Sedimentation of particles in Stokes flow

Abstract

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. H\"ofer, Sedimentation of inertialess particles in Stokes flows, arXiv:1610.03748, (2016)] 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 and P. E. Jabin, Particle approximation of Vlasov equations with singular forces : propagation of chaos, Ann. Sci. Ec. Norm. Super. (4), (2015)] and [M. Hauray, Wasserstein distances for vortices approximation of Euler-type equations, Math. Models Methods Appl. Sci. 19, (2009), pp. [1357,1384]].