Particles from gravitational force

As an illustration, consider the problem of removing solids and water droplets from deaerated bituminous froth produced from the oil sands hot water flotation process (see Chapter 13 and reference 35). This is a nonaqueous suspension from which the particles and water droplets must be removed before upgrading and refining. At process temperature (80 °C) the suspension viscosity is similar to that of bitumen alone, but the density, because of the dispersed solids, is higher. Taking rj = 500 mPa s (35), px = 1.04 g/mL and p2 = 2.50 g/mL, the rate of settling of 10 pm diameter solid particles under gravitational force will be very slow ... 

Settling and sedimentation. In settling processes, particles are separated from a fluid by gravitational forces acting on the particles. The particles can be solid particles or liquid drops. The fluid can be a liquid or a gas. 

Sedimentation (qv) techniques, whether based on gravitational forces or centrifugation, derive the particle size from the measured travel rates of particles in a Hquid. Before the particle analysis is carried out, the sample is usually dispersed in a medium to break down granules, agglomerates, and aggregates. The dispersion process might involve a simple stirring of the powder into a Hquid, but the use of an ultrasonic dispersion is preferred. 

The basic operations in dust collection by any device are (1) separation of the gas-borne particles from the gas stream by deposition on a collecting surface (2) retention of the deposit on the surface and (3) removal of the deposit from the surface for recovery or disposal. The separation step requires (1) application of a force that produces a differential motion of a particle relative to the gas and (2) a gas retention time sufficient for the particle to migrate to the coUecting surface. The principal mechanisms of aerosol deposition that are apphed in dust collectors are (1) gravitational deposition, (2) flow-line interception, (3) inertial deposition, (4) diffusional deposition, and (5) electrostatic deposition. Thermal deposition is only a minor factor in practical dust-collectiou equipment because the thermophoretic force is small. Table 17-2 lists these six mechanisms and presents the characteristic... 

In the preceding processes, the particles were separated from the fluid by gravitational forces acting on the particles. Sometimes gravity separation may be too slow because of the closeness of the densities of the particles and the fluid, because of small particle size leading to low settling velocity or, in the case of liquid-liquid separations, because of the formation of a stable emulsion. 

Most of the rocks that make up the upper crust of the earth lie hidden beneath layers of sediments, unconsolidated accumulations of particles derived from the weathering of minerals and rocks (see Fig. 44 and Textbox 45) (Keller 1957). Once formed, the particles are either carried away or moved by the wind, rain, and gravitational forces into the seas and oceans or, before they get there, into depressions in the land. There they accumulate in a wide range of shapes and sizes (see Table 49) (Rocchi 1985 Shackley 1975). 

Many engineering operations involve the separation of solid particles from fluids, in which the motion of the particles is a result of a gravitational (or other potential) force. To illustrate this, consider a spherical solid particle with diameter d and density ps, surrounded by a fluid of density p and viscosity /z, which is released and begins to fall (in the x = — z direction) under the influence of gravity. A momentum balance on the particle is simply T,FX = max, where the forces include gravity acting on the solid (T g), the buoyant force due to the fluid (Fb), and the drag exerted by the fluid (FD). The inertial term involves the product of the acceleration (ax = dVx/dt) and the mass (m). The mass that is accelerated includes that of the solid (ms) as well as the virtual mass (m() of the fluid that is displaced by the body as it accelerates. It can be shown that the latter is equal to one-half of the total mass of the displaced fluid, i.e., mf = jms(p/ps). Thus the momentum balance becomes... 

A force that is as large as the gravitational force can be used to suspend a particle against gravity, provided that it can be controlled and directed upward to balance gravity. One such force is the radiation pressure force or radiometric force. Ashkin and Dziedzic (1977), whose work is discussed in the next section, were the first to use the radiation pressure to levitate a microsphere stably. It was demonstrated by Allen et ai (1991) that the radiometric force can be measured with the electrodynamic balance, and they used the technique to determine the absolute intensity of the laser beam illuminating a suspended particle. This was accomplished in the apparatus displayed in Fig. 13. The laser illuminated the microparticle from below, and... 

Note When precipitation occurs in sol-gel processing, sol particles have aggregated to a size where gravitational forces cause them to sink or float. Generally, aggregation arises from a change in the sol that reduces the interparticle repulsion. 

From the analysis presented in the last two paragraphs, it is evident that the gravitational force acting upon the particle is used for the derivation of the equations for the terminal velocity and the pressure drop in the fluidized bed. Then, it is clear that the hydraulic density should be used in these equations as well as in any other equations that are derived from a similar force-balance analysis. For instance, this is the case of the Foscolo-Gibilaro criterion for determining the fluidization pattern (Section 3.8.2). 

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