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# Particle size analysis by sieving

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which may be due to wear. Ideally, sieves should have apertures of identical shape and size. However, due to the methods of fabrication, woven wire sieves have a range of aperture sizes and weaving gives a three dimensional effect. Fairly wide tolerances are accepted and specified in standards but even these are sometimes exceeded in practice. Leschonski [4] examined eight 50 |Lim woven wire sieves with the results presented in Figure 4.7. The median varied between 47.3 and 63.2 |um (almost certainly an incorrectly labeled 63 }xm sieve) and the standard deviation between 1.8 and 8.6 |Lim. Ilantzis [49] gave a rigorous statistical analysis of microscopic measurements on a set of 13 different sieves (Table 4.2). Most of the sieves had rectangular openings with wider variations on the warp than the weft, and with a coefficient of variation rising from 3% to 5% with large aperture sieves and up to 10% with small apertures. Only four of the sieves met the standard specifications. All aperture widths shown in Figure 4.7 are for nominal 50 |Lim sieves but comparative tests on the same material using these sieves could yield enormous differences in the residual weight. In order to obtain agreement between different sets of sieves it is therefore necessary to calibrate them and thenceforth to monitor them to detect signs of wear. One way of standardizing a single set of sieves is to analyze the products of comminution. It is known that the products are usually log- normally distributed hence, if the distribution is plotted on a log- probability paper, a straight line should result. The experimental data are fitted to the best straight line by converting the nominal sieve aperture to an effective sieve aperture. The traditional way of determining the median and spread of aperture sizes for a woven wire sieve is to size a randomly selected set of apertures using a microscope. Due to the method of manufacture, the measurements for the warp and weft will tend to differ. The limiting size may also be determined by using spherical particles. These are fed on to the sieve which is then shaken and the excess removed. Many spheres will have 222 Powder sampling and particle size determination 40 50 6 0 Aperture size in microns Fig. 4.7 Cumulative distribution by number of aperture widths of eight 50 |j.m woven wire sieves. Table 4.2 Means and standard deviations of 13 different sieves as reported by Ilantzis [50] Nominal aperture width (urn) 40 50 63 80 100 125 160 200 250 315 400 500 630 Warp Median (urn) 44.1 53.2 62.9 82.6 103.2 121.5 167.7 200.8 258.9 299.3 414.5 512.9 639.0 Standard deviation 4.85 6.12 4.20 5.68 4.44 4.89 10.48 11.51 14.60 22.63 22.00 28.70 20.70 Weft Median (|Lim) 45.2 50.8 64.0 84.3 106.1 123.8 155.2 214.8 260.9 295.9 467.6 500.5 634.0 Standard deviation 4.56 5.19 3.75 4.02 2.91 5.59 6.79 16.46 14.40 17.29 1 26.40 25.00 43.20 Sieving 223 jammed into the sieve cloth and may be removed for examination. In such an examination, Kaye et al [51] showed that both methods yielded similar data for a 65-mesh Tyler sieve, with 90% of the apertures falling between 0.91 and 1.07 of the nominal size. Kaye recommends monitoring sieves every few months using glass beads to find out whether the sieve apertures are deteriorating or enlarging. These beads are available from the National Institute of Standards and Technology. Table 4.3 NBS Standard reference materials designated for calibration of sieves SRM 1003 b 1004b 1017b 1018b 1019b Particle diameter in microns 10 to 60 40 to 150 100 to 400 220 to 750 750 to 2450 Standard polystyrene spheres are also available for calibration purposes from Gilson and Duke Standards. Stork Screens Inc. measure apertures and screen wire dimensions using wax impressions and the impressions are examined with an automatic image analyzer. Sieves may also be calibrated by a counting and weighing technique applied to the fraction of particles passing the sieve immediately prior to the end of an analysis. These will have a very narrow size range and the average particle size may be taken as the cut size of the sieve. A minimum number {n) of particles need to be weighed to obtain accurate volume diameters {d^)\ let this weight be m and the particle density be /? then: < - \f^. (4.7) Particles larger than 250 |im can easily be counted by hand and, if weighed in batches of 100, d^ is found to be reproducible to three significant figures. For particles between 100 and 250 |Lim in size, it is necessary to count in batches of 1000 using a magnifier. For sizes smaller than this, the Coulter Principle can be used to obtain the number concentration in a known suspension. An alternative procedure using tacky dots has also 224 Powder sampling and particle size determination been described [52]. Sieve analyses are then plotted against volume diameter in preference to the nominal sieve diameter. The method is tedious and time consuming and BCR have prepared quartz samples by this method that may be used as calibration material [53]. The quartz is fed to a stack of sieves and the analytical cut size is read off the cumulative distribution curve of the calibration material. A method for measuring accurately the aperture and wire diameter using wax impressions has also been described [54]. Rideal et. al. [55] describe the preparation, measurement and use of microspheres for calibrating individual test sieves. Broad distribution glass microspheres were first sieved at 75 |Lim and the undersize re-sieved on a 53 |am sieve using a production sonic sifter from Gilson. This was repeated three times to give about 90% by weight of powder between 53 and 75 |im. The resulting samples were then analyzed using a nest of electroformed sieves in the 45 to 75 [im aperture range and a calibration graph of percent, passing against mean aperture size was the generated. This graph was then used to calibrate a 63 |am sieve. Results were confirmed by microscope analysis of the sieve mesh. The calibration method gave a mean aperture of 59.6 |Lim with a standard deviation of 0.08 |Lim; by microscopy the sieve apertures were 60.5 |im; the near mesh method gave 63.5 |Lim. This last method is expected to generate a larger size since the particles measured are those trapped in the sieve mesh at the end of the analysis. Centerline sieve measurements service from ATM evaluate the wire and opening sizes in wire cloth and electroformed mesh used in test sieves. Service provides a data set of opening sizes for verifying compliance with applicable standards. 4.8 Sieving errors Hand sieving is the reference technique by which other sieving techniques should be judged. For instance, in the French standard NFX 11-57, it states: If sieving machines are used, they must be built and used in such a way that the sieve analysis must, within the agreed tolerances, agree with the analysis obtained by hand sieving. The apertures of a sieve may be regarded as a series of gauges that reject or pass particles as they are presented at the aperture. The probability that a Sieving 225 particle will present itself to an aperture depends upon the following factors: \u2022 The particle size distribution of the powder. The presence of a large fraction of near-mesh particles reduces the sieving efficiency. An excess of fines also reduces sieving efficiency. It is recommended that fines should be removed before carrying out the sieve analysis. This is effected by pre-sieving, by hand, on the finest sieve to be used in the subsequent analysis. If this is not done, the fines will have to pass through the whole nest of sieves, thus prolonging the analysis and increasing the risk of high powder loss. Since small particles often adhere to large ones it may be necessary to carry out this operation by wet sieving.