Abstract

This talk discusses various strategies for deriving models for spray flows involving a fluid dynamic equation for the propellant and a kinetic model for the dispersed phase.

A first approach is based on the homogenization of the Stokes or Navier-Stokes equation for an incompressible fluid with a prescribed distribution of spherical particles assumed to be far enough from each other so that the drag force on each particle is given by the Stokes formula. This leads to a rigorous derivation of the Brinkman force in the Navier-Stokes or the Stokes equation.

A second approach involves a coupled system of Boltzmann type equations for a binary gaseous mixture, where the dispersed phase and the propellant are described by the methods of kinetic theory. Asymptotic regimes leading to the Vlasov-Stokes and Vlasov-Navier-Stokes systems are identified.