Size Reduction RICHARD H. SNOW
echnical meetings continue to provide interplay between T theoretical grinding research that is striving to become applied and practical grinding research that is striving to make use of newly available tools of computer simulations. 4 t the February 1969 AIME meeting in Washington, D.C., there was a session on simulation and also a stimulating panel discussion on the problems of scale-up of large mills. I t was concluded that plant performance is usually 307, below that predicted by scale-up methods in use. Another session a t the September 1969 AIME meeting in Salt Lake City presented representative papers on current developments in computer applications, particularly to milling circuit simulation. The Engineering Foundation Research Conference on Particulate Matter Systems, held a t Deerfield, Massachusetts, in August 1969, attracted a number of well-known research workers from abroad as well as representatives of U.S. and Canadian industry and academic researchers, and provided a more extended forum for these discussions. A session on comminution a t the November 1969 AIChE meeting in Washington, D.C., will continue this exchange of information. At the September AIME meeting it was agreed that the term “selection function” is misleading and should be replaced by “rate function.” This change will be made in next year’s annual review. Fracture Behavior
Bond (78) reviews attempts to induce breakage without wastefully applying pressure and concludes that inherent practical limitations have been found for the following methods: spinning particles, resonant vibration, electrohydraulic crushing, induction heating, sudden release of gas pressure, and chisel effect breakers. He suggests that research to improve the efficiency of comminution start with the fundamental mechanisms of fracture as it depends on the physical structure of rocks. A new journal, Engineering Fracture Mechanics, has started publication on this subject. New tools for studying fracture include the scanning electron microscope. I t can reveal crystal dislocations and flaws, and may be a useful tool to study the mechanism of fracture propagation. Examples of such use are shown in a n article by Willard (794). For example, the microscope can distinguish between fracture along grain boundaries and across them, and could be used to settle some long-standing questions about fracture of heterogeneous materials. Another new tool, called acoustic emission, is used by 102
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Dunegan, Harris and Tatro (50) to detect incipient fracture in flawed metal specimens far below the general yield stress. Kerkhof (94) continues his pioneering work on fractography, or the study of lines induced on fracture surfaces by interaction of the crack front with impressed acoustic waves. Krushchov (96) reviews scratch test methods and concludes that the scratch test is a useful rough measure of the microhardness of minerals, although its fundamental significance is not clear. Glathart and Preston (63)elucidate by high-speed photographs the mechanism of impact breakage of glass sheets. Failure may begin under the impactor, when it is governed by the Hertz formula; or on the opposite side of the sheet, when it is governed by a flexural formula. Shand (768)gives further results on this subject. Solntsev and Fridman (773)study 10,000 cases of cracks or fracture in glass, vitreous enamels, and other silicate materials. They observe that one of the cracks is normal to the maximum tensile stress, and the length and shape of this crack depend strongly on both applied load conditions and the inherent strength and shape of the sample. Kambour (89) investigates the part played by crazing in the fracture mechanism of glassy polymers, while Heijboer (75)reports on the impact behavior of polymers. I t is commonly thought that crack-branching occurs when a crack reaches a definite velocity in a given material, but Congleton and Petch ( 3 9 ) find that it can vary with the stress on the crack. They give a theory for inducing persistent growth of a new crack ahead of a running crack. Their work is extended to alumina (40). Under special loading conditions, fracture can originate a t internal flaws in brittle materials, since stresses are concentrated there. Brady (20) assumes a statistical flaw distribution and determines a criterion for brittle fracture when a uniform stress field is applied. Edmonds and Beevers (53)consider the opposite problem and analyze the stress state around hard inclusions by means of a photoelasticity technique. Peter (733) further investigates this subject. Austin and Klimpel ( 7 ) correct previous analyses of the random fracture of solids based on assumed flaw distributions. Davidge and Tappin (46) compare prediction of grain boundary cracks with experiments, and point out that the theory cannot explain the experimentally observed strength/grain size relationship for polycrystalline BeO. All of the above approaches assume a uniform stress field within the sample. Barsom (9) shows that the fracture of thermally tempered glass sheets is related to the stored nonuniform strain energy, and they correlate the maximum tensile stress with the particle size produced.
lnformation interplay between theoretical grinding research and practical grinding research is heading toward further use of computer simulation
Hildinger (77) reports experimental results on the probability of breakage of single particles by drop-weights, an experimental condition for which few data were previously available. He tests glass spheres and particles of quartz, cement clinker, and limestone of sizes 1 to 12 mm and gives fragment size distributions. Cahn and Karpinski (24) report compression breakage results with iron ore pellets, and also find the breaking load to be normally distributed. They emphasize the need for a standardized test procedure in the industry. Hall (69) finds that decreased porosity increases the strength of ceramic materials, as does decreased grain size, the addition of sintering compounds, and other effects. Lund (709) reports that fine grinding of the raw materials increases strength of ceramic products. Hall (69) states that strength is often affected by surface conditions; Gutshall and Cross (67) suggest that a strong ceramic will result from a fine-grained surface layer with a large-grained interior. The small-grain surface reduces the size of cracks on the surface resulting from loading, thus increasing the stress required to cause fracture. The coarse-grained interior increases the stress required to propagate a crack through it. Experimental results on fracture by thermal shock in disks is given by Wilson (797), who correlates the results with surface stress, which can conveniently be calculated for this geometry. Mill Performance
