Momentum density kinetic theory

Kinetic Theory. In the kinetic theory and nonequilibrium statistical mechanics, fluid properties are associated with averages of pruperlies of microscopic entities. Density, for example, is the average number of molecules per unit volume, times the mass per molecule. While much of the molecular theory in fluid dynamics aims to interpret processes already adequately described by the continuum approach, additional properties and processes are presented. The distribution of molecular velocities (i.e., how many molecules have each particular velocity), time-dependent adjustments of internal molecular motions, and momentum and energy transfer processes at boundaries are examples. 

There is a close connection between molecular mass, momentum, and energy transport, which can be explained in terms of a molecular theory for low-density monatomic gases. Equations of continuity, motion, and energy can all be derived from the Boltzmann equation, producing expressions for the flows and transport properties. Similar kinetic theories are also available for polyatomic gases, monatomic liquids, and polymeric liquids. In this chapter, we briefly summarize nonequilibrium systems, the kinetic theory, transport phenomena, and chemical reactions. 

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 (/ ... 

Does it exist , can, of course, not yet be answered on these grounds alone. Experience shows that the MBPT procedure yields energy barriers that are too high. This will be demonstrated later in this report for the N4 molecule. To estimate the kinetic stability of 8 more accurately, other calculation methods such as MP2, MP4, CC, or MCSCF-CI should also be employed. Meanwhile, density functional theory (DFT) has been developed and the available basis sets are extended to higher angular momentum quantum numbers. Therefore, the author of this report applied himself... 

The kinetic theory of dense gases began with the work of Enskog, who in 1922, generalized Boltzmann s derivation of the transport equation to apply it to a dense gas of hard spheres. Enskog showed that for dense gases there is a mechanism for the transport of momentum and energy by means of the intermolecular potential, which is not taken into account by the Boltzmann equation at low densities, and he derived expressions for the transport coeffi-... 

Force surface density and pressure. The notion of pressure is traditionally thought of as a surface density of force and therefore more as a mechanical concept than a thermodynamic one. The classical development of the kinetic theory of gases uses this concept of force surface density, leading through the previously reasoning made for linking momentum and force to the following expression of the pressure ... 

As the density of the fluid is increased above values for which a linear term in the expansion of equation (5.1) is adequate (crudely above values for which a third virial coefficient is adequate to describe the compression factor of a gas), the basis of even the formal kinetic theory is in doubt. In essence, the difficulty arises because it becomes necessary, at higher densities, to consider the distribution function, in configuration and momentum space, of pairs, triplets etc. of molecules in order to formulate an equation for the evolution of the single-particle distribution function. Such an equation would be the generalization to higher densities of the Boltzmann equation, discussed in Chapter 4 (Ferziger Kaper 1972 Dorfman van Beijeren 1977). 

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