On pressure and thermal flux in gas-mixture flows and in two-phase flows

To begin with, two different definitions of pressure, thermal flux, etc. in the diffusion model and two-fluid model are given. Then the physical interpretations of the pressure and the thermal flux are provided by introducing the momentum and energy fluxes,M and ε, through a surface dS in the flow field. The quantities defined in the diffusion model are suggested when the motion of the mixture is studied as a whole, while the quantities defined in the two-fluid model are suggested when the motion of individual species is studied. The collision pressure and thermal flux in dense gas-mixtures are also discussed in detail, i.e. their origin, their expressions in the momentum and energy equations, and their distinctions from the normal partial pressure and thermal flux. A gas-particle flow can be treated as a flow of dense gas-mixtures. The long-standing controversy whether the “inertial coupling term” should exist in the momentum equation can be clarified by the two different definitions of pressure.