Beds of particles

Another separation device that may be used is the mineral jig. This unit produces a loose vibrating bed of particles in a Hquid medium. The vibrations segregate the soHds into layers of density. The dense nonferrous metals, primarily lead, 2inc, and copper are at the bottom while organics are at the top. The middle layer is primarily glass. 

In packed beds of particles possessing small pores, dilute aqueous solutions of hydroly2ed polyacrylamide will sometimes exhibit dilatant behavior iastead of the usual shear thinning behavior seen ia simple shear or Couette flow. In elongational flow, such as flow through porous sandstone, flow resistance can iacrease with flow rate due to iacreases ia elongational viscosity and normal stress differences. The iacrease ia normal stress differences with shear rate is typical of isotropic polymer solutions. Normal stress differences of anisotropic polymers, such as xanthan ia water, are shear rate iadependent (25,26). 

Percolation Leaching. Ground material coarse enough to permit circulation of a solution through a bed of particles can be leached by percolation of the solvent through the material placed ia a tank or vat. The process usually takes several days. 

Sedimentation. Gravity makes all particles that ate mote dense than the suspending Hquid move downward, and also causes beds of particles to compress toward the state of minimum-included Hquid. The sedimentation force,for a single spherical particle (not part of a bed) submerged in a Hquid is as foUows ... 

Fig. 3. Stressing mechanisms (a) single particles or (b) a bed of particles cmshed between two solid surfaces impact of a particle against (c) a solid surface or (d) another particle (e) cutting (f) shearing forces or pressure waves and (g) plasma reaction, an example of size reduction by nonmechanical energy.

Stressing between Two Solid Surfaces Crushing. Either single particles (Fig. 3a) or a bed of particles (Fig. 3b) are cmshed between two solid surfaces. The amount of stress that can be applied is governed by the force applied to the solid surfaces. 

Crushers and Roller Mills. In this equipment group, stress is applied by either cmshing single particles or a bed of particles between two sohd surfaces. In general, most machines are used for coarse and medium-size reduction, with the exception of the high pressure roUer mill which can achieve extremely fine particle distributions. 

Mass-Transfer Coefficient Denoted by /c, K, and so on, the mass-transfer coefficient is the ratio of the flux to a concentration (or composition) difference. These coefficients generally represent rates of transfer that are much greater than those that occur by diffusion alone, as a result of convection or turbulence at the interface where mass transfer occurs. There exist several principles that relate that coefficient to the diffusivity and other fluid properties and to the intensity of motion and geometry. Examples that are outlined later are the film theoiy, the surface renewal theoiy, and the penetration the-oiy, all of which pertain to ideahzed cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flowthrough banks of tubes, in fixed beds of particles, and the like, correlations have been developed that follow the same forms as the above theories. Examples of these are provided in the subsequent section on mass-transfer coefficient correlations. 

To determine the mass-transfer rate, one needs the interfacial area in addition to the mass-transfer coefficient. For the simpler geometries, determining the interfacial area is straightforward. For packed beds of particles a, the interfacial area per volume can be estimated as shown in Table 5-27-A. For packed beds in distillation, absorption, and so on in Table 5-28, the interfacial area per volume is included with the mass-transfer coefficient in the correlations for HTU. For agitated liquid-liquid systems, the interfacial area can be estimated... 

Fluidized Beds When gas or liquid flows upward through a vertically unconstrained bed of particles, there is a minimum fluid velocity at which the particles will begin to move. Above this minimum velocity, the bed is said to be fluidized. Fluidized beds are widely used, in part because of their excellent mixing and heat and mass transfer characteristics. See Sec. 17 of this Handbook for detailed information. 

Fluid bed boilers have also been applied as a cure to sulfur dioxide air pollution from power plants. Various schemes have been developed in which combustion of a sulfur containing fuel takes place in a fluidized bed of particles which absorb or react with sulfur dioxide. The particles are usually regenerated to recover sulfur, which often has enough by-product value to make a significant contribution to process economics. 

Adlington and Thompson (Al) measured the gas-liquid interfacial area in beds of particles of from 0.3- to 3-mm diameter by oxygen absorption in a sodium sulfite solution. They found that the interfacial area decreased with decreasing bed porosity, and was less sensitive to changes in particle size. 

If Ihe particles tend to form a bed, they will be affected by the lateral dispersive forces described by Bagnold<69-70). A fluid in passing through a loose bed of particles exerts a dilating action on the system. This gives rise to a dispersion of the particles in a direction at right angles to the flow of fluid. 

Fluid bed electrodes consist of a bed of particles supported by a structure such as a coarse sinter and fluidized by an upward stream of electrolyte and two different configurations have been described where the current path is parallel or perpendicular to the direction of fluidization (Backhurst et al., 1969). Such electrodes have been used for electrosynthetic reactions and, in particular, a pilot plant for the reduction of... 

A well-defined bed of particles does not exist in the fast-fluidization regime. Instead, the particles are distributed more or less uniformly throughout the reactor. The two-phase model does not apply. Typically, the cracking reactor is described with a pseudohomogeneous, axial dispersion model. The maximum contact time in such a reactor is quite limited because of the low catalyst densities and high gas velocities that prevail in a fast-fluidized or transport-line reactor. Thus, the reaction must be fast, or low conversions must be acceptable. Also, the catalyst must be quite robust to minimize particle attrition. 

However, in contrast to the two classes of dispersive mixers mentioned before, the attached flow-through channel contains a packed bed of particles which may carry a catalyst. This chamber is much larger than the typical dimensions of the inlet channels (e.g. compare with Section 5.1.2). The packed bed and its interstices influence the gas/liquid flow patterns, e.g. a trickle-bed operation may be established. 

Method Polishing treatment after chemical precipitation and sedimentation by filtration through a bed of particles of several distinct size ranges. 

A majority of the models incorporate what are essentially curve fitting parameters or functions. Some (C11, K12) are more pertinent to the pressed, briquetted, or tableted beds of particles rather than to granulated ensembles of particles, even though the distinction between the two kinds of pellets is necessarily somewhat arbitrary. 

A water stream contacts a bed of particles with diameters ranging from 1 to 1000 gm and SG = 2.5. The water stream flows upward at a rate of 3 cm/s. What size particles will be carried out by the stream, and what size will be left behind ... 

Wemer, A., Haider, M., and Linzer, W., Modelling of Particle Population in Fluidized Beds of Particles Differing in Size and Physico-chemical Behaviourf Preprint Fluidization VIII, 1 557 (1995)... 

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