Extensive data on wet grinding in laboratory ball mills is reported by Clarke and Kitchener (34). The main effect of slurry viscosity is to alter the lift of the balls by the mill walls, and hence change power consumption and grinding rate. Independent of this, there is another effect of viscosity that gives a flat maximum a t about 100 cP. Results are in agreement with the traditional rule that for fine grinding, the slurry should be thick enough to coat the balls, but not s o thick as to be impenetrable to impacts. Sterne and Stratton (775) experimentally determine scale-up of dry ball mills for grinding ceramic alumina from 9 in. to 6 ft diam mills. Effect on production, power consumption, and wear of media are presented for milling times u p to 24 hr, and media/ charge ratios of 4/1 and 8/1. No evidence of material packing occurs, but addition of a grinding aid improves efficiency by about
35%. I n continuous ball milling there is a n optimum load of balls that should be maintained as the balls wear. Rauth (747) obtains a formula for the optimum load by combining the Davis torque con-
cept with Bond’s empirical relation for the power consumed by the mill, assuming that best results are obtained when power consumption is maximized. The results check a few available plant data, and can be used for control of milling conditions. Patat and Schulz (137)assume that the optimum milling conditions are those under which the order of grinding kinetics is zero, and deduce these conditions from their previous kinetic studies. Harris (72) presents a general equation relating size reduction to time in batch grinding. This equation includes most cases deduced from kinetic studies. Agar ( 7 ) reviews correlations between energy consumption and size reduction, and shows that these are all statements of the same basic concept. Chandler (28) experimentally compares methods of measuring the grindability of 11 coals with roll crushing, attrition, scratch hardness, and surface energy. There is no good correlation among the standard grindability methods or these tests, except under limited conditions of low grindability and fines removal. The tests are either too laborious or do not simulate well the industrial conditions of coal milling. A spiral arrangement (6) of lifters over the length of a ball-mill chamber tends to distribute the media so that large balls are a t the feed end and small ones a t the discharge end. Ball mill liner wear in South African practice is throughly reported by French and Lissner (59), including photographs and data on wear of liners and discharge grates. The parts are designed to have the most metal in regions of greatest wear rate. When wear rate is plotted against metal hardness, the curve increases abruptly a t a hardness equal to that of the feed, and hardness has less effect outside this region. Thus the wear rate with feldspar is twice as much for pearlitic steel as for martensitic, while the difference is less for quartz. But the choice of material is limited by the resistance to impact of harder steels, and it depends on the extent of impact occurring in the mill. The greatest wear rate occurs at the inlet end of the mill and primary mills suffer the most impact. Osborn liner bars, which accumulate an autogenous lining, are very effective in reducing wear. So far they have not been used in mills larger than 9 ft in diameter because of the difficulty in installing them. Gommel (64) compares the comminution and wear rates in impact mills. The grinding rate increases with increasing hardness of the impact elements, while the wear rate decreases, so long as the feed and elements are of the same hardness range. Kriegel (98)finds that the wear rate of materials caused by flow of particles in a jet of air is influenced by the elastic modulus of the materials. VOL. 6 1
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Bombled (17) proposes a rapid method of predicting wear in cement mills by grinding corundum in a planetary mill, and finds that the rate accelerated 60 times. H e claims that the results agree with practice, although the results discussed above would deny this. A French conference (143) on ore-dressing includes papers by Regnier, Martin, Barthelmes, Gabillat, Huyet, Bombled, a n d Dours on experience of wear of media and linings in mills grinding bauxite, uranium ores, cement, and a survey of 15 ore treatments. Peter (732) finds that the wear of media in cement tube mills can be greatly reduced by using very hard alloys, which are replacing manganese steel. T h e latest developmcnt is a metal lining without bolts that assures a long life. German experience in use of rubber mill linings is presented by Lange (99) and Mohr ( 7 78). Both Swedish and domestic rubber linings are now available in the U.S. Minutes of a discussion (25)on rubber linings concern noise level, operating experience, grinding efficiency, and cost data. Bisson (74)reviews fundamental mechanisms of friction and wear and discusses the influence of crystal structure and hardness. Tsesnek (780) interprets data on abrasive wear by a microscopic model of the system of contact. Parameters of the model are known properties : friction coefficient, size of abrasive grain, and a n additional modulus which can be estimated theoretically or empirically. The problem of wear is found to be a problem of fluctuations of the friction forces with contacts. Although the advantages of high density alumina as grinding media are well known, Gendel et al. (62) state that the advantages of zirconia have not been fully appreciated for use in paint milling applications. Rich (745)describes the concept of a ball mill which has no gear drive because the mill itself serves as the armature of the motor, being surrounded by the windings. I t could be of value if mills increase from their present maximum size of 6600 hp. Planetary ball milling is a method of increasing the gravitational force acting on balls in a ball mill. Burke (22) reports that thoriaurania can be ground to 80y0 -5 pm in 90 min, while 40 hr are required by conventional ball milling. Majac fluid-energy mills can do the job quickly, but there is danger from the toxic dust. Dobrovol’skii et al. (47) explore the grinding of refractory metals and carbides in a planetary ball mill. The useful centrifugal force can reach 10 to 50 g, and the apparatus is capable of producing 1 to 2.6 pm particles in 5 to 20 min.
