Boltzmann Equation - General Equation (for A Mixture)

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

\left(\frac{\partial f_i}{\partial t} \right)_{\mathrm{coll}} = \sum_{j=1}^n \iint g_{ij} I_{ij}(g_{ij}, \Omega) \,d\Omega\,d^3\mathbf{p'}.

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.

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