall. We examine three different cases, i.e., intermediate, strong, and weak interaction energies. For an intermediate interaction, two distinct peaks are observed in the mobility of the particle as the first two adsorbed fluid layers form. On the other hand, a monotonously increasing mobility is found for a strong interaction energy, and a nearly constant mobility is observed for a weak interaction.

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47.85.Np	Fluidics
47.55.Kf	Particle-laden flows
47.61.Fg	Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)
47.61.Jd	Multiphase flows
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.11.Mn	Molecular dynamics methods

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Hovering of a passive body in an oscillating airflow

Stephen Childress, Nicolas Vandenberghe, and Jun Zhang

Phys. Fluids 18, 117103 (2006); http://dx.doi.org/10.1063/1.2371123 (9 pages) | Cited 10 times

Online Publication Date: 14 November 2006

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Small flexible bodies are observed to hover in an oscillating air column. The air is driven by a large speaker at frequencies in the range 10–65 Hz at amplitudes 1–5 cm. The bodies are made of stiffened tissue paper, bent to form an array of four wings, symmetric about a vertical axis. The flapping of the wings, driven by the oscillating flow, leads to stable hovering. The hovering position of the body is unstable under free fall in the absence of the airflow. Measurements of the minimum flow amplitude as a function of flow frequency were performed for a range of self-similar bodies of the same material. The optimal frequency for hovering is found to vary inversely with the size. We suggest, on the basis of flow visualization, that hovering of such bodies in an oscillating flow depends upon a process of vortex shedding closely analogous to that of an active flapper in otherwise still air. A simple inviscid model is developed illustrating some of the observed properties of flexible passive hoverers at high Reynolds number.

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47.85.Gj	Aerodynamics
47.35.Lf	Wave-structure interactions
47.20.Cq	Inviscid instability
47.53.+n	Fractals in fluid dynamics
47.80.Jk	Flow visualization and imaging
47.32.cb	Vortex interactions

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Three-dimensional direct numerical simulation for film-boiling contact of moving particle and liquid droplet

Yang Ge and Liang-Shih Fan

Phys. Fluids 18, 117104 (2006); http://dx.doi.org/10.1063/1.2386027 (19 pages)

Online Publication Date: 15 November 2006

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The hydrodynamics and heat transfer phenomena during the collision process of a liquid droplet and a hot particle, both in motion, are illustrated by direct numerical simulation in this study. The three-dimensional level-set method is used to portray the surface deformation of the droplet. The immersed boundary method is employed by means of the particle level-set function so that the particle-fluid boundary conditions are satisfied. The governing equations for the droplet and the surrounding gas phase are solved using the finite-volume method. To account for the multiscale effect due to lubrication resistance induced by the vapor layer between the droplet and solid surface or solid particle formed by the film-boiling evaporation, a vapor flow model is developed, which quantifies the pressure and velocity distributions along the vapor layer. The temperature fields in all phases and the local evaporation rate on the droplet surface are illustrated using a full-field heat transfer model. The convergence of the simulation model is analyzed and verified by using different grid sizes in the computation. The normal and oblique collisions between the droplet and the particle are simulated. It is found that the particle sizes have a significant effect on the collision dynamics in a normal collision. When the droplet size is larger than the particle size, the contact time is shorter than the droplet vibration period and is controlled by the dynamics of the particle. In an oblique collision, the increasing obliquity causes a decrease in contact area and contact time, and hence, a reduction in the heat loss of the particle during the collision process.

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47.55.dp	Cavitation and boiling
47.55.Kf	Particle-laden flows
47.27.te	Turbulent convective heat transfer
47.11.Df	Finite volume methods
47.85.Dh	Hydrodynamics, hydraulics, hydrostatics
64.70.F-	Liquid-vapor transitions

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Experimental investigation of the electromagnetic effect on a shock layer around a blunt body in a weakly ionized flow

Yuji Takizawa, Atsushi Matsuda, Shunichi Sato, Takashi Abe, and Detlev Konigorski

Phys. Fluids 18, 117105 (2006); http://dx.doi.org/10.1063/1.2375076 (10 pages) | Cited 8 times

Online Publication Date: 20 November 2006

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A reentry vehicle is exposed to a partially ionized flow during the reentry flight. For such a flight, a strong magnet mounted on the vehicle, which generates the magnetic field around the vehicle, is suggested to affect a surrounding ionized flow and make it possible to control the flow. Such an electromagnetic effect on the flow is investigated experimentally by using a small arc-jet wind tunnel. In the experiment, the translational temperature distribution in the shock layer around a magnetized blunt body in a supersonic, weakly ionized, argon flow is determined by applying an absorption spectroscopic technique. For the absorption spectrum affected by the magnetic field, the temperature determination method was newly developed. The temperature distribution thus determined for the shock layer shows that the applied magnetic field significantly affects the shock layer or, specifically, the shock standoff distance and enhances it.

