Sedimentation of particles in Stokes flow

Amina Mecherbet (1)

1 IMAG - Institut Montpelliérain Alexander Grothendieck

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)].

Mots clés: Key-words: Suspension flows; Interacting particle systems; Stokes equations; Vlasov-like equations

Domaines: Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]

Amina Mecherbet. Sedimentation of particles in Stokes flow. 2020. ⟨hal-01824278v2⟩