摘要:

An experimental validation of a recent statistical model [Phys. Rev. Lett.72, 336 (1994)] is reported. The analysis is focused on the transverse components of the velocity structure functions, and extend previous tests conducted only on longitudinal velocity components. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869144

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Experiments show that, when two drops are brought in contact and pushed toward each other in the presence of temperature differences, coalescence is inhibited. Axisymmetric numerical solutions of the Navier–Stokes problem have been obtained to give an explanation of the phenomenon, assuming that a thin air film exists between the contacting drops and that, provided that well-defined dynamic conditions prevail on the liquid surfaces, the film experiences a suitable pressure that balances the pressure in the drops. The numerical results agree with the experimental ones, qualitatively explain why an air film between the drops could be created by Marangoni effects and show that the suppression of coalescence is obtained as long as films sufficiently large exhibit excess pressures of the same order of magnitude of the pressure needed to deform the drops. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869145

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

We show that vortex breakdown appears as a jump bifurcation due to structural instability of swirling flows when their solution locally fails to exist and the flow transits to another stable or metastable state. The flow pattern inside the steady separation zone and, consequently, the vortex breakdown features depend on the flow history. Therefore, we take into account theflow pattern inside the separation zone. The stagnation zone model (without velocity jump) excels the traditional analytic continuation method (leading to a recirculation zone) in that solutions always exist, and, for large enough inflow swirl, exhibit nonuniqueness and folds due to smooth variations of flow parameters, thus predicting the experimentally observed hysteretic jump transitions.©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869146

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

The problem of interaction of a drop with a solid boundary is formulated in the framework of a recently developed theory of the three-phase contact line motion and analyzed in the case of finite Bond and small capillary and Weber numbers. Evolution of the free-surface shape in a quasi-static regime of the drop spreading under gravity on a horizontal plane and on the surface of a rotating disk is investigated. In the considered regime, the free-surface shape deformation in time is independent of the initial conditions of the drop deposition onto the solid surface, while the three-phase contact-line motion is described by the same equations as in a general case. This feature makes the quasi-static regime informative and desirable from the point of view of investigation of the wetting phenomenon. Accuracy of the so-called “spherical cap approximation’’ often used in experimental studies of wetting is discussed. The theory describes both the “spontaneous” and “forced” regimes of the drop spreading and the transition between them. The results are compared with experimental data. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869147

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Linear nonaxisymmetric oscillations of liquid bridges are analyzed in the limit of large capillary Reynolds numberC−1. A boundary layer analysis is used that yields a second approximation of the damping rate and frequency in terms of the capillary Reynolds number, the slenderness of the bridge and the axial and azimuthal wave numbers of the mode being excited. Very good agreement with previous numerical results is obtained forC≲0.01, while the first correction of the damping rate gives a poor approximation, except for unrealistically small values ofC(C≲10−5). ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869148

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Asymptotic solutions are developed for miscible displacements at Stokes flow conditions between parallel plates or in a cylindrical capillary, at large values of the geometric aspect ratio. The single integro-differential equation obtained is solved numerically for different values of the Pe´clet number and the viscosity ratio. At large values of the latter, the solution consists of a symmetric finger propagating in the middle of the gap or the capillary. Constraints on conventional convection-dispersion-equation approach for studying miscible instabilities in planar Hele–Shaw cells are obtained. The asymptotic formalism is next used to derive—in the limit of zero diffusion— a hyperbolic equation for the cross-sectionally averaged concentration, the solution of which is obtained by analytical means. This solution is valid as long as sharp shock fronts do not form. The results are compared with recent numerical simulations of the full problem and experiments of miscible displacement in a narrow capillary. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869149

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

The transport in vortical and stagnation point flow fields is analyzed for particles across the entire range of density ratios, based on the Maxey–Riley equation [Phys. Fluids26, 883 (1983)] without history effects. For these elementary flow fields, the governing equations simplify substantially, so that analytical progress can be made towards quantifying ejection/entrapment trends and accumulation behavior. For a solid body vortex, the analysis shows that optimal ejection or entrapment occurs for all density ratios, as the difference between inward and outward forces reaches a maximum for intermediate values of the Stokes number. The optimal Stokes number value is provided as a function of the density ratio. Gravity is shown to shift accumulation regions, without affecting the entrapment or ejection rates. For a point vortex flow, the existence of up to three different regimes is demonstrated, which are characterized by different force balances and ejection rates. For this flow, optimal accumulation is demonstrated for intermediate Stokes numbers. The stagnation point flow gives rise to optimal accumulation for heavy particles, whereas light particles do not exhibit optimal behavior. The analysis furthermore indicates that nonvanishing density ratios give rise to a finite Stokes number regime in which the particle motion is oscillatory. Above and below this regime, the motion is overdamped. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869150

