摘要:

The use of formaldehyde‐killed single‐cell organisms as scattering particles for laser Doppler velocimetry studies in water and salt solutions is discussed. Advantages over traditional scattering particles include ready availability in large quantities, uniformity in size, monodispersity, and the ability to stay suspended in solution for several days. The tracers are colloidal sols for a wide range of densities of aqueous solutions. The microorganisms can be easily stained with a large variety of fluorescent and nonfluorescent dyes before they are used as tracer particles.

ISSN:0031-9171    

DOI:10.1063/1.866913

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The hydrodynamic transport properties of hard‐sphere dispersions are calculated for volume fractions (&fgr;) spanning the dilute limit up to the fluid–solid transition at &fgr;=0.49. Particle distributions are generated by a Monte Carlo technique and the hydrodynamic interactions are calculated by Stokesian dynamics simulation. The effects of changing the number of particles in the simulation cell are investigated, and the scaling laws for the finite‐size effects are derived. The effects of using various levels of approximation in computing both the far‐ and near‐field hydrodynamic interactions are also examined. The transport properties associated with freely mobile suspensions—sedimentation velocities, self‐diffusion coefficients, and effective viscosities—are determined here, while the corresponding properties of porous media are determined in a companion paper [Phys. Fluids31, xxxx (1988)]. Comparison of the simulation results is made with both experiment and theory. In particular, the short‐time self‐diffusion coefficients and the suspension viscosities are in excellent agreement with experiment.

ISSN:0031-9171    

DOI:10.1063/1.866914

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The hydrodynamic transport properties of hard‐sphere dispersions are calculated for volume fractions (&fgr;) spanning the dilute limit up to the fluid–solid transition at &fgr;=0.49. Particle distributions are generated by a Monte Carlo technique and the hydrodynamic interactions are calculated by Stokesian dynamics simulation. The effects of changing the number of particles in the simulation cell are investigated, and the scaling laws for the finite‐size effects are determined. The effects of using various levels of approximation in computing both the far‐ and near‐field hydrodynamic interactions are also examined. The transport properties associated with porous media—permeabilities and hindered diffusion coefficients—are determined here. The corresponding properties of freely mobile suspensions are determined in a companion paper [Phys. Fluids31, xxxx (1988)].

ISSN:0031-9171    

DOI:10.1063/1.866915

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

In this work natural convection within a two‐dimensional fluid saturated Darcy porous layer is considered. The porous material is in a large aspect ratio rectangle with its sides inclined with respect to the gravity vector. All four faces are exposed to uniform heat fluxes, opposite faces being heated and cooled, respectively. Analytical solutions for the streamfunction and temperature fields in the central region are deduced using a parallel flow assumption. Numerical confirmation of the analytical results is also obtained. For high enough Rayleigh numbers multiple steady states around the rest state are found. These states represent unsymmetrical flows in opposite directions. The critical Rayleigh number for the onset of motion determined from a stability analysis corresponds to that for the existence of unicellular convection using the parallel flow approximation. Linear stability limits of each of the multiple states are also calculated. One of the convective flows is found to be stable to higher Rayleigh numbers than the other.

ISSN:0031-9171    

DOI:10.1063/1.866916

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The base‐state convective flows, which are set up when a nondilute sedimenting suspension is placed beneath an inclined wall, are analyzed theoretically using a two‐fluid model. Their hydrodynamic stability and the corresponding spatial growth of small two‐dimensional disturbances at the clear fluid–suspension interface are then determined over the entire range of the governing parameters through numerical solutions of the relevant Orr–Sommerfeld equations. Two mechanisms for the growth of instability waves at the interface are identified. The results demonstrate that the base‐state flow becomes more unstable as inertial effects in the base state become more pronounced and thus, contrary to what has been suggested by earlier investigators, there is no restabilization as the base state approaches the inviscid limit. Increasing the concentration of the suspension is found to have a stabilizing effect on the two‐phase interface, particularly when inertial effects dominate in the base state. Similarly, increasing the angle of inclination enhances the stability of the interface when viscous forces are dominant in the base flow.

