Collisional transfer of momentum and energy

The fundamental postulate is that as a dilute gas is compressed two novel effects become important because the molecules have finite volumes. First, it is expected that during a molecular collision momentum and energy are transferred over a distance equal to the separation of the molecules. In the particular case of rigid spherical molecules this collisional transfer of momentum and energy takes place instantaneously and results in a transfer over the distance between their centers. Second, the collision frequency may be altered. One possible mechanism is that the collision frequency is increased... 

Fig. 17. The instantaneous collisional transfer of momentum and energy across a distance a when two bard spheres, each of diameter a, collide head on. The figure on the left represents the velocity and positions of the two spheres immediately before the collision, and the figure on the right represents them immediately after the collision.

The stress and the flux of fluctuation energy are due to both transport between collisions and transfer in collisions. The transport parts are -p(CC)and p CC /2, respectively. The collisional transfers, expected to dominate at relatively high number densities, depend upon the exchange of momentum and energy in a collision and the frequency of collision. As an alternative to the number density, the solid volume fraction, v = Ttno /b, is often employed to characterize the density of the system. Then, p = p v, where p is the mass density of the material of the spheres. 

The Enskog theory for diffusion (equation (5.2)) just scales in time the solution of the Boltzmann equation valid at low densities. However, whereas for diffusion the particles themselves must move, in the case of viscosity and thermal conductivity there is the additional mechanism of collisional transfer, which becomes increasingly important as the density increases, whereby momentum and energy can be passed to another molecule upon collision. The Enskog theory for the viscosity rjg and the thermal conductivity... 

Collisional stresses resulting from inter-particle collision, which result in transfer of both momentum and kinetic energy. 

Here we will discuss the phenomena that result in chemical conversion reactions when transfer of energy and momentum become important. As demonstrated, the removal of translational energy (or momentum) is crucial in association reactions. The reverse process, collisional excitation of reactants is also important, for two types of unimolecular reactions, namely dissociation... 

In reality, more complicated expressions apply because of the multi-step character of the reaction ki and k i depend on the energy E and the angular momentum (quantum number J), and the collisional energy transfer is a multi-step process with activations and deactivations, to be characterized by a master equation. It has become customary to consider "strong collisions" first and to introduce "weak collision effects" afterwards. For strong collisions, equation (6) takes the form... 

In this representation, particular emphasis has been placed on a uniform basis for the electron kinetics under different plasma conditions. The main points in this context concern the consistent treatment of the isotropic and anisotropic contributions to the velocity distribution, of the relations between these contributions and the various macroscopic properties of the electrons (such as transport properties, collisional energy- and momentum-transfer rates and rate coefficients), and of the macroscopic particle, power, and momentum balances. Fmthermore, speeial attention has been paid to presenting the basic equations for the kinetie treatment, briefly explaining their mathematical structure, giving some hints as to appropriate boundary and/or initial conditions, and indicating main aspects of a suitable solution approach. 

A consideration of collisional dissociation near threshold requires an understanding of the amount of energy transferred in a single encounter, the role of angular momentum in the decay of activated molecules, and the lifetimes for decay of such species. Accurate determination of apparent thresholds has been achieved by modeling the threshold behavior of the system with a cross-sectional form as follows ... 

For the purposes of modeling, it is convenient to factor the rate coefficient for collisional energy and angular momentum transfer into an overall rate coefficient for collisions between the molecule and bath gas (irrespective of the amount of energy transferred), z, and a collisional energy and angular momentum transfer probability distribution function (TPDF) P E,J E, J ),... 

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