RET of Dense Polyatomic Gas with Six Fields

A RET theory of dissipative dense gases is presented. In this chapter, we study, in particular, the RET theory with six fields, where we ignore the shear viscosity and heat conductivity and we treat the internal (rotational and vibrational) motion of a molecule as a unit. We postulate a principle of duality between rarefied gas and dense gas. This principle is based on the microscopic analysis of the energy exchange between different modes of the molecular motion. The basic system of field equations satisfies all principles of RET, that is, Galilean invariance and objectivity, entropy principle, and thermodynamic stability (entropy convexity), and, as in the RET theory of rarefied gases, the constitutive equations are completely determined by the thermal and caloric equations of state. The present theory includes the RET theory of rarefied polyatomic gases with six fields (ET6) explained in Chap. 12 as a special case in the rarefied-gas limit. The system is the simplest one after the Euler system, but, in contrast to the Euler system, we may have a global smooth solution due to the fact that the system is dissipative symmetric hyperbolic and satisfies the K-condition. Similar to the ET6 theory, there emerge two nonequilibrium temperatures. Furthermore we evaluate the characteristic velocities associated with the hyperbolic system, and address the fluctuation-dissipation relation of the bulk viscosity. As a typical example, we analyze van der Waals fluids by using the present theory.