摘要:

A special theory of rectilinear flow of a polarizable liquid is developed by introducing a polarization parameter into the stress‐rate‐of‐strain relationship of the liquid. The viscosity of the liquid is thus dependent on its state of polarization, and this in turn is determined by the shear rate, the strength and direction of any applied electromagnetic field, and the proximity to an interface. Formulas for the effects of these influences on the apparent viscosity are developed for the case of large shear rates. Comparison of these formulas with three published sets of viscometric data—Couette flow with an electric field, Poiseuille flow with a magnetic field, and Poiseuille flow with interfacial effects—on nematic liquid crystals show excellent agreement of the theory with the data.

ISSN:0031-9171    

DOI:10.1063/1.1694154

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

A theoretical and experimental study is made of the phenomenon. It is shown that for inertial waves, just as for gravity waves in a two‐component liquid, there are discontinuities in the tangential particle velocities at the interface, a fact implying the existence of a vortex sheet for a real liquid. For the particular case wherein the two liquids completely fill the cylinder, other results are obtained that are analogous to those for gravity waves. In particular, if the liquids are nearly of the same density, there are two sets of frequencies, one set characterizing oscillations of the liquid mass as a whole, the other set characterizing very low frequency oscillations at the interface. For the case in which the two liquids have markedly different densities, there are again two sets of frequencies, one set characterizing oscillations of the inner liquid as though the outer liquid were a solid mass, the other set characterizing oscillations of the outer liquid as though the inner liquid were absent. For the general case, physical interpretations are difficult; hence, a table of frequencies versus composition is given.

ISSN:0031-9171    

DOI:10.1063/1.1694178

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

The problem of turbulent spectrum engenders two coupled hierarchies: one originates from the development of stress, leading to a transfer function, and the other from the development of an eddy viscosity. In order to incorporate physical roles among scales, the turbulent velocity fluctuation is decomposed into a series of ranks in the increasing order of randomness, contributing successively to energy or stress, eddy viscosity, relaxation frequency, and higher‐rank frequencies in the memory chain. As a result, the first hierarchy mentioned above becomes closed at the quadrupole correlation. The second hierarchy governs the eddy viscosities of different ranks, related to relaxation frequencies of such ranks, in the form of a memory chain. It is cut off by an implicit viscous mechanism. For zero wind gradient, the spectrum in the inertial subrange recovers the Kolmogoroffk−5/3law with a numerical constant 1.58, in good agreement with experiments. For a strong wind gradient, the spectrum in the production subrange has ak−1law. In the viscous subrange, a law of approach confirming the Heisenbergk−7power spectrum, and a viscous cut‐off in the form of an exponential tail are obtained, insuring the convergence of high‐order spectral moments. The critical wavenumbers characteristic of the production, inertia, viscous subranges, and the cutoff are determined, together with their numerical coefficients.

ISSN:0031-9171    

DOI:10.1063/1.1694158

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

The coupling of the translational and rotational Brownian motion of a particle due to its arbitrary geometric shape is studied. The generalized kinetic equation for the Brownian particle distribution function is derived from the Liouville equation. The correlation functions for random force and torque are calculated from hydrodynamic fluctuation theory. It is found that the coupling effect plays an appreciable role in the diffusivities of asymmetric particles. For the special case of a sphere where there is no coupling, the autocorrelation function for the random torque in rotational Brownian motion is given in closed from. Its asymptotic from at large times is proportional to (time)−5/2. As an example of an asymmetric particle, the diffusivity tensor is worked out for two disks connected by a rigid rod.

ISSN:0031-9171    

DOI:10.1063/1.1694169

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

A study of an asymptotic theory of hyperthermal flow past a blunt object for large Knudsen number is presented. The greatest demands on such a theory are present for flow past two‐dimensional bodies. This is because the large lateral extent of the emitted molecules in free molecular flow gives rise to a singularity in the integrated collision frequency of the incoming free stream molecules. This singularity is removed by accounting for the effects of collisions upon the emitted molecules which augments the usual geometric free molecular decay. The method of matched asymptotic expansions is applied to regions near the body and far from the body (one mean free path and greater). For two‐dimensional bodies, the surprising result is obtained that the first correction to free molecular flow [Kn−1ln(Kn)−1] cannot be obtained without explicitly taking into account the collisional effects on the emitted particles in the far region. For three‐dimensional bodies, although there is no problem in the determination of the leading term (Kn−1), the evaluation of the next order term [Kn−2ln(Kn)−1involves precisely the same difficulties as the leading term for two‐dimensional bodies.

