摘要:

Molecules at the air–water interface often form inhomogeneous layers in which domains of different densities are separated by sharp interfaces. Complex interfacial pattern formation may occur through the competition of short‐ and long‐range forces acting within the monolayer. The overdamped hydrodynamics of such interfacial motion is treated here in a general manner that accounts for dissipation both within the monolayer and in the subfluid. Previous results on the linear stability of interfaces are recovered and extended, and a formulation applicable to the nonlinear regime is developed. A simplified dynamical law valid when dissipation in the monolayer itself is negligible is also proposed. Throughout the analysis, special attention is paid to the dependence of the dynamical behavior on a characteristic length scale set by the ratio of the viscosities in the monolayer and in the subphase. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868893

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

The motion of a test sphere falling through an otherwise monodisperse suspension of different settling velocity has been examined experimentally. Marked test spheres of different sizes and densities were tracked in a monodisperse suspension of unmarked glass spheres, made optically transparent by matching the index of refraction of the suspending fluid to that of the glass spheres. The ratio,Rs, between the Stokes’ velocity of the test particle and that of an isolated sphere of the suspension was varied from 1 to 13 while the particle volume fraction of the suspension was kept constant at 20%. Statistical analyses of the velocities of the test sphere yield the mean settling velocities, the velocity fluctuations and the velocity autocorrelation functions. The long time motion of the test sphere is shown to be diffusive in nature. Correlation times and self‐diffusivities are measured as a function ofRs. A change in the behavior of the motion of the test particle is observed forRs≥5. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868885

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Spatially resolved velocity profiles and spatially nonresolved velocity distributions of steady flow in a tube and bead packs were measured. Two different NMR experiments were used to measure velocity distributions. In one, the velocity histogram was calculated from spatially resolved velocity phase encoded images acquired in a 6 mm bead pack. In the other, a Fourier flow method was used to measure the velocity distribution directly in a 0.25 mm bead pack. Axial velocity profiles in the pore space of the 6 mm bead pack at Reynolds numbers of 14.9, 29.9, and 44.8 proved to be roughly parabolic, with maxima near the pore centers. Both NMR methods yielded the same dimensionless velocity distributions that contain negative as well as positive velocity components. The velocity distribution function derived from a bundle‐of‐tubes‐model accounts for the positive part of the velocity distribution. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868867

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Experiments were performed on the motion of isolated drops and bubbles in a Dow‐Corning silicone oil under the action of an applied temperature gradient in a reduced gravity environment aboard the NASA Space Shuttle in orbit. Images of the interior of the test cell during these experiments were recorded on cine film and later analyzed to obtain data on the migration velocity as a function of size and the applied temperature gradient. The data are presented in scaled form. Predictions are available in the case of gas bubbles, and it is found that the scaled velocity decreases with increasing Marangoni number qualitatively as expected even though there are quantitative discrepancies. The scaled velocity also appears to approach a theoretical asymptote predicted in the limit of large values of the Marangoni number for Stokes motion. Finally, sample results from a preliminary experiment on a pair of drops are presented. They display the remarkable feature that a small drop which leads a large drop in a temperature gradient can significantly retard the motion of the large trailing drop while itself moving as though it is virtually unaffected by the presence of the large drop. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868868

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

The dynamics of bubbles at high Reynolds numbers is studied from the viewpoint of statistical mechanics. Individual bubbles are treated as dipoles in potential flow. A virtual mass matrix of the system of bubbles is introduced, which depends on the instantaneous positions of the bubbles, and is used to calculate the energy of the bubbly flow as a quadratic form of the bubbles’ velocities. The energy is shown to be the system’s Hamiltonian and is used to construct a canonical ensemble partition function, which explicitly includes the total impulse of the suspension along with its energy. The Hamiltonian is decomposed into an effective potential due to the bubbles’ collective motion and a kinetic term due to the random motion about the mean. An effective bubble temperature—a measure of the relative importance of the bubbles’ relative to collective motion—is derived with the help of the impulse‐dependent partition function. Two effective potentials are shown to operate: one due to the mean motion of the bubbles, dominates at low bubble temperatures, where it leads to their grouping in flat clusters normal to the direction of the collective motion, while the other, temperature‐invariant, is due to the bubbles’ position‐dependent virtual mass and results in their mutual repulsion. Numerical evidence is presented for the existence of the effective potentials, the condensed and dispersed phases, and a phase transition. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868869

