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

Select this Article

On intra- and intersubject variabilities of airflow in the human lungs

Jiwoong Choi, Merryn H. Tawhai, Eric A. Hoffman, and Ching-Long Lin

Phys. Fluids 21, 101901 (2009); http://dx.doi.org/10.1063/1.3247170 (17 pages) | Cited 11 times

Online Publication Date: 13 October 2009

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

The effects of intra- and intersubject variabilities in airway geometry on airflow in the human lungs are investigated by large eddy simulation. The airway models of two human subjects consisting of extra- and intrathoracic airways are reconstructed from CT images. For intrasubject study, airflows at two inspiratory flow rates are simulated on the airway geometries of the same subject with four different levels of truncation. These airway models are the original complete geometry and three geometries obtained by truncating the original one at the subglottis, the supraglottis, and the laryngopharynx, respectively. A comparison of the airflows in the complete geometry model shows that the characteristics of the turbulent laryngeal jet in the trachea are similar regardless of Reynolds number in terms of mean velocities, turbulence statistics, coherent structures, and pressure distribution. The truncated airway models, however, do not produce the similar flow structures observed in the complete geometry. An improved inlet boundary condition is then proposed for the airway model truncated at the laryngopharynx to improve the accuracy of solution. The new boundary condition significantly improves the mean flow. The spectral analysis shows that turbulent characteristics are captured downstream away from the glottis. For intersubject study, although the overall flow characteristics are similar, two morphological factors are found to significantly affect the flows between subjects. These are the constriction ratio of the glottis with respect to the trachea and the curvature and shape of the airways.

+

Show PACS

87.19.Wx	Pneumodyamics, respiration
47.63.Ec	Pulmonary fluid mechanics

Select this Article

Entrainment of a film on a surface from the meniscus of a liquid wedge during coating

S. N. Reznik, W. Salalha, Y. Sorek, D. Avramov, and E. Zussman

Phys. Fluids 21, 102001 (2009); http://dx.doi.org/10.1063/1.3240396 (14 pages) | Cited 1 time

Online Publication Date: 1 October 2009

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

The shape evolution of an entrained film from the meniscus of a liquid wedge is studied, both experimentally and theoretically. The liquid wedge is formed by a droplet of liquid injected between a substrate and a tilted plate. When the substrate moves relative to the tilted plate with a constant velocity, a film of a constant slope is entrained on it, while another film remains on the tilted plate. The numerical and analytical investigation of the process provides the dependence of the length and slope of the entrained film after the end of drawing process, as well as the maximum thickness of the film on the tilted plate, on the capillary number. The length of the entrained film was found to be minimal for infinitely large capillary numbers when the surface tension effects are negligibly small. Experimental data confirm the predicted characteristic geometry of the film for capillary numbers up to 0.75.

+

Show PACS

47.55.Hd	Stratified flows
68.08.Bc	Wetting
68.03.Cd	Surface tension and related phenomena
47.55.dr	Interactions with surfaces
47.55.nb	Capillary and thermocapillary flows
68.15.+e	Liquid thin films

Select this Article

Transport properties of Brownian particles confined to a narrow channel by a periodic potential

Xinli Wang and German Drazer

Phys. Fluids 21, 102002 (2009); http://dx.doi.org/10.1063/1.3226100 (7 pages) | Cited 1 time

Online Publication Date: 2 October 2009

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

We investigate the transport of Brownian particles in a two-dimensional potential moving under the action of an external force or convected by a flow field. The potential is periodic in one direction and confines the particles to a narrow channel of varying cross section in the other direction. We apply the standard long-wave asymptotic analysis in the narrow dimension and show that the leading order term is equivalent to that obtained previously from a direct extension of the Fick–Jacobs approximation. We also show that the confining potential has similar effects on the transport of Brownian particles to those induced by a solid channel. Finally, we compare the analytical results with Brownian dynamics simulations in the case of a sinusoidal variation of the width of a parabolic potential in the cross section. We obtain excellent agreement for the marginal probability distribution, the average velocity of the Brownian particles, and the asymptotic dispersion coefficient over a wide range of Péclet numbers.

