Binary Particle Collisions with Mass Exchange

We investigate a kinetic model for interacting particles whose masses are integer multiples of an elementary mass. These particles undergo binary collisions which preserve momentum and energy but during which some number of elementary masses can be exchanged between the particles. We derive a Boltzmann collision operator for such collisions and study its conservation properties. Under some adequate assumptions on the collision rates, we show that it satisfies a H-theorem and exhibit its equilibria. We formally derive the system of fluid equations that arises from the hydrodynamic limit of this Boltzmann equation. We compute the viscous corrections to the leading order hydrodynamic equations on a simplified collision operator of BGK type. We show that this diffusive system can be put in the formalism of nonequilibrium thermodynamics. In particular, it satisfies Onsager’s reciprocity relation and entropy decay.