CHAPTER
10
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). 
By suitable choice of sizes for the wire from which the sieves are woven,
the ratio of opening sizes has been kept approximately constant in moving
from one sieve to the next. Actually, the ratio of 2:1 is rather large
so that the normal series progresses in the ratio of Ö2:1
and if still closer ratios are required intermediate sieves are available
to make the ratio between adjacent sieves in the complete set ^{4}Ö2
: 1.
The standard British series of sieves has been based on the available standard wire sizes, so that, although apertures are generally of the same order as the Tyler series, aperture ratios are not constant. In the SI system, apertures are measured in mm. A table of sieve sizes has been included in Appendix 10. 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.
where F ' (D) is the derivative of F(D) with respect to D.
and so integrating between D_{1 }_{and D2 }gives the cumulative fraction between two sizes D_{2} (larger) and D_{1} which is also that fraction passing through sieve of aperture D_{2} and caught on that of aperture D_{1}. The F'(D) graph gives a particle size distribution 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. From
the above table:
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.
For industrial sieving, it is seldom worthwhile to continue until equilibrium is reached. In effect, a sievingefficiency 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 particlesize 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 multideck 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 flourmilling 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.
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