摘要:

In this Letter, experimental evidence of shocklets in a counterflow Mach 2 shear layer is presented. Schlieren photography reveals shock waves emanating from the turbulent structure; they are normal in the vicinity of the structure and weaken into Mach waves a short distance away from the shear layer. The slope of the Mach waves suggests that the turbulent structures are nonstationary, even though the shear layer is symmetric. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868621

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

In this paper an experimental and theoretical study of the deformation of a spherical liquid droplet colliding with a flat surface is presented. The theoretical model accounts for the presence of inertia, viscous, gravitation, surface tension, and wetting effects, including the phenomenon of contact‐angle hysteresis. Experiments with impingement surfaces of different wettability were performed. The study showed that the maximum splat radius decreased as the value of the advancing contact angle increased. The effect of impact velocity on droplet spreading was more pronounced when the wetting was limited. The experimental results were compared to the numerical predictions in terms of droplet deformation, splat radius, and splat height. The theoretical model predicted well the deformation of the impacting droplet, not only in the spreading phase, but also during recoiling and oscillation. The wettability of the substrate upon which the droplet impinges was found to affect significantly all phases of the spreading process, including the formation and development of a ring structure around the splat. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868622

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

A two‐dimensional volatile liquid droplet on a uniformly heated horizontal surface is considered. Lubrication theory is used to describe the effects of capillarity, thermocapillarity, vapor recoil, viscous spreading, contact‐angle hysteresis, and mass loss on the behavior of the droplet. A new contact‐line condition based on mass balance is formulated and used, which represents a leading‐order superposition of spreading and evaporative effects. Evolution equations for steady and unsteady droplet profiles are found and solved for small and large capillary numbers. In the steady evaporation case, the steady contact angle, which represents a balance between viscous spreading effects and evaporative effects, is larger than the advancing contact angle. This new angle is also observed over much of the droplet lifetime during unsteady evaporation. Further, in the unsteady case, effects which tend to decrease (increase) the contact angle promote (delay) evaporation. In the ‘‘large’’ capillary number limit, matched asymptotics are used to describe the droplet profile; away from the contact line the shape is determined by initial conditions and bulk mass loss, while near the contact‐line surface curvature and slip are important. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868623

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Simple scaling analysis of temperature‐ and stress‐dependent viscosity convection with free‐slip boundaries suggests three convective regimes: the small viscosity contrast regime which is similar to convection in a fluid whose viscosity does not depend on temperature, the transitional regime characterized by self‐controlled dynamics of the cold boundary layer and the asymptotic regime in which the cold boundary becomes stagnant and convection involves only the hottest part of the lid determined by a rheological temperature scale. The first two regimes are usually observed in numerical experiments. The last regime is similar to strongly temperature‐dependent viscosity convection with rigid boundaries studied in laboratory experiments. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868624

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The steady transport of Brownian particles convected by a periodic flow field is studied by following the motion of a randomly chosen tagged particle in an otherwise uniform solute concentration field. A nonlocal, Fickian constitutive relation is derived, in which the steady mass flux of Brownian particles equals a convolution integral of the concentration gradient times a (tensorial) diffusion functionDL(R). In turn, the diffusion function is uniquely determined via thenth diffusivities, which are determined analytically in terms of thenth cumulants of the probability distribution by exploiting the translational symmetry of the velocity field. The Lagrangian, long‐time self‐diffusion functionDL(R) is shown to be equal to the symmetric part of the Eulerian, gradient diffusion functionDE(R). Since the latter characterizes the dissipative steady‐state mass transport, whileDL(R) describes the fluctuations of the concentration field about its uniform equilibrium value, the equality betweenDE(R) andDL(R) can be seen as an aspect of the fluctuation–dissipation theorem. Finally, the present results are applied to study the transport of solute particles immersed in a fluid flowing in rectilinear pipes and through periodic fixed beds of spheres at low Pe´clet number. In the first case, the first sixnth diffusivities are determined; in the second, the first two diffusivities are calculated, showing that the enhancement to the second diffusivity due to convection is eight times larger in the direction parallel to the fluid flow than in the transversal direction. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868625

