摘要:

The displacement of water molecules associated with the flow of water inside a nonconsolidated packing of 800 &mgr;m OD glass spheres has been measured by a pulsed gradient NMR technique. Using a stimulated spin‐echo sequence, mean displacements of up to 300 &mgr;m corresponding to measurement times of up to 200 ms can be analyzed. The measurement can be quantitatively calibrated using the pure molecular self‐diffusion of water at zero flow conditions. For molecular displacements much smaller than the pore size, the distribution of the flow velocity component along the mean flow direction is determined at Reynolds numbers high enough so that longitudinal molecular diffusion is negligible. An exponential decay of the probability distribution of the displacements is observed at large distances. The results are very similar to those obtained by numerical solution of the Stokes equation in random sphere packings. At longer displacement distances, a secondary peak of the displacement distribution is observed: It is interpreted as the first step toward the transition toward classical dispersion at displacements much larger than the pore size. The influence of molecular diffusion and of the heterogeneities of the magnetic permeability also are discussed. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868839

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Meniscus shapes from a simulation of a plate immersing into an infinitely deep liquid bath, for a range of outer length scales, have been obtained numerically. These have been compared with the leading‐order prediction from a three‐region asymptotic analysis done in the double limit, Capillary number, Ca→0,LS/LC→0, with Ca ln(LC/LS) ofO(1), whereLSandLCrepresent the slip length and an outer macroscopic length, respectively. For Ca<0.01, the numerically computed and the perturbation solutions show excellent agreement. Within this range of Ca, the meniscus slope at a distance 10LSfrom the dynamic contact line is geometry independent, that is, does not vary with changes in the outer lengthLC. The interface slope at this point can serve as an appropriatematerialboundary condition for the outer problem. For 0.01<Ca<0.1, the intermediate region solution continues to closely fit the numerically generated solution, while the match in the outer region begins to degrade. By monitoring the pressure difference between the surrounding inviscid gas phase and arbitrarily chosen point in the liquid, we attribute this breakdown to infiltration of viscous effects into the outer region, so that static capillarity does not adequately describe meniscus shapes in this regime. For Ca≳0.1, there is no match between the numerical and perturbation solutions in both the intermediate and outer regions, indicating that higher‐order contributions must be accounted for in the perturbation solutions. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868840

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Experiments and numerical simulations of rising spherical bubbles in quiescent surfactant solutions are presented. The rise velocities versus the concentration in the bulk are measured using three surfactants, Triton X100, Brij30and SDS for different bubble sizes, between 0.4 and 1 mm equivalent radius. We also present a brief description of the finite‐difference numerical method developed to solve the full Navier‐Stokes equations around the contaminated bubble for Reynolds numbers ranging from 50 to 200. The distributions of the tangential velocity, the vorticity, the pressure and the surfactant concentration on the bubble surface are calculated. In the case of high Peclet numbers surfactant molecules, which adsorb on the surface are convected and collected at the rear part of the bubble forming a stagnant cap where the no‐slip condition holds. The concentration on the bubble interface is obtained for surfactants having a desorption rate much slower than the convective rate. The sudden increase of the shear stress and pressure at the leading edge of the cap contributes mainly to decrease the rise velocity. This rapid slowdown of the bubble occurs when nearly half of the bubble surface is covered by the surfactant layer, and this is due to the particularly high values obtained for the shear stress and the pressure at the leading edge of this cap‐angle. Measured and calculated rise velocities for bubbles of 0.4 mm equivalent radius show good agreement when the sorption kinetics controls the surfactant exchange between the bulk and the surface. Calculated critical concentrations needed to cover completely the bubble agree with the measurements even for larger bubbles. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868787

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Numerical and experimental studies of the transient shock wave phenomena in a liquid containing non‐condensable gas bubbles are presented. In the numerical analysis, individual bubbles are tracked to estimate the effect of volume oscillations on the wave phenomena. Thermal processes inside each bubble, which have significant influence on the volume oscillation, are calculated directly using full equations for mass, momentum and energy conservation, and those results are combined with the averaged conservation equations of the bubbly mixture to simulate the propagation of the shock wave. A silicone oil/nitrogen bubble mixture, in which the initial bubble radius is about 0.6 mm and the gas volume fraction is 0.15% – 0.4%, is used in the shock tube experiments. The inner diameter of the shock tube is chosen to be 18 mm and 52 mm in order to investigate the multidimensional effects on the wave phenomena. In a fairly uniform bubbly mixture, the experimental results agree well with the numerical ones computed using a uniform spatial distribution of bubbles. On the other hand, in all the other experiments, the bubbles in the shock tubes are not distributed uniformly, being relatively concentrated along the axis of the tube. This non‐uniformity substantially alters the profile of the shock waves. The numerical predictions where such a distribution is taken into account agree well with those experimental data. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868788

