Fluid Mechanics for Chemical Engineering

Chapter 16

Movement of a Solid Particle in a Fluid Flow

This chapter deals with the movement of a small solid particle in a fluid flow. We start by presenting the equations governing particle movements, which we refer to as the Basset, Boussinesq, Oseen, and Tchen (BBOT) equations, to name a few key contributors to this modeling. Rather than deriving the equations, we endeavor to identify and discuss the physical meaning of the different terms: acceleration, added mass, Basset term, etc.

This approach is embodied by applying the BBOT equations to describe the behavior of a particle in three configurations of particular significance by their applications:

1. the movement of a fluid particle under the effect of gravity in a fluid at rest,

2. the movement of a particle in a unidirectional sheared fluid flow, and

3. the centrifugation of a particle in a rotating flow.

The BBOT equations allow the determination of the characteristic time with which the dynamics of a solid particle placed in a fluid flow adapts to its environment. This chapter is quite theoretical, although we have presented few derivations. This enables the reader to understand the hypotheses used in Chapters 15 (behavior of particles within gravity field) and 17 (centrifugation).

In section 16.5, we discuss the lift force applied on a particle in a unidirectional flow. This force is not taken into account by the BBOT equations. Finally, we conclude with the application of the results presented in this chapter to laminar ...