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This lecture, the second in a series, explores the rigorous derivation of fluid-kinetic models for suspensions, focusing on homogenization of Stokes-Brinkman type models and mean field limits. Delve into the mathematical analysis of suspensions that are common in nature (sediments, clouds, biological fluids) and industry (paints, polymers). The presentation reviews main results in deriving effective models from microscopic systems where particle positions and velocities are fixed or given, examining asymptotic analysis when particle numbers increase while their radius decreases. Learn about the derivation of the Brinkman term in simplified cases and understand the rigorous derivation of fluid-kinetic models that account for fluid-particle interactions and particle dynamics. The lecture connects to mean field limit theory for interacting particles and presents approaches using the method of reflections and stability estimates through Wasserstein distance. Recorded during the thematic meeting "Kinetic theory and fluid mechanics: couplings, scalings and asymptotics" at the Centre International de Rencontres Mathématiques in Marseille, France.