+

Show PACS

05.40.Jc	Brownian motion
47.60.Dx	Flows in ducts and channels

Select this Article FREE

Nucleation threshold and deactivation mechanisms of nanoscopic cavitation nuclei

Bram M. Borkent, Stephan Gekle, Andrea Prosperetti, and Detlef Lohse

Phys. Fluids 21, 102003 (2009); http://dx.doi.org/10.1063/1.3249602 (9 pages) | Cited 14 times

Online Publication Date: 19 October 2009

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

The acoustic nucleation threshold for bubbles trapped in cavities has theoretically been predicted within the crevice theory by Atchley and Prosperetti [“The crevice model of bubble nucleation,” J. Acoust. Soc. Am. 86, 1065 (1989) ]. Here, we determine this threshold experimentally, by applying a single pressure pulse to bubbles trapped in cylindrical nanoscopic pits (“artificial crevices”) with radii down to 50 nm. By decreasing the minimum pressure stepwise, we observe the threshold for which the bubbles start to nucleate. The experimental results are quantitatively in good agreement with the theoretical predictions of Atchley and Prosperetti. In addition, we provide the mechanism which explains the deactivation of cavitation nuclei: gas diffusion together with an aspherical bubble collapse. Finally, we present superhydrophobic nuclei which cannot be deactivated, unless with a high-speed liquid jet directed into the pit.

+

Show PACS

47.55.dp	Cavitation and boiling
68.08.Bc	Wetting
47.55.D-	Drops and bubbles

Select this Article

Measurements of tangential momentum accommodation coefficient for various gases in plane microchannel

I. A. Graur, P. Perrier, W. Ghozlani, and J. G. Méolans

Phys. Fluids 21, 102004 (2009); http://dx.doi.org/10.1063/1.3253696 (9 pages) | Cited 13 times

Online Publication Date: 30 October 2009

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

Mass flow rate measurements in a single silicon microchannel were carried out for various gases in isothermal steady flows. The results obtained from hydrodynamic to near free molecular regime by using a powerful experimental platform allowed us to deduce interesting information, notably about the reflection/accommodation process at the wall. In the 0–0.3 Knudsen range, a continuum analytic approach was derived from the NS equations, associated with first or second order slip boundary conditions. Identifying the experimental mass flow rate curves to the theoretical ones the tangential momentum accommodation coefficient (TMAC) of various gases was extracted. Over the full Knudsen range [0–30] the experimental results were compared with theoretical values calculated from the kinetic approaches: using variable accommodation coefficient values as fitting parameter, the theoretical curves were fitted to the experimental ones. Whatever the Knudsen range and whatever the theoretical approach, the TMAC values are found decreasing when the molecular weights of the gas increase (as long as the different gases are compared using the same approach). Moreover, the values of the various accommodation coefficients are rather close to one another but sufficiently smaller than unity indicating that the full accommodation modeling is not satisfactory to describe the gas/wall interaction.

+

Show PACS

47.60.Dx	Flows in ducts and channels
47.61.-k	Micro- and nano- scale flow phenomena
47.45.Gx	Slip flows and accommodation
47.10.ad	Navier-Stokes equations

Select this Article

Nonmodal and nonlinear dynamics of a volatile liquid film flowing over a locally heated surface

Naveen Tiwari and Jeffrey M. Davis

Phys. Fluids 21, 102101 (2009); http://dx.doi.org/10.1063/1.3241967 (14 pages) | Cited 1 time

