摘要:

A new frequency selection criterion valid in the fully nonlinear regime is presented for extended oscillating states in spatially developing media. The spatial structure and frequency of these modes are dominated by the existence of a sharp front connecting linear to nonlinear regions. A new type of fully nonlinear time harmonic solutions calledsteep global modesis identified in the context of the supercritical complex Ginzburg–Landau equation with slowly spatially varying coefficients. A similar formulation is likely to be applicable to fully nonlinear synchronized global oscillations in spatially developing free shear flows. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869784

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

An analytical model for predicting the universal time scale for formation of vortex rings generated through impulsively started jets is considered. The model is based on two assumptions, namely the validity of the slug model in simulating the discharge process of the fluid out of the cylinder and the approximation of the vortex at the pinch off moment by a vortex in the Norbury family. The nondimensional stroke lengthL/D(referred to as “formation number,” following Gharib &etal; [J. Fluid Mech.360, 121 (1998)]) predicted by the model satisfactorily matches the experimental observation of Gharib &etal; The model introduces two nondimensional parameters that govern the limiting formation number: nondimensional energyEndand circulation&Ggr;nd.The predicted value ofEndmatches very well with the experimental data. It is also predicted that there is a limiting value for the nondimensional circulation in the range1.77≲&Ggr;nd≲2.07.©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869785

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

An infinite, conductive cylindrical column of electrolyte lying inside another electrolyte flattens when it is submitted to a transverse continuous electric field. This “ribbon” effect can be canceled by a second oscillatory field whose direction is perpendicular to both the column axis and to the first electric field. The linear stability of the equilibrium with respect to elliptic perturbations of the cross section is studied, and it is shown that the stability of the circular shape depends on the sign of a discriminating function of the conductivity and permittivity ratios. Possible applications of the results to continuous flow electrophoresis are discussed: Even for unstable situations the growth rate of disturbances is reduced by the application of a second field so that we expect the efficiency of the separation to be improved. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869763

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

Experiments on flow stability and pattern formation in Couette flow between two cylinders with highly elastic polymer solutions are reported. It is found that the flow instabilities are determined by the elastic Deborah number, De, and the polymer concentration only, while the Reynolds number becomes completely irrelevant. A mechanism of such “purely elastic” instability was suggested a few years ago by Larson, Shaqfeh, and Muller [J. Fluid Mech.218, 573 (1990)], referred to as LMS. It is based on the Oldroyd-B rheological model and implies a certain functional relation between De at the instability threshold and the polymer contribution to the solution viscosity,&eegr;p/&eegr;,that depends on the polymer concentration. The elastic force driving the instability arises when perturbative elongational flow in radial direction is coupled to the strong primary azimuthal shear. This force is provided by the “hoop stress” that develops due to stretching of the polymer molecules along the curved streamlines. It is found experimentally that the elastic instability leads to a strongly nonlinear flow transition. Therefore, the linear consideration by LMS is expanded to include finite amplitude velocity perturbations. It is shown that the nature of the elastic force implies major asymmetry between inflow and outflow in finite amplitude secondary flows. This special feature is indeed exhibited by the experimentally observed flow patterns. For one of the flow patterns it is also shown that the suggested elastic force should be quite efficient in driving it, which is important evidence for the validity of the mechanism proposed by LMS. Further, the predicted relation between De and&eegr;p/&eegr;is tested. At fixed&eegr;p/&eegr;the elastic instability is found to occur at constant Deborah number in a broad range of the solution relaxation times in full agreement with the theoretical prediction. The experimentally found dependence of the Deborah number on&eegr;p/&eegr;also agrees with the theoretical prediction rather well if a proper correction for the shear thinning is made. This provides further support to the proposed instability mechanism. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869764

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

Viscous fingering phenomena in a circular geometry are studied for a magnetic fluid submitted to a perpendicular magnetic field. Air is injected at the center of a Hele-Shaw cell filled with a viscous magnetic fluid. The instability of the interface between the air and the magnetic fluid is favored by the presence of a magnetic field. More precisely, the threshold of the instability is magnetic field dependent. The patterns obtained for high values of the magnetic field with a low injection rate are similar to those obtained in the absence of an external field and at high flow rates. We also give a linear analysis for the stability of radial flow under the influence of a magnetic field. This calculation provides us with an understanding of the magnetic field effect. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869765

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

The stability of an axisymmetric liquid bridge between unequal circular disks in an axial gravity field is examined for all possible values of the liquid volume and disk separation. The parameter defining the disk inequality isK, the ratio between the radii of the smaller and larger disks. Both axisymmetric and nonaxisymmetric perturbations are considered. The parameter space chosen to delimit the stability regions is the&Lgr;-Vplane. Here, &Lgr; is the slenderness (ratio of the disk separation to the mean diameter,2r0,of the two support disks), andVis the relative volume (ratio of the actual liquid volume to the volume of a cylinder with a radius equal tor0). Wide ranges of the Bond number and the ratioKare considered. Emphasis is given to previously unexplored parts of the stability boundaries. In particular, we examine the maximum volume stability limit for bridges of arbitrary &Lgr; and the minimum volume stability limit for small &Lgr; bridges. The maximum volume stability limit was found to have two distinct properties: large values of the critical relative volume at small &Lgr;, and the possibility that stability is lost to axisymmetric perturbations at small values ofK. For a set ofK, the maximum Bond number beyond which stability of the bridge is no longer possible for any combination ofVand &Lgr; is determined. In addition, the maximum value of the actual liquid volume of a stable bridge that can be held between given disks for all possible disk separations was examined for fixed Bond number. It is found that this volume decreases asKdecreases and (depending on the sign of the Bond number) tends to the critical volume of a sessile or pendant drop attached to the larger disk. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869783

