Modeling Theory of the Linearized Collision Operator for a Gas Mixture

Kinetic models are developed for the linearized Boltzmann collision operator which describes the collisions between different kinds of molecules. From the known eigentheory of this operator and the method of Gross and Jackson, a sequence of increasingly more accurate model operators is generated. All of the models satisfy the conservation laws, and all except the single-relaxation time model lead to the proper transport coefficients. Explicit expressions are given for some models, including the simplest one compatible with hydrodynamics. In the context of the present development, a unified discussion of the linearized versions of several existing models is given.