ISSN:0031-9171    

DOI:10.1063/1.866917

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The linear stability of two immiscible liquid layers heated from below through a rigid perfectly conducting boundary with a free deformable upper surface and a deformable liquid–liquid interface is examined. Three modes of instability are allowed simultaneously in the analysis: surface tension driven at each of the two interfaces, buoyancy driven because of the presence of adverse density gradients in each liquid, and an interfacial mode (the Rayleigh–Taylor instability), related to the density difference and interfacial tension at the interfaces. For purely surface tension driven convection, the presence of a middle interface that can suppress normal deformations makes the two liquid layers more stable than a single layer of the same total depth. The interaction of the buoyancy and interfacial modes leads to overstability when the physical properties of the two liquids are only slightly different from each other. For certain Rayleigh numbers, both stationary and oscillatory modes display positive growth constants over a certain range of wavenumbers. As the Marangoni number is increased, the coupling between the surface tension and buoyancy mechanisms makes the system more unstable but removes the oscillatory eigenmodes. The addition of trace amounts of insoluble surface active agents at the two interfaces has a very strong stabilizing influence by introducing the expected hydrodynamic rigidity to the surfaces. However, their more interesting effect is their ability to change the nature of the most unstable eigenmode from stationary to oscillatory.

ISSN:0031-9171    

DOI:10.1063/1.867022

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

The effect of dispersion on the stability of miscible displacement in rectilinear porous media is examined. Following a convection–dispersion (CDE) formalism, the base state of Tan and Homsy [Phys. Fluids29, 3549 (1986)] at conditions of unfavorable mobility contrast is analyzed. Emphasis is placed on the dependence of the dispersion coefficient on flow rate (e.g., mechanical dispersion). It is found that such a dependence induces a destabilizing contribution at short wavelengths. This effect, which is in contrast to the stabilization commonly associated with dispersion, is highly pronounced near the onset of the displacement. It is also near this onset that, for a certain condition, the cutoff wavenumber becomes infinitely large. An analytical expression is derived for this condition and the origin and implications of the instability are discussed. It is also suggested that the present CDE formulation may be inadequate in providing stability criteria for a range of unstable flows.

ISSN:0031-9171    

DOI:10.1063/1.866918

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

An averaged two‐fluid model is used to study the motion of a cloud of bubbles. The linearized equations of motion are shown to be a wave equation with both dissipation and dispersion. The fully nonlinear equations are also examined and it is demonstrated that the cutoff frequency of the cloud is equal to the natural frequency of a single bubble. The steady linear response of a periodically driven bubble cloud is then derived. Resonances are seen to arise when the driving frequency is below the cutoff frequency. The inner core of the cloud is shielded by an outer layer when the driving is above the cutoff frequency. The nonlinear dynamics of periodically driven bubble clouds is studied numerically. It is found that the cutoff frequency is crucial in determining whether or not the cloud will behave like a single bubble. Also, under some conditions the cloud is seen to behave like a damped and driven single‐degree‐of‐freedom Hamiltonian system.

ISSN:0031-9171    

DOI:10.1063/1.866919

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

Vortex rings are usually formed by a brief discharge of fluid from an orifice. In previous investigations, the geometry of the vortex generator has varied greatly from one experiment to another, with important consequences for the ensuing flow. The present work categorizes the generating conditions for vortex rings and classifies the conditions under which a given vortex generator produces either an initially laminar ring, which may or may not undergo instability and transition to turbulence, or an initially turbulent ring. A particularly simple vortex generator was devised and measurements were carried out to provide systematic data over a range of the important dimensionless parameters. The results of this survey are used to construct a transition map that reveals a reasonably well defined boundary separating vortex rings that are turbulent upon formation from those that are not. High‐speed cinephotography of the formation and evolution of turbulent vortex rings suggests a possible connection between the generating conditions and the transition to turbulence.

ISSN:0031-9171    

DOI:10.1063/1.866920

出版商:AIP    

年代:1988

数据来源: AIP

摘要:

An analysis is presented of the influence of steady quasiperiodic streamwise vortices on Tollmien–Schlichting (TS) waves. The vortices act as parametric exciters for the TS waves. The present analysis is for the subharmonic resonance in which the spanwise wavenumber of the vortices is twice that of the TS wave. Floquet theory is used to derive an eigenvalue problem for the complex streamwise wavenumber, which is then solved using a shooting technique. The results show that there are two components of the solution, one is stabilized and the other is destabilized by the vortices. For the same flow characteristics, calculations were obtained from the theory which Nayfeh [J. Fluid Mech.107, 441 (1981)] developed using the method of multiple scales. The results obtained from both approaches are in excellent agreement.

ISSN:0031-9171    

DOI:10.1063/1.866921

出版商:AIP    

年代:1988

数据来源: AIP