Collision dynamics simple kinetic theory

These ring collision events are now a familiar part of the kinetic theory description of dynamic processes in simple dense fluids. A brief comparison of the theory for the velocity autocorrelation function with that for the chemically reacting fluid will help motivate our description. Recent developments in the theory of the velocity autocorrelation function have arisen out of an attempt to understand the slow t power law decay observed by Alder and Wainwright in a computer simulation of a dense hard-sphere fluid. This work also showed that the translational motion of a small hard sphere in a fluid of similar hard spheres has a significant collective (hydro-dynamic) component. On the theoretical side, this type of behavior was discussed from the kinetic theory point of view in terms of the ring collision events described above and provided a microscopic basis for the introduction of collective effects. In addition, it was shown that mode... 

The validity of the viscoelastic model (5.32) has been tested against experimental and molecular dynamics simulation results [26, 27, 28]. The detailed comparison has established that the viscoelastic model works remarkably well for wavenumbers k km, where km denotes the first peak position of the static structure factor S k). However, it has also been found that the situation is not so satisfactory for smaller wavenumbers, where the viscoelastic model is shown in some circumstances to yield even qualitatively incorrect results. This failure was attributed to the fact that the single relaxation time model (5.31) cannot describe both the short-time behavior of the memory function, dominated by the so-called binary collisions, and in particular the intermediate and long-time behavior where in the liquid range additional slow processes play an important role (see the next subsection). It is obvious that these conclusions demand a more rigorous consideration of the memory function, which lead to the development of the modern version of the kinetic theory. Nevertheless, the viscoelastic model provides a rather satisfactory account of the main features of microscopic collective density fluctuations in simple liquids at relatively large wavenumbers, and its value should not be undervalued. 

Collision theory, which only suffices for simple gas reactions, essentially views reactants as if they were particles with a certain kinetic energy. Matter dynamic considerations play no role here. In the following, we will get to know a more comprehensive theory that can, in principle, be applied to every possible type of reaction. 

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