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Acknowledgment Financial support of this work was provided by the National Science Foundation through Grant CBT 8516449.
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Liquid States of Water in SI Units; Hemisphere Publishing: New York, 1984. Hales, J. L.; Ellender, J. H. J. Chem. Thermodyn. 1976,8 , 1177. Hales, J. L.; Gundry, H. A.; Ellender, J. H. J. Chem. Thermodyn. 1983, 15, 211. Kay, W. B.; Donham, W. E. Chem. Eng. Sci. 1955,4 , 1. Kemp, J. D.; Giaugue. W. F. J. Am. Chem. SOC.1937, 5 9 , 79. Kennedy, R. M.; Sagenkahn, M.; Aston, J. G. J. Am. Chem. SOC. 1941,63, 2267. Kim, H.; Lin. H. M.; Chao, K. C. Ind. Eng. Chem. Fundam. 1986, 25, 75. Kirk-Othmer Encyclopedia of Chemical Technology, 3rd ed.; Wiley-Interscience: New York, 1982; Vol. 19, p 246. Kobe, K . A.; Ravicz, A. R.; Vohra. S. P. J. Chem. Eng. Data 1958, 1 , 50. Kratzke, H.; Muller. S. J. Chem. Thermodyn. 1985, 17, 151. Machado, J. R. S.; Streett, W. B. J. Chem. Eng. Data 1983. 2 8 , 218. Medir. M.; Giralt, F. AIChE J. 1982,28,341. Meyer, E. F.; Awe, M. J. J. Chem. Eng. Data 1980,25,371. O'Brien, L. J.; Alford, W. J. Ind. Eng. Chem. 1951, 43,506. Ohgaki, K.; Katayama, T. J. Chem. Eng. Data 1975,20,3. Partington, J. R.; Neville, N. H. J. Phys. Colloid Chem. 1956, 55, 1550. Pozo, M. E.; Streett, W. B. J. Chem. Eng. Data 1984,29, 324. Radosz, M. J. Chem. Eng. Data 1986, 31, 43. Reamer, H. H.; Olds, R. H.; Sage, B. H.; Lacey, W. N. Ind. Eng. Chem. 1944. 36,381. Reamer, H. H.; Sage, B. H. J. Chem. Eng. Data 1959a, 4 , 152. Reamer, H. H.; Sage, B. H. J. Chem. Eng. Data 1956b,4 , 303. Robinson, D. 6.; Senturk, N. H. J. Chem. Thermodyn. 1979, f l , 461. Sage, B. H.; Lacey, W. N. Monograph of API Research Project 37; American Petroleum Institute: New York. 1955. Schnaible, H. W.; Smith, J. M. Chem. Eng. Prog.. Symp. Ser. 1953, 7(4), 159. Schroeder, M. R.; Poling, B. E.; Manley, D. B. J. Chem. Eng. Data 1982,27, 256. Terent'eva, A. A,; Krumgal'z B. S.; Gerzhberg, Yu. I . Z h . Prikl. Khim. (Leningrad) 1973, 46, 1143. Ter Gazarian, G. J. Chim. Phys. Phys.-Chim. Biol. 1906, 4 , 140. Timmermans. J. Sci. Proc. R . Dublin SOC. 1912, 73,327. Thies, M. C.; Paulaitis, M. E. J. Chem. Eng. Data 1984, 29. 438. Wade, F,;Merriman, P. W. J. Chem. SOC. 1912, 101, 2437. Young, S. J. Chem. SOC. 1891, 59,903. Young, S. Sci. Proc. R . DublinSoc. 1910, 12,374. Zinov'ev, A. A,; Rosolovskii, V. Y. J. Inorg. Nucl. Chem. 1960, 5. 1239.
School of Chemical Engineering Purdue Uniuersity West Lafayette, Indiana 47907
William A. Leet Ho-Mu Lin Kwang-Chu Chao*
Received for review J u n e 16, 1986 Revised manuscript received July 29, 1986 Accepted August 11, 1986
Performance Evaluation of Particle Size Classifiers
Performance evaluation of a particle size classifier strongly depends on both the agglomeration properties of feed powders and the erroneous results of particle size analysis. Several calculated examples of the grade or partial separation efficiency curves are presented in order to show the trends for an assumed ideal (perfect) classifier.
Introduction Exact size classification is a severe requirement for micron size powders, for example, new ceramic materials, toner suspensions, coating powders, etc. It is desirable that the classification performance be as sharp as possible. The criterion of performance is usually based on the grade or partial separation efficiency curve. The grade efficiency is calculated from measured particle size distributions of both fine and coarse or feed powders. However, particle size measurements often give erroneous results, especially for the submicron size range, even with liquid sedimentation methods, and agglomeration of the feed powder deteriorates the classification performance. Therefore, the evaluation of classifier performance depends on both the measurement accuracy of particle size analyzers and the adhesion property of feed powders that are fed to the classifier. 01 96-4313/86/ 1025-0701$0 1.50/0
If a classifier has really ideal (perfect) performance, its grade efficiency must change in steps from zero for very small particles to 100% at the classification cut size, Dpc. The measured or apparent efficiency usually becomes much deteriorated or unexpected. This fact creates confusion for the performance evaluation of size classifiers in practice. This paper discusses the effects of both feed agglomeration and erroneously measured size distributions on the apparent grade efficiency of an ideal classifier, assuming a simple uniform size distribution of feed powder. The results are shown in several calculated examples.