Online Publication Date: 1 October 2009

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

The stability of a thin, volatile liquid film falling under the influence of gravity over a locally heated, vertical plate is analyzed in the noninertial regime using a model based on long-wave theory. The model is formulated to account for evaporation that is either governed by thermodynamic considerations at the interface in the one-sided limit or limited by the rate of mass transfer of the vapor from the interface. The temperature gradient near the upstream edge of the heater induces a gradient in surface tension that opposes the gravity-driven flow, and a pronounced thermocapillary ridge develops in the streamwise direction. Recent theoretical analyses predict that the ridge becomes unstable above a critical value of the Marangoni parameter, leading to the experimentally observed rivulet structure that is periodic in the direction transverse to the bulk flow. An oscillatory, thermocapillary instability in the streamwise direction above the heater is also predicted for films with sufficiently large heat loss at the free surface due to either evaporation or strong convection in the adjoining gas. This present work extends the recent linear stability analysis of such flows by Tiwari and Davis [Phys. Fluids 21, 022105 (2009) ] to a nonmodal analysis of the governing non-self-adjoint operator and computations of the nonlinear dynamics. The nonmodal analysis identifies the most destabilizing perturbations to the film and their maximum amplification. Computations of the nonlinear dynamics reveal that small perturbations can be sufficient to destabilize a linearly stable film for a narrow band of wave numbers predicted by the nonmodal, linearized analysis. This destabilization is linked to the presence of stable, discrete modes that appear as the Marangoni parameter approaches the critical value at which the film becomes linearly unstable. Furthermore, the thermocapillary instability leads to a new, time-periodic base state. This transition corresponds to a Hopf bifurcation with increasing Marangoni parameter. A linear stability analysis of this time-periodic state reveals further instability to transverse perturbations, with the wave number of the most unstable mode about 50% smaller than for the rivulet instability of the steady base state and exponential growth rate about three times larger. The resulting film behavior is reminiscent of inertial waves on locally heated films, although the wave amplitude is larger in the present case near the heater and decays downstream where the Marangoni stress vanishes. The film’s heat transfer coefficient is found to increase significantly upon the transition to the time-periodic flow.

+

Show PACS

47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking
47.27.te	Turbulent convective heat transfer
47.55.nb	Capillary and thermocapillary flows
47.52.+j	Chaos in fluid dynamics

Select this Article

Enhanced slip on a patterned substrate due to depinning of contact line

Peng Gao and James J. Feng

Phys. Fluids 21, 102102 (2009); http://dx.doi.org/10.1063/1.3254253 (10 pages) | Cited 15 times

Online Publication Date: 26 October 2009

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

We perform numerical simulations of a shear flow over a periodically patterned substrate with entrapped gas bubbles. A diffuse-interface model is employed to handle the liquid-gas interface deformation and the three-phase contact line. Depending on the shear rate and the pattern geometry, four flow regimes are observed. The contact lines can be pinned, depinned, or eliminated depending on the competition between the shear force and the surface tension. The effective slip length is found to be dependent on the morphology of the menisci and hence on the shear rate. In particular, the bubbles are transformed into a continuous gas film when the shear rate is larger than a critical value, resulting in a significantly enhanced slip length proportional to the liquid-gas viscosity ratio. The present results have interesting implications for effective slip on superhydrophobic surfaces.

+

Show PACS

47.45.Gx	Slip flows and accommodation
02.60.-x	Numerical approximation and analysis
68.03.Cd	Surface tension and related phenomena
47.55.D-	Drops and bubbles
66.20.-d	Viscosity of liquids; diffusive momentum transport
83.50.-v	Deformation and flow

Select this Article

Electrowetting with contact line pinning: Computational modeling and comparisons with experiments

Shawn W. Walker, Benjamin Shapiro, and Ricardo H. Nochetto

Phys. Fluids 21, 102103 (2009); http://dx.doi.org/10.1063/1.3254022 (16 pages) | Cited 12 times

