Particles Within the Gravity Field

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

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, Browruan 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 the particles in suspension. 

Finally, we present in section 15.6 the mechanical principles governing fluidized beds. By directing an upward flrud stream through a bed of particles deposited on a sieve, it is observed that the flow of the fluid inside the bed places the particles in 

---

The BBOT equations lead to the classic results on the sedimentation of a small particle within the gravity field when the surrounding fluid is at rest. They describe the acceleration of the particle which is dropped with zero velocity, and determine the characteristic time needed to reach Stokes fall velocity. Since Ui = 0, eqnations... 

The left-hand-side terms in equations [16.43], [16.47], and [16.49] are in identical form to those derived when we stndied the fall of a small particle within the gravity field (section 16.3) or its displacement in a nnidirectional fluid flow (section 16.4). The time periods characterizing the acceleration phase of the particle are identical (equations [16.11] and [16.18]). We recall that these were short. Our discussion regarding the Basset terms (section 16.3) also transposes to the case of centrifiigatioa... 

The force acting on a particle within a centrifugal field is defined by Newton s fundamental force equation FM = mu. Acceleration acting upon the particle, directed loward the center of rotation is a = nr2. Therefore, the centrifugal force ading on the particle is F — mru 2. or expressed as multiples of gravity. 

Particle Manipulation Using Ultrasonic Fields, Fig. 2 Enhanced sedimentation. Particles within an ultrasonic field left) are agglomerated by the field center) and then tend to sediment under gravity right)... 

Particle Positions Under Gravity and Other Forces Yosioka and Kawasima also considered the direction in which an acoustic force will act on a particle in suspension. The equilibrium position of a particle within the field will be determined by the resolution of this acoustic force and any other forces acting on the particle. Typically this would be gravity, although it applies to any force. In the case of a planar resonant field in which the positive x-axis points vertically upwards, the particle will be in equilibrium when... 

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). 

---