摘要:

The theory of transport phenomena in a gas is considered from a statistical mechanical viewpoint. The formalism is based on the Liouville equation for the time evolution of an ensemble of systems and the Bogoliubov‐Born‐Green‐Kirkwood‐Yvon equations which are integrals of the Liouville equation. The BBGKY hierarchy is truncated by a factorization principle which is a generalization of the molecular chaos assumption. For purely repulsive potentials, the set of equations obtained by truncating atf(3)is shown to give rise to the three‐body interaction term obtained by Hollinger and Curtiss and by a different argument by Bogoliubov. The two coupled equations obtained by truncating the BBGKY hierarchy atf(3)are considered in detail. An approximation to these equations leads to a Boltzmann equation which is a soft potential generalization of the Enskog dense gas equation for rigid spheres. This Boltzmann equation includes both collisional transfer and three body collision effects.

ISSN:0031-9171    

DOI:10.1063/1.1711097

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

A limiting case of the interaction between particles in a viscous fluid is described by a linear form of Boltzmann's equation. The distribution function,f(v), is found for small particles falling under the action of gravity and viscous drag, and colliding with large particles. Several approximate procedures for computingf(v) and the connection with flows of gases containing solid particles are examined.

ISSN:0031-9171    

DOI:10.1063/1.1711098

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

Measurements were made of the heat transfer to the stagnation point of a cylinder in partially ionized monatomic gases, and the effect of free electrons on the total gas thermal conductivity was assessed. Shock‐heated argon and xenon were used as the test media, thus bypassing the dissociation phase present in diatomic gas heat transfer, and passing directly from the ideal gas to the ionized gas. Comparison of the experimental data is made with two real‐gas estimates, the first including the effects of ionization only on the thermodynamic properties involved, and a second including the effects of ionization on both the thermodynamic and transport properties. The experimental results are in substantial agreement with the latter prediction where equilibrium is attained, and confirm the prediction of an increased gas thermal conductivity due to the presence of free electrons. An estimate of the contribution of radiative heating is made both numerically and experimentally, and found to be less than 10% of the aerodynamic heating for the test conditions. The test gas is shown to be in thermochemical equilibrium under those conditions where ionization is significant.

ISSN:0031-9171    

DOI:10.1063/1.1711099

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

Through a generalization of Coleman and Noll's discussion of steady extension we find a new class of flows which are dynamically possible in every incompressible simple fluid. An interesting aspect of this treat is that the two material functions which describe the behavior of the fluid are not the same as those found by Coleman and Noll, although they do become identical in the limit of steady‐state behavior.

ISSN:0031-9171    

DOI:10.1063/1.1711100

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

The stability of a non‐Newtonian inelastic viscous liquid moving between two rotating coaxial circular cylinders was considered by Graebel. Recently Thomas and Walters have considered the same problem for an elasticoviscous liquid with memory, which they call liquid of the typeB′. In this note this problem is considered for an incompressible second‐order liquid. For the particular case when the outer cylinder is at rest a particularly simple solution is given which brings out the dependence of the critical Taylor number on the viscoelastic parameter quite distinctly. It is also shown that for particular values of the viscoelastic parameters one obtains the equations considered by Graebel and Thomas and Walters.

ISSN:0031-9171    

DOI:10.1063/1.1711101

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

A turbulent boundary layer is assimilated to a laminar layer of large and variable viscosity. This viscosity represents the eddy viscosity. A stability analysis is performed for small perturbations by the use of a digital computer. It is found that a typical turbulent layer is stable, even if the eddy viscosity vanishes at the wall. However, if the mean velocity profile has a weak inflection near the outer edge, instabilities do occur. Various observations of the intermittent part of the layer suggest the existence of such inflections and lead to acceptable values of the wavelengths and phase velocities. It is also found that the laminar sublayer has a negligible effect on this type of oscillation.

