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In this short paper, we formally derive the thin spray equation for a steadyStokes gas, i.e. the equation consists in a coupling between a kinetic (Vlasovtype) equation for the dispersed phase and a (steady) Stokes equation for thegas. Our starting point is a system of Boltzmann equations for a binary gasmixture. The derivation follows the procedure already outlined in[Bernard-Desvillettes-Golse-Ricci, arXiv:1608.00422 [math.AP]] where theevolution of the gas is governed by the Navier-Stokes equation.

A Derivation of the Vlasov-Stokes System for Aerosol Flows from the Kinetic Theory of Binary Gas Mixtures