The book’s final chapter pays attention to various issues that can be encountered when investigating multiphase flows. This chapter can be read independently, although on a few occasions it refers to some selected problems from the prior topics. First, this chapter treats a multiphase flow as a system of spherical particles with some given concentration and with some average distance between the particles. Later, the chapter looks into the particle reaction as immersed in a fluid (discussion so-called response times), and it is shown how the presence of the particles influences the fluid flow by discussing the concept of phase coupling and suspension viscosity. Next, we consider the issue of the dispersion of particles as they are subject to turbulent flows, and how the particles may gather in some selected flow zones (preferential concentration). The fact that the particles may be of different sizes is later analysed by investigating the particle size distribution. The final sections of the chapter are dedicated to collision frequency and a particular case of a flow through a particle bed.

Chapter 5 delineates the Eulerian–Lagrangian modeling commonly used for dilute-phase multiphase flows. The most essential part is the formulation of a Lagrangian trajectory model to describe the transport of individual particles, which requires proper formulation of particle–fluid and particle–particle interactions involved. The basic modeling considerations include the type of Lagrangian trajectory models such as deterministic trajectory model, stochastic trajectory model, particle-cloud tracking model, or discrete element method; the degree of phase coupling between Lagrangian models of discrete phases and Eulerian model of continuum phase such as one-way or two-way particle–fluid coupling or four-way particle–fluid and particle–particle coupling flow; the field coupling with particle transport such as the electrostatic field induced by the suspended charged particles or thermal radiation among particles; and the turbulence modulation between particles and eddy transport. The Lagrangian model of particle motion, typically in a simplified form of additivity of individual modes of fluid–particle interactions, is employed in the Lagrangian modeling of discrete phase transport.