Notes on Mathematical Problems on the Dynamics of Dispersed Particles Interacting through a Fluid (original) (raw)

This chapter explores mathematical problems concerning the dynamics of dispersed particles interacting with a fluid, focusing on dilute cases. Key topics include the derivation of transport equations for particle density influenced by fluid dynamics, specifically in potential flow and Stokes flow conditions. The chapter presents the formulation of Vlasov-type equations for particle density, discussing the mathematical challenges involved in transitioning between Lagrangian and Hamiltonian representations, and introduces recent improvements in mathematical modeling as applied to these fluid interactions.