摘要:

Solder drops spreading on metallic substrates are a reactive form of the wetting problem. A metallic component may diffuse in the liquid toward a metal substrate, where it is consumed by a reaction that forms a solid intermetallic phase. The resulting spatial variation in the composition of the drop may cause composition gradients along the free surface of the drop. Together with any thermal gradients along the free surface, Marangoni effects may, in turn, modify the bulk transport in the spreading drop. Motivated by this situation, we extend lubrication theory for the spreading of thin drops in the presence of gravity and thermocapillarity to include mass transport and solutocapillarity. We use an approximate solute profile in the drop to derive coupled evolution equations for the free surface shape and concentration field. Numerical solutions for the nonreactive (single component) drop agree well with previous theory. In the reactive case, we are only able to compute results for parameters outside of the range for solder materials. Including reactive effects in the model impacts the flow patterns and spreading rates at relatively early times; but by the end of the spreading, solutal effects have died out in the model. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868497

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Fibers in a planar extensional flow tend to align parallel to the axis of extension, with a small orientational dispersion resulting from hydrodynamic, fiber–fiber interactions. We have visualized the orientation of an opaque, tracer fiber in the midst of an index of refraction and density matched fiber suspension in a four‐roll mill and determined the mean squares of the components of the fiber orientation in the compressional and neutral directions. The observed mean‐square orientations in suspensions in Newtonian fluids withnL3=5–17 are qualitatively consistent with the dilute limit of the theory of Shaqfeh and Koch [Phys. Fluids A31, 728 (1988)]. Herenis the number of fibers per unit volume andLis the fiber length. It was not possible to perform the experiment for higher fiber concentrations, because of difficulties in keeping the tracer fiber at the stagnation point, which were attributed to translational, hydrodynamic diffusion. Measurements of orientational dispersion in polyacrylamide solutions indicated that the non‐Newtonian stresses increase fiber alignment, as predicted by Harlen and Koch [Phys Fluids A4, 5 (1992)]. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868758

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Three‐dimensional granular dynamics simulations are carried out to investigate macroscopic behavior of granular materials subjected to vibrations. Particles, idealized as smooth inelastic, uniform spheres, are gravitationally loaded into a rectangular periodic cell having an open top and plane floor. Vibrations to the bed are subsequently imposed through the sinusoidally oscillated floor. Significant differences in the character of the bed are found, depending on the strength of the applied floor accelerations &Ggr;=a&ohgr;2, even if the boundary input energy is fixed. At high acceleration values, a dense upper region is supported on a fluidized low‐density region near the floor. The temperature is maximum at the floor and monotonically attenuates upward, while the solids fraction profile peaks at some intermediate depth. When lower accelerations are applied, the granular temperature no longer decreases monotonically from the bottom to the top and the solids fraction depth profile bulges at approximately three diameters from the floor. The surface of the bed appears chaotic and fluidized, where a low solids fraction and high temperature occurs. The bed height, which remains almost constant below 1.2g, undergoes a pronounced expansion when 1.2g≤&Ggr;≤2.0g, and subsequently flattens out at &Ggr;&bartil;2.8g. Computed granular temperature and solids fraction depth profiles are in good agreement with recent kinetic theory predictions when the acceleration is large enough, while bed expansion at lower accelerations is quantitatively consistent with existing experimental data. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868498

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The nonlinear long‐wave stability and lifetimes of thin free films subjected to the excess Lifshitz–van der Waals (LW) forces are studied based on numerical solutions, and a weakly nonlinear theory (WNT), which neglects mode interactions. The WNT works best for the fastest growing (dominant) disturbances of small initial amplitudes, and also for relatively thick films. For such cases, the nonlinear viscous effects (stabilizing) and inertia (destabilizing) are usually less significant than the LW force (destabilizing), surface tension force, and the unsteady effects (both stabilizing). For large initial amplitudes, linearly stable disturbances can engender strong subcritical instabilities and film rupture due to the greatly enhanced LW forces, inertia and mode interactions. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868499

