Particles settling

Figure 3.3 shows a simple type of classifier. In this device, a large tank is subdivided into several sections. A size range of solid particles suspended in vapor or liquid enters the tank. The larger, faster-settling particles settle to the bottom close to the entrance, and the slower-settling particles settle to the bottom close to the exit. The vertical baffles in the tank allow the collection of several fractions. 

Figure 3.5 shows centrifuges in which a cylindrical bowl is rotated to produce the centrifugal force. In Fig. 3.5a, the cylindrical bowl is shown rotating with a feed consisting of a solid-liquid mixture admitted at the center. The feed is immediately thrown outward toward the walls of the container. The particles settle horizontally... 

Since the radial acceleration functions simply as an amplified gravitational acceleration, the particles settle toward the bottom -that is, toward the circumference of the rotor-if the particle density is greater than that of the supporting medium. A distance r from the axis of rotation, the radial acceleration is given by co r, where co is the angular velocity in radians per second. The midpoint of an ultracentrifuge cell is typically about 6.5 cm from the axis of rotation, so at 10,000, 20,000, and 40,000 rpm, respectively, the accelerations are 7.13 X 10, 2.85 X 10 , and 1.14 X 10 m sec" or 7.27 X 10, 2.91 X 10, and 1.16 X 10 times the acceleration of gravity (g s). 

In a solution of molecules of uniform molecular weight, all particles settle with the same value of v. If diffusion is ignored, a sharp boundary forms between the top portion of the cell, which has been swept free of solute, and the bottom, which still contains solute. Figure 9.13a shows schematically how the concentration profile varies with time under these conditions. It is apparent that the Schlieren optical system described in the last section is ideally suited for measuring the displacement of this boundary with time. Since the velocity of the boundary and that of the particles are the same, the sedimentation coefficient is readily measured. 

Measurement of single particle settling velocity in a turbulent field is not easy. However, it is known to be a function of free settling velocity which for spherical particles can be estimated from the following ... 

A single particle settling in a gravity field is subjected primarily to drag force, gravity force, Ta-g-, and buoyancy, which have to be in... 

The length of time the particles stay in the pool determines the distance the particles settle in the pool. Thus, the feed entrance must be located so that the velocity of the pulp toward the weir, together with the distance, allows sufficient time for the fine particles to be carried out over the weir as the... 

Glassification. Classification (2,12,26,28) or elutriation processes separate particles by the differences in how they settle in a Hquid or moving gas stream. Classification can be used to eliminate fine or coarse particles, or to produce a narrow particle size distribution powder. Classification by sedimentation iavolves particle settling in a Hquid for a predetermined time to achieve the desired particle size and size distribution or cut. Below - 10 fim, where interparticle forces can be significant, gravitational-induced separation becomes inefficient, and cyclone and centrifugation techniques must be used. Classification also separates particles by density and shape. Raw material separation by differential sedimentation is commonly used in mineral processiag. 

Hindered Settling When particle concentration increases, particle settling velocities decrease oecause of hydrodynamic interaction between particles and the upward motion of displaced liquid. The suspension viscosity increases. Hindered setthng is normally encountered in sedimentation and transport of concentrated slurries. Below 0.1 percent volumetric particle concentration, there is less than a 1 percent reduction in settling velocity. Several expressions have been given to estimate the effect of particle volume fraction on settling velocity. Maude and Whitmore Br. J. Appl. Fhys., 9, 477—482 [1958]) give, for uniformly sized spheres,... 

Wall Effects When the diameter of a setthng particle is significant compared to the diameter of the container, the settling velocity is reduced. For rigid spherical particles settling with Re < 1, the correction given in Table 6-9 may be used. The factor k is multiplied by the settling velocity obtained from Stokes law to obtain the corrected set-... 

Stokes-Cunningham correction foctor is included for fine particles settling in air. 

Top-Feed Procedure The sequence of operations with a top-feed leaf test is the same as in a bottom-feed test, except that the leaf is not immersed in the sluriy. The best method for transferring the slurry to the top-feed leaf is, of course, a function of the characteristics of the sluriy. If the particles in the sluriy do not settle rapidly, the feed can usually be transferred to the leaf from a beaker. If, however, the particles settle veiy rapidly, it is virtually impossible to pour the slurry out of a beaker satisfactorily. In this case, the best method is to make use of an Erlenmeyer flask, preferably one made of plastic. The slurry is swirled in the flask until it is completely suspended and then abruptly inverted over the leaf. This technique will ensure that all of the sohds are transferred to the leaf. 

For dilute systems, Stoke s law is applicable to particle settling. References cited at the end of this chapter provide design and sizing information. 

Parameter x can be expressed in terms of the ratio of the mass of solid particles settled on the filter plate to the filtrate volume, x, and, instead of r , a specific mass cake resistance, r , is used. That is, r, is the resistance to the flow presented by a uniformly distributed cake in the amount of 1 kg/m. Replacing units of volume by mass, the term r x into the above expression changes to r x,j,. Neglecting the filter plate resistance (i.e., R, = 0), then ... 

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