Flow of spatially non-uniform suspensions - Part II: Systematic derivationof closure relations

This paper presents a systematic method by which closure relations for the ensemble-averaged equations of disperse two-phase flows of solid spheres ca n be derived. The method relies on the direct numerical simulation of three flow situations: equal forces or couples applied to the spheres, and an im posed macroscopic shear flow. A crucial aspect of the work is that it focus es on systems that are spatially non-uniform on average. It is shown that, due to this feature, several new terms arise in the constitutive relations that would vanish for a uniform system. For example, while the usual effect ive viscosity is recovered in the closure of the stress tensor, it is found that other terms are also present, which confer a markedly non-Newtonian n ature to the rheological constitutive equation. (C) 2001 Elsevier Science L td. All rights reserved.