摘要:

Transport processes in fluids are discussed in the framework of ensemble theory. A nonequilibrium ensemble is constructed by explicit consideration of the external forces which bring about the deviation from equilibrium. The resulting ensemble has the form of a product of factors, one characteristic of local equilibrium and the other containing a description of the irreversible processes. For states near equilibrium (to which the discussion is restricted) the ensemble depends linearly on the thermodynamic parameters which specify the deviation from equilibrium. Transport relations are obtained which are, in general, nonlocal in space and time; that is, the transport coefficients are frequency and wavelength dependent. An approximation procedure is used which amounts to an expansion in powers of the wave number, and in the lowest approximation one obtains the familiar local transport relations.

ISSN:0031-9171    

DOI:10.1063/1.1706081

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

In previous studies treating the problems of linear shear and heat flow in parallel plate geometry, a half‐range moment expansion of the distribution function was given for arbitrary values of the Knudsen number. The half‐range collision integrals for Maxwellian molecules are now evaluated numerically. The inverse fifth law of molecular interaction can be regarded as a lower bound for neutral gases. The problems of shear and heat flow are reconsidered in this light.

ISSN:0031-9171    

DOI:10.1063/1.1706082

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

Experimental values of the diffusion coefficient and the thermal diffusion factor for the systems He&sngbnd;Ar, He&sngbnd;CO2, and H2&sngbnd;CO2, over a temperature range of about −78° to 325°C, are analyzed for the purpose of testing the Lennard‐Jones (12−6) and the exp‐6 intermolecular potentials, as well as the combination rules usually used in conjunction with these potentials. The exp‐6 potential gives excellent results for He&sngbnd;Ar, but the 12−6 potential is not satisfactory. This system affords no opportunity to choose between the various combination rules. The 12−6 potential works fairly well for He&sngbnd;CO2and H2CO2. On the whole, the combination rules are surprisingly good, being no worse than the potentials themselves. The importance of considering the higher theoretical approximations for the thermal diffusion factor is emphasized. An expression interrelating the transport properties and independent of any particular intermolecular potential is proposed, which can be used to test how well a mixture conforms to the basic assumptions of the Chapman‐Enskog theory or to indicate the consistency of the experimental measurements.

ISSN:0031-9171    

DOI:10.1063/1.1706083

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

An integral representation of the general solution to the Hopf &phgr; equation is reported. Integral representations for the spatial correlation functions are derived from the characteristic functional &phgr;. These exact results are applied to Navier‐Stokes fluid turbulence.

ISSN:0031-9171    

DOI:10.1063/1.1706084

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

Proofs are given which show that the integral representations for the Navier‐Stokes spatial correlation functions satisfy the reality conditions, the continuity conditions, and the Navier‐Stokes condition. With the aid of the integral representations for the correlation functions an analysis of the decay of homogeneous turbulence is developed. For the initial period of decay the theory predicts the empirical lawu2&agr; &ngr;(t″ −t′)−1, as well as a universal and shape‐preserving two‐point correlation tensor.

ISSN:0031-9171    

DOI:10.1063/1.1706085

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

A method is introduced by which experimental measurements of two‐ and three‐velocity correlation functions can be used to provide a direct test of energy transfer hypotheses in a turbulent fluid. By using this method, the optimal values for the three empirical parametersm, n, and &ggr;, which appear in the general transfer function proposed by T. von Ka´rma´n, are determined from the correlation function data of R. W. Stewart and A. A. Townsend. This optimal transfer function is found to be:Toptimal(k)=1.2 [k−5/2E1/4∫ 0kk′3E5/4(k′)dk′−k3E5/4∫k∞k′−5/2E1/4(k′)dk′],and a comparison, based on the data, is made between this transfer function and transfer functions proposed by W. Heisenberg and L. Kovasznay.

ISSN:0031-9171    

DOI:10.1063/1.1706086

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

A variational principle is given which describes the steady laminar motion of simple non‐Newtonian fluids, for which the viscosity is a function of the second invariant of the rate of deformation tensor. This principle simplifies to von Helmholtz's principle for the Newtonian fluid, and to Tomita's principle for the Ostwald‐de Waele fluid. For the latter two types of fluids, the equations of continuity and motion are equivalent to the statement that the rate of entropy production in the system is a minimum; for more general fluids, the variational principle does not admit this simple interpretation.

ISSN:0031-9171    

DOI:10.1063/1.1706087

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

The coefficient for tangential momentum transfer &sgr; between the boundary and a flow of rarefied gas has been investigated by the rotating cylinder technique. Systematic perturbation of the pressure history of the active surfaces were made and correlated with observed variation of &sgr;. A high‐pressure history is found to result in a lowering of &sgr; with time (order of days) from values in the range 0.9 to 1.0 values approaching 0.6. A low‐pressure history is found to result in constant values of &sgr; in the range 0.9 to 1.0. The observations were of the same character for all gases.

ISSN:0031-9171    

DOI:10.1063/1.1706088

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

Experiments with electrostatic and magnetic probes were performed to investigate the electron diffusion ahead of shock waves ofMs= 8 to 12 in argon. Negative electrostatic signals of several volts were obtained with pronounced fronts propagating with velocities up to several times the shock velocity. The current produced by the diffusing electrons was determined from a measurement of the azimuthal magnetic field and found to be of the order of 10−5amp forMs= 12. By assuming that the electron flow velocity is approximately equal to the velocity of the electrostatic front, the measured current corresponds to an electron density ofne≈ 107cm−3at about 1 m ahead of the shock front.

ISSN:0031-9171    

DOI:10.1063/1.1706089

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

Consideration is given to the possible steady one‐dimensional flows which can occur in a medium in which an arbitrary number of chemical reactions proceed behind an initiating shock, and the stability of solutions to the chemical rate equations is investigated. The theoretical apparatus is that of irreversible thermodynamics and nonlinear mechanics, with neglect of transport processes. Most of the discussion is concerned with detonations, but the analysis applies to all such reacting systems. For detonations, it is shown that under suitable conditions on the rate functions, there are stable solutions resulting in an equilibrium final state for detonation velocities equal to or greater than the ``equilibrium Chapman‐Jouguet (C‐J)'' value corresponding to tangency of the Rayleigh line and the equilibrium Hugoniot. The final state in such a flow is the high‐pressure intersection of the Rayleigh line and the equilibrium Hugoniot. We suggest that these solutions correspond to piston‐supported detonations after decay of initiation transients, and we further suggest that the equilibrium C‐J detonation is stable with respect to removal of the piston support at sufficiently late times.The ``normal frozen C‐J condition,'' corresponding to attainment of chemical equilibrium at a point where the flow velocity is sonic with respect to the ``frozen'' or high frequency sound speed, is shown to result in an unstable solution. Solutions corresponding to ``pathological detonations,'' in which the region of steady flow terminates at a point of incomplete reaction, are identified, but the conditions necessary or sufficient for their realization have not been obtained, nor has the nature of the subsequent time‐dependent flow been elucidated. Thus their physical significance remains somewhat doubtful.

ISSN:0031-9171    

DOI:10.1063/1.1706090

出版商:AIP    

年代:1960

数据来源: AIP