Mathematical analysis of the sieving process

The tolerances on sieve cloth are extremely wide, particularly for small aperture cloth. For example, the British Standard Specification (BS 410) for a 200-mesh sieve requires a median diameter of 75 plus or minus 33 pm. It is clear that oversize apertures are more undesirable than undersize, since the latter are merely ineffective whilst the former permit the passage of oversize particles. In order to reduce differences between analyses using different sets of sieves (differences of up to 42% have been recorded) manufacturers such as ATM make specially selected sieves [45] available that can reduce the differences by a factor of 10. 

Whitby assumed a to be a function of several variables total load on sieve (W), Particle density (pj, mesh opening (5), percentage open area (Aq), sieve area (A), particle size (d) and bed depth on sieve (7). This function reduces to  

Using the conventional rate test, the sieving operation is terminated some time during region 2. The true end-point, when every particle capable of passing through a sieve has done so, is not reached unless the sieving time is unduly protracted. 

Kaye [47] and Jansen and Glastonberry [48] assumed m = 1 and plotted log(/ , - 7 oo) against t, which yields a straight line if the (assumed) value for R is correct. 

In practice, this value of R is of limited practical value, since it cannot apply to the nominal aperture of the sieve. As sieving progresses, the smaller apertures become ineffective since all the particles finer than these apertures will have passed through the sieve. The largest aperture in the sieve therefore controls the sieving operation and the final particle to pass through the sieve will only do so when presented to this aperture in its most favorable orientation, i.e. for a 75 pm sieve, the true end-point could be 100 pm or more. 

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