Online Publication Date: 30 October 2009

Full Text: Read Online (HTML) | Download PDF

multimedia

+

Show Abstract

This work describes the modeling and simulation of planar electrowetting on dielectric devices that move fluid droplets by modulating surface tension effects. The fluid dynamics are modeled by Hele-Shaw type equations with a focus on including the relevant boundary phenomena. Specifically, we include contact angle saturation and a contact line force threshold model that can account for hysteresis and pinning effects. These extra boundary effects are needed to make reasonable predictions of the correct shape and time scale of liquid motion. Without them the simulations can predict droplet motion that is much faster than in experiments (up to 10–20 times faster). We present a variational method for our model, and a corresponding finite element discretization, which is able to handle surface tension, conservation of mass, and the nonlinear contact line pinning in a straightforward and numerically robust way. In particular, the contact line pinning is captured by a variational inequality. We note that all the parameters in our model are derived from first principles or from independent experiments except one (the parameter D_visc that accounts for the extra resistive effect of contact angle hysteresis and is difficult to measure directly). We quantitatively compare our simulation to available experimental data for four different cases of droplet motion that include splitting and joining of droplets and find good agreement with experiments.

+

Show PACS

85.50.-n	Dielectric, ferroelectric, and piezoelectric devices
68.08.Bc	Wetting
68.03.Cd	Surface tension and related phenomena
47.11.Fg	Finite element methods
47.55.D-	Drops and bubbles
47.65.-d	Magnetohydrodynamics and electrohydrodynamics

Select this Article

Axisymmetric instabilities in electrospinning of highly conducting, viscoelastic polymer solutions

Colman P. Carroll and Yong Lak Joo

Phys. Fluids 21, 103101 (2009); http://dx.doi.org/10.1063/1.3246024 (10 pages) | Cited 9 times

Online Publication Date: 12 October 2009

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

In this paper the axisymmetric instabilities observed during the electrospinning of highly electrically conducting, viscoelastic poly(ethylene oxide) (PEO)/water solutions are investigated. In our theoretical study, a linear stability analysis is coupled with a model for the stable electrospun jet. The combined model is used to calculate the expected bead growth rate and wave number for given electrospinning conditions. In the experimental section of the study, PEO/water solutions are electrospun and the formation of axisymmetric beads is captured using high-speed photography. Experimental values for the bead growth rate and wave number are extracted and compared with the model predictions. An energy analysis is then carried out on the stability results to investigate the mechanism of instability via the coupling between base flow and perturbation. The analysis reveals that the unstable axisymmetric mode for electrically driven, highly conducting jets is not a capillary mode, but is mainly driven by electrical forces due to the interaction of charges on the jet. We note that this axisymmetric, conducting mode often exhibits a growth rate too small to be observed during electrospinning. However, both our experiments and stability analysis demonstrate that the axisymmetric instability with a high growth rate can be seen in practice when the electrical force is effectively coupled with viscoelastic forces.

+

Show PACS

47.57.Ng	Polymers and polymer solutions
47.55.nb	Capillary and thermocapillary flows
81.20.-n	Methods of materials synthesis and materials processing
47.60.Kz	Flows and jets through nozzles

Select this Article

Coating flow of viscous Newtonian liquids on a rotating vertical disk

Nilesh H. Parmar, Mahesh S. Tirumkudulu, and E. J. Hinch

Phys. Fluids 21, 103102 (2009); http://dx.doi.org/10.1063/1.3250858 (8 pages) | Cited 1 time

Online Publication Date: 22 October 2009

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

We study a Newtonian viscous liquid coating a vertical rotating disk in the creeping flow regime. Experiments were performed at varying disk rotation speeds and liquid volumes, and the thickness profile at steady state was measured. While the maximum liquid supported by the rotating disk varied with rotation rate and liquid viscosity, the numerical value of a dimensionless number signifying the ratio of gravity to viscous forces was the same in all the cases, γ = 0.30. A lubrication analysis for the time evolution of the film thickness that accounted for gravity, surface tension, and viscous forces was solved numerically to steady state. The predicted thickness profiles are in quantitative agreement with those obtained experimentally. The lubrication equation at steady state was solved analytically in the absence of surface tension to obtain constant height contours that were circular and symmetric about the horizontal axis. However to obtain a complete solution, knowledge of the height variation across the contours is required, and this is controlled by the surface tension. On including this effect, we derived an asymptotic solution to predict thickness profiles that agree well with measurements for large values of viscosity or rotation rates.

