摘要:

Viscous fingering patterns of aqueous hydroxypropyl methyl cellulose (HPMC) solutions pushed by air in the Hele–Shaw cell were observed as a function of isopropyl alcohol content under a constant pressure of 15 cm H2O. A morphological transition from side branching patterns to tip splitting ones with increasing isopropyl alcohol content, accompanied with a decrease in surface tension and an increase in viscosity is found. The observed morphology transition was correlated with the dimension of the fingering pattern, as well as the average tip velocity in the fingering. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868643

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

In the present paper, experiments are reported for the measurement of the complete meniscus profile in asymmetric forward roll coating. A thin laser sheet technique is used to recover accurately the shape and position of the interface for an extensive database of operating conditions. Knowledge of the interface profile and position is then used to measure the total flow rate and its distribution on each cylinder. The results provide for the first time validation of numerical predictions for the extended shape of the meniscus. Comparison with existing theoretical and numerical predictions validates both these approaches, but reveals the need to model the whole flow region, including gravity, instead of restricting to the region downstream of the nip separating the rotating cylinders. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868644

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The three‐dimensional evolution of the viscous fingering instability has been visualized directly with magnetic resonance imaging (MRI). Miscible displacement of thin solute bands by aqueous solvent was investigated in packed beds of 30 &mgr;m chromatographic particles. Fingering behavior into samples of glycerol and a protein, bovine serum albumin (BSA), with viscosity ratios ranging from 1 to approximately 4, were compared. The three‐dimensional morphology and dynamics of fingers were monitored to approximately millimeter spatial resolution using MRI. Linear and nonlinear fingering behavior were observed. Permeability heterogeneities with length scales on the order of the finger wavelength induced complex three‐dimensional fingering patterns. Sample and column boundary effects on fingering dynamics were also noted. The differences in fingering behavior observed between albumin and glycerol samples are consistent with the wavelength predictions of linear stability analysis and the large differences in molecular diffusivity. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868645

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Tracer diffusion in a steady shear flow state is analyzed. A kinetic model incorporating a temperature dependence in the collision frequencies is used. This allows for the consideration of a general repulsive intermolecular interaction. A perturbative scheme is applied to get the shear rate dependence of the tracer diffusion tensor in terms of the mass ratio, the force constants ratio, and a parameter characterizing the interaction potential considered. In addition, the heat flux arising from the concentration gradient of the tracer species is also evaluated. The results are illustrated for the two extreme cases of Maxwell molecules and hard spheres. ©1995 American Institute of Physics. 

ISSN:1070-6631    

DOI:10.1063/1.868646

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

A single, non‐Brownian fiber suspended in a viscous, Newtonian fluid undergoing simple shear flow rotates in one of a set of closed orbits known as Jeffery orbits. In a fiber suspension, the hydrodynamic interactions among the fibers determine the distribution of fibers among these orbits. The hydrodynamic interactions in dilute and semidilute suspensions have been studied using slender‐body theory. Hydrodynamic, orientational diffusivities were obtained from an ensemble average of the fiber–fiber interactions. The steady‐state fiber orientation distribution is controlled by the anisotropy and orientation dependence of the diffusivities. The steady‐state and transient fiber orientation distributions are derived using a perturbation analysis for weak hydrodynamic orientational diffusion that is an extension of the work of Leal and Hinch [J. Fluid Mech.46, 685 (1972)] for weak, isotropic, rotary Brownian motion. In the dilute regime, the steady‐state experimental distributions of Anczurowski and Mason [J. Colloid Interface Science23, 522 (1967)] do not agree with the theoretical predictions. An explanation for these discrepancies accompanied with new experimental results is presented in this work. The theoretical predictions for the steady‐state orientation distribution, and the temporal orbit constant correlation function in the semidilute regime are in good agreement with the experimental results of Stoveretal. [J. Fluid Mech.238, 277 (1992)]. The correlation time for the fiber orientation is approximately inversely proportional to fiber concentration in both the dilute and semidilute regimes. ©1995 American Institute of Physics. 

ISSN:1070-6631    

DOI:10.1063/1.868647

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The question whether one‐dimensional granular systems can be described by hydrodynamic equations is the main theme of the present work. Numerical simulations are used to create a database with which theory is compared. The system investigated in the numerical work is that of a one‐dimensional collection of point particles colliding inelastically. The dependence of the dynamical properties on both the degree of inelasticity and the number of particles is investigated. A hydrodynamic theory which describes the large‐scale motion of such systems has been developed. It is shown that the standard set of hydrodynamic fields (density, velocity, and granular temperature) is insufficient for this purpose and that an additional hydrodynamic field corresponding to the third moment of the fluctuating velocity field must be added to that set. The results of a linear stability analysis of the derived hydrodynamic equations are in a close agreement with those of the numerical simulations. The question of the effects of velocity correlations on the hydrodynamics is addressed as well. It is shown that these correlations, though not negligible, do not affect the hydrodynamic equations. The form of the single particle initial distribution function is shown to slightly affect the form of the hydrodynamic equations for transient times. Except for this minor effect the hydrodynamic equations possess a universal form. Possible implications for higher dimensional systems are mentioned. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868648

