Résumé
In this paper, we consider N identical spherical particles sedimenting in a uniform gravitational field. Particle rotation is included in the model while inertia is neglected. Using the method of reflections, we extend the investigation of [R.M. Höfer, Sedimentation of Inertialess Particles in Stokes Flows. Commun. Math. Phys. (2018) 360: 55. https://doi.org/10.1007/s00220-018-3131-y] by discussing the optimal particle distance which is conserved in finite time. We also prove that the particles interact with a singular interaction force given by the Oseen tensor and justify the mean field approximation of Vlasov-Stokes equations in the spirit of [M. Hauray, Wasserstein distances for vortices approximation of Euler-type equations, Math. Models Methods Appl. Sci. 19, (2009), pp. [1357,1384]] and [M. Hauray and P. E. Jabin, Particle approximation of Vlasov equations with singular forces : propagation of chaos, Ann. Sci. Ec. Norm. Super. (4), (2015)].