Hindered Settling of Well-Separated Particle Suspensions

TL;DR

This paper analyzes how particle interactions in a suspension affect sedimentation velocity, deriving the order of hindering effects and explicit corrections under specific conditions.

Contribution

It provides a rigorous analysis of hindered settling in particle suspensions, including explicit leading order corrections for certain configurations.

Findings

Hindered sedimentation velocity is smaller than single-particle velocity.

Order of hindering effects is identified under convergence and separation assumptions.

Explicit corrections are computed for specific particle configurations.

Abstract

We consider $N$ identical inertialess rigid spherical particles in a Stokes flow in a domain $\Omega \subset \mathbb R^3$. 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.