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

In this paper numerical simulations of the irrotational fluid flow associated with the entry of circular disks of a given mass into a semi-infinite fluid domain in the limits of very low to moderate Froude numbers are reported. This work is motivated by an experimental study performed by Glasheen and McMahon who investigated the low-Froude-number water entry of circular disks and found a linear relationship between the cavity seal depth and the Froude number and also showed that a single value of a modified drag coefficient is sufficient to predict the drag force on the disk. The numerical calculations performed in this paper confirm these experimental findings for steady cavity regimes and identify the ranges of Froude number and dimensionless mass values for which these results hold. Excellent agreement between the numerical computations and analytical velocity predictions, as well as the experimental cavity seal depth measurements, are obtained although the agreement between the measured and the computed drag coefficient values is not as good. The cavity seal depth and the drag coefficient are also found to depend on the disk mass and the numerical results in this paper show that for any disk of dimensionless massMthere exists a value of the Froude number for which the cavity dynamics are steady. Also, a very low-Froude-number regime in which gravitational forces are dominant and for which the cavity dynamics are qualitatively different than for low-to-moderate-Froude-number cases is also numerically explored in this paper. Finally, a bifurcation in the cavity seal mechanism from deep seal to surface seal was found at a Froude numberF=105.©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869787

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

The unsteady flow of an annular and axisymmetric film under gravity is examined. This moving boundary problem is solved by mapping the inner and the outer interface of the film in the radial direction onto fixed ones and by transforming the governing equations accordingly. The ratio of the film thickness to its inner radius at the exit of the die is small in relevant processes with polymer melts. This ratio, &egr;, is used as the small parameter in a perturbation expansion of the general Navier–Stokes equations. Forces applied on the film include gravity, surface tension, inertia, and viscous forces. Their ratios give rise to three dimensionless numbers, St, Ca, and Re. When these dimensionless numbers are up to order one, the base state is quite deformed and it is calculated numerically by simultaneously solving three nonlinear partial differential equations in time and the axial direction. Intuitively it is expected that when the dimensionless numbers are small the base state in the perturbation scheme is a uniformly falling film. This is confirmed by analysis and the two next orders in the perturbation scheme are calculated analytically. In both cases, it was found that increasing the St number (i) accelerates the downward motion of the film, (ii) deflects its inner and outer surfaces towards its axis of symmetry, and (iii) decreases its thickness around the middle of its length. The latter effect may lead to breakup of the film in two parts. It was also found that increasing the Ca number deflects these two interfaces towards its axis of symmetry and increases its thickness monotonically with time and the axial distance. Increasing the Re number from zero, but to not very large values, generally decelerates the film and decreases its deflection from the vertical. Given typical fluid properties and process conditions the St number is up toO(&egr;0),i.e., much larger than the other two dimensionless numbers, and affects the film shape more significantly. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869766

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

The influence of the spacecraft’s rotation on the convection in a nonuniformly heated fluid under microgravity conditions has been studied. This influence is determined by action of the buoyancy force generated by the resultant microacceleration vector and the inertia force related to variations in the angular rotational velocity of the spacecraft. It is shown that the solenoidal part of the resulting rotational force acting upon the nonuniformly heated fluid strongly depends on the angle between the temperature gradient at some point in the fluid and the radius vector of this point relative to the spacecraft’s centroid. To minimize the influence of the spacecraft’s rotation, it is necessary to make this angle close to zero. The thermal convection which could have arisen in a rectangular box with rigid walls under rotation of the Space Shuttle orbiter has been simulated numerically. It is shown that the intensity of this kind of convection may be rather appreciable. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869767

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

The influence of impulsive spin-up on Rayleigh–Be´nard convection in a cylindrical cell with radius-to-height ratio&Ggr;=0.5is investigated. Velocity and temperature fields in the thin layer adjacent to the top of the cell are measured by means of particle image velocimetry and thermochromic liquid crystal visualization. The cell, initially in steady nonrotating convection, is rapidly accelerated to steady rotation about its vertical axis with dimensionless rotation rates4×103⩽&OHgr;⩽8×104.Rayleigh numbers Ra vary from5×107to5×108.In a large part of this domain of the parameter space, axisymmetric structures appear near the top of the cell. In most cases, a single ring forms with a radius close to 3/4 of the radius of the cell. The same experiment without heating produces typical Ekman spin-up devoid of ring structures. The ring is characterized by a local decrease in temperature and azimuthal velocity. As the flow evolves, an azimuthal velocity gradient forming across the ring causes shear instability and leads to the emergence of Kelvin–Helmholz vortices.

ISSN:1070-6631    

DOI:10.1063/1.869768

出版商:AIP    

年代:1998

数据来源: AIP