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The Stokes drag coefficients for conglomerates of between two and 167 spheres are obtained from a recently developed scheme for numerical calculations of hydrodynamic interactions [J. Chem. Phys.100, 3780 (1994)]. Experimental data for these conglomerates were provided by Lasso and Weidmann [Phys. Fluids29, 3921 (1986)]. The numerical results and the experimental data agree very well. It is shown that in numerical calculations of hydrodynamic interactions, all long‐range contributions must be included exactly. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868626

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Buoyancy driven convection induced by a fluctuating acceleration field is studied in a two dimensional square cavity. This is a simplified model of, for example, fluid flow in a directional solidification cell subject to external accelerations, such as those encountered in a typical microgravity environment (g‐jitter). The effect of both deterministic and stochastic acceleration modulations normal to the initial density gradient are considered. In the latter case, the acceleration field is modeled by narrow band noise defined by a characteristic frequency &OHgr;, a correlation time &tgr;, and an intensityG2. If the fluid is quiescent att=0 when the acceleration field is initiated, the ensemble average of the vorticity at the center of the cavity remains zero for all times. The mean squared vorticity ⟨&xgr;2⟩, however, is seen to exhibit two distinct regimes: Fort≪&tgr;, ⟨&xgr;2⟩ oscillates in time with frequency &OHgr;. Fort≫&tgr;, ⟨&xgr;2⟩ grows linearly in time with an amplitude equal to R2Pr/(1+(&OHgr;&tgr;))2, where R is a new dimensionless number which reduces to the Rayleigh number in the case of a constant gravity, and Pr is Prandtl number. At yet later times, viscous dissipation at the walls of the cavity leads to saturation, with ⟨&xgr;2⟩sat={(Pr &tgr;+1)R2/[(Pr &tgr;+1)2+&OHgr;2&tgr;2]}. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868627

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Linear stability of the rectangular cell flow: &PSgr;=cos kx cos y(0<k<1), is studied, both numerically and analytically. Owing to its spatial periodicity, the disturbances are characterized by the Floquet exponents (&agr;,&bgr;). Based on numerical results, it is found that two types of the critical modes with vanishingly small exponents exist. One type (large‐scalemode) has an almost uniform spatial structure. The other type (periodicmode) has a structure with the same periodicity as the main flow. The large‐scale mode gives the critical Reynolds number in a more isotropic case (i.e.,k≳0.6), while the periodic mode does so in the less isotropic case (i.e.,k<0.6). Asymptotic expansions from (&agr;,&bgr;)=(0,0) agree with the numerical results. Using the periodic mode, a possible explanation is given for the merging process of a pair of counter‐rotating vortices observed in the experiments of a linear array of vortices by Tabelingetal. [J. Fluid Mech.213, 511 (1990)]. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868628

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The effect of an insoluble, elastic surface film on the drift velocity of capillary–gravity waves is studied theoretically on the basis of a Lagrangian description of motion. There is no forcing from the atmosphere, and the wave amplitude is taken to attenuate in time. Defining a nondimensional parameter &agr;, which combines film elasticity, fluid viscosity, and wave frequency, maximum damping of the linear waves occurs when &agr;=1 (the Marangoni effect). In this case the frequency of capillary–gravity waves nearly coincides with that of elastic film waves. The nonlinear drift velocity is obtained for general values of &agr;. In particular, it is found that the absolute maximum of the transient drift current is locatedbelowthe surface when &agr;≳2/3. At the surface, maximum drift velocity (in time domain) occurs for values of &agr; that are somewhat less than one. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868629

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Convection in the form of thermal Rossby waves is studied in the low Prandtl number regime. An anomalous Eckhaus instability is found in the range between 10−3and 10−2for a moderately strong Coriolis parameter, where no supercritical stable solution can exist near the onset. Numerical results for higher Rayleigh numbers show detachment of the stability limit from the neutral curve, shrinkage and distortion of the stable region, and the onset of a second sideband mode of instability, which is characterized by a maximum growth rate at a finite modulation parameter. The new mode is more pronounced at higher Rayleigh numbers, and appears to destabilize all spatially periodic waves for the whole supercritical band for all Prandtl numbers below the anomalous range. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868764

出版商:AIP    

年代:1995

数据来源: AIP