| Abstract: |
| The kinetic description of a mixture of gases with different particle masses (and possibly with different internal energies) is not a trivial generalization of the classical Boltzmann theory for a single gas, since the collision operators have to take into account exchanges of momentum and energy among the different species (and also mass exchanges, in the case of reacting mixtures). Moreover, the analysis of the gas-mixture equations is more difficult than the comparable single component gas theory because of the many different scales which now enter in the approach to equilibrium. There is the approach of the distribution function to a Maxwellian distribution (referred to as Maxwellization) and, in addition, there is the equilibration of the species (i.e., the vanishing of differences in velocity and temperature among the species). In kinetic theory, the evolution of a mixture of $N$ elastically scattering gases is usually described by a set of $N$ integro-differential equations of Boltzmann type for the species distribution functions. Since it is difficult, in general, to manage the collision integral operator as such, simplified kinetic models have been developed in the literature and widely used in practice. In the present work, we will analyze different linearized kinetic model equations for binary gas mixtures describing time-dependent problems and we will focus in particular on those allowing a semi-analytical representation of the solution. |
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