Fluidization represents an important particulate and multiphase operation, featuring dynamic interactions between a continuum fluid and a discrete phase. It is typically realized in a vertical column or pipe. Various fluidization regimes occur, depending on the property of the fluidizing particles, flow rate, and external field force applied. This chapter describes gas–solid fluidization represented by dense-phase fluidized beds and circulating fluidized beds. Fluidization under the gas–liquid–solid flow conditions is also illustrated with the inclusion of its limiting condition of two-phase flows. Basic topics of fluidization include the fluidization regime classification and characteristics, phase-interaction mechanisms in the dense and dilute phase fluidization as well as nanoparticle fluidization, fluidized bed systems, and multiscaled transport phenomena, such as clustering, agglomeration, breakup, and coalescence of dispersed particles or bubbles. For the numerical modeling of fluidization systems, the Eulerian–Eulerian modeling is extensively used and often coupled with the DEM models or kinetic theory models for collision-induced transport in the dispersed phase.

Multiphase pipe flows are represented by gas–solid pneumatic transport and solid–liquid slurry transport in pipes, and gas–liquid pipe flows with either gas or liquid as the continuous phase. Fully developed multiphase pipe flows can be characterized by several transport regimes with distinctively different flow patterns and phase interactions dominated by factors such as mass flow ratio of phases, density ratio of phases, pipe orientation relative to gravity direction, transport velocity of continuum phase, and sizes of pipe and particles. Basic topics include the regime classification and flow characteristics in each regime for gas–solid pneumatic transport, solid–liquid slurry transport, and gas–liquid pipe flows, critical transport conditions such as saltation and pickup velocities, mechanisms dominating the pressure drop, suspended flow characteristics in straight pipes and effects of particle loading, electrostatic charges and pipe orientation, characteristics of flow over a bend, such as roping phenomena and bend erosion, and stratified multiphase pipe flow with wavy interfaces.

The phase separation of a multiphase flow is primarily achieved with an application of a specific mechanism that can lead to a distinctively different dynamic response of each phase in a multiphase medium. Such mechanisms include the gravitational settling (e.g., solids in fluids, droplets in immiscible fluids, bubbles in liquids or slurries), flow-induced alternation of phase inertia (e.g., centrifugal acceleration by flow rotation, jet dispersion, impaction on a surface), selective interception or blockage of phase transport (e.g., sieving; filtration), and separation using externally controlled field forces (e.g., electrostatic precipitation). A separation system or method can be developed by using one or a combination of these mechanisms. High separation efficiency and low mechanical energy loss are among the most important objectives for system design or selection. Actual separation of multiphase flows involves complicated phase transport, flow regimes, particle size distributions, and system geometries. Thus, aside from numerical modeling, much simplified analytical models with empirical correlations are still popular in practice.

Chapter 7 introduces the basic algorithms used to solve the governing equations of multiphase flows. The algorithms for incompressible, isothermal single-phase Newtonian fluid flow form the basis for more complex multiphase flow algorithms. Numerical techniques for the microscopic descriptions of fluid–particle interactions are focused on the discrete particle phase with rigid or nonrigid surfaces. Such methods are associated with the direct numerical simulation and can be categorized into the conformal mesh technique and the nonconformal mesh technique. Numerical techniques for the macroscopic descriptions of multiphase flow include the Eulerian–Lagrangian algorithm for continuum-discrete modeling, and the Eulerian–Eulerian algorithm for continuum modeling. The lattice Boltzmann method is a unique numerical technique for flow simulation. It is based on the discrete Boltzmann equation, rather than the typical Navier–Stokes equation in other CFD techniques. Its computational efficiency and some special treatment for multiphase models make it a suitable tool for flows with complex phase interactions.

Chapter 1 provides an overview of the concepts and exemplified applications of multiphase flows. It illustrates the distinctly different transport patterns or phenomena of individual phase in a multiphase flow, which have either naturally caused or intentionally designed consequences.

The chapter conveys the basic definitions of a multiphase flow, the phase interactions, and the associated modeling approaches, which include the difference between a multiphase flow and a multicomponent single-phase flow, the difference between a dilute-phase multiphase flow and a dense-phase multiphase flow, the difference between a continuum phase and a discrete phase in describing the flow regimes, and the difference in Eulerian–Lagrangian modeling and Eulerian–Eulerian modeling. Some interesting and unique phenomena of multiphase flows are discussed by case studies.