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Two‐dimensional unsteady separated flow past a semi‐infinite plate is considered. The rolling up of the separated shear layer is modeled by a point vortex, whose time‐dependent circulation is predicted by an unsteady Kutta condition. The equation of motion for the starting vortex is derived and solved in closed form for any free‐stream condition. A time‐dependent scaling that captures the universality of the flow is proposed. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868765

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Two radially spreading adjacent streams, which differ in their radial velocities and thus form a radially spreading shear‐layer flow, are considered here. The theory presented by the authors for sprays suspended inunidirectional[Katoshevski and Tambour, Phys. Fluids A5, 3085 (1993)] shear layers is extended here forradiallyspreadingshear layer flows. The behavior of a multisize (polydisperse) evaporating spray, which is suspended in one of the streams, is studied. The spray spreads in the lateral direction towards the other coflowing stream, resulting in lateral changes in spray densities and in local droplet size distributions across the shear layer. These effects are analyzed here via similarity solutions of the governing equations. A comparison between the behavior of the multisize sprays and their vapors inradiallyspreadingversusunidirectionalshear‐layer flows is also presented and discussed here. The dynamics of the radially spreading spray is essentially different from that of the unidirectional spray. In the radial case, streamlines of the host‐gas flow become more crowded with radial distance, and thus, it is shown here how lateral evolution in size histograms and lateral Sauter mean diameter (SMD) profiles are affected by this feature of the radially spreading flow. The effects of initial drop‐size histograms on lateral distributions of: droplet SMD, overall spray densities, and vapor are also studied here for three basic initial drop‐size distributions: monodisperse, bimodal, and polydisperse. It is shown how the behavior exhibited by polydisperse (and bimodal) sprays differs intrinsically from the behavior of monodisperse sprays. For example, for sprays which are initially monodisperse the lateral profile of the spray’s SMD across the shear layer always decreases, whereas for polydisperse or bimodal sprays it may increase or assume an ‘‘S’’ shaped curve. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868649

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Hyperdiffusion, a simple linear eddy diffusivity scheme, is commonly used in atmospheric and oceanic simulations because it increases the range of inertially behaving spatial scales for a given model resolution. Compared with molecular diffusion (which is utterly negligible in the atmosphere and oceans), hyperdiffusion more sharply confines the dissipation to the smallest scales of the numerical model. But is this all that hyperdiffusion does? In this paper, the inelastic interaction of two distributed vortices of unequal size is examined. Contour surgery (CS) simulations are compared with pseudospectral (PS) simulations employing hyperdiffusion or molecular diffusion. The example illustrates what is believed to be the most fundamental characteristic of two‐dimensional (2‐D) (and layerwise‐2‐D) vortex dynamics, namely, the formation of exceedingly high vorticity gradients. There is an excellent agreement between the hyperdiffusive PS and CS calculations at early times (i.e., for a few vortex rotation periods). Thereafter, significant discrepancies develop, beginning abruptly from the time when vorticity‐gradient intensification is arrested by diffusion. A rapid inward erosion of the smaller of the two vortices then takes place. This erosion takes place under the joint action of (hyper) diffusion and stripping (the peeling of the vortex periphery by the external flow). With hyperdiffusion, the erosion is accompanied by a serious numerical artifact: a climb in the peak vorticity by 30% in this example. Eventually, the erosion reaches the vortex center and the vortex is sheared into a filament. In the CS calculation, there is no erosion, no climb in peak vorticity, and the vortex appears to last indefinitely.In the PS calculations, the viscosity or hyperdiffusion is adjusted according to the resolution to give the largest possible inertial range while ensuring numerical stability. It is found that vortices that are spanned by fewer than 10–20 grid points are eroded away in only a few vortex rotation periods (a time scale that is very much shorter than one would estimate from pure viscous decay). These findings bring into question the results of many 2‐ turbulence simulations using hyperdiffusion, for hyperdiffusion simulates neither inviscid dynamics nor molecular‐diffusive dynamics. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868650

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Axial velocity deficit is a source of instability in vortices that may otherwise be stable. Temporal large‐eddy simulation is performed to study the response of vortices with axial velocity deficits to random and controlled disturbances at high Reynolds numbers. Theqvortex [Batchelor, J. Fluid Mech.20, 321 (1964)] is used as a model of such vortices. When the vortex is linearly unstable, the disturbances grow and result in the appearance of large‐scale helical sheets of vorticity. Later, these large‐scale helical structures break up into small‐scale filaments. Associated with the formation of the large‐scale structures is a redistribution of both angular and axial momentum between the core and the surroundings. The redistribution weakens the axial velocity deficit in the core while strengthens the rigid‐body‐like rotation of the core. The emerging mean velocity profiles drive the vortex core to a stable configuration. The vortex eventually returns to a laminar state, with an insignificant decay in the tangential velocity, but with a much weakened axial velocity deficit. A direct numerical simulation obtained at a lower Reynolds number confirms the above conclusions. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868582

出版商:AIP    

年代:1995

数据来源: AIP