CHAPTER 10
MECHANICAL SEPARATIONS (cont'd)

SIEVING

In the final separation operation in this group, restraint is imposed on some of the particles by mechanical screens that prevent their passage. This is done successively, using increasingly smaller screens, to give a series of particles classified into size ranges. The fluid, usually air, can effectively be ignored in this operation which is called sieving. The material is shaken or agitated above a mesh or cloth screen; particles of smaller size than the mesh openings can pass through under the force of gravity.

Rates of throughput of sieves are dependent upon a number of factors:
nature and the shape of the particles,
frequency and the amplitude of the shaking,
methods used to prevent sticking or bridging of particles in the apertures of the sieve and
tension and physical nature of the sieve material.

Standard sieve sizes have been evolved, covering a range from 25 mm aperture down to about 0.6 mm aperture. The mesh was originally the number of apertures per inch. A logical base for a sieve series would be that each sieve size have some fixed relation to the next larger and to the next smaller. A convenient ratio is 2:1 and this has been chosen for the standard series of sieves in use in the United States, the Tyler sieve series. The mesh numbers are expressed in terms of the numbers of opening to the inch (= 2.54 cm).

In order to get reproducible results in accurate sieving work, it is necessary to standardize the procedure. The analysis reports either the percentage of material that is retained on each sieve, or the cumulative percentage of the material larger than a given sieve size.

The results of a sieve analysis can be presented in various forms, perhaps the best being the cumulative analysis giving, as a function of the sieve aperture (D), the weight fraction of the powder F(D) which passes through that and larger sieves, irrespective of what happens on the smaller ones. That is the cumulative fraction sums all particles smaller than the particular sieve of interest.

 Thus F = F(D),
   dF/dD = F ' (D)

where F ' (D) is the derivative of F(D) with respect to D.

So dF = F ' (D) dD                                                                                                (10.15)

and so integrating between D_{1 and D2} gives the cumulative fraction between two sizes D₂ (larger) and D₁ which is also that fraction passing through sieve of aperture D₂ and caught on that of aperture D₁. The F'(D) graph gives a particle size distribution analysis.

EXAMPLE 10.7. Sieve analysis
Given the following sieve analysis:

plot a cumulative sieve analysis and estimate the weight fraction of particles of sizes between 0.300 and 0.350 mm and 0.350 and 0.400 mm.

This has been plotted on Fig. 10.9 and the graph F(D) has been smoothed. From this the graph of F'(D) has been plotted, working from that slope of F(D), to give the particle size distribution.

FIG. 10.9 Particle-size analysis

To find the fraction between the specified sizes, eqn. (10.15) indicates that this will be given directly by the fraction that the area under the F ' (D) graph and between the sizes of interest is to the total area under the
F' (D) curve. Counting squares, on Fig. 10.9, gives:
           between 0.300 and 0.350 mm as 13%
           and        0.350 and 0.400 mm as 9%.

For industrial sieving, it is seldom worthwhile to continue until equilibrium is reached. In effect, a sieving-efficiency term is introduced, as a proportion only of the particles smaller than a given size actually get through. The sieves of a series are often mounted one above the other, and a mechanical shaker used.

Sieve analysis for particle-size determination should be treated with some caution especially for particles deviating radically from spherical shape, and it needs to be supplemented with microscopical examination of the powders. The size distribution of powders can be useful to estimate parameters of technological importance such as the surface area available for a reaction, the ease of dispersion in water of a dried milk powder, or the performance characteristics of a spray dryer or a separating cyclone.

Industrial sieves include rotary screens, which are horizontal cylinders either perforated or covered with a screen, into which the material is fed. The smaller particles pass through as they tumble around in the rotating screens. Other industrial sieves are vibrating screens, generally vibrated by an eccentric weight; and multi-deck screens on which the particles fall through from one screen to another, of decreasing apertures, until they reach one which is too fine for them to pass. With vibrating screens, the frequency and amplitude of the vibrations can significantly affect the separation achieved. Screen capacities are usually rated in terms of the quantity passed through per unit area in unit time. Particles that can conveniently be screened industrially range from 50 mm diameter, upwards.

Continuous vibrating sieves used in the flour-milling industry employ a sieve of increasing apertures as particles progress along the length of the screen. So the finer fraction at any stage is being removed as the flour particles move along. The shaking action of the sieve provides the necessary motion to make the particles fall through and also conveys the oversize particles on to the next section. Below the sieves, in some cases, air classification may be used to remove bran.


Mechanical separations > SUMMARY, PROBLEMS

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