+

Show PACS

47.15.gm	Thin film flows
47.85.mf	Lubrication flows
47.32.Ef	Rotating and swirling flows
68.03.Cd	Surface tension and related phenomena
68.15.+e	Liquid thin films

Select this Article

Thermal convection of a viscoplastic liquid with high Rayleigh and Bingham numbers

A. Vikhansky

Phys. Fluids 21, 103103 (2009); http://dx.doi.org/10.1063/1.3256166 (7 pages) | Cited 17 times

Online Publication Date: 28 October 2009

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

We consider the effect of yield stress on the Rayleigh–Bénard convection of a viscoplastic material. First we consider the model problem of convection in a differentially heated loop, which is described by the (modified) Lorenz equations. The presence of the yield stress significantly alters the dynamics of the system. In particular, the chaotic motion can stop suddenly (sometimes, after a period of chaotic oscillations). Guided by the model equations we performed direct numerical simulations of convection of the Bingham liquid in a square cavity heated from bellow. Our interest has been concentrated on the situation when both buoyancy and plastic forces are large. The obtained results are in a reasonable agreement with the predictions by the Lorenz equations.

+

Show PACS

47.50.-d	Non-Newtonian fluid flows
47.52.+j	Chaos in fluid dynamics
47.55.pb	Thermal convection

Select this Article

Lattice Boltzmann simulation of the rise and dissolution of two-dimensional immiscible droplets

Cheng Chen and Dongxiao Zhang

Phys. Fluids 21, 103301 (2009); http://dx.doi.org/10.1063/1.3253385 (11 pages) | Cited 4 times

Online Publication Date: 22 October 2009

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

We used a coupled multiphase lattice Boltzmann (LB) model to simulate the dissolution of immiscible liquid droplets in another liquid during the rising process resulting from buoyancy. It was found that there existed a terminal rise velocity for each droplet, and there was a power law relationship between the Eötvös (Eo) number and the terminal Reynolds (Re) number. Our simulation results were in agreement with the empirical correlation derived for predicting bubble rise. When more than two identical droplets rose simultaneously in a close proximity, the average terminal rise velocity was lower than that of a single droplet with the same size because of the mutual resistant interactions. The droplet trajectories at the noncentral positions were not straight because of the nonzero net horizontal forces acting on the droplets. The Damkohler (Da) and Peclet (Pe) numbers were varied to investigate the coupling between droplet size, flow field, dissolution at the interface, and solute transport. For a given Pe, increasing Da led to a higher dissolution rate. For a given Da, increasing Pe led to a higher dissolution rate. For a large Da and a small Pe, the process near the interface was diffusion limited, and the advective flow relative to the droplet resulting from droplet rise was unable to move the accumulated solute away from the interface quickly. In this case, it was favorable to split the single droplet into as many small ones as possible in order to increase the interface area per unit mass and consequently enhance the whole dissolution process. For a small Da and a large Pe, the process was dissolution limited near the interface. The mass of accumulated solute near the interface was little, so the advective flow at the top side of the droplet was able to clean the solute quickly. In this case it was favorable to keep the droplet as a single one in order to obtain a high rise velocity and consequently enhance the whole dissolution process. By studying the coupling between Da and Pe, we qualitatively proposed to construct a Da-Pe phase plane and found the interface dividing the plane into regions 1 and 2. Region 1 was the collection of points where it was favorable to break down the droplet into as many small ones as possible in order to accelerate dissolution, while region 2 was the collection of points where it was favorable to keep the droplet in a single one for the same purpose. Based on our LB simulations, we found that the interface was an increasing function of Pe. Region 1 was the portion above the interface, while region 2 was the portion below it. In real applications, if both Pe and Da are obtained, it will be easy to judge whether it is favorable to break down the droplet or not in order to accelerate dissolution by checking whether (Pe, Da) falls in region 1 or 2.

