This chapter is dedicated to the elementary problem, which concerns interactions between a single particle and the surrounding fluid. First, we explore the drag force, which is the most common interaction. It is shown how this force is derived and applied in practice. This topic is further expanded upon by introducing Basset and added mass force – both are crucial for unsteady cases such as accelerating particles. Next, lift forces (Magnus and Saffman) are shown that may result in the particle’s motion in the lateral direction. To some extent, this is associated with the next issue explained in the chapter: the torque acting on a particle. The following sections pay attention to other interactions: Brownian motion, rarefied gases and the thermophoretic force. These interactions play a role for tiny particles, perhaps of nano-size. Ultimately, we deliberate heat effects when the particle and fluid have different temperatures. Thus, this last section scrutinise convective and radiative heat transfer.

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.