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 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(c2) terms (c = volume concentration of spheres) for the suspension viscosity which have previously been obtained by assuming a priori that the suspension is both unbounded and statistically homogeneous.