Modeling of macroscopic stresses in a dilute suspension of small weakly inertial particles

TL;DR

This paper derives an asymptotic model for the macroscopic stresses in a dilute suspension of small inertial particles, highlighting how inertia modifies classical particle-stress theories for ellipsoidal particles.

Contribution

It introduces an asymptotic framework to incorporate inertial effects into the macroscopic stress modeling of dilute suspensions, extending classical theories.

Findings

Inertia alters the classical particle-stress relationships.

The asymptotic model applies specifically to ellipsoidal particles.

Modified stress expressions account for inertial effects.

Abstract

In this paper we derive asymptotically the macroscopic bulk stress of a suspension of small inertial particles in an incompressible Newtonian fluid. We apply the general asymptotic framework to the special case of ellipsoidal particles and show the resulting modification due to inertia on the well-known particle-stresses based on the theory by Batchelor and Jeffery.