Kinetic theory absolute Maxwellian

In a series of impressive publications. Maxwell [95-98] provided most of the fundamental concepts constituting the statistical theory recognizing that the molecular motion has a random character. When the molecular motion is random, the absolute molecular velocity cannot be described deterministically in accordance with a physical law so a probabilistic (stochastic) model is required. Therefore, the conceptual ideas of kinetic theory rely on the assumption that the mean flow, transport and thermodynamic properties of a collection of gas molecules can be obtained from the knowledge of their masses, number density, and a probabilistic velocity distribution function. The gas is thus described in terms of the distribution function which contains information of the spatial distributions of molecules, as well as about the molecular velocity distribution, in the system under consideration. An important introductory result was the Maxwellian velocity distribution function heuristically derived for a gas at equilibrium. It is emphasized that a gas at thermodynamic equilibrium contains no macroscopic gradients, so that the fluid properties like velocity, temperature and density are uniform in space and time. When the gas is out of equilibrium non-uniform spatial distributions of the macroscopic quantities occur, thus additional phenomena arise as a result of the molecular motion. The random movement of molecules from one region to another tend to transport with them the macroscopic properties of the region from which they depart. Therefore, at their destination the molecules find themselves out of equilibrium with the properties of the region in which they arrive. At the continuous macroscopic level the net effect... 

It is important to note that this distribution function (2.244), defined so that it resembles (2.243) but with the constant values of n, v and T in (2.243) replaced by the corresponding functions of r and t, remains a solution to (2.242). This distribution function, which is called the local Maxwellian, makes the kinetic theory much more general and practically relevant. Both the absolute- and local Maxwellians are termed equilibrium distributions. This result relates to the local and instantaneous equilibrium assumption in continuum mechanics as discussed in Chap. 1, showing that the assumption has a probabilistic fundament. It also follows directly from the local equilibrium assumption that the pressure tensor is related to the thermodynamic pressure, as mentioned in Sect. 2.5. 

The standard theories of chemical kinetics are equilibrium theories in which a Maxwell-Boltzmann energy (or momentum or internal coordinate) distribution of reactants is postulated to persist during a reaction. In the collision theory, mainly due to Hinshelwood,7 the number of energetic, reaction producing collisions is calculated under the assumption that the molecular velocity distribution always remains Maxwellian. In the absolute... 

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