Collective behavior of particles in fluids

Paris, December 14-17, 2020

**Matthieu Hillairet** (Université de Montpellier)

*Modelling the interactions between a cloud of particles and a viscous fluid*

When a solid moves inside a viscous fluid, it induces a perturbation of the flow as well as a force acting on the fluid. Extrapolating computations for one single sphere moving in a Stokes fluid, A. Einstein (1906) and then H. Brinkman (1947) derive respectively formulas for the effective viscosity of a fluid/solid mixture and the friction force between the solid and fluid phase velocities. In my talk, I shall present recent results tackling a rigorous analytical justification of these formulas.

See slides.