Search Documents

By H. M. Zoerb

Based on the belief that operating details are a definite contributing factor to major economies, this paper traces the development of crushing cavity design in Symons cone crushers to attain maximum liner utilization. Wear rates are analyzed and compared in this presentation and drawings illustrate succeeding design changes. IN these times of rising labor and material costs, it has become more and more necessary that attention be paid to some operating details which, in their obscurity, may he the key to major economies. Liner wear in crushing cavities of secondary and tertiary crushers can become an appreciable cost item when the material to be crushed is hard and abrasive. This item of cost not only includes the value of the crushing members, but also more intangible costs such as labor and lost production due to more frequent replacement. The variables which are encountered in ores and minerals to be reduced; the design of plant and machine application; the sizes, shape, and fineness, characteristics of the crushed product; the moisture; hardness; friability; and abrasiveness of the material to be crushed are all influencing factors which must be taken into consideration in the selection of a crusher, and particularly in the design of crushing cavity and liners to be used in a crusher. Through a research program undertaken in cooperation with many operators of Symons cone crushers a new approach to crusher cavity design was made, resulting in the development of liners for specific operations which showed: 1—maximum utilization, as high as 70 to 80 pct of original weight of metal, and 2— maximum capacity of unit during the greater portion of its life. It has been found that liners so designed for a given operation will show added economies in power consumption, maintenance, and general wear and tear on the crushing unit. Initial work in the so-called tailoring of crushing cavitles was begun on the tertiary or fine crushing units where as a rule reduction ratios were low, varying from 3 to 6. Parallel or sizing zones in the lower portion of the crushing cavity were too long, resulting in a tendency to pack. It was found that very little additional crushing was done in the parallel zone after the initial impact in that zone and that a relatively small amount of' additional crushing was done by attrition, which required very careful feed control. A small amount of over-feeding would result in packing which not only consumed power but caused unnecessary liner wear as well. The illustrations which follow in this discussion will show only contours of crushing cavities, and for purposes of simplification the cavities will be considered only in their closed position. The first step, therefore. was to reduce the sizing zone to a minimum. This was done by removing the lower portion of the liner as shown in Fig. 1. The result of the change was a saving of 15 to 20 pct in liner cost, less power consumption, with no change in capacity. This change in design, while an improvement, did not go far enough. As wear took place, the change in the liner was not uniform throughout its entire length, resulting in a restriction of the feed opening and thereby loss of capacity. Furthermore, progressive wear of the liner had the effect of lengthening the parallel zone until finally the entire crushing cavity was all parallel zone, see Fig. 2. It is obvious from the reduced feed opening of the worn liner that the ability of the machine to receive material is lessened considerably. Furthermore, the long parallel zone with its worn, irregular profile did not operate at its highest efficiency. The first attempt to overcome this difficulty was carried out on a 5 1/2-ft crusher installed in a plant producing roofing granules. The material being crushed was a very hard graywacke and the crusher was closed-circuited with a screen having .232-in. slotted openings. A radical change in contour was developed, as illustrated in Fig. 3. Equal wear lines on both concave and mantle are designated 1, 2, 3, etc. The method of development of this contour is as follows: Since adjustment for wear is vertical, corresponding intersections of wear lines and vertical lines developed concave and mantle contours which maintained equal but lengthening wear surfaces in the parallel zone. The ideal contour, of course, is one in which the length of the parallel zone remains constant, but because of present foundry practice and heat treating characteristics this is impossible.