ISSN:0031-9171    

DOI:10.1063/1.1694170

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

A critical evaluation is made of the first iterate of integral iteration of the Boltzmann equation for nearly‐free molecular flow over isolated bodies. It is demonstrated that, for two‐dimensional bodies with diffuse reflection, the first iterate is incapable of describing the correct physics governing nearly‐free molecular flow. Spurious sources and sinks of mass are shown to exist which result in errors of the same order as is being computed.

ISSN:0031-9171    

DOI:10.1063/1.1694171

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

Normal solutions to the Boltzmann equation are investigated using a reordering of the various collision integrals which is expected to be appropriate for binary gas mixtures in which the species masses are very different from each other but the number densities are comparable. The resulting predictions for the temperatures and flow velocities of the species are obtained and discussed. Conservation and relaxation equations are obtained and compared with results of others. Predictions for a uniform mixture indicate that the approach used is a consistent way of treating disparate‐mass binary gases. Finally, it is shown that the results presented here also apply to Lorentzian mixtures.

ISSN:0031-9171    

DOI:10.1063/1.1694172

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

An exact solution is obtained for the suction flow problem. Hydrodynamical theory is shown to be valid only under a certain limit. The neighborhood of the boundary and the neighborhood of infinity are shown to always be kinetic layers. The exact solution is then used for a general determination of slip coefficients to be used as perturbation boundary conditions in the Chapman‐Enskog‐Hilbert method. One explicit result of this, is the resolution of the problem of slip velocity in a pressure gradient field.

ISSN:0031-9171    

DOI:10.1063/1.1694173

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

Shock structure during ionization of a hydrogen‐helium mixture has been followed using hydrogen line and continuum emission measurements. A reaction scheme is proposed which includes hydrogen dissociation and a two‐step excitation‐ionization mechanism for hydrogen ionization by atom‐atom and atom‐electron collisions. Agreement has been achieved between numerical calculations and measurements of emission intensity as a function of time for shock velocities from 13 to 20 km/sec in a 0.208 H2‐0.792 He mixture. The electron temperature was found to be significantly different from the heavy particle temperature during much of the ionization process. Similar time histories forH&bgr;and continuum emission indicate upper level populations of hydrogen in equilibrium with the electron concentration during the relaxation process. The expression for the rate constant for excitation of hydrogen by atom‐atom collisions that best fit the data waskAA = 4.0×10−17 (8kT/&pgr;&mgr;)1/2 exp (−10/kT) cm3 sec−1, where it has been assumed that the excitation cross section is the same for hydrogen and helium collision partners. The electron‐atom excitation rate constant,k8 = 7.5 × 10−16 (8kTe/&pgr;&mgr;e)1/2 exp ( −10/kTe), determined from this investigation, was in agreement with recent electron beam cross‐section measurements.

ISSN:0031-9171    

DOI:10.1063/1.1694174

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

A continuum electrostatic probe theory is developed for a slightly ionized, collision‐dominated plasma in the presence of a uniform magnetic field. The governing equations are nonlinear and coupled. A quasilinearization technique is applied to solve the equations numerically using finite difference approximations, in the case of spherical probes larger than a Debye length, the magnetic field being weak. When the probe size is not very large or the probe potential is small, the detailed analysis of the sheath is not necessary. But when the probe potential is large, the sheath needs a separate treatment. The sheath equations are essentially one‐dimensional and the magnetic field parameters do not appear explicitly. In the absence of an analytic solution for either the sheath or the main region, both solutions are matched numerically in an overlap region. The effect of magnetic field on the nature of the distribution of the charged particles and the potential in space and on the probe surface is investigated in detail. The phenomenon of “potential overshoot” in the case of a probe biased near plasma potential is clearly revealed. A few representative current‐voltage characteristics at various magnetic fields are drawn. A systematic procedure for the interpretation of the probe characteristics is developed.

ISSN:0031-9171    

DOI:10.1063/1.1694175

出版商:AIP    

年代:1973

数据来源: AIP