Effect of Agglomeration of Feed Powder If the classification is assumed to be perfect (ideal), the stepwise grade efficiency curve will appear as shown in Figure 1and 2. If the particle size measurements are also
0 1986 American
Chemical Society
702
Ind. Eng. Chem. Fundam., Vol. 25, No. 4, 1986
f c‘
\y
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Figure 1. Particle size classifier flowsheet.
m
0
(’
Feed f c
’
50
1
(%I
Dpc
AR
Figure 4. Second example of particle size distributions (fo and fo‘) and grade efficiency (AT) of an ideal (perfect) classifier for an agglomerated feed powder, measured by a precise size analyzer.
Figure 2. Particle size distributions (fo) and grade efficiency (Aq) of an ideal (perfect) classifier for a completely dispersed feed powder, measured by a precise size analyzer.
-
0 DPC
DP
Figure 5. Third example of particle size distributions (fo and fo’) and grade efficiency (Aq) of an ideal (perfect) classifier for an agglomerated feed powder, measured by a precise size analyzer.
A q0=50%
u0
Figure 3. First example of particle size distributions and fd) and grade efficiency ( A q ) of an ideal (perfect) classifier for an agglomerated feed powder, measured by a precise size analyzer.
exactly accurate, agglomeration of feed powders will give deteriorated grade efficiency curves, especially for the smaller size ranges. Figures 3-6 show a few model examples of grade or partial separation efficiency curves, 117,in the case of the feed agglomeration, assuming an uniform frequency size distribution, f o (solid lines), of a fully dispersed feed powder. The agglomerated size distributions are assumed to be the distributions, fd (the broken lines), in these figures. If there is no agglomeration, the efficiency curve, AQ, should be just a vertical step at the cut size, Dpc.
f
% qz’% 6 1 ?/o
Effect of Erroneous Particle Size Measurement
Figure 6. Fourth example of particle size distributions (fa and fo’j and grade efficiency (Sq)of an ideal (perfect) classifier for an agglomerated feed powder, measured by a precise size analyzer.
If a size-measuring instrument gives an erroneously broader distribution, fd’,than the real uniform (rectangular) distribution, fo, for the feed powder and an erroneous
(false) one, fl”, for the coarse product, the grade efficiency curve, 2q,becomes an inclined step like the one in Figure
Ind. Eng. Chem. Fundam., Vol. 25, No. 4, 1986 Fine
)”;
Coarse ~
70’’ f,”
703
hand, if the measured distributions, fo” and f1”, are narrower than the real, uniform ones, as shown in Figure 8, the grade efficiency curve, Aq, reaches more than 100% and the apparent cut size deviates from the real value. In practice, light-diffraction methods for particle size measurement often show broader size distributions and may give inferior evaluation of a classifier’s performance.
Conclusion From the above explanation, it is shown that both the exact measurements of particle size distributions and the complete dispersion of the feed powder are very important factors for the evaluation of a classifier’s performance. If the feed dispersion and/or the particle size analysis are not good enough, the performance evaluation of any classifier will be badly distorted. DPC
Figure 7. An example of erroneously measured, broader particle size distributions (f,,,.f{, and q{f?) and grade efficiency (A?) of an ideal (perfect) classifier for a completely dispersed feed powder.
rT
Figure 8. Another example of erroneously measured, narrower particle size distributions (io, fd‘, and q{fl”) and grade efficiency (A?) of an ideal (perfect) classifier for a completely dispersed feed powder.
7 instead of a vertical step a t the cut size, Dpc. An example without agglomeration is shown in Figure 7. On the other
Nomenclature Dp = particle size or diameter, km Dpc = classification (cut) size, km fo = frequency distribution of particle size for fully dispersed feed powder, % /Apm f,,’ = frequency distribution of particle sizes for agglomerated feed powder, % /AMm f / = erroneously measured frequency distribution of completely dispersed particle sizes for feed powder, % /AFm fl” = erroneously measured frequency distribution of completely dispersed particle sizes for coarse powder, % / Akm to= recovery efficiency of coarse powder for fully dispersed feed powders, dimensionless or % A t = grade or partial separation efficiency of a size classifier, dimensionless or % q,,’ = recovery efficiency of coarse powder for agglomerated feed powders, dimensionless or % Q,,” = recovery efficiency of coarse powder for an erroneously measured size distribution, dimensionless or % The Society of Powder Technology Shibunkaku-Kaikan, 2-7 Tanakasekiden-cho, Sakyo-ku Kyoto 606, J a p a n
Koichi Iinoya
Received for review June 12, 1986 Revised manuscript received J u n e 18, 1986 Accepted July 30, 1986