+

Show PACS

47.11.Qr	Lattice gas
47.55.D-	Drops and bubbles
64.70.fh	Boiling and bubble dynamics
64.75.Bc	Solubility

Select this Article

Effects of geometric shape on the hydrodynamics of a self-propelled flapping foil

Xing Zhang, Saizhen Ni, Shizhao Wang, and Guowei He

Phys. Fluids 21, 103302 (2009); http://dx.doi.org/10.1063/1.3251045 (7 pages) | Cited 5 times

Online Publication Date: 22 October 2009

Full Text: Read Online (HTML) | Download PDF

multimedia

+

Show Abstract

The hydrodynamics of a free flapping foil is studied numerically. The foil undergoes a forced vertical oscillation and is free to move horizontally. The effect of chord-thickness ratio is investigated by varying this parameter while fixing other ones such as the Reynolds number, the density ratio, and the flapping amplitude. Three different flow regimes have been identified when we increase the chord-thickness ratio, i.e., left-right symmetry, back-and-forth chaotic motion, and unidirectional motion with staggered vortex street. It is observed that the chord-thickness ratio can affect the symmetry-breaking bifurcation, the arrangement of vortices in the wake, and the terminal velocity of the foil. The similarity in the symmetry-breaking bifurcation of the present problem to that of a flapping body under constraint is discussed. A comparison between the dynamic behaviors of an elliptic foil and a rectangular foil at various chord-thickness ratios is also presented.

+

Show PACS

47.20.Ky	Nonlinearity, bifurcation, and symmetry breaking
47.32.-y	Vortex dynamics; rotating fluids
47.15.Tr	Laminar wakes
47.40.-x	Compressible flows; shock waves
89.20.Kk	Engineering
47.52.+j	Chaos in fluid dynamics

Select this Article

Effects of viscosity ratio and three dimensional positioning on hydrodynamic interactions between two viscous drops in a shear flow at finite inertia

Rajesh Kumar Singh and Kausik Sarkar

Phys. Fluids 21, 103303 (2009); http://dx.doi.org/10.1063/1.3253351 (9 pages) | Cited 2 times

Online Publication Date: 26 October 2009

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

Drops driven toward each other by shear at finite inertia follow two distinct types of trajectories. Type I trajectory is similar to the one in Stokes flow where drops slide past each other. However, at finite inertia, drops display a new type II trajectory, where they reverse their paths. Increasing viscosity ratio results in a transition from type II to type I trajectory. The transition is caused by decreased drop deformation and increased alignment with the flow at higher drop viscosity; both decrease the zone of reversed streamlines that accompanies a drop at finite inertia. The transition is delineated in a phase diagram of Reynolds number and viscosity ratio for different capillary numbers. The critical viscosity ratio, where a type II transitions into type I, increases with Reynolds number except at higher capillary numbers, where the critical viscosity ratio shows a slight nonmonotonic variation with Reynolds number. Also, it is nonmonotonic with capillary numbers in that for a fixed Reynolds number, the critical viscosity ratio first increases with increasing capillary number and then decreases. Similar to the Stokes regime, increased viscosity ratio leads to a decreased postcollision cross-stream separation effectively decreasing the shear induced diffusion. Higher viscosity ratio results in an increased separation between drops during encounter, which results in a smaller interaction time. With drops placed initially at different shear planes, drops come under the influence of the reversed flow zone around a single drop that broadens off the central shear plane. Consequently, the trajectory changes from type I to type II as the offset in the vorticity direction increases. The change depends on the initial offset in the shear direction as well. The final displacement in the shear direction varies linearly with the initial offset. The net relative displacement in the shear direction shows a gradual decrease with increasing offset. The net relative displacement in the vorticity direction with increasing offset first increases from a zero value when drops are placed at the same shear plane to a maximum and then decreases. For certain cases, it reaches a negative value.

