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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 reduced. Sieving 217 50 60 70 W(iiominal) 100 110 W, W^ Fig 4.5 Effective aperture width distribution with increasing sieving time. 100 CO a 10 ^ h h L V ' \u2022 \u2022 " \u2022 \u2014 \u2022 1 j Region 1 ]X ^ 1 J 1 i.....L Lnii. l i Region 2 1 ^ r Transition region 1 1 1 1 I 1 1 i i l _ _ __.! 1 1\u20141 1 t i l l 10 100 Sieving time in minutes looq 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^ (4.3) 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 (4.4) Whitby found f aW \u2014 ^ 1 A^S h vMm ^^S^gpj (4.5) 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- point. 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