ISSN:0031-9171    

DOI:10.1063/1.1711102

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

A phenomenological treatment is given for the fluid dynamics and thermodynamics of strongly polarizable magnetic fluid continua in the presence of nonuniform magnetic fields. Examples of the fluids treated here have only recently been synthesized in the laboratory. It is found that vorticity may be generated by thermomagnetic interaction even in the absence of viscosity and this leads to the development of augmented Bernoulli relationships. An illustration of a free‐surface problem of static equilibrium is confirmed by experiment and information is obtained regarding a fluid's magnetic susceptibility. Another illustration elucidates the mechanism of an energy conversion technique. Finally, an analytical solution is found for the problem of source flow with heat addition in order to display the thermomagnetic and magnetomechanical effects attendant to simultaneous heat addition and fluid motion in the presence of a magnetic field.

ISSN:0031-9171    

DOI:10.1063/1.1711103

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

The response of a homogeneous plasma to the sudden application of a strong, uniform electric field,E0, is studied by solving, self‐consistently, the coupled equations for the one‐ and two‐particle distribution functions. The field is assumed to be large compared to that which produces a ``runaway'' current, so that particle‐particle collisions have a negligible effect on the current flow, and particle‐wave interactions dominate. The principal approximations are the neglect of intrinsic three‐particle correlations (i.e., linearization in fluctuations) and the use of an adiabatic ansatz for the time dependence of the fluctuations. For the case of unequal temperatures,Te≫Ti, two different methods of solution are employed: a moment approximation, in which the distribution functions are assumed Maxwellian, with mean velocity and width determined self‐consistently; and a more exact treatment in which the distribution function for velocities parallel to the applied field is determined by direct numerical solution of the kinetic equation using on‐line computational techniques. In both cases, it is found that the unstable ion acoustic waves grow from the thermal fluctuation level to a magnitude sufficient to cause a sharp and sudden decrease in the current. Examination of the kinetic equation shows this drop to be ascribable to the dynamic friction associated with the unstable waves. Although waves propagating parallel to the applied field are most important at early times, those propagating at finite angles soon become dominant; this casts some doubt on one‐dimensional approximations to this problem. The limitation of the exponential growth of unstable waves resulting from the non‐linear (or quasilinear) effects is clearly evident, notwithstanding the presence of the external driving force,E0.

ISSN:0031-9171    

DOI:10.1063/1.1711104

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

A kinetic theory of a fully ionized plasma with the transverse electromagnetic field expanded in vacuum normal modes is developed. The Bogoliubov, Born, Green, Kirkwood, and Yvon hierarchy of equations is terminated using only an expansion in the plasma discreteness parameterse, m, and 1/n. The renormalization of the vacuum field on a fast time scale is discussed for an infinite homogeneous plasma, and a superposition principle for dressed test particles is derived.

ISSN:0031-9171    

DOI:10.1063/1.1711105

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

A detailed examination is made of a large‐amplitude beam‐excited electron plasma wave, and of the acceleration to high energies of favored electrons by the electric field of this wave. In laboratory experiments x rays with energies greater than 100 keV have been observed coming from a plasma in a magnetic field, typically 2000 G, penetrated by an electron beam, typically one ampere at 10 keV. To account for the impressive energies reached by the electrons producing these x rays, an acceleration process is invoked in which individual steps of coherent cyclotron acceleration are summed stochastically. The increase in the perpendicular energy of the favored electrons enhances their magnetic mirror confinement and enables the acceleration process to occur within a small volume of plasma. The overstable mode under consideration is the double‐hump‐excited electrostatic wave in a magnetic field, withkandEnot quite parallel toB0. The wave frequency is close to the electron plasma frequency, the phase velocity is close to the beam velocity. It is electrons, often with low parallel energy, which feel the wave at their own cyclotron frequency (or a harmonic thereof) which are favored in the acceleration process. The rapid growth of the electric fields to the large amplitudes requisite for the acceleration mechanism is difficult to account for, however, since electron trapping would be expected to occur and the linearized Vlasov‐equation theory loses validity. An efficientuntrappingprocess is therefore invoked: The plasma is thought of as a conglomerate of wave regions which are individually coherent but mutually incoherent. As an electron passes from one coherent region to another it is subjected to a new electric field randomly phased with respect to the first. A short correlation length improves the ability to account for overstability growth to large amplitude, but lengthens somewhat the calculated time for electron acceleration. Computations show efficient acceleration when the electron plasma frequency is of the same order or larger than the electron cyclotron frequency.

ISSN:0031-9171    

DOI:10.1063/1.1711106

出版商:AIP    

年代:1964

数据来源: AIP