A derivation of the Vlasov-Stokes system for aerosol flows from the kinetic theory of binary gas mixtures

In this paper, we formally derive the thin spray equation for a steady Stokes gas (i.e. the equation consists in a coupling between a kinetic -Vlasov type- equation for the dispersed phase and a -steady- Stokes equation for the gas). Our starting point is a system of Boltzmann equations for a binary gas mixture. The derivation follows the procedure already outlined in [Bernard-Desvillettes-Golse-Ricci, Commun.Math.Sci, in press] where the evolution of the gas is governed by the Navier-Stokes equation