Relaxation Processes of Molecular Rotation and Vibration: ET₁₅

Abstract

In the previous Chaps. 6 and 7, we have studied RET of rarefied polyatomic gases under the assumption that molecular internal modes can be treated as a whole in terms of the single variable I. However, by dividing the internal modes into the molecular rotational and vibrational modes, we can obtain a more refined version of RET of rarefied polyatomic gases with a wider applicability range. To study this subject is the main purpose of the present chapter. In this case, we need to introduce (at least) two variables instead of I, and as a result we have a triple (or multiple) hierarchy of the moment system. As the simplest model, we derive explicitly the closed system of field equations with 15 variables (ET₁₅) by using the maximum entropy principle (MEP). Three different types of the production terms, which are suggested by a generalized BGK-type collision term in the Boltzmann equation, are adopted. The Navier-Stokes and Fourier (NSF) theory is again derived from the ET₁₅ theory as a limiting case of small relaxation times via the Maxwellian iteration. The relaxation times introduced in ET₁₅ are related to the shear and bulk viscosities and heat conductivity.