Figure I , 104
Vibratory ball mills continue to receive attention. Lesin (107) surveys the sizes, capacities, and construction details of Soviet vibratory mills. Hartman and Wyman (73) examine experimentally the operating conditions, and report that fineness increases with decreasing throughput rate, or increasing amplitude and frequency. Melman ( 7 76) finds that limestone develops caking in a vibratory mill under conditions of greatest impact, which decreases with increasing mill filling. Bertume (12)surveys the art of vibratory grinding in East Europe. He reviews formulas for inertial force of eccentric mechanisms and pictures several designs. The larger number of ball impacts makes the method more effective than conventional ball milling, so materials can be ground to 1 ym size. This results in greater strength of ceramics, produces settable plaster without dehydrating, and gives 5% greater enrichment of iron ore. Echalaz (52) reports tests on vibratory milling of gold ore in South Africa. The mill consists of two rigidly connected chambers vibrated a t 17 Hz, containing 1-1/2- to 2-in. balls. Tabular data indicates that power consumption compares favorably with conventional ball milling. Electrohydraulic crushing is a n exotic method that has not yet been found practical. The method applies a spark under water in the presence of pieces to be broken. Yigit, Johnson, and Maroudas (200)measure the shape and size distribution of aggregate crushed in this way. Ohme (728) reports an extensive investigation to try to make the method practical. The most severe experimental problem was obtaining a suitable electrical insulator for the electrodes, but a suitable one is found. Brass is most suitable for the electrodes themselves. Shock waves or friction cause comminution of grains; cavitation appears to play a minor role. Performance is rated in terms of kwh per unit of new surface formed. I t is best when the water has a low conductivity, and the material to be crushed completely surrounds the spark. Product particle sizes are mostly below 0.06 mm, and fineness increases with sparking time. The energy consumption is still 10 times that of conventional methods. Sarapuu (755) demonstrates electrical heating to break rock in several iron ore mines in Missouri and Minnesota. Heating is due to electrical contact resistance and internal resistance and performance depends on electrical conductivity of the rock. Equipment is commercially available. Multipoint electrodes are depicted in Figure l and electrified drill bits are also used. Electric power consumption is 1 to 2 kwh/ton rock. Another development
Multiple-point electrodes breaking taconite by electrical heating ( 155)
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Figure 2. Variation of selection function with size of feed particles and size of balls in ball mill (92) Courtesy of Powder Technology
by the Institute of Gas Technology is the breaking of street pavement by microwave heating. The main advantage is that the method does not make disturbing noise. Planiol's (737) impact grinder operating under vacuum is described in an English article. A rotor in this device throws particles of ore against a metal ring. Data tabulated in the article indicate less power consumption than a ball mill. Popelnik (738)studies performance of hammer crushers on coal, and finds that neither number of hammers nor their arrangement on the rotor has much effect, nor does the weight of hammers within a range from 7 to 13 kg. Breaker plates play little or no part in the impact crushing process. Economical jaw crushers are constructed so that the deadtime is minimized, according to Molling (727). I t depends on the drive speed, the resistance of the feed, and its tendency to pack. Marasanov ( 7 72) also reports the dynamic characteristics ofjaw crushers. A study by Mukai and Ichidate (723) indicates that multistage crushing of iron ore results in less fines than crushing in a single high-reduction stage. Data on the performance of spring-loaded roll mills for grinding weakly burned limestone is reported by B8rner (79). Zimmerman and Levine (203) describe Kady colloid mills and give capacities as well as costs. Rumpf (749)surveys the costs and methods of selection of comminution equipment. Equations are given for the component costs of cement clinker tube-milling, for which power cost is more than half the total. Mill Circuit S i m u l a t i o n a n d Control
Development of grinding circuit simulation mathematics has outstripped the ability to apply the results because of a lack of data concerning coefficients in the theory. Most published examples of simulation applications have been based on hypothetical data. I n fact the selection and breakage functions have never been measured in pilot- or full-sized mills, because laborious tracer methods are required to determine these functions directly and independently. Tracer experiments reported by Kelsall, Reid, and Restarick (92) show for the first time some features of the behavior of the selection function. Kelsall uses quartz of a particular size as a AUTHOR Richard H. Snow is a Senior Engineer at the IIT Research Institute, Chicago, Ill.
tracer in a mixture of sizes of calcite feed, and by dissolving the calcite he measures the appearance of quartz in the screen fractions of the product from a 10-in. diameter mill. Selection function of the finer feed sizes decreases exponentially with size according to Figure 2, and this agrees with results of the kinetics of grinding; see for example Herbst and Fuerstenau (76). I n addition, Kelsall's data shows that there is a maximum selection function, as was also shown by tracer experiments of Szantho and Furhmann reviewed last year. Curves of the form of Figure 2 can be fitted by the following equation containing three parameters
where = selection function = feed particle size, pm S,,, = maximum value of selection function X,,, = value of Xfor which S = S, a = slope of curve for fine feed particle sizes e = 2.70
S
X
That a maximum must exist should be apparent from the 1933 observation of Coghill and Devaney (36)that there is an optimum ball size for each feed size; conversely there must be a size of feed for which the selection function is a maximum. The data of Figure 2 show that the position of this maximum depends on the ball size. I n fact the feed size for which S is a maximum can be estimated by inverting the formula for optimum ball size given by Coghill and Devaney. Herbst and Fuerstenau (76) analyze data on the kinetics of ball milling with a view to deduce values of selection and breakage function from this data. They conclude that zero-order kinetics follow if there is a certain relationship between the selection and breakage functions. Harris (77) shows that the batch grinding differential equation can be solved to give a product size distribution in the form of a previously published (70)size law that includes many of the standard laws as special cases. Hukki and Allenius (87) investigate, by laboratory grinding experiments, the effect of sharpness of classification on the performance of a closed grinding circuit. This is also one objective of VOL. 6 1
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mathematical studies of grinding circuits. Kelsall, Stewart, and Reid (93) compute the performance of a closed-circuit grinding system with a cyclone classifier and confirm the results by comparison with their experimental data. Lynch et al. ( 7 7 7 ) model the performance of a rake classifier, calculate performance of a ballmill system in closed circuit with this classifier, and compare the results with experiment. Plant operating experience indicates that control of transients is important to obtain good grinding system performance. Bilan (73) gives extensive data to compare the uniformity of particle size analysis and assay of various streams in closed-circuit wet milling of iron ore with rod mill and cyclones. Slurry feed rate to the cyclone is kept constant and ore feed to the rod mill is controlled to maintain constant slurry density as determined by a gamma-gage. Such control decreases variability of the rod mill discharge and minimizes overgrinding. Daniel (42) also reports automatic control of a rod mill-ball mill circuit. A Russian cement-clinker tube mill is controlled by the combined signals from an electric ear attached to the primary chamber and the power demand of the product conveyor, as described by Gal’fand et al. (67). Applications