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Gravitational settling of solid heavy particles in a dilute suspension is studied analytically and numerically. The particle Reynolds number is assumed to be less than unity, for which the viscous drag force on the particle is well approximated by the linear Stokes law. The particulate volume fraction (or concentration)cis assumed to be small enough for the effects of particle–particle interactions to be negligible. The ratio&dgr;=&rgr;p/&rgr;fof the particle and fluid densities is considered large enough however, so that the momentum exchange between the two phases caused by the viscous drag forces (which is of the order of the particulate mass loading factorc&dgr;)is significant. The particulate base concentration,c0(y), is assumed to be a smooth function of the vertical coordinatey(hence, a stratified suspension) and a perturbation of the initially stationary settling regime is considered in the form of a horizontally propagating monochromatic wave with wavenumberkand frequency&ohgr;(k). Analytical solutions for the perturbations in the limit of small particle inertia (such that&ohgr;&tgr;p≪1, where&tgr;pis the particle response time) are found to be similar to those for internal waves propagating in a stratified fluid with effective density&rgr;eff=&rgr;f(1+c0(y)&dgr;). On the other hand, it is found that in the opposite limit of large particle inertia(&ohgr;&tgr;p≫1)the perturbations are damped. As an example, we consider a suspension consisting of two layers with uniform concentrations of particlesc1(fory>+h/2)andc2(fory<−h/2)separated by the interface layer of thicknessh, where the concentration gradient is substantial. The solutions obtained in the long-wave limitkh≪1show that if the concentration in the lower layer exceeds that in the upper layer(c2>c1), the disturbance of the interface brings about wavy motions analogous to internal waves in a two-layer fluid. In the case of inverse stratification(c2<c1)the disturbance grows exponentially and generates plume-like “bubbles,’’ similar to those produced due to the Rayleigh–Taylor instability in a two-layer fluid. The results of the numerical simulations show that, as expected, the waves are damped and the instability growth rate is reduced for particles having larger inertia. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869151

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

In this paper the initial “spin-up” stage of the flow field generated by the slow axial motion of a symmetric particle or drop in a rotating fluid in a “short cylinder” of length2His considered for small Rossby and Ekman numbers,RoandE. The motion starts from solid body rotation. Attention is focused on time-dependent effects in the extended core (outside theE1/2Ekman andE1/3Stewartson layers) and their influence on the behaviour of the drag force. When the particle velocity is established by an impulsive start, the flow-field and the drag build up on the spin-up time scale; the particle advances∼2RoE−1/2Hduring the transient stage. Results for the time-dependent geostrophic case, and also for various values of&Vegr;=(12H)1/2E1/4, for both sphere and disk particles, are presented. It is shown that when the particle velocity is established by release under a constant axial (say, buoyant) force, during the spin-up some rapid inertial oscillations may appear which are inconsistent with some of the assumption of the present analysis and require a separate investigation. The present theory is in qualitative agreement with available experiments, but a quantitative comparison requires new experiments. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869234

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

The Poiseuille–Be´nard flow (PBF) is studied by a two-dimensional numerical simulation for a Prandtl number equal to 6.4 (that of water at 23 °C) and for a wide range of Rayleigh (Ra) and Reynolds (Re) numbers: Ra⩽6000 and Re⩽3. The two observed flow configurations are (1) thermally stratified Poiseuille flow and (2) thermoconvective transversal rolls superimposed to the basic Poiseuille flow. The time evolution of the velocity components, the spatial development of the transversal rolls, their frequency, wavelength and velocity, the Nusselt number, together with the stability map in the Ra–Re plane, are studied in detail. Whenever possible, quantitative comparisons are made with published results: most of the experimental data, based on laser-Doppler anemometry (LDA), are recovered with amazing accuracy; a good agreement with results of convective stability deduced from a weakly nonlinear Ginzburg–Landau theory is also obtained. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869235

出版商:AIP    

年代:1997

数据来源: AIP