Global homogenization of a dilute suspension of spheres: Suspension rheology

Abstract

A new method for rheologically homogenizing a dilute suspension composed of freely-suspended spherical particles dispersed in a Newtonian fluid is presented: The ensemble-averaged velocity and stress fields obtained for the neutrally-buoyant sphere suspension are compared with the respective velocity and stress fields obtained for a hypothetical homogeneous Newtonian fluid continuum possessing a spatially {\em non-uniform} viscosity for the same specified boundaries and ambient flow. The method is global in nature; that is, wall effects and spatial dependence of both the ambient flow and the particle number density are encountered, thereby confirming known classical results up to $O(c^2)$ terms ($c$ = volume concentration of spheres) for the suspension viscosity which have previously been obtained by assuming {\em a priori} that the suspension is both unbounded and statistically homogeneous.

This paper has been rejected by several journals many years ago. Since in recent years it has been cited several times, I am putting it here for the benefit of those interested. This submission is dedicated to the memory of my coauthor: the late Howard Brenner