The state of the art of milling is reviewed by Schneider (759) including selective grinding of inhomogeneous matcrials, grindability, and activation of surfaces. Smith (777) considers comminution as a laboratory problem, and describes techniques. I n the large-scale grinding of ores such as iron ore, the efficiency of the operation can make a substantial difference in annual costs. Dor (49)compares primary grinding circuits used in several ironore concentrating plants. A dry circuit uses Aerofall mills, air classifiers, and screens, while a wet circuit uses a screen and wet cyclones. The dry circuit gives a product with a few per cent higher iron assay for the same amount passing 325 mesh, and it also requires less grinding energy to produce the same grade of product. This is attributed to the use of a dry magnetic separator to remove a tailing from the mill recycle stream. Iron recoveries are about 1 7, higher for the wet circuit, however. I n general, wet primary grinding has lower capital and operating costs than dry grinding, although this depends on circumstances. For second-stage ball milling of iron ore, Vetrova et al. (784)compare ore pebbles with steel balls as media. The per cent of slimes was less with pebbles (17 us. 2lYc), and the flotation concentrate was more consistent in iron content. A German symposium on ore-milling practice is edited by Clement (35). Experience in Chile, Finland, and South Africa is compared concerning mill rotation speed and size. Included in the symposium is a paper by Burghardt and Kortmann (23)comparing milling of iron ore in a 2.4 X 2.2-m autogenous mill with a tube mill 1.8 X 2.2 m. The milling capacity is determined as a function of rotation speed and filling, and costs are compared. The application of jet-milling to iron ore is suggested by Pevnikova et al. (734). The specific energy consumption is 25 kwh/ton a t a throughput of 1.5 tons/hr. The part of the product below 60 mesh has 2 7 , greater iron content than with ball milling, indicating selective breakage of the iron mineral. Michaelson (777)discusses the use of portable crushers in openpit mining, so that the ore can be conveyed to the concentrator, avoiding expensive truck haulage. Larger mills are being used for coal grinding in current European practice. Werkmeister ( 7 9 7 ) reports brown-coal beater mills with outputs of 120 tons/hr; Veitsman et al. (783)discuss 63 tons/hr attrition mills for brown coal; Zehetner and Hammerschmid (202) describe 60 tons/hr bowl mills for anthracite; and Schuler and Hess (764)describe 60 tons/hr bowl mills that compete with 43 tons/hr beater mills. I n grinding coal for coke, Fomin et al. (57) predict the optimum degree of crushing, and Blagov et al. ( 7 5 )find that sulfur content can be reduced 30y0 by separating particles 0.07 to 0.5 mm in size. Further sulfur reduction would require flotation. 106
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Rao and Hohmann (740) study the selective crushing of limestone to remove silica by screening. Silica content of material above 0.35 mm size is reduced from 12 to 67,. Tliargalla (788) gives examples of problems of wet milling of bauxite. Tompa (778) describes a low-temperature grinding technique to prepare propellants for analysis. A patent by Windle (798) makes it possible to grind chalk whiting to - 2 pm using a grinding aid, so that the product compares with precipitated chalk as a pigment. Solov’ev et al. (774)investigate grinding of organic pigments in disk mixers with sand media, including effects of sand/pigment ratio, speed, size distribution of sand and its density, viscosity, and time, and compare results with other dispersion techniques. Influence of titanium pigment concentration in ball mill dispersion in alkyd resins is experimentally determined by Rehacek (742). Numerous articles deal with cement milling. Schneider (757) surveys current German practice. Spring-loaded roll mills are making some inroads. Ball mills are still mostly used, and are close-circuited in the larger sizes of 6- to 12-ft diameter. The largest cement mill is 4 min diameter, 14 m long, and has a drive power of 2700 kw, which makes it smaller than some U.S. mills. Grinding aids are chiefly advantageous for grinding of cements with high specific surfaces. Cernes et al. (27) find that closed-circuit grinding of clinker is 207, more efficient than open-circuit for cement of 3900 specific surface, and 35yc more efficient for 4300 specific surface. I t is more efficient to grind separately lime, clay, and sand as raw materials for cement, according to Thormann (777). Serafin (767) patents use of a urea compound that serves not only as a cement grinding aid but also improves fluidity of the product. Beke ( 7 7 ) notes that surfactants can help cement milling when sticking of fines to the walls interferes with milling. A most popular subject for research seems to be the surface chemical effects of extended grinding. Gregg ( 6 G ) brings up to date his findings on this subject, and notes that the general effect of grinding is to make a substance more reactive. Usually the specific surface area increases u p to a maximum and thereafter decreases, owing to re-adhesion of the particles. Distortion of the lattice may occur, and, in extreme instances, polymorphic transitions. Compaction also affects some of these properties. Schrader et al. (767-763) note a n increase in catalytic activity or solubility of bohmite, hydrargillite, corundum, and bauxite on increasing grinding, and attribute this to lattice deformation or amorphotization as determined by X-ray, magnetic, and kinetic measurements. Khodakov and Edelman (95)study the solubility of ground quartz in water. The defect energy valuc and solubility of amorphous surface layers depends on grinding parameters. Solubility increases on precalcination due to surface cleaning. Lidstrom ( 708) observes formation of amorphous surface layers up to 0.15 pm thick, depending on the method of grinding. Coal pulverizing is approached from the viewpoint of coal as a high-molecular-weight organic material by Dzhaparidze et al. (57). Chemical composition changes are determined by extracting the product. The usefulness of many drugs depends on their particle size distribution. Fincher ( 5 6 )presents a review with 118 references on the subject. Small particle size increases the solution rate in the body, but sometimes too large a rate is avoided by using larger particles. Difficult experimental problems of measuring these effects are discussed. Particle size knowledge is not always a determining factor, but more knowledge is often needed. There are important problems of size reduction applied to food products. One is the possibility of dry milling and de-germing of corn. A literature review on this subject is presented by Vantwisk (787). Vrigazov (785)determines the distribution of strontium-90 in ground fractions of wheat. Niediek, Rumpf, and co-workers ( 7 79, 727, 753)report studies to improve the process of milling and preparing chocolate. Usually the partly ground cocoa and sugar are masticated in conches. A more efficient and economical new process is described, in which the materials are separately ground and then blended. A symposium with 10 papers on woodpulp grinding is summarized (729).
