Rarefied gases

McCourt F R, Beenakker J, Kohler W E and Kuscer I 1991 Nonequilibrium Phenomena In Polyatomic Gases. 2. Cross-sections, Scattering and Rarefied Gases (Oxford Clarendon)... 

Maxwell, J., On Stress in Rarefied Gases Arising from Inequalities of Temperature," Philos. Trans. R. Soc. London, Vol. 170,1879,pp.231-261. 

Immense clouds of cold and rarefied gases float between and around the stars. These clouds are mainly composed of hydrogen, the most widespread element in nature. Stars form there and contribute their ashes to them when they reach the end of their evolution (Fig. 6.1). 

Sir William Crookes will probably be longest remembered for his study of rarefied gases and for his discoveries in radioactivity and molecular physics. After Sir William Ramsay discovered helium in 1895, it was Crookes who established its identity with the helium that Sir Norman Lockyer had observed spectroscopically in the sun s atmosphere. Crookes also invented the radiometer and the spinthariscope. As early as 1886-88 he recognized the existence of atomic species of identical... 

S.A. Schaaf and P.L. Chambre, Flow of Rarefied Gases, Princeton University Press, Princeton, NJ, 1961. 

In the free molecular limit (Kn > 10), the coagulation coefficient is obtained from the kinetic theory of rarefied gases as (4)... 

When the particle size is very small compared to the mean free path, i.e., Kn > 10, the particle can be regarded as a large spherical molecule undergoing independent binary collisions with the gas molecules and the coagulation coefficient is obtained from the kinetic theory of rarefied gases as (5)... 

McCourt FRW, Kohler WE, Beenakker JJM, Kuscer I (1991) Nonequilibrium phenomena in gases Cross sections, scattering, and rarefied gases. Clarendon Press, Oxford... 

Interactions of electromagnetic radiation with particles Transport and deposition Atmospheric visibility radiative transfer in combustors analytical chemistry of particles military applications Process equipment fouling thin-film deposition microcontamination filtration kinetic theory of rarefied gases hydrodynamics atmospheric dry and wet deposition. 

Flame has already been defined as a mass of gas raised to incandescence. It will be observed that this definition does not limit flame to such phenomena as are attendant upon combustion it simply postulates the existence of vapour or gas. Whilst flames may and often do exist under conditions excluding all types of combustion, as for example during the electric discharges through rarefied gases, in the majority of cases flames are the result of rapid oxidation. 

Springer, G. S. Heat Transfer in Rarefied Gases A Survey, Univ. Mich., Fluid Dyn. Lab. Publ. 69-1, May, 1969. 

No exact general criterion is available when it is necessary to include the relaxation terms in the equations of change however, relaxation terms are necessary for viscoelastic fluids, dispersed systems, rarefied gases, capillary porous mediums, and helium, in which the frequency of the fast variable transients may be comparable to the reciprocal of the longest relaxation time. 

At constant temperature of the system, when r -> 0 (because of the van der Waals repulsion between two molecules at small intermolecular distances, Un -> oo), the ratUal rUstribution function g(ri tends to zero for impermeable atoms and simple molecules. In cases when r 2 -> at T = const., or when T- oo, the molecules are completely independent (highly rarefied gases and vapours, U12 0), and 12) 1- The above... 

Generally speaking, the moments y, y induced by a field E — 1 e.s.u. — 300 volt/cm. are of the following magnitude (in rarefied gases and dilute liquids) ... 

Actually, computational convenience has almost always suggested using pairwise additive potentials for simulations of condensed phases also, though strictly two-body potentials are only acceptable for rarefied gases. The computational convenience of two-body potentials is maintained, however, if non-additive effects are included implicitly, i. e. with the so called two-body effective potentials. All empirical or semi empirical functions whose parameters have been optimized with respect to properties of the system in condensed phase belong to this class. As already observed, this makes these potentials state-dependent, with unpredictable performance under different thermodynamic conditions. 

Deissler, R.G., An analysis of second-order slip flow and temperature-jump boundary conditions for rarefied gases, Int. J. Heat Mass Transfer, Vol. 7, pp. 681-694, (1964). 

Heat transfer by forced convection inside micro tube, generally referred as the Graetz problem, has been extended by Barron et al. [11] and Larrode and al. [12] to include the velocity slip described by Maxwell in 1890 [13] and the temperature jump [14] on tube surface, which are important in micro scale at ordinary pressure and in rarefied gases at low-pressure. 

Schaaf, S., and Chambre, P., (1961) Flow of Rarefied Gases, Princeton University Press. Beskok, A., Kamiadakis, G. E., (1995) Models and Sealing Laws for Rarefied Internal Gas Flows Including Separation, 48 Annual Meeting of the American Physical Society Division of Fluid Dynamics, Irvine, Ca. Nov 1995. 

Morini, G. L., Lorenzini, M., and Spiga, M., (2004) A Criterion for the Experimental Vahdation of the Shp-Flow Models for Incompressible Rarefied Gases through Mieroehannels, Proceedings of the International Conference on Mieroehannels and Minichannels, June 17-19, 2004 Rochester, New York, USA, pp. 351-368. 

We mention that, by contrast, the more familiar Raman spectra arising from the permanent polarizabilities of the individual (noninteracting) molecules of the complex are not considered a part of the supermolecular spectra, or of CILS. In ordinary Raman spectroscopy of rarefied gases the invariants of the permanent molecular polarizability tensor are conveniently considered to be not affected by intermolecular interactions, an approximation that is often justified because induced spectral components are usually much weaker than ordinary allowed Raman bands. 

The simphcity of the relationship between the thermodynamic scale and the gas thermometer scale is due principally to the simple properties of rarefied gases, and also to the fortunate choice of mercury as thermometric substance by Celsius and Reaumur before the discovery of the gas laws. The coefficient of expansion of mercury happens to be almost exactly proportional to the coefficient of expansion of rarefied gases. All our thermodynamical relationships would have been very much more comphcated had water or alcohol, for example, or the resistance of a metal, been used for the definition of the practical scale of temperature. Their strict validity, however, would not have been affected. 

F. R. McCourt. J. Beenakker, W. E. Kohler, and I. Kuifer Nonequilih-rium phenomena in polyatomic gases. I olume 2 Cross-sections, scattering, and rarefied gases... 

Andries, R, Bourgat, J.-R, le Tallec, P. Perthame, B. 2002b Numerical comparison between the Boltzmann and ES-BGK models for rarefied gases. Computer Methods in Applied Mechanics and Engineering 191, 3369-3390. 

Grad, H. 1949b On the kinetic theory of rarefied gases. Communications on Pure and Applied Mathematics 2, 331 07. 

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