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

The equations of motion for interacting elliptical vortices in a background shear flow are derived from a Hamiltonian moment formulation. The equations reduce to the sixth order system of Melanderetal. [J. Fluid Mech.167, 95 (1986)] when a pair of vortices is considered and shear is neglected. The equations for a pair of identical vortices are analyzed using a number of methods, with particular emphasis on the implications for vortex merger. The splitting distance between the stable and unstable manifolds connecting the hyperbolic fixed points of the intercentroidal motion—the separatrix splitting—is estimated with a Melnikov analysis. This analysis differs from the standard time‐periodic Melnikov analysis on two counts: (a) the ‘‘periodic’’ perturbation arises from a second degree of freedom in the system which is not wholly independent of the first degree of freedom, the intercentroidal motion; (b) this perturbation has a faster time scale than the intercentroidal motion. The resulting Melnikov integral appears to be exponentially small in the perturbation as the latter goes to zero. Numerical simulations, notably Poincare´ sections, provide a global view of the dynamics and indicate that, as observed in previous studies, there are essentially two modes of merger. The effect of the shear on chaotic motion is also discussed. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868870

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

We report an experimental study of the swirling flow generated in the gap between two coaxial corotating disks. We use a free geometry, i.e., unshrouded disks in air, with moderate to high Reynolds numbers. When the relative rotation rate is varied, transitions in the flow can be observed by global power measurement and are related to the geometry of the external recirculating flow. The mean flow is studied in details with hot‐wire measurements using a boxcar‐type averaging technique. It involves a single turbulent vortex undergoing a slow precession motion. We show that statistical properties of the turbulent fluctuations are affected by the dynamics of the mean flow, which also displays a correlation with the global power fluctuations. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868871

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

The flow of an electrically conducting fluid in an open channel in the presence of a strong magnetic field of oblique incidence to both the channel walls and the force of gravity is explored. This type of flow has possible applications to the protection of high heat flux surfaces in magnetic confinement fusion reactors. The governing equations of fully‐developed flow are derived retaining all viscous terms. They are then solved in the strong field limit in an asymptotic, iterative fashion, carrying the first two terms in the expansion with powers of the effective Hartmann number. The asymptotic solutions for the velocity, induced magnetic field and the flow rate are compared with a numerical solution of the complete governing equations. Good agreement is seen between the asymptotic and numerical predictions of velocity and electric current distribution when the core regions are dominated by magnetic forces. One novel feature of open channel flow of this type is the existence, predicted by the asymptotic analysis and confirmed by the numerical integration, of a second‐order Hartmann layer on the free surface. Its presence is required to ensure the condition of no shear stress on this boundary. Also seen is the presence of strong discontinuities across free shear layers, which form along the field lines that extend from the free surface/sidewall corner. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868872

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

This paper concerns electroconvectional stability of a conduction state in an electrolyte layer flanked by cation‐permselective walls (electrodialysis membranes, electrodes) under potentiostatic conditions. It is shown through a numerical finite difference solution of the linear stability problem that above a certain voltage threshold the basic conduction state becomes electroconvectionally unstable. Marginal stability curves in the voltage/wave number plane are calculated and the dependence of the critical threshold characteristics on the system’s parameters (ionic diffusivities ratio, electroconventional Pe´clet number) studied. Electroconvectional instability is shown to occur for an arbitrary ionic diffusivities ratio. A model problem of electroconvection in a loop under potentiostatic conditions is solved explicitly for a steady state. It is shown that above a certain voltage threshold, the quiescent conduction in the loop bifurcates into a pair of electroconvectional steady state circulations. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868873

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

This paper treats the buoyant convection of a liquid metal in a circular cylinder with a uniform, steady, axial magnetic field and with the random residual accelerations encountered on earth‐orbiting vehicles. The objective is to model the magnetic damping of the melt motion during semiconductor crystal growth by the Bridgman process in space. For a typical process with a magnetic flux density of 0.2 T, the convective heat transfer and the nonlinear inertial effects are negligible, so that the governing equations are linear. Therefore, for residual accelerations or ‘‘g‐jitters’’ whose directions are random functions of time, the buoyant convection is given by a superposition of the convections for two unidirectional accelerations: an axial acceleration which is parallel to the cylinder’s axis and a transverse acceleration which is perpendicular to this axis. Similarly, the response to accelerations whose amplitudes are random functions of time is given by a Fourier‐transform superposition of the buoyant convections for sinusoidally periodic accelerations for all frequencies. Since the temperature gradient in the Bridgman process is primarily axial, the magnitude of the three‐dimensional buoyant convection for the transverse acceleration is much larger than the magnitude of the axisymmetric convection for the axial acceleration. At a low frequency, only the magnetic damping limits the magnitude of the buoyant convection. As the frequency is increased, linear inertial effects augment the magnetic damping, so that the magnitude of the convection decreases, and its phase shifts to a quarter‐period lag after the acceleration. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868892

出版商:AIP    

年代:1996

数据来源: AIP