Mono-atomic gas

The value of k is not universal and depends on the nature of the reactive mixture (for example, fhe value of k may be around 26 for mixtures highly diluted with a mono-atomic gas [29], or around 20 for hydrogen/air mixtures [30]), as well as on the diffraction process at the tube... 

In the gaseous state at room temperature helium (He) is a mono-atomic gas, and the formula of the element helium is written as He. However, the gaseous form of hydrogen and oxygen at room temperature involves diatomic molecules, namely, H2 and O2. This difference is largely determined by the individual electron configuration of the el-... 

A collection of mono-atomic gas molecules are characterized by their position r in space and their velocity c at time t. An infinitesimal spatial space containing the point r is denoted by dr (e.g., in Cartesian coordinates = dxdydz). In a similar manner, an infinitesimal element in a hypothetical velocity space containing the velocity c is denoted by dc (e.g., in Cartesian coordinates = dcx dcy dcz). The imaginary or hypothetical space containing both dr and dc constitutes the six-dimensional phase space. Therefore, by a macroscopic point (r, c, t) in phase space is meant an infinitesimal volume, dr dc, centered at the point (r, c,t), having an extension sufficient to contain a large number of molecules as required for a statistical description to be valid, but still small compared with the scale of the natural changes in the macroscopic quantities like pressure, gas velocity, temperature and density of mass. 

In a non-equilibrium gas system there are gradients in one or more of the macroscopic properties. In a mono-atomic gas the gradients of density, fluid velocity, and temperature induce molecular transport of mass, momentum, and kinetic energy through the gas. The mathematical theory of transport processes enables the quantification of these macroscopic fluxes in terms of the distribution function on the microscopic level. It appears that the mechanism of transport of each of these molecular properties is derived by the same mathematical procedure, hence they are collectively represented by the generalized property (/ ... 

In practice the local pressure variable is assumed to be independent on the state of the fluid. If the gradients in the flow field of a mono-atomic gas are sufficiently large, viscous stresses and heat conduction phenomena emerge. 

These relations are called the generalized Maxwell-Stefan equations and are the inverted counterparts of the Pick diffusion equations (2.281). These two descriptions contain the same information and are interrelated as proven by Curtiss and Bird [18] [19] for dilute mono-atomic gas mixtures. 

A more rigorous derivation of these relations were given by Curtiss and Hirschfelder [16] extending the Enskog theory to multicomponent systems. FYom the Curtiss and Hirschfelder theory of dilute mono-atomic gas mixtures the Maxwell-Stefan diffusivities are in a first approximation equal to the binary diffusivities, Dgr Dsr- On the other hand, Curtiss and Bird [18] [19] did show that for dense gases and liquids the Maxwell-Stefan equations are still valid, but the strongly concentration dependent diffusivities appearing therein are not the binary diffusivities but merely empirical parameters. 

The transport coefficients like viscosity, thermal conductivity and self-diffusivity for a pure mono-atomic gas and the diffusivity for binary mixtures obtained from the rigorous Chapman-Enskog kinetic theory with the Lennard-Jones interaction model yield (e.g., [39], sect 8.2 [5], sects 1-4, 9-3 and 17-3) ... 

Assuming an ideal, mono-atomic gas, the kinetic correction becomes -kT / 2 for adsorption into an (ideal) 2D gas phase and +kT/2 for adsorption into a 2D sohd. A detailed account of the thermodynamics of adsorption can be found in [97B2]. 

A temperature-dependent expression for gas viscosity of a pure mono-atomic gas is given by Chapman-Enskog s kinetic theory as... 

The Chapman-Enskog solution method, as discussed in Sect. 2.8 for a dilute mono-atomic gas, can be applied to the Enskog s equation as well. Solving the Enskog s equation by the perturbation method to determine /, we find that the zero-order approximation (i.e., / / ° ) of the pressure tensor and the heat flux vector are... 

The limiting viscosity for the dilute regime can be approximated from the dilute mono atomic gas relation (2.620) by converting the molecular temperature (2.200) to the granular temperature (4.70). The result is [49] ... 

Except for the adaption to granular temperature, this relation coincides with the dilute mono-atomic gas viscosity closure given by the bracket integral (7.41 -1) and the first approximation (10.21,1) in Chapman and Cowling [25]. 

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