Undersize
Air
Oversize
/
Figure 3. Schematic design of a new gravity classifier with short cylindrical sefiaration of zone and accelerated removal of j n e s ( 706) Courtesy of Powder Technology
Clessiflera
Despite the publication of 400 papers on hydrocyclones, lack of knowledge has prevented successful design, according to Cohen (37). Too many industrial cyclones use the wrong design, or the right design under the wrong conditions. This stems partly from misleading results of research using plain water instead of slurries; partly from failure to distinguish the different behavior under three flow regimes; partly from failure to realize that Kelsall’s brilliant research is misleading because his cyclone had an unusual feature of low feed entry; and partly because of reliance on equilibrium models, which Cohen’s recent work shows to be false. Particles in a cyclone do not have time to establish equilibrium orbits. A paper on the residence time of particles in cyclones shows the effect of particle size and flow regime, and indicates the importance of entry turbulence in determining the trajectory of the particle. Further work on the dynamic flow characteristics of a small spiral classifier is reported by Stewart and Restarick (776), who use an impulse of tracer material. Lynch and Rao ( 7 7 7 ) conduct extensive tests on classification of ores in a 20-in. diam hydrocyclone to develop a method to predict performance as a function of dimensions, operating pressure, and feed solids content, Results are expressed in terms of parameters of equations from their previously reported model of flow and separation. Warren and Hinchliffe (789) describe the use of a hydrocyclone for closed-circuit milling of ceramic slips, and recommend a solids content below 25%. Trawinski (779) recognizes that a sharp classifier will improve efficiency of a closed-circuit grinding system. He discusses application of wet classifiers suitable a t the finenesses usually required for minerals, such as rake classifiers, thickener-separators, elutriators, hydrocyclones, and centrifuges, and gives examples of their use in circuits. Ruger et al. (748) describe the properties of a centrifugal dry separator, and Ruegg (747) discusses the efficiency data for the Escher-Wyss centrifugal classifier. Nagel ( 726) groups classifiers into 20 groups in accordance with the forces of gravity and drag that they employ. Rumpf et al. (752) analyze, in terms of dimensionless groups, the behavior of cyclone dust collectors, and optimize design by developing a relation between the separation limit and the pressure-drop coefficient. Wessel and Hermann (792) report on the production of narrow particle-size fractions by air classification. Mayer (774) considers that the separation efficiency curves of separators operating in closed circuit with mills are
far from ideal because some feed passes over without being subjected to classification. Equipment for dry and wet sieving of material in the range 0.2 to 0.5 mm is described by Kreller (97). Hoffmann et al. (78)present a techno-economic comparison between drum-sieves and rapidvibrating sieves. Selection of scalping screens for use with crushers is discussed by Westerfeld (793). A capacity formula multiplies the per cent oversize in the feed by the per cent smaller than half the screen opening as a measure of the fines. Type of screen surface, largest piece to be handled, and type of installation are also discussed. Wehner (790)reviews the state of the art, with particular reference to “impact mesh screening,” “tension wave screening,” and the Umbra sieve. Jansen and Glastonbury (87) review the factors affecting the performance of various types of screens, and discuss the mechanics of motion of a particle on a screen surface. The random-path model is shown to explain several of the empirical screening relationships. Several articles consider the fundamental behavior of settling suspensions. Rumpf and Alex ( 7 5 7 ) derive efficiency curves for decanting, based on Stokes law. Davies (44) discusses the behavior of unflocculated suspensions a t high concentrations and shows experimentally that particle segregation occurs u p to a limiting concentration above 30 ~017~. At this concentration the suspension settles en masse. The deceleration of particlcs in a vertically pulsating flow field can be deduced from the nonlinearity of the law of resistance governing flow around particles, according to Molerus and Werther (720). A similar result has been obtained from solution of the basic flow equations by Iloughton (80). The drag coefficient of small particles depends on acceleration as well as velocity, and experimental results on this behavior are given by Selberg and Nicholls (766). Poriicle Size Analysis
Leschonski and Rumpf (706) describe two new laboratory air classifiers which are available from Geoscience Instrument Corp., Mount Vernon, N . Y . 10553. A gravity elutriator, shown in Figure 3, is effective down to a cut size of 10 Fm. This classifier overcomes inherent physical interferences in the Gonnell, Roller, and Alpine classifiers. The sample is subjected to a uniform flow ofairover the whole width of the inlet screen, owing to high pressure drop across the screen. T o prevent resedimentation of fines once they are entrained, the air flow is accelerated by the decreasing cross-section of the conical chamber. Stirring and vibration of VOL. 6 1
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the sample tend to break u p agglomerates. The cut size can be precalculated, so that trial runs are not necessary. Air classification of finer sizes can be done only with centrifugal classification. For sizes down to 15 pm, a classifier such as the Bahco gives good results. A new type that makes use of transverse flow classification is also described by Leschonski and Rumpf (706). I t extends the useful range down to 2 pm cut size. Wolf (799)reports that to obtain a sharp separation below 10 Mm with a Bahco separator, one must repeatedly pass through the oversize to remove the fines. Lauer (704)describes a new laboratoryscale centrifugal air classifier with a wide separation range. A book by Allen (5)on particle size measurement is published, as well as a literature search by Essick (54)on methods of particle size measurement. Some common size distribution equations are compared by Harris (70), including the characteristics of their differential forms, and their parameters such as size