+

Show PACS

47.55.D-	Drops and bubbles
47.55.nb	Capillary and thermocapillary flows
47.32.-y	Vortex dynamics; rotating fluids
66.20.-d	Viscosity of liquids; diffusive momentum transport
66.10.C-	Diffusion and thermal diffusion

Select this Article

Sedimentation of a sphere in a fluid channel

Olivier Pitois, Christelle Fritz, Laurentiu Pasol, and Michèle Vignes-Adler

Phys. Fluids 21, 103304 (2009); http://dx.doi.org/10.1063/1.3253408 (5 pages) | Cited 2 times

Online Publication Date: 26 October 2009

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

We studied both experimentally and numerically the sedimentation velocity of small solid particles through liquid channels merging at the intersection of three soap films. The wall mobility induces a nontrivial behavior for the particle drag coefficient, providing particular transport properties that are not observed for channels with rigid walls. It is shown that for sufficiently small particles, slow and fast motions are observed for the particle along the channel, depending on the particle position within the channel cross section and the sphere/channel size ratio. The velocity corresponding to fast motions can be as high as twice the Stokes velocity in an unbounded fluid. Moreover, the fast motions are not observed anymore when the size ratio exceeds a critical value, which has been found to be approximately equal to 0.5. As another major difference with the solid wall channel, the sphere velocity does not vanish when the size ratio reaches unity. Instead, the smallest value is found to be ¼ of the Stokes velocity.

+

Show PACS

47.55.-t	Multiphase and stratified flows
47.15.Rq	Laminar flows in cavities, channels, ducts, and conduits
47.60.Dx	Flows in ducts and channels
47.50.-d	Non-Newtonian fluid flows

Select this Article

Sound propagation through a rarefied gas confined between source and receptor at arbitrary Knudsen number and sound frequency

Denize Kalempa and Felix Sharipov

Phys. Fluids 21, 103601 (2009); http://dx.doi.org/10.1063/1.3247159 (14 pages) | Cited 3 times

Online Publication Date: 13 October 2009

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

A sound propagation through a rarefied gas is investigated on the basis of the linearized kinetic equation taking into account the influence of receptor. A plate oscillating in the normal direction to its own plane is considered as a sound source, while a stationary parallel plate is considered as being the receptor of sound. The main parameters determining the solution of the problem are the oscillation speed parameter, which is defined as the ratio of intermolecular collision frequency to the sound frequency, and the rarefaction parameter defined as the ratio of the distance between source and receptor to the molecular mean free path. The kinetic equation is solved via a discrete velocity method with a numerical error of 0.1%. The numerical calculations are carried out for wide ranges of the oscillation and rarefaction parameters. The concept of integral phase parameter is introduced to obtain the sound speed correctly in all regimes of the gas rarefaction and sound frequency. Analytical solutions are obtained in the limits of small and large parameters of frequency and rarefaction.

+

Show PACS

47.45.-n

Rarefied gas dynamics

Select this Article

Influence of inlet radius on Stokes flow in a circular tube via the Hamiltonian systematic method

G. P. Wang, X. S. Xu, and Y. X. Zhang

Phys. Fluids 21, 103602 (2009); http://dx.doi.org/10.1063/1.3250302 (9 pages) | Cited 1 time

Online Publication Date: 23 October 2009

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

This paper presents a new semianalytical method, Hamiltonian systematic method, for solving axisymmetric problems of Stokes flow. In the system, nonzero-eigenvalue solutions can describe local effect near the boundary and therefore the influence of inlet radius on the flow can be investigated. A rule of minimal entrance length is discussed on the basis of the criteria which are defined by axial flow deviating from the full developed (Hagen–Poseuille) flow. Numerical results show that the entrance length is related to the inlet radius, and there is one minimal point on the relationship curve, namely, there is one minimal entrance length. Besides, pressures have the characteristic too and the minimal point is same. The method can also be generalized to other fields.

