Derivation of models for thin sprays from a multiphase Boltzmann model

We shall consider a class of models for thin sprays where the evolution of the two-phase system is modelled through an hydrodynamic equation, describing the fluid phase, coupled to a Vlasov type equation, describing the dispersed phase. We shall illustrate how to derive systems of equations in such a class of models from a multiphase Boltzmann model, obtaining, when considering different asymptotics for the characteristic parameters, different hydrodynamic equations for the fluid component