On the collective effect of a large system of heavy particles immersed in a Newtonian fluid

TL;DR

This paper investigates how a large system of very heavy particles influences fluid flow, demonstrating that their collective effect resembles a Brinkman-type perturbation in the Navier-Stokes equations through homogenization analysis.

Contribution

It introduces a homogenization framework for understanding the collective impact of infinitely dense particles on fluid dynamics, linking particle properties to Brinkman perturbations.

Findings

Heavy particles induce a Brinkman-like perturbation in the fluid equations.

The collective effect can be characterized via homogenization techniques.

The results connect particle density growth to modifications in fluid flow behavior.

Abstract

We consider the motion of a large number of heavy particles in a Newtonian fluid occupying a bounded spatial domain. When we say "heavy", we mean a particle with a mass density that approaches infinity at an appropriate rate as its radius vanishes. We show that the collective effect of heavy particles on the fluid motion is similar to the Brinkman perturbation of the Navier-Stokes system identified in the homogenization process.