Introduction

Developing a mathematical model for general description of a particulate multiphase flow system has long been a challenging issue for researchers in the field. Although at this stage comprehensive constitutive relationships for modeling have not been fully established, several approaches which have proved useful are available for predicting the gas–solid flow behavior, particularly for engineering application purposes. Among them are the Eulerian continuum approach, Lagrangian trajectory approach, kinetic theory modeling for interparticle collisions, and Darcy's law and the Ergun equation for flows through packed beds. These approaches are the most commonly used and are introduced in this chapter.

The Eulerian continuum approach, based on a continuum assumption of phases, provides a “field” description of the dynamics of each phase. The Lagrangian trajectory approach, from the study of motions of individual particles, is able to yield historical trajectories of the particles. The kinetic theory modeling for interparticle collisions, extended from the kinetic theory of gases, can be applied to dense suspension systems where the transport in the particle phase is dominated by interparticle collisions. The Ergun equation provides important flow relationships, which are useful not only for packed bed systems, but also for some situations in fluidized bed systems.