Fluid Mechanics for Chemical Engineering

Chapter 15

Particles Within the Gravity Field

In this chapter, we discuss several aspects of the mechanical behavior of particles situated within the gravity field.

The density ρ_s of the particles often differs from the density ρ_f of the fluid in which they are immersed. Within the gravity field, this produces a relative movement of the particles with respect to the fluid, either upward (rising) or downward (settling), depending on whether the particles are less or more dense than the fluid. In section 15.1 we study how to evaluate the fall velocity of a rigid spherical particle in a fluid at rest, before discussing in section 15.2 the settling of a set of particles. The relative gravitational movement of a small-sized fluid particle is then discussed in section 15.3 for a gas bubble in a liquid, a drop of liquid in a gas, or a drop of non-miscible liquid in another liquid.

We then study, in sections 15.4 and 15.5, how the stirring of a fluid can maintain a dispersed set of particles in suspension. Practitioners of underwater diving have remarked that water becomes turbid in the event of a storm; sediments are kept in suspension within the water layer by turbulence. In a fluid at rest, Brownian motion can also maintain a colloidal suspension (e.g. paint), which is composed of very fine particles. Both physical awareness and observation show that the denser and the larger the particles are, the greater is the energy of turbulence or the molecular stirring energy required to keep ...