Derivation of a Multi-Species Mix Model
Multi-species flow takes place when two or more gases, plasmas or fluids are flowing and interacting with one another through particle collisions, chemical reactions, turbulence, and thermonuclear processes; this list is not exhaustive. It has a wide range of applications in geological, biological and engineering systems. In what follows species refers to different species of atoms or molecules that may or may not be partially or fully ionized. The interactions between these species takes place at an atomic or molecular level. The species are electrically neutral. These are very important points, because the coupling between species that are interacting on a mesoscale level or are immiscible would be very different than what is being considered in this work. In addition, in section 4, we present a heuristic argument to enhance the collisional mean free path to incorporate the effects of turbulent eddies by use of Prandtl’s assumption that the integral scale length of a turbulent boundary layer is proportional to the width of the turbulent layer. This leads to coupling terms that are non-Newtonian, because they are a function of the dynamics of the flow. It is also assumed that the turbulent stress terms are much smaller than the species partial pressures. This may be a good assumption if the species are hot, dense plasmas that exist in ICF targets.