Chapter 8 introduces the principles of experimental methods to determine various transport properties in multiphase flows. Typical properties include geometric characteristics of dispersed phase, phase volume fractions, mass fluxes or flow rates, velocities, and electrostatic charges. Specifically, the particle size and morphology are measured via the optical image, sieving, sedimentation, cascade impaction, and laser-scattering method. The volume fraction can be determined by the beam-attenuation, permittivity, and tomography principles. The mass flow rate can be determined from the isokinetic sampling and ball probe method. Phase velocities can be measured using the cross-correlation, LDV, and PIV methods. The electrostatic charge is typically measured by Faraday cup and induction probe. The introduction is focused on the basic mechanisms and applicability of the measurement techniques. The chapter also discusses the data analysis methods describing the particle size distribution from overlapped size sampling, such as the deconvolution method. It is also important to identify the equivalent diameter of nonspherical particles that a size measurement reveals.

Chapter 3 provides basic formulation of various fluid–particle interactions of an isolated object that has a relative motion in a fluid flow and in the absence of any interactions with other transported objects in the same fluid flow. The chapter describes the distinctly different transport mechanisms governing the fluid–particle interactions, their basic mathematical formula, and the corresponding ranges of validation. The most essential interactions are represented by the drag force, carried mass, Basset force, Saffman force, Magnus force, Stefan flux, and d2-law of diffusive evaporation. The most essential formulation of these fluid–particle interactions is derived with the Newtonian fluid flowing over a rigid sphere and under the creeping flow conditions. This approximated method leads to the basic formulation of the Lagrangian modeling approach for the discrete phase transport in a multiphase flow. Application of the fluid–particle interactions for the transport of isolated objects in a carrying fluid flow are illustrated. The usefulness of the order-of-magnitude analysis of the transport mechanisms in modeling simplification also is discussed.

Multiphase flows refer to the flows with distinctively different dynamic responses of each phase in the transport and phase interactions that impact the transport phenomena. Aimed to serve as an educational, learning-oriented text that introduces multiphase flows to engineering students, advanced researchers, and other readers, this unified textbook methodically encompasses a broad range of the important elements of knowledge in the multiphase flow field, along with sufficient theoretical and applied details in a manner suitable to both introductory and advanced level learning in an instructional setting. The book has twelve chapters, with six on a systematic introduction of multidisciplinary fundamentals critical to understanding multiphase flows, two on the numerical methods and experimental techniques of multiphase flows, and four on selected subjects of multiphase flow systems. Aided with ample examples and problems in each chapter (with available solution manual), this book can be used for advanced undergraduate and graduate courses in many engineering disciplines including mechanical, power, chemical, pharmaceutical, environmental, and process system engineering.

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.

Chapter 12 is focused on multiphase flows with phase changes, where the phase interactions are further complicated by the mass transfer and mass-transfer-induced momentum and energy transfer. Basic topics include the regime classification and flow characteristics in each regime for boiling and spray dispersion, phase interaction mechanisms involving phase changes, flow characteristics of atomized spray jetting with evaporation, characteristics of gas–solid reacting flows in risers, characteristics of bubbling flow in sparged stirred tanks, and their impact on reactions, and combustion characteristics and coupling of transport mechanisms of dispersed fuel particles. Multiphase flow modeling with phase changes is quite incomplete compared to that without phase changes. More physical understanding is necessary and hence the mathematical descriptions of flow-influence phase changes, multiscaled phase changes, and transport phenomena of multiphase flows under highly pressurized and high-temperature operation conditions. Progress in both modeling and numerical solution techniques is evidenced in the case studies as given for the applications of multiphase flows with phase changes.

Chapter 2 provides a detailed account of the transport theories on continuum single-phase flows that include the laminar or turbulent flows of viscous fluids, the viscous fluid flows through porous media, and flows of granular particles. The most essential one is the continuum modeling of laminar flows of Newtonian fluids, which is the foundation of the Eulerian modeling approach of multiphase flows. The distinctly different transport mechanisms between a laminar flow and a turbulence flow as well as the flow regime transition conditions are presented. The essential aspects of the modeling of a turbulent flow of Newtonian fluid are also given. The basic theories of flows through porous media are represented by Darcy’s law, Ergun’s equation, and Brinkman's equation. The chapter also illustrates the continuum theory of granular flow, represented by the kinetic theory of granular flows whose transport mechanisms are dominated by inertia and interparticle collisions.

Chapter 4 discusses the mechanisms and formulation of various basic particle–particle interactions. The essential modes of these interactions include a pair of spheres interacting by head-on approaching or by wake attraction, flow through a uniformly suspended sphere, electrostatic field induced by the suspended charged particles, normal collision dynamics involving forces, deformation, contact area and duration for a pair of elastic spheres, van der Waals force, and capillary force due to liquid bridge between two particles. The chapter further discusses the nonidealized particle–particle interactions and associated formulation, including the radiation transport equation for thermal radiation within a particle cloud, collision dynamics with tangential friction and torsional traction of elastic spheres, inelastic collisions, and the concept of restitution coefficient, heat and charge transfer by particle collisions, and deformation, breakup, and coalescence of fluid particles. These particle–particle interactions are critical to the model formation of dense-phase multiphase flows.