modulus and slope. Lapple (702) reviews particle size representation and common techniques for size analysis. Inability to sense particle size directly has hampered industrial process control. An indirect method based on slurry viscosity is patented by Brown (27). Ricci et al. (744) describe a real-time particle-size analyzer that uses a flying-spot laser beam to count particles in slurries containing less than 2 wt%i, of particles 5 to 1000 pm in size. The pulses are electronically analyzed to determine particle size distributions of latex, glass spheres, and ore slurries. Kelsall et al. ( 9 7 ) describe a method of modifying a cyclone to obtain a rapid measure of coarse sizes that are of interest for plant use. I n this device the vortex finder extends an adjustable distance close to the bottom of the unit. This distance governs the available time for material to be centrifuged out, and allows a coarse cut. T o obtain sharpness, a dilute slurry is used and the material is recycled about 10 times. T h e range of effective cut sizes is from 16 mesh to sub-sieve sizes. The availability of electroformed microprecision sieves is sparking a number of studies to establish practical procedures for their use. Lauer (703) states that dry sieving is possible down to 33 pm and wet sieving down to 10 wm with the aid of ultrasonic vibrations. Crawley (47) obtains good precision with 800 kHz ultrasound to assist the passage of slurries through 11 and 5 pm sieves. Yudaev and Kokorev (207)investigate the movement of particles in stagnant acoustic waves, and find that density of the medium, particle concentration, rate of sound distribution in medium and particles, and particle diameter affect the movement. Schmidt and Geisel (760) compare the sieving capacity of laboratory sieving machines. For particles larger than 150 pm mechanical sieving gives the largest capacity, while air-jet sieving works better for smaller sizes. A critical review (705) of sedimentation methods is given in the symposium proceedings of the Society for Analytical Chemistry. A simplified method (30)of measuring suspension concentration a t a known depth makes use of absorption of a finely collimated beam of x-rays. The methods of calculating particle size from hindered settling measurements are critically discussed by Dollimore and McBride (48). Experimental results agree with results by wet sieving and Coulter Counter analysis. Barnett et al. ( 8 ) indicate that, for accurate results, temperature control is important in Coulter Counter analysis. An acoustical particle counter is described by Langer (700). A particle passing through a Venturi in a glass tube produces a click, with an acoustical form that depends on particle size. Hoffmann and Mohnen (79) discuss the theoretical principles of this intriguing device. Izrailevich and Novikov (85) note that surface area measurements of powder based on permeametry depend on packing of the powder. A modified method overcomes this uncertainty by measuring ratios of flow rates under varying conditions. Light-scattering has long been used to count particle size distributions. Tiallace and Kratohvil (786)develop a new method of analysis based on measuring the polarization ratio, fitting this parameter to latex size distributions. Jacobi et al. (86)calibrate a 108
INDUSTRIAL AND ENGINEERING CHEMISTRY
laser-beam light-scattering device with mono-disperse latex aerosols. A simple instrument intended to fill the gap between manual and automatic microscope analysis can focus two images on a screen in rapid succession. Persistence of vision makes comparison easy, according to Gardiner (GO). Chatfield (29)describes another device for the same purpose, which simply projects an image onto each side of a translucent screen. A Zeiss electronic particlesize analyzer is adapted by Boggs (76) to measure roundness and sphericity rapidly. An Automatic Microscope Electronic Data Accumulator contains logic circuitry to scan a microscope image and count particles in 10 size ranges. The instrument and applications are discussed by Bayer et al. (70). Schwartz (765) discusses use of a field-ion microscope for particle size analysis. Mukherjee (724) assesses errors arising from the replication process used in measuring particle size with an electron microscope. Droplet size measurement involves problems more difficult than for particles. Direct photography of droplets for size measurement is possible with an electronic image analyzer, in a method described by Ramshaw (739). Two articles discuss use of X-ray diffraction patterns. Langford (707)reviews variance measures of line broadening, and Ward (787) determines particle size from composite data. The BET gas adsorption method of surface area measurement is compared with a negative adsorption method by van den Hul and Lyklema (82). Meffert and Langenfeld ( 7 7 5 ) propose a rapid BET method. I t is a single-point method with precautions to eliminate sources of error, and is claimed to give the same deviation as the regular BET method. Several articles consider sampling problems. Davies (43) discusses entry of aerosols into sampling tubes. He states that isokinetic sampling is necessary to obtain correct samples in strong winds. Parker (730) discusses methods for obtaining isokinetic samples, and the effect of the shape of the probe inlet. Ruping (754) shows that the importance of isokinetic sampling is usually overestimated, and argues that other factors, such as the number of measuring points in a pipe in relation to the total number of flow currents, are much more important. Montgomery (722) describes a 15-in. revolving riffle that can cut a large sample into small fractions which gives a much more representative fraction than the Jones riffle. Particle Behavior
A broad summary of powder technology is given by Rumpf (750), including specific examples in photos, tables, and figures on
