## Discrete settling

The settling of a discrete non-flocculating particle in a dilute suspension can be described by means of classical mechanics. Such a particle is not affected by the presence of other particles, and settling is therefore a function only of the properties of the fluid and the characteristics of the particles. As shown in Fig. 11.5 the particle is affected by three forces:

(1) Gravity, Fg; (2) the buoyant force, Fb and (3) the frictional force, Ff.

In accordance with Newton's second law of motion, the following equation can be set up:

dt where vs = the linear settling velocity of the particles, m = the mass of the particles and t = time.

The gravity effect is given by:

where p = the particle density, V = the particle volume and g = the acceleration due to gravity.

The buoyant force is:

Figure 11.5. The settling particle is affected by three forces: The gravity, Fg, the buoyant force, Fb and the frictional force, Ff.

The frictional force is a function of different particle parameters, such as roughness, size, shape and velocity of the particle, and of the density and viscosity of the fluid. It can be described by the following relationship:

where pe = the fluid density.  