Species continuity equation:(1.5)
Equation of motion:
The single underlined terms are the convective fluxes of species mass, momentum, and energy, respectively, and the doubly underlined terms are the corresponding molecular fluxes. In the energy equation (which can be thought of as a generalization of ) there is a molecular heat flux q and a molecular work flux . The internal energy for an ideal monatomic gas mixture in Eq. 1.7 is obtained from equilibrium statistical mechanics.
At the same time that one gets the above three conservation equations, one also obtains the expressions for the molecular fluxes: