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Hindered settling of well-separated particle suspensions

Matthieu Hillairet and Richard M. Höfer

Vol. 6 (2024), No. 2, 581–609
Abstract

We consider N identical inertialess rigid spherical particles in a Stokes flow in a domain Ω 3. We study the average sedimentation velocity of the particles when an identical force acts on each particle. If the particles are homogeneously distributed in directions orthogonal to this force, then they hinder each other leading to a mean sedimentation velocity which is smaller than the sedimentation velocity of a single particle in an infinite fluid. Under suitable convergence assumptions of the particle density and a strong separation assumption, we identify the order of this hindering as well as effects of small scale inhomogeneities and boundary effects. For certain configurations we explicitly compute the leading order corrections.

Keywords
suspension, Stokes flow, sedimentation
Mathematical Subject Classification
Primary: 35Q70, 76D07, 76M50, 76T20
Milestones
Received: 15 September 2023
Revised: 15 January 2024
Accepted: 13 April 2024
Published: 16 May 2024
Authors
Matthieu Hillairet
Institut Montpelliérain Alexander Grothendieck
Université de Montpellier, CNRS
Montpellier
France
Richard M. Höfer
Fakultät für Mathematik
Universität Regensburg
Regensburg
Germany