heterogeneity of useful minerals, strength of powders, settling and optical properties of powders, and the mechanical action of jet mills. Cheng and Valentin (37) develop a theory in which powder is considered to exist in three states (elastic, consolidating, or flowing) depending on the stresses acting upon it. Each state and the transition from one state to another is characterized by the appropriate stress-strain relation, equation of state and rate equations. I n another article Cheng (32)further analyzes the tensile strength of powders. Schneider (758) explains the rheology of powders in contrast to liquids by stating that a higher pressure is to be assumed in the direction of pressure application than perpendicular to this direction. The ratio of the two pressures may be considered a constant of the material in many cases. The ratio and the pressure drop resulting from wall friction in a packed bed are measured for various packings, such as granulated and powdered plastics, steel balls, and quartz sand. Williams and Birks (796) consider shear failure tests to measure the i-iternal friction angle of the powder, which is a resultant of the applied stress and the tensile strength. They derive a theoretical equation for the yield locus that reduces the number of tests needed to determine the failure properties of a powder. Several articles describe improvements in shear cells for measur-
ing the cohesiveness of powders. Pilpel (736)describes a basic instrument adapted from Jenike and gives results for cement and pigments. I t consists of three rings which are held together while being filled with powder. One of the rings is then pulled sideways and the shear stress on the powder is measured. A modification by Scarlett and Todd (756)uses a concentric annular guard ring principle to eliminate wall effects. Carr and Walker (26) describe improvements in accuracy under low-loading conditions. Farley and Valentin (55)measure five powders in two flow testers, correlate the yield locus with particle size and bulk density, and find that cohesion is roughly twice the tensile strength. Harwood and Pilpel (74)state that the shear cell is useful for fine particles, but a discharge hopper is more suitable for study of the flow of coarse granules. One application of these basic measurements is the design of bins to promote discharge. Johanson (88)points out that theory developed so far is based on equilibrium of forces, while bin flow is dynamic; that theory treats powder as a continuum, while powders have discrete particles. Actual bin operation therefore requires discuss the existence of a safety factors. Shinohara et ~ l (769) . dynamic arch which does not stop the flow from a bin. Their simplified model assumes that every particle coming into the arch can fall out freely under gravity, and they deduce the flow rate from the location of the arch. Results agree with empirical flowrate equations. Forbes et ~ l(58) . show mechanical modifications to convert a storage bunker to a mass-flow bin. Colijn and Carroll (38) discuss inter-relation of bin design and feeders. The filling pressure on the feeder is usually two to four times the steady-state flow discharge pressure. Ikekawa and Kaneniwa (83)discuss the effect of particle size on the flow properties of pharmaceutical powders. A book on the packing of solid particles is published by Gray (65). A series of articles by Aim and le Goff (2-4) discuss the packing of binary mixtures of spheres or cylinders. The model is based on a concept from crystal lattice theory, determining the number of nearest neighbors. The excess porosity due to contact with a wall is also explained. An empirical relationship is given by Hager (68) to deduce the packing density of a binary mixture from that of its pure components. The maximum compaction occurs with a mixture of 70% coarse and 307, fine particles, with a sizeratioof10:l. Williams ( 795)discusses the methods of describing, specifying, and testing the mixing of powders. The operation of a mixer is regarded as a counterbalancing of simultaneous mixing and segregating effects. Both mixers themselves and powders differ in their tendencies to segregate, and the causes are discussed. Smalley (770)describes some commercially available types of powder mixers, and Ciborowski and Wolny (33)establish that the rate of axial mixing can be increased by increasing the humidity of the particles, provided that a diffusion mixing mechanism is preserved. The vibratory mill can be used for high-efficiency dry blending, according to Smith (772). The method is particularly suited to pm-sized powders and can give a throughput of 50 lb/hr. Roessler and Willis (746)also discuss applications of mixing with vibrations. A research proposal (45)is available for a fundamental study of blending and mixing. I t includes a survey of the state of the art. The three-year project is to be funded by a group of industrial companies. The aggregation of powders is a n important industrial process for making pellets of iron ore, fertilizer, and other materials. Proceedings of a symposium on aggregation (84)include papers on granulation of sand as a n aid to understanding fertilizer granulation, relationship between liquid content and average granule size, preparation of high density ceramics, tablet machine development and pharmaceutical tabletting, and pelletizing wastes. Pietsch, Hoffman and Rumpf (735)study the tensile strength of moist agglomerates in terms of capillary forces. Musschoot and Thomson (725)patent a method for flowing aggregates in a trough, such that the larger particles move toward the lower end while the smaller ones move toward the upper end. A coalescence model for gran-
ulation is presented by Kapur and Fuerstenau (90). Data on the size distribution of particles in compacts are presented by Varma et ~ l (782). . T o end on an exotic note, Mason (773)gives an application for the determination of particle size distribution of lunar surface material. REFERENCES (l),Agar, G. E., “Grindability measurements and the determination of energysize parameters,” Trans. A I M E , 241 (4), 384 (1968). (2) Aim, R. B., and Le Goff, P., “The wall eflect in disordered ackings of spheres and its application to the porosity of binary mixtures,” Powder gech., 1 (5), 281--90 (1968) (Fr.). (3) Aim, R. B., and Le Gofl, P., “ T h e co-ordination of randomly packed spheres, application t o binary mixtures of spheres,” Powder Tech., 2 (l), 1-12 (1968): (Fr.). (4) Aim, R. B., and Le Gofl, P.%,“Porosit of binary assemblages of spheres and objects of cylindrical symmetry, Powder h h . , 2 (31, 169-74 (1969) (Fr,). (5) Allen, T., “Particle size measurement,” 248 pp, Chapman and Hall, London, 1968. (6) Aufbereitungr-Tech., “Self-sorting mill linings,” 9 (11, 39 (1968) (Ger.). (7) Austin L G. and Klimpel, R. R., !