Collective behavior of particles in fluids

Paris, December 14-17, 2020

**Amina Mecherbet** (Sorbonne Université)

*Derivation of sedimentation models as a mean-field limit and analysis of the transport-Stokes model*

The rigorous justification of models for sedimenting particles can be investigated as a mean-field analysis for a large system of interacting particles through a singular kernel corresponding to the Oseen tensor and its derivatives. Using a method of reflections I will first recall the type of ODEs obtained for the interacting particles in the case of well separated particles and the case of clustering particles. I will then describe how to obtain the mean-field limit using the infinite Wasserstein distance in the spirit of the works by M. Hauray. In the second part I will focus on the analysis of the limit transport-Stokes model and derive a hyperbolic equation describing the surface evolution of axisymmetric falling droplets. I will finish by explaining how to recover the Hadamard and Rybczynski result which states that a falling spherical viscous droplet in a viscous fluid remains spherical all the time.

See slides.