The gas-phase working fluids in the combustion engine are modeled as a mixture of individual gas components, or species, and this composition changes during the engine cycle due to flow convection, molecular diffusion, turbulent transport, interactions with fuel sprays, and combustion. The conservation equation for the mass of species is:

(2–1)

where is the density, subscript is the species index, is the total number of species, is the flow velocity vector, and is the mass fraction of species . Application of Fick’s Law of diffusion results in a mixture-averaged molecular diffusion coefficient . The Φ term accounts for the effects of ensemble-averaging or filtering of the convection term, that is, , which has to be modeled. and are source terms due to chemical reactions and spray evaporation, respectively.