‘Statistics of random fracture,” Trans. A I M E , i41 13), $19 (1968). (8) Barnett, M . I., Harania, V. R., and James, K . C., “The importance of temperature control in Coulter Counter analysis,” Powdcr Tech., 2 (l),60-2 (1968). (9) Barsom, J. M., “Fracture of tempered glass,” J . Amer. Ceram. S a , 51 (Z), 75-8 (1968). (10) Bayer, J. L., Denton, G. H., and Hassel R. E “Use of the AMEDA microscope in quantitative microscopy,” ASTM Sped: Tech. Publ., (430), 118-28 (1968). (11) Beke, B., and 0 oczk L “Structure changes in milling clinker to extreme fineness,” Zement-dlki’0 (6), 267-70 (1967) (Ger.). (12) Bertume, I., “Vibration grinding,” Min. €3 Minerals Engr., (5), 46-53 (1969). (13) Bilan B. B “Semiautomatic grinding control at the Moose Mountain Mine,” Can. Mi;. Mei.’Bull. 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Instrum., 44 ( 8 ) , 615-17 (196j). (30) Chem. Eng. News, “Particle size determination simplified,” 47 (5), 34 (1969). (31) Cheng, D. C.-H and Valentin, F. H. H. ‘iSome fundamental aspects of powder behavior,” &hem. Eng. Sci., 23 (7), 723-3)8 (1968). (32) Cheng, D. C.-H., “ T h e tensile strength of powders,” Chem. Engr. Sci., 23 (12), 1405-20 (1968). (33) Ciborowski, J., and Wolny A “The influence of moisture content of loose materials on the dynamics of‘ th& mixing,” I n t . Chem. Engr., 8 ( Z ) , 199-204 (1968). (34) Clarke, B., and Kitchener J. A. “ T h e influence of pulp viscosity o n fine grinding in a ball mill,” Brit. dhem. E&., 13 (7), 991-5 (1968). (35) Clement, M., Auge! P., and Kerl, H “Survey of the state of the art and of several roblems of milling of mineral &es,” Tech. Mitt. Essen., 59 (5), 222-8 (1966) (36) Coghill, W. H., and Devaney, F. D., “Ball mill grinding,” U.S. Bur. Mines Tech. Paper, (5811, 56 pp., (1937). 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(40) Congleton J Petch N. J and Shiels S A , , “Brittle fracture of alumina below 1 0 0 O 0 d , ” ~ h i 1 M&., . 19 ?160), 795 ( i k j . (41) Crawley, D F. C “Micromesh sieve analysis using high-frequency ultrasonic vibrations,” J.’Sci. Inytrum. (Series 2 ) , 1, 576 (1968). (42) Daniel S. W “Automatic control of a rod mill-ball mill circuit,” Can. M i n . Met. Bull.: 60 (621), 568-70 (1967). (43) Davies C. N. “The entr of aerosols into sampling tubes and heads,” Brit. J . Appl. Phys: (Seriis 21, 1 (7), $21-32 (1968). (44) Davies R . “The experimental study of the differential settling of particles i n suspensioi at high concentrations,” Powder Tech., 2 (l), 43-51 (1968). (45) Davies, R. “Mixing and blending research proposal,” I I T Research Institute, Chicago, Ill.,kO616 (1969). (46) Davidge, R . W. and Tappin G. “Internal strain energy and the strength of brittle materials,” -?. Mater. Sci., (3j, 297 (1968). (47) Dobrovol‘skii, Y u . I., e t al., “Preparation of powders on a planetary mill,” Porosh. M e t . , 7 (6), 1-7 (1967) (Russ.); CA, 67, 7 5 7 8 1 ~ (1967). (48) Dollimore, D., and McBride, G. B., “Alternative methods of calculating particle size from hindered settling measurements,” J . Appl. Chem. (London), 18 ( 5 ) , 136-40 (1968). (49) Dor, A. A,, and Morrow, J. B., “Wet and dry primary grinding,” Mining Congress J., 55 (5), 44-52 (1969). (50) Dunegan, H . L., Harris, D . O., and Tatro, C. A,, “Fracture analysis by the use of acoustic emission,” Engr. Fracture Mech., 1, 105-22 (1968). (51) Dzhaparidze, P. N., Landau I. N. and Ades V I , “Some effects of subjecting coal to mechanical action,” D o h . A h d . ”fauk SSR, ‘179 (4), 923-5 (1968) (Russ.); CA, 69, 29144k (1968). (52) Echalaz A . J “Vibration milling tests at Durban Roodepoort Deep Ltd.,” J . S. Afr. I’st. Mi;. Met., 6 8 ( l l ) , part 1, 501-10 (1968). (53) Edmonds, D . V., and Beevers C. J., “ T h e effect of inclusions on the stress distribution in solids,” J . Mater. Si’;.3, (5), 457 (1968). (54) Essick M . L. “Literature search on methods of particle-size measurement,” Report kD4838i7, Clearinghouse Fed. Sci. Tech. Info., (1968). (55) Farley, R . and Valentin F. H . H . “Effect of particle size upon the strength ofpowders,” >owder Tech., 1 ’(G), 344-5i (1968). (56) Fincher J H “Particle size of drugs and its relationship to absorption and activity,” .?.+ha,;. Sci.,57 ( l l ) , 1825-35 (1968). (57) Fomin, A. P., et al. “Predicting optimum degree of crushing of coal blends for carbonization,” Code b Chem. Russia (Engl. ed.) (4), 3 (1968). ( 5 8 ) Forbes, F., e t al., “Applying the principles of scientific bin design,” Mining Ener., 20 (5), 69 (1968). (59) French, J. H., and Lismer, 0. E., “Rotar mill liner practice in the South African gold mining industry,’’ J . S. Ajr. Inst. h i n . C3 Mel., 71-102 (Sept. 1968); Discussion, 229-37 (Dec. 1968); 475 (1969). (60) Gardiner, J. A , , “Size analyser for images and particles,” Instr. Pract., 22 (l), 50-3 (1968). (6l),Gel’fand, Ya. E., Val’sonok, A. M., and Dubinin Y u . I “Automation of a milling plant for dry milling of raw material,” Cement, $2 (6), i’8-9 (1966) (Russ.). (62) Gendel, S. Z . , Adams, J. H., and Kanost H. S “High density zirconia in grinding and milling applications,” Am. Cerarn.’Soc. &I., 47 (9), 878 (1968). (63) Glathart, J. L., and Preston F. W. “Behavior of lass under impact- theo89-100 (19687. retical considerations,” Glnss Tich., 9 (i), (64) Gommel G “Interrelation between comminution and wear in impact mills,” Aufbereituns8Ti;h., 8 (12), 679-87 (1967) (Ger.). (65) Gray, M’. A , , “The packing of solid particles,” 134 pp., Barnes & Noble, N.Y. (1968). (66) Gregg S. J., “Surface chemical study of comminuted and compacted solids,” Chem. B’Ind., (191, 611-7 (1968). 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of dispersed materials’ comparison of the negative adsorption method with some other methods,” J . A;. Chem. Soc., 90 (12), 3010-15 (1968). (83) Ikekawa, A., and Kaneniwa, N., “Influence of article size on physicochemical properties of harmaceutical powders,” Chem. Plarm., 1 6 (8), 1433; (E), 1543 (1968); 1 7 (4f 827 (1969). (84) Inst. Chem. Eng. Trans., “Symposium on Aggregation,” (2201, CE196-236 (1968). (85) Izrailevich, I. S., and Novikov, S. M., “Determination of specific surface of powders from the ratio of flow rates measured under different conditions of gas flow in a porous medium,” Sou. Powder M e t . Metal. Ceram., (5), 386-95 (1966) (Engl. ed.). (86) Jacobi W Eichler, J., and Stolterfoht, K.,“Particle size spectrometry 03 aerosols dsing’iight scattering in a laser beam,” Staub-Reinhalt. Lujt, 28 (81, 314-9 (1968) (Engl.). (87) Jansen, h< L. and Glastonburv J. R. “ T h e size separation of particles by screening,” P;wdlr Tech., 1 (6), 334 ’(1968): (88) Johanson, J. 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