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

It has been known for some time that two‐dimensional numerical simulations of flow over nominally two‐dimensional bluff bodies at Reynolds numbers for which the flow is intrinsically three dimensional, lead to inaccurate prediction of the lift and drag forces. In particular, for flow past a normal flat plate (InternationalSymposiumonNonsteadyFluidDynamics, edited by J. A. Miller and D. P. Telionis, 1990, pp. 455–464) and circular cylinders [J. Wind Eng. Indus. Aerodyn.35, 275 (1990)], it has been noted that the drag coefficient computed from two‐dimensional simulations is significantly higher than what is obtained from experiments. Furthermore, it has been found that three‐dimensional simulations of flows lead to accurate prediction of drag [J. Wind Eng. Indus. Aerodyn.35, 275 (1990)]. The underlying cause for this discrepancy is that the surface pressure distribution obtained from two‐dimensional simulations does not match up with that obtained from experiments and three‐dimensional simulations and a number of reasons have been put forward to explain this discrepancy. However, the details of the physical mechanisms that ultimately lead to the inaccurate prediction of surface pressure and consequently the lift and drag, are still not clear. In the present study, results of two‐dimensional and three‐dimensional simulations of flow past elliptic and circular cylinders have been systematically compared in an effort to pinpoint the exact cause for the inaccurate prediction of the lift and drag by two‐dimensional simulations. The overprediction of mean drag force in two‐dimensional simulations is directly traced to higher Reynolds stresses in the wake. It is also found that the discrepancy in the drag between two‐dimensional and three‐dimensional simulations is more pronounced for bluffer cylinders. Finally, the current study also provides a detailed view of how the fluctuation, which are associated with the Ka´rma´n vortex shedding in the wake, affect the mean pressure distribution and the aerodynamic forces on the body. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868500

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

It is shown that viscosity stratified plane Poiseuille flow may exhibit a long‐wavelength instability of a purely kinetic nature formally resembling the so‐called alpha effect known in magnetohydrodynamics or in anisotropic three‐dimensional flows of homogeneous fluids. In the absence of the alpha effect, the system may display a peculiar type of long‐wavelength instability, where the latter is controlled by the surface tension. The weakly nonlinear equation for the evolving interfaces is derived and solved numerically. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868501

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The study of capillary wave scattering by a circular region with different interfacial properties from the rest of an otherwise homogeneous interface is motivated by experiments on wave attenuation at a monolayer‐covered air–water interface where domains of one surface phase are dispersed in a second surface phase. Here the scattering function is calculated for an incident wave of frequency &ohgr; (wavevectork0) scattering from an isolated circular domain of radiusawith surface tension &sgr;1which is imbedded in an otherwise infinite interface of surface tension &sgr;0. The underlying fluid is treated as irrotational and the three‐dimensional flow problem coupling the heterogeneous surface to the underlying liquid is reduced to a set of dual integral equations, which are solved numerically. With this solution the scattering amplitudes and the total scattering cross sections are calculated as a function of the surface tension ratio &sgr;0/&sgr;1and incident wavenumberk0a. The analogous problem of a discontinuous change in bending rigidity is also considered and the solution to the complete viscous problem is outlined in the Appendix. Experimental implications of these results are discussed. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868502

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

A new model describing the dynamics of large‐amplitude waves on laminar falling wavy films at high Reynolds numbers (Re≳300) is presented. The model is based on second‐order boundary layer theory and includes the pressure variation across the film as well as higher‐order viscous terms. The consistency and accuracy of the model is verified by comparing the linear stability results with Kapitza’s classical boundary layer model and Orr–Sommerfeld studies of the two‐dimensional Navier–Stokes equations. Numerical integration of a traveling wave simplification of the model predicts the existence of chaotic large‐amplitude, nonperiodic waves, as observed in the experiments. The computed wave statistics such as wave celerities, root‐mean‐square (RMS) values of film thickness, probability density function (PDF), and film thickness power spectrum using the present model are in reasonable agreement with those measured on naturally excited fully developed flows at Re≳300. The present model also overcomes the main deficiency of the classical boundary layer model (namely, negative wall shear stress) predicts large‐amplitude waves (with peak to substrate ratios of 3 to 4) and gives better agreement with data. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868503

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The formulation of a nonlinear frequency domain parabolic mild‐slope model is detailed. The resulting model describes two‐dimensional wave transformation and nonlinear coupling between frequency components. Linear dispersion and transformation characteristics are dictated by fully‐dispersive linear theory, an improvement over weakly‐dispersive Boussinesq theory. Both the present model and a weakly‐dispersive nonlinear frequency domain model are compared to laboratory data for both two‐dimensional wave transformation and pure shoaling. It is found that, in general, data‐model comparisons are enhanced by the present model, particularly in instances where the wave condition is outside the shallow water range. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868504

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The nonlinear response of an initially flat sea bed to a monochromatic surface progressive wave was studied using the multiple scale perturbation method. Two opposite‐traveling subliminal internal ‘‘mud’’ waves are selectively excited and form a resonant triad with the surface wave. The amplitudes of the internal waves grow on a time scale much longer than the period of the surface wave. It was found that the sea bed response is critically dependent on the density ratio of water and soil, depth of water, and depth and viscosity of the saturated soil. The result of instability analysis is in qualitative agreement with the result of a wave flume experiment. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868505

出版商:AIP    

年代:1995

数据来源: AIP