Global homogenization of a dilute suspension of spheres: Suspension rheology
arXiv:2003.01480
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 terms ( = 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.
arXiv commentThis 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