摘要:

This work addresses the sensitivity of a calculated global quantity to the smoothing of discontinuous variation of properties. The analysis is based on the very simple model problem of a fully developed, thermocapillary channel flow. The predictions of this simple model are shown to be in excellent agreement with the results for the Navier–Stokes simulations of the thermocapillary migration of a spherical drop. The main conclusion is that the migration velocity depends very strongly on the smearing of the driving interfacial force whereas it is rather insensitive to the smearing of the discontinuous viscosity distribution. This hints at the indispensability of grid adaption for modeling interfacial forces.

ISSN:1070-6631    

DOI:10.1063/1.868145

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

Photographs from high‐speed movies of the profiles of a mechanically generated, gentle spilling breaking water wave are presented. It is found that as the wave steepens a bulge forms on the forward face of the wave near the crest and capillary waves form on the water surface ahead of the ‘toe’ of the bulge (see Fig. 1). The toe of the bulge then moves rapidly down the forward face of the wave and a train of large‐amplitude waves with short wavelength grows rapidly on the surface of the bulge. These waves quickly break down into a random pattern indicating that the flow has become turbulent.

ISSN:1070-6631    

DOI:10.1063/1.868146

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

Couette and parallel plate viscometers are two commonly used flow geometries to characterize shear viscosity of concentrated suspensions. In Couette flow, it is well documented that prolonged shearing causes a decrease in the apparent viscosity of concentrated suspensions due to shear‐induced particle migration from the annulus region to the stagnant region under the bob. In this study, the technique of nuclear magnetic resonance imaging (NMRI) was used to measure the evolution of suspension concentration profiles in Couette and parallel‐plate flow devices upon shearing. Neutrally buoyant suspensions of nearly monodisperse, non‐Brownian spherical particles at a volume fraction of 0.5 in a Newtonian fluid were used. The same flow cells and suspensions were also used in a rheometer to measure the changes in shear stress under identical experimental conditions such that a direct comparison can be made between the stress and concentration data. For Couette flow, the NMRI data correlated very well with the stress measurements and directly confirmed the Leighton–Acrivos [J. Fluid. Mech.181, 415 (1987)] shear‐induced migration theory. In torsional flow between parallel plates, no detectable change was found in particle concentration in the radial direction, but some decrease in the apparent viscosity was observed. These results provide some important clues for developing and evaluating more general descriptions of particle migration for nonrectilinear shear flows.

ISSN:1070-6631    

DOI:10.1063/1.868147

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

To study rapid and laminar flow of a mud layer down a gentle slope, a shallow layer of Bingham fluid is considered. Attention is focused on long waves of finite amplitude. Convective inertia is kept in the approximate equations which are simplified by Ka´rma´n’s momentum integral approach with an assumed velocity profile. A linearized instability analysis is first carried out for periodic disturbances. The nonlinear development of unstable disturbances is computed numerically to study the formation of periodic shocks, or roll waves. Nonlinear motion caused by external influx to an otherwise steadily flowing mud layer is also investigated.

ISSN:1070-6631    

DOI:10.1063/1.868148

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

A collision between two bubbles of radiiawith an initial relative velocity 2U∞is studied in the limit, Re≡&rgr;U∞a/&mgr;≫1 and We≡&rgr;U2∞a/&ggr;≪1. Here &rgr; and &mgr; are the density and viscosity of the liquid and &ggr; is the surface tension of the air–liquid interface. In the absence of colloidal forces, Chesters and Hoffman [Appl. Sci. Res.38, 353 (1982)] showed that this situation leads to coalescence. The case where there is a nonhydrodynamic repulsive force between the gas–liquid interfaces of the two bubbles that is sufficient to prevent coalescence is considered. Such a force may arise due to ionic salts in aqueous solution or due to surfactants. The analysis shows the bubbles undergo a nearly elastic bounce on anO(a We1/2/U∞) time scale and the repulsive force per unit area must be at least 2&ggr;/afor rebound. Also, experimental observations of bubble collisions in aqueous solutions using high‐speed video photography are presented.

