The Boltzmann Equations for a Mixture of Chemical Species

It is first necessary to generalize the definitions of the important functions. If we denote the chemical species in a gas mixture by s, then rip, ms, fs, Ci, Q, Fj, etc. wiU in general be different for each species. 

The starting point for the kinetic theory of low density, non-reacting mixtures of mono-atomic gases is the knowledge of the distribution function /j(r, Cj,t). fs(r, Cs,t) is defined in such a way that the quantity /j(r, Cj, t)dcsdr represents the probable number of molecules of the s-th species which at the time t lie in a unit volume element dr about the point r and which have velocities within the range dc about Cj. It is emphasized that Cj denotes the molecular velocity of a species s with respect to a coordinate system fixed in space. 

The total number of molecules of species s per unit spatial volume yields  

The mean (number average) values of any function ipsicg) over all the molecules of a particular species, s, yield  

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