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RESEARCH PRODUCT

Derivation of Models for Thin Sprays from a Multiphase Boltzmann Model

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We shall review the validation of a class of models for thin sprays where a Vlasov type equation is coupled to an hydrodynamic equation of Navier–Stokes or Stokes type. We present a formal derivation of these models from a multiphase Boltzmann system for a binary mixture: under suitable assumptions on the collision kernels and in appropriate asymptotics (resp. for the two different limit models), we prove the convergence of solutions to the multiphase Boltzmann model to distributional solutions to the Vlasov–Navier–Stokes or Vlasov–Stokes system. The proofs are based on the procedure followed in Bardos et al. (J Stat Phys 63:323–344 (1991), [2]) and explicit evaluations of the coupling terms due to the interaction between the two components of the mixture. The results reviewed in this article are proved in detail in Bernard et al. (A derivation of the Vlasov-Navier-Stokes model for aerosol flows from kinetic theory (2016), [4], A derivation of the Vlasov-Stokes system for aerosol flows from the kinetic theory of binary gas mixtures (2016), [5]).