Kinetic theory intermediate density range

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. 

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