Homogenization of Stokes-Brinkman Type Models and Mean Field Limit - Lecture 1

This lecture explores the rigorous derivation of fluid-kinetic models for suspensions, which are prevalent in nature (sediments, clouds, biological fluids) and industry (paints, polymers). Learn about the mathematical framework for analyzing suspensions through homogenization techniques and mean field limits. The first session introduces both microscopic and limiting equations with formal derivations, while examining Stokes-Brinkman type models. The presentation covers asymptotic analysis when particle numbers increase while their radius decreases, resulting in different limit equations (Stokes, Darcy, or Stokes-Brinkman) depending on the scale of holes and their typical distance. Discover the mathematical approaches used to derive fluid-kinetic models when accounting for fluid-particle interactions and particle dynamics, including the Transport-Stokes equation. The lecture concludes by highlighting mean-field arguments for deriving suspension models, presented by Amina Mecherbet at the "Kinetic theory and fluid mechanics: couplings, scalings and asymptotics" thematic meeting at the Centre International de Rencontres Mathématiques in Marseille, France.