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

The Rayleigh–Taylor instability arises when a heavy fluid adjacent to a light fluid is accelerated in a direction against the density gradient. Under this unstable configuration, a perturbation mode of small amplitude grows into bubbles of the light fluid and spikes of the heavy fluid. Taylor discovered the steady state motion with constant velocity for a single bubble or periodic bubbles in the Rayleigh–Taylor instability. Read and Youngs studied the motion of a randomly perturbed fluid interface in the Rayleigh–Taylor instability. They reported constant acceleration for the overall bubble envelope. Bubble merger is believed to cause the transition from constant velocity to constant acceleration. In this paper, we present a numerical study of this important physical phenomenon. It analyzes the physical process of bubble merger and the relationship between the horizontal bubble expansion and the vertical interface acceleration. A dynamic bubble velocity, beyond Taylor’s steady state value, is observed during the merger process. It is believed that this velocity is due to the superposition of the bubble velocity with a secondary subharmonic unstable mode. The numerical results are compared with experiments. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868789

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

We provide numerical and analytic evidence for the formation of a singularity driven only by surface tension in the mathematical model describing a two‐dimensional Hele–Shaw cell with no air injection. Constantin and Pugh have proved that no such singularity is possible if the initial shape is close to a circle; thus we show that their result is not true in general. Our evidence takes the form of direct numerical simulation of the full problem, including a careful assessment of the effects of limited spatial resolution, and comparison of the full problem with the lubrication approximation. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869102

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

A probabilistic criterion is derived for the onset of wetting front instability during surface water infiltration into a randomly stratified soil. It is based on the common assumption that the natural log hydraulic conductivity of the soil is a random, multivariate Gaussian function of space. Whereas the mean (expectation) of this function may exhibit a drift, its fluctuations about the mean are statistically homogeneous with constant variance and autocorrelation scale. The wetting front is taken to form a sharp boundary. Closed‐form expressions for the probability of instability, and for the mean critical wave number, are obtained either directly or via a first‐order reliability method. Monte Carlo simulations are used to verify these analytical solutions as well as to determine the mean maximum rate of incipient finger growth and corresponding mean wave number. The effects of applied pressure gradient, capillary pressure head at the wetting front, and statistical parameters of the hydraulic conductivity field on instability and incipient finger growth are investigated for a wide range of these variables. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868790

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

In the fundamental (l=2) mode, the frequency spectrum of a magnetically levitated inviscid droplet exhibits three distinct peaks. If the modes that correspond to each of these peaks is known, the surface tension of the droplet may be calculated. In experiments that make use of this principle, there is nounambiguousmethod of assigning mode numbers to these peaks. The dynamics of the oscillating droplet depend on the magnetic pressure on the droplet surface. Consequently, the order of the peaks in thel=2 mode oscillations is determined by the magnetic pressure distribution. In this paper, the magnetic pressure distribution on the surface of the droplet is calculated as a function of the parameters that govern the external magnetic field. The frequencies of the droplet oscillation and its static shape deformation are also expressed in terms of these same parameters. The frequencies of oscillation are used to determine the surface tension of the liquid droplet. Finally, the magnetic pressure distribution on the droplet is shown to yield the well‐known ‘‘pear‐like’’ shape that is assumed by liquid metal droplets in a conical levitator. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868791

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Planar flow induced in a viscous fluid by a small cylinder oscillating in the direction normal to its axis is modeled theoretically and reproduced experimentally. In the model, a line force dipole (force doublet) was used as the source of motion. In an initially quiescent unbounded fluid this source produces zero net momentum and generates symmetrical quadrupolar flow consisting of two dipolar vorticity fronts propagating in opposite directions from the source. For starting flow at low Reynolds numbers, a second‐order unsteady solution is obtained in terms of a power series of the Reynolds number, Re=Q/4&pgr;&ngr;2, whereQis the forcing amplitude and &ngr; is the kinematic viscosity. This solution demonstrates that, as timet→∞, the flow in the vicinity of the source becomes steady and radial. To describe this steady asymptote, the Jeffery–Hamel nonlinear solution for radial flow is used. A particular solution is derived using the nondimensional intensity Re of the force dipole as a governing parameter. It is shown that the problem permits a similarity solution for all values of Re when a mass sink of prescribed intensityq=q(Re) is added to the flow. This steady asymptote is reproduced experimentally, using a vertical porous cylinder that oscillates horizontally in the shallow upper layer of a two‐layer fluid and sucks fluid through its porous walls. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868792

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

In this paper we study steady capillary‐gravity waves in a two‐layer fluid bounded above by a free surface and below by a horizontal rigid boundary with a small obstruction. Two critical speeds for the waves are obtained. Near the smaller critical speed, the derivation of the usual forced KdV equation (FKdV) fails when the coefficient of the nonlinear term in the FKdV vanishes. To overcome this difficulty, a new equation, called a forced extended KdV equation (FEKdV) governing interfacial wave forms, is obtained by a refined asymptotic method. Various solutions and numerical results of this equation are presented. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868793

出版商:AIP    

年代:1996

数据来源: AIP