+

Show PACS

47.60.Dx

Flows in ducts and channels

Select this Article

On steady rotational cyclonic flows: The viscous bidirectional vortex

Joseph Majdalani and Martin J. Chiaverini

Phys. Fluids 21, 103603 (2009); http://dx.doi.org/10.1063/1.3247186 (15 pages) | Cited 3 times

Online Publication Date: 28 October 2009

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

This study is focused on the tangential boundary layers of a bidirectional vortex, specifically those forming at the core and the sidewall of a swirl-driven cyclonic chamber. Our analysis is based on the regularized, tangential momentum equation which is rescaled in a manner to capture the forced vortex near the chamber axis and the no slip requirement at the sidewall. After identifying the coordinate transformations needed to resolve the rapid changes in the regions of nonuniformity, two inner expansions are constructed. These expansions are then matched with the outer, free vortex solution that is sandwiched between the core and the hard wall. By combining inner and outer expansions, uniformly valid approximations are subsequently obtained for the swirl velocity, vorticity, and pressure. These are shown to be strongly influenced by a dimensionless grouping that we refer to as the vortex Reynolds number, V. This keystone parameter appears as a ratio of the mean flow Reynolds number and the product of the swirl number and the chamber aspect ratio. Based on V, several fundamental features of the bidirectional vortex are quantified. Among them are the thicknesses of the viscous core and sidewall boundary layers; these decrease with V^1/2 and V, respectively. The converse may be said of the peak velocity which increases with V^1/2. In the same vein, the angular speed of the rigid-body rotation of the forced vortex is found to be linearly proportional to V. Our laminar swirl velocity is reminiscent of Sullivan’s two-cell vortex except for its additional dependence on the aspect ratio of the chamber. For the purpose of verification, theoretical predictions are compared to particle image velocimetry measurements and Navier–Stokes simulations at high vortex Reynolds numbers. By properly accounting for the turbulent eddy viscosity in the analytical model, local agreement is obtained with both laboratory measurements and computer simulations.

+

Show PACS

47.10.ad	Navier-Stokes equations
47.15.ki	Inviscid flows with vorticity
47.32.-y	Vortex dynamics; rotating fluids

Select this Article

Influence of flow confinement on the drag force on a static cylinder

B. Semin, J. P. Hulin, and H. Auradou

Phys. Fluids 21, 103604 (2009); http://dx.doi.org/10.1063/1.3253324 (9 pages) | Cited 5 times

Online Publication Date: 30 October 2009

Full Text: Read Online (HTML) | Download PDF

+

Show Abstract

The influence of confinement on the drag force F on a static cylinder in a viscous flow inside a rectangular slit of aperture h₀ has been investigated from experimental measurements and numerical simulations. At low enough Reynolds numbers, F varies linearly with the mean velocity and the viscosity, allowing for the precise determination of drag coefficients λ_∥ and λ_⊥ corresponding, respectively, to a mean flow parallel and perpendicular to the cylinder length L. In the parallel configuration, the variation in λ_∥ with the normalized diameter β = d/h₀ of the cylinder is close to that for a two-dimensional (2D) flow invariant in the direction of the cylinder axis and does not diverge when β = 1. The variation in λ_∥ with the distance from the midplane of the model reflects the parabolic Poiseuille profile between the plates for β⪡1 while it remains almost constant for β ∼ 1. In the perpendicular configuration, the value of λ_⊥ is close to that corresponding to a 2D system only if β⪡1 and/or if the clearance between the ends of the cylinder and the side walls is very small: in that latter case, λ_⊥ diverges as β→1 due to the blockage of the flow. In other cases, the side flow between the ends of the cylinder and the side walls plays an important part to reduce λ_⊥: a full three-dimensional description of the flow is needed to account for these effects.

+

Show PACS

47.60.Dx	Flows in ducts and channels
47.50.-d	Non-Newtonian fluid flows
47.27.nf	Flows in pipes and nozzles
47.50.Cd	Modeling
47.27.E-	Turbulence simulation and modeling
89.20.Kk	Engineering