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47.85.Gj	Aerodynamics
47.65.Md	Plasma dynamos
47.40.Nm	Shock wave interactions and shock effects
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.40.Ki	Supersonic and hypersonic flows
47.80.Fg	Pressure and temperature measurements

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An approximate method in transport theory. II

S. K. Loyalka and S. Naz

Phys. Fluids 18, 117106 (2006); http://dx.doi.org/10.1063/1.2391736 (9 pages) | Cited 1 time

Online Publication Date: 22 November 2006

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Maxwell had constructed first approximate solutions of the basic slip problems in the rarefied gas flows by distinguishing between incident and outgoing distributions at a surface. He used a single parameter approximation to the incident distribution and a conservation relation. The method has been improved in the recent past through the use of two conservation relations and two-parameter approximations to the incident distribution. We have explored in this work a method to improve upon these latter approximations by using an arbitrary order parameter representation of the incident distribution. For a test problem, we have considered the Milne problem of one speed transport [ S. K. Loyalka, Phys. Fluids 24, 1912 (1982) ]. We have found that a three-parameter representation yields a result for extrapolation distance that is accurate to four figures. We have explored approximations up to order 512, and we have found that the accuracy of results is improved systematically with the order of the approximation, and results of any desired accuracy can be obtained.

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47.45.Gx	Slip flows and accommodation
47.10.ab	Conservation laws and constitutive relations
02.60.Ed	Interpolation; curve fitting

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Nonlinear analysis of periodic modulation in resonances of cylindrical and spherical acoustic standing waves

Eru Kurihara and Takeru Yano

Phys. Fluids 18, 117107 (2006); http://dx.doi.org/10.1063/1.2393437 (11 pages)

Online Publication Date: 22 November 2006

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The nonlinear resonance of cylindrical acoustic standing waves of an ideal gas contained between two coaxial cylinders is theoretically investigated by the method of multiple scales. The wave motion concerned is excited by a small-amplitude harmonic oscillation of the radius of the outer cylinder, and the formulation of the problem includes the wave phenomenon in a hollow cylinder without the inner one as a limiting case. The spherical standing wave in two concentric spheres is also studied in parallel. The resonance occurs if the driving frequency falls in a narrow band around the linear resonance frequency, and in the weakly nonlinear regime, no shock wave is formed in contrast to the plane wave resonance. A cubic nonlinear equation for complex wave amplitude can then be derived by the method of multiple scales. Using a first integral of the cubic nonlinear equation, we shall demonstrate that the resonant oscillation is accompanied by a periodic modulation of amplitude and phase when the dissipation effect due to viscosity and thermal conductivity is negligible. The period of the modulation varies as the minus two-thirds power of the acoustic Mach number defined at the outer cylinder or sphere and decreases with an increase in the radius ratio of the inner and outer cylinders or spheres. When the dissipation effect is small but not negligible, the modulation is slowly weakened and the resonant oscillation approaches a steady state oscillation, which corresponds to the steady solution examined in earlier works.

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47.35.Rs	Sound waves
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.40.Nm	Shock wave interactions and shock effects
47.11.St	Multi-scale methods
02.30.Rz	Integral equations

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On electro-osmotic flows through microchannel junctions

G. Yossifon, I. Frankel, and T. Miloh

Phys. Fluids 18, 117108 (2006); http://dx.doi.org/10.1063/1.2391701 (9 pages) | Cited 26 times

Online Publication Date: 29 November 2006

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We study the electro-osmotic flow through a T-junction of microchannels whose dielectric walls are weakly polarizable. The present global analysis thus extends earlier studies in the literature concerning the local flow of an unbounded electrolyte solution around nearly insulated wedges. The velocity field is obtained via superposition of an irrotational part associated with the equilibrium zeta potential and the induced-charge electro-osmotic flow originating from the interaction of the externally applied electric field and the charge cloud it induces owing to field leakage through the polarizable dielectric channel walls. Along the channel walls the latter component gives rise to fluid velocities converging toward the corner which dominate the flow in its immediate vicinity. Recent experimental observations in the literature regarding the appearance and subsequent expansion of flow reversal and vortices downstream (initially) and upstream (subsequently) of the junction, are both rationalized in terms of the growing relative importance of this induced contribution to the global velocity field with increasing intensity of the externally applied electric field.

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47.61.Fg	Flows in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS)
47.65.-d	Magnetohydrodynamics and electrohydrodynamics
47.60.-i	Flow phenomena in quasi-one-dimensional systems
47.85.Np	Fluidics
47.32.cb	Vortex interactions
47.57.jd	Electrokinetic effects

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Higher-order Föppl models of steady wake flows

Bartosz Protas

Phys. Fluids 18, 117109 (2006); http://dx.doi.org/10.1063/1.2389033 (13 pages) | Cited 3 times

Online Publication Date: 30 November 2006

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In this paper we construct two-dimensional steady potential flows past a circular cylinder as generalizations of the point-vortex Föppl system. For a given classical Föppl system, these higher-order systems form a two-parameter family depending on the truncation order N and the area A of the vortex region desingularizing the original Föppl solution. We characterize the higher-order equilibria analytically and numerically, and show that their modified linear stability properties make the higher-order systems useful models for a class of flow control problems.

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