摘要:

Recently, Mallier and Maslowe [Phys. Fluids A5, 1074 (1993)] found an exact nonlinear solution of the inviscid, incompressible, two‐dimensional Navier–Stokes equations, representing an infinite row of counter‐rotating vortices, which extended the previous Kelvin–Stuart vortices. The aim of this work is to establish explicit sufficient conditions for the nonlinear stability of this solution. The result is derived with the energy‐Casimir stability method as a function of the parameters of the solution and the domain size. The size of the domain over which the street of vortices is unstable is exhibited.

ISSN:1070-6631    

DOI:10.1063/1.868225

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

The viscosity of a monolayer of a suspension of bimodally distributed hard spheres is determined for area fractions, &fgr;a, from 0.15 to 0.74 with different particle size ratios, &lgr; (diameter of large sphere/diameter of small spheres=1, 2, and 4), and different fractions of small spheres of total solids, &xgr; (0.07, 0.27, 0.49, 0.64, and 0.83). Particle distributions are generated by a Monte Carlo technique and the hydrodynamic interactions are calculated by Stokesian dynamics. These results, which correspond to the high‐frequency dynamic viscosities, are compared with those from the dynamic simulation of hydrodynamically interacting spherical particles [Chang and Powell, J. Fluid Mech.253, 1 (1993)]. Dynamic simulation is found to yield higher relative viscosities, &eegr;r, as compared with the results of Monte Carlo simulation at high concentrations. This results from the absence of long clusters that completely cross a periodic cell in the Monte Carlo simulations that are present in the dynamic simulations. When &fgr;ais normalized by the maximum packing fraction, &fgr;m2‐D, all the viscosity data fall onto a master curve. This is the same trend as that found in dynamic simulations, except that the Monte Carlo simulation gives lower relative viscosities for &fgr;a/&fgr;m2‐D≳ 0.3. When &lgr; and &fgr;aare fixed, &eegr;rdecreases as &xgr; increases from zero, reaches a minimum, and then increases as &xgr;→1, similar to the trend found in the dynamic simulations. Good agreement is found among the results of two‐dimensional simulations, experiments, and three‐dimensional simulations for monodispersed suspensions.

ISSN:1070-6631    

DOI:10.1063/1.868226

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

A method for computing Stokes flow interactions in suspensions of spherical objects is described in detail and applied to the suspensions of porous particles, drops, and bubbles to determine their hydrodynamic transport coefficients.

ISSN:1070-6631    

DOI:10.1063/1.868227

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

A new method is described for incorporating close‐field, lubrication forces between pairs of particles into the multiparticle Stokes flow calculations. The method is applied to the suspensions of both spherical as well as cylindrical particles, and results computed by the method are shown to be in excellent agreement with the exact known results available in the literature.

ISSN:1070-6631    

DOI:10.1063/1.868228

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

This paper examines theinsitugrowth and stability of a single bubble in an effective porous medium, where the pore microstructure is neglected. The main objective of the study is the effect of mass transfer and flow parameters on bubble stability. Because it is necessary for flow in both phases to be considered, this is actually a generalized phase‐change problem involving two fluids in a porous medium. Similarity solutions are developed in both three‐dimensional (3‐D) and two‐dimensional (2‐D) geometries, the stability of which is subsequently analyzed. In the absence of capillarity, an instability analogous to Mullins–Sekerka is found, which is independent of the process parameters, including the viscosity ratio,M. Capillary effects are next considered for the 2‐D geometry of a Hele–Shaw cell (the analysis is also extended to 3‐D geometries). At the largeMlimit, the stability condition is identical to Patterson’s [J. Fluid Mech.113, 513 (1981)] for the displacement of a liquid by a gas. This theory is found consistent with bubble growth experiments in Hele–Shaw cells. At finiteM, the theory predicts that the interface becomesmorestable asMincreases, which is directly opposite to the effect ofMin viscous fingering. This is a novel mechanism of convective stabilization and it is intrinsic toinsituphase growth. Higher solubility and diffusion coefficients also have a stabilizing effect. For conditions typical to bubble growth, however, the sensitivity to these parameters is very weak.

ISSN:1070-6631    

DOI:10.1063/1.868229

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

Air flow between a spinning annular disk and a flat baseplate has been studied both experimentally and computationally. The Ekman number, Ek, has been determined to be the single important dimensionless parameter required to characterize this problem. A numerical solution which predicts spacing‐dependent axisymmetric flow has been developed. It has been found to agree with experimental data over a wide range of parameter space. The calculated flow predicts unusual complexity; counter‐rotating recirculation cells are likely to be present.

ISSN:1070-6631    

DOI:10.1063/1.868230

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

The linear stability of a plane layer of dielectric liquid subjected to an electric field and a thermal gradient is studied. The liquid is supposed to have a non‐negligible residual conductivity and to exhibit an injection of charge from one of the electrodes. Both effects are due to the dissolution of a given salt in the liquid. The ionic mobility and the dielectric constant are temperature dependent. The stability of this configuration is studied with the help of an heuristic model and a precise discussion of the physical mechanisms of instability is made. Complete sets of the stability maps corresponding to different cases are presented.  

ISSN:1070-6631    

DOI:10.1063/1.868231

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

The development and interaction of solitary wave pulses is critical to understanding wavy film flows on an inclined (or vertical) surface. Sufficiently far downstream, the wave structure consists of a generally irregular sequence of solitary waves independent of the conditions at the inlet. The velocity of periodic solitary waves is found to depend on their frequency and amplitude. Larger pulses travel faster; this property, plus a strong inelasticity, causes larger pulses to absorb others during interactions, leaving a nearly flat interface behind. These wave interactions lead to the production of solitary wave trains from periodic small amplitude waves. The spacings between solitary waves can be irregular for several different reasons, including the amplification of ambient noise, and the interaction process itself. On the other hand, this irregularity is suppressed by the addition of periodic forcing.

ISSN:1070-6631    

DOI:10.1063/1.868232

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

The method of multiple scales is used to investigate the nonlinear stability behavior of a thin molten laser cutting. In this analysis, the balance of momentum and energy with the effects of phase change is considered. Under the assumption of long wavelength, a corresponding nonlinear generalized kinematic equation for the film thickness is thereby derived. The result shows that there exist supercritical stability in the linearly unstable region and subcritical instability in the linearly stable region. For higher cutting speeds, the surface roughness could be improved by decreasing the cutting speed or increasing the gas velocity due to the decreasing of the maximum equilibrium finite amplitude. On the other hand, for lower cutting speeds, the surface roughness could be improved by increasing the cutting speed or decreasing the gas velocity due to the increasing of the minimum threshold amplitude.

ISSN:1070-6631    

DOI:10.1063/1.868233

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

New experimental results at the onset of turbulence in a gravity‐driven pipe flow are presented, and a simple phenomenological model is introduced to describe the intermittent behavior observed. In this model slugs are stochastically produced at the pipe inlet, and the decrease in velocity due to turbulent friction is taken into account. The present approach shows that stochastic arguments account well for several experimental observations at low intermittency factors. In particular, it is shown that special intermittency routes to chaos are not needed to explain the exponentially decaying inverse cumulative distribution of laminar times.

ISSN:1070-6631    

DOI:10.1063/1.868234

出版商:AIP    

年代:1994

数据来源: AIP