Particle size analysis by sieving
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Particle size analysis by sieving

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micromesh sieves are much better than those for 
woven-wire sieves; the apertures being guaranteed to ±2 jiim of nominal 
size apertures except for the smaller aperture sieves. Each type of sieve 
has advantages and disadvantages [38]; e.g. sieves having a large 
percentage open area are structurally weaker but measurement time is 
Sieving 217 
50 60 70 
100 110 
W, W^ 
Fig 4.5 Effective aperture width distribution with increasing sieving time. 
a 10 
' \u2022 \u2022 " \u2022 \u2014 \u2022 1 
Region 1 ]X 
^ 1 
J 1 i.....L Lnii. l i 
Region 2 1 
^ r Transition region 
1 1 1 I 1 1 i i l _ _ __.! 1 1\u20141 1 t i l l 
10 100 
Sieving time in minutes 
Fig. 4.6 The rate at which particle pass through a sieve. 
218 Powder sampling and particle size determination 
Size and shape accuracy are improved by depositing successive layers of 
nickel, copper and nickel on a stainless steel plate followed by etching 
through a photolithographic mask additional layers of copper and nickel. 
The holes are filled with dielectric, after which the additional nickel is 
removed down to the copper layer [39]. A description of electroforming 
methods for making multilayer matrixes for precision screens has been 
patented [40]. A process, which is claimed to give better bonding of the 
mesh on to the support grid, has also been described [41]. 
Niklas [42] discusses edge weaknesses in nickel electroformed sieves 
due to acute angle comers. Additives used during photo-etching increases 
these defects [43] Stork [44] also describe sieve preparation by 
electrodepositing a thin metal skeleton on to a substrate, removal of the 
skeleton from the substrate, followed by deposition of two or more layers 
of metal on both sides of the substrate. Additives encourage growth 
perpendicular to the surface of the skeleton. 
4.6 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 
|Lim. 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. 
The nominal wire thickness for a 75 |Lim sieve is 52 |Lim hence, at the 
commencement of a sieving operation, the nominal open area comprises 
35% of the total area [i.e. (75/127))^]; the apertures may range in size from 
42 to 108 |Lim (Figure 4.5). The number of particle that can pass through 
the smaller apertures decreases as sieving progresses and this results in a 
decrease in the effective percentage of available open area. Thus, the 
effective sieve size increases, rising, in the example given above, to 84 )Lim 
and then to 94 \xm and, eventually to the largest aperture in the sieve cloth. 
Hence, the mechanism of sieving can be divided into two regions with a 
transition region in between [46], an initial region that relates to the 
passage of particles much finer than the mesh openings and a second 
region that relates to the passage of near-mesh particles (Figure 4.6). Near-
mesh particles are defined as particles that will pass through the sieve 
Sieving 219 
openings in only a limited number of ways, and the ultimate particle is the 
one that will pass only through the largest aperture in only one orientation. 
The first region is governed by the law: 
P = afi (4.2) 
where P is the cumulative weight fraction through the sieve, t is the sieving 
time, a is the fraction passing through the sieve in unit time or per tap for 
hand sieving and Z? is a constant nearly equal to unity. 
Whitby assumed a to be a function of several variables; total load on 
sieve {W), Particle density (/T^), mesh opening (5), percentage open area 
(^Q), sieve area {A\ particle size {d) and bed depth on sieve (7). This 
function reduces to: 
a = f 
p^SA^ ' d' A' d' S^ 
an identity with seven variables and two dimensions; hence a is a function 
of five dimensionless groups. A^A is constant for any sieve, A/Sis so large 
that it is unlikely to have any appreciable effect, and the effect of variation 
in T/d is negligible so that the equation reduces to: 
' w s^ 
Ps^^o d 
Whitby found 
\u2014 ^ 1 
vMm ^^S^gpj 
where k^d^ is a linear function of the geometric mass mean of the particle 
size distribution, Cj and h are constants and a is the geometric standard 
deviation at a particular size on the distribution curve. This expression 
was found to hold for wheat products, crushed quartz, St Peter's sand, glass 
beads and other similar materials. 
Whitby suggested that the end-point of sieving be selected at the 
beginning of region 2. This can be done, by plotting the time-weight curve 
on log-probability paper, and selecting the end-point at the beginning of 
220 Powder sampling and particle size determination 
region 2. It is difficult to do this in practice and an alternative procedure is 
to use a log-log plot and define the end-point as the intersection of the 
extrapolation for the two regions (Figure 4.6). 
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. 
The second region refers to the passage of 'near-mesh' particles. These 
are defined as particles that will pass through the sieve openings, in only a 
limited number of ways, relative to the many possible orientations with 
respect to the sieve surface. The passage of such particles is a statistical 
process, that is, there is always an element of chance as to whether a 
particular particle will or will not pass through the sieve. In the limit, the 
largest aperture through which the ultimate particle will pass in only one 
particular orientation controls the sieving process. In practice there is no 
'end-point' to a sieving operation, so this is defined in an arbitrary manner. 
The rate method is fundamentally more accurate than the time method but 
it is more tedious to apply in practice and, for most routine purposes, a 
specified sieving time is adequate. Several authors have derived equations 
for the rate of sieving during region 2 where the residual particles are near 
mesh. The general relationship is of the form: 
'-^ = k{R,-Rj' (4.6) 
where 7?^ is the residue on the sieve at time t and R^ is the ultimate end-
Kaye [47] and Jansen and Glastonberry [48] assumed m = 1 and plotted 
\og(Rf - R^) against t, which yields a straight line if the (assumed) value 
for R^ is correct. 
In practice, this value of 7? 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 |im sieve, the true end-point could 
be 100 jam or more. 
Sieving 221 
4.7 Calibration of sieves 
It is not widely realized that analyses of the same sample of material, by 
different sieves of the same nominal aperture size, are subject to 
discrepancies that may be considerable. These discrepancies may be due 
to non-representative samples, differences in the time the material is 
sieved, operator errors, humidity, different sieving actions and differences 
in the sieves themselves