General Equation (for A Mixture)
For a mixture of chemical species labelled by indices i = 1,2,3...,n the equation for species i is:
where fi = fi(r, pi, t), and the collision term is
where f′ = f′(p′i, t), the magnitude of the relative momenta is
and Iij is the differential cross-section as before, between particles i and j. The integration is over the momentum components in the integrand (which are labelled i and j). The sum of integrals describes the entry and exit of particles of species i in or out of the phase space element.
Read more about this topic: Boltzmann Equation
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