Calculations for Extended Thermodynamics of dense gases up to whatever order and with only some symmetries

The 14 moments model for dense gases, introduced in the last years by Ruggeri, Sugiyama and collaborators, is here considered. They have found the closure of the balance equations up to second order with respect to equilibrium; subsequently, Carrisi has found the closure up to whatever order with respect to equilibrium, but for a more constrained system where more symmetry conditions are imposed. Here the closure is obtained up to whatever order and without imposing the supplementary conditions. It comes out that the first non symmetric parts appear only at third order with respect to equilibrium, even if Ruggeri and Sugiyama found a non symmetric part proportional to an arbitrary constant also at first order with respect to equilibrium. Consequently, this constant must be zero, as Ruggeri, Sugiyama assumed in the applications and on an intuitive ground.

On a non approximated approach to Extended Thermodynamics for dense gases and macromolecular fluids

Recently the 14 moments model of Extended Thermodynamics for dense gases and macromolecular fluids has been considered and an exact solution, of the restrictions imposed by the entropy principle and that of Galilean relativity, has been obtained through a non relativistic limit. Here we prove uniqueness of the above solution and exploit other pertinent conditions such us the convexity of the function $h$ related to the entropy density, the problem of subsystems and the fact that the flux in the conservation law of mass must be the moment of order 1 in the conservation law of momentum. Also the solution of this last condition is here obtained without using expansions around equilibrium. The results present interesting aspects which were not suspected when only approximated solutions of this problem were known.