Ensemble-Average Equations of a Particulate Mixture

Abstract

A method of evaluating the transfer terms appearing in the ensemble-average fluid transport equation is developed and applied to obtain the transport equations describing flow of a dilute particulate mixture containing solid spherical particles. The equations apply in the limit where interactions between phases are both quasi-steady and viscous, which is defined as flows that meet the three criterion Ref(a/ℒ)2 ≪ 1, vfτ/a2 ≫ 1, and Rep ≪ 1. In this limit, the terms describing transfer of momentum between the two phases of the mixture are evaluated to O(1) in the particle radius and O(γp) in the particle phase density. The continuity equations and consistency principle are exact. When the first two conditions are not met, the transport equations require the terms that describe virtual mass forces; when the third is not met, the transport equations require terms that describe Oseen corrections to the drag term.