Interactions between particles in multiphase flow may also involve adhesion – i.e., an attraction between the particles. This issue is the main topic of this chapter. The first sections of the chapter, however, focus on a primary case: forces acting between two solid surfaces close to each other. A typical example is an interaction between two spherical bodies, which mimic two particles in a multiphase flow. This situation is later extended to a more complex case: the bodies change their shape due to these adhesive interactions. For this, two theories were developed in the literature (JKR and DMT), and they are fully described in the chapter. Later, it is shown how these theories can be adopted to investigate particle-particle collisions in a multiphase flow. In other words, this topic constitutes an extension of the previous chapter, where the focus was on purely “mechanical” interactions without considering any adhesive forces. Finally, the last section of the chapter describes rough surfaces. There is a brief description of how this real-life issue influences the adhesion between two bodies in contact.

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.