ISSN:1070-6631    

DOI:10.1063/1.868149

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

The complex dispersion relation of capillary waves on water has been measured in a wavelength regime (&lgr;∼1–2 cm) of interest to radar imaging. Two noninvasive sensors: a capacitive wave height antenna and a one‐dimensional scanning laser slope gauge, are used to study the alteration of surface tension and surface elastic modulus in the presence of monomolecular surface films. On a static water surface, these sensors are compared to accepted standard techniques. The surface tension results are compared to a Wilhelmy plate while the elastic modulus results are compared to equations of state obtained by Langmuir trough techniques. The sensors are then employed to measure the response of surface film properties to surface areal strains for film pressures and strain rates, which are comparable to natural films in the presence of ship‐generated surface currents. In the experiments reported in this paper, onlyinsolublesurfactants are used. The monolayer surface films considered in this study are found to exhibit higher elastic modulus (∼8 mN/m) at small surface pressure (&pgr;≤1 mN/m) than expected from previous work reported in the literature. The response of these films to surface strain is consistent with our static surface measurements. The modulation of film parameters is found to be in phase with internal wave‐generated oscillatory surface strain with periods on the order of 9 s. This implies that the film conforms to the strained water surface with negligible slippage in this regime. These measurements demonstrate the capability of this approach to continuously monitor surface filmsinsituwith detector system response time of the order of 1 s. The technique is suited to large or deep containers and is applicable to sheltered ocean environments.

ISSN:1070-6631    

DOI:10.1063/1.868150

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

A numerical solution of linear differential equations governing the stability of the nonaxisymmetric wide‐gap circular Couette flow was present in this study. The numerical solution took into account the presence of a radial temperature gradient between the two rotating cylinders. Boussinesq approximation was applied in the analysis so as to examine the interaction of radial temperature difference with the centrifugal potential but neglect the gravity effect. The critical Taylor number and corresponding critical axial and azimuthal wave numbers were shown graphically for various values of radius ratio, ratio of angular velocities of the inner and outer cylinders, and temperature gradient parameterNfor Prandtl number 0.7. Not only the critical Taylor number but the oscillatory onset mode of nonaxisymmetric disturbances could be altered by the effects of a temperature gradient, as indicated by the calculated results.

ISSN:1070-6631    

DOI:10.1063/1.868151

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

The viscous stability analysis of Long’s vortex is performed. Some quantitative disagreements with the inviscid results of previous investigators are reported. The truncation of the infinite radial domain into a small computational domain utilized in past investigations is found to be the source of these discrepancies. More important, for small flow forces, a type‐II Long’s vortex is shown to be destabilized by perturbations having positive azimuthal wave number. Based on previous numerical computations, it had been conjectured that these unstable eigenmodes may not exist. The stability characteristics of the unstable modes are fully mapped and are presented in detail.

ISSN:1070-6631    

DOI:10.1063/1.868152

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

The oscillating convective structures appearing at the threshold of the two‐layer Rayleigh–Be´nard instability are analyzed in the nonlinear regime. By deriving the amplitude equations for left‐ and right‐traveling waves from the infinite Prandtl number Boussinesq equations, it is shown that one of these waves should generally appear, rather than standing waves, in sufficiently large cells. Numerical results show that these waves have a limited range of existence, because a hysteretic transition to stationary convection occurs when the Rayleigh number is increased (via approach of a heteroclinic orbit for standing waves, and steady‐state bifurcation for traveling waves). From numerical evidence and by comparison with similar behaviors encountered in the one‐layer two‐component problem, it is inferred that the overall behavior is typical of a codimension‐2 Takens–Bogdanov bifurcation.

ISSN:1070-6631    

DOI:10.1063/1.868153

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

The axisymmetric, dynamic breakup of a Newtonian liquid jet injected vertically into another immiscible Newtonian liquid at various Reynolds numbers is investigated here. The full transient from jet start‐up to breakup into drops was simulated numerically by solving the time‐dependent axisymmetric equations of motion and continuity using an algorithm based on the Volume of Fluid (VOF) method that was previously proven successful in simulations of steady‐state liquid jets (i.e., of the jet region close to the nozzle before breakup). The algorithm has been further refined here based on its performance on transient problems such as the solution of the free liquid–liquid capillary jet breakup problem. The comparison of the simulation results with previous experimental measurements of jet length under conditions where all forces, i.e., viscous, inertial, buoyancy, and surface tension, are important, can be judged satisfactory given the sensitive dependence of the results on details of the experimental setup that are not available. The comparison involves the jet length till breakup as well as the jet and drop shapes, often far from regular. In comparison with experiment, the results of the present numerical method show a greater sensitivity of the jet length to the Reynolds number than the best predictions previously available based on the linear stability analysis of the free liquid–liquid capillary jet breakup problem.

ISSN:1070-6631    

DOI:10.1063/1.868154

出版商:AIP    

年代:1994

数据来源: AIP