Jan 1, 1954

By Nathaniel Arbiter, Norman L. Weiss

Factors now accelerating the trend to larger concentrators and larger equipment units are reviewed. After almost 40 years of stability with unit sizes less than 100 cu ft, 200 and 300-cu-ft flotation-cell units are now operating and a 500-cu-ft machine is being built. The design of these cells is considered, as is the design and operation of flotation circuits against the background of the need to achieve greater process efficiency while holding down operating and investment costs. Particular attention is paid to the scale-up problem. With the newer cells having five to ten times higher unit capacities, the advantages resulting from this in sampling, mill operation nnd control, testing and plant layout are indicated, as well as the broad direction for changes in the overall design of 50,000 to 100,000-tpd concentrators. A comparison is given of the available larger cells of U.S. manufacture with analysis of differences and similarities. After almost 60 years of application in this country, froth flotation is still by far the most important process for concentrating metallic ores as well as a number of nonmetallic ores including fluorspar, phosphate rock, and potash. Its use on iron ores and coal is increasing. In the metals groups, the largest plants and the greatest progress are found in copper and molybdenum mills, and the section of this paper that deals with applications will be found most pertinent to that field. During its long reign, the flotation process has passed through several phases of evolution and has achieved progress in economy, efficiency. and simplicity of operation. Much of today's success in the flotation of low-grade ores can be attributed to that progress. Even more important to us than our ability to cope with today's conditions are tomorrow's problems, which we can contemplate with some prescience and confidence. Our annual production of copper, lead, zinc, and molybdenum—to mention only the most important metals occurring in the U.S. as sulfides- must be held at a high level in the face of a declining grade of ore. It is probable that the tonnage of such ores mined and processed will double in this country before the turn of the century. Not only will many of the existing flotation mills be enlarged again and again, but larger mills will be built here and abroad to meet our needs. At this moment, in fact, there are at least three proposed new foreign mills or expansions that envision 100,000-tpd milling rate on copper ores. Table 1' shows the trend in copper ore grades in U.S. in recent years. Table 2' shows the projected annual growth rate of consumption 1966-1985. A study by one of the authors 25 years ago showed that of 32 copper mills in North America with more than 100-tpd capacity, only eight had capacities exceeding 10,000 tpd. The average for these eight was 25,000 tpd. These included the three giants of that day, Magna, Arthur, and Morenci; the other five averaged a little over 10,000 tpd. Today instead of the eight mills with capacities exceeding 10,000-tpd capacity we have 25, and the mill with less than 1000-tpd capacity is fast becoming extinct. Much less range is found in lead and zinc mills, which are still generally small except for the few with over 1000-tpd capacity in Missouri, Utah, and Idaho, and a few zinc ore mills in the same size category. Molybdenum and potash operations are the fastest growers in North America today, but when one considers the projected increase in consumption of copper together with the projected decrease in grade of ore (3% annually), he can foresee that copper ore milling will soon lead the list. Technological improvements to meet the challenge of lower-grade ores have taken the wholly predictable path toward bigger equipment. In mining, shovels, draglines, scrapers, and trucks have led the way; in ore processing, we have seen a rapid increase in size of grinding mills, flotation cells, and pumps. Twenty-five years ago, for example, the 10-ft-diam ball mills treating 2000 tpd at Morenci were considered the giants, but today some grinding mills in similar service have five times that capacity. The specific matters to be dealt with in this paper are 1) the underlying principles that affect flotation-machine design, and the conditions required to produce

Jan 1, 1971

By Shiou-Chuan Sun

THE presence of an excessive amount of tough froth in the flotation of minerals, particularly coals, may create trouble in dewatering, filtering, and handling. Froth is also a nuisance in many chemical industries.' This paper presents a study on the destruction of extremely tough froths with intense high-frequency sound. The data indicate that sound waves can be employed for continuous atandsoundwavescan instantaneous defrothing. A powerful high-frequency siren was used in obtaining the data. Also tested was an ultrasonorator of the crystal type with a frequency range of 400, 700, 1000, and 1500 kc per sec and a maximum power output from its amplifier of 198 w. The results, not presented, indicate that as now designed this machine is not suitable for defrothing. Although the sound generators of the magnetostriction type2,3 and of the electromagnetic type'.' were not available, it is beelectromagneticlieved they are capable of producing the required sound intensity for defrothing. The use of ultrasonics for defrothing was suggested by Ross and McBain1 in 1944. Ramsey8 reported in 1948 that E. H. Rose mentioned a supersonic device that broke down flotation froth but with low capacity. The writer has not been able to find any published literature containing practical experiments. Theoretical Considerations The mechanism of defrothing by sound is attributed to the periodically collapsing force of the propagated sound waves and the induced resonant vibration of the bubbles. The collapse of froth is further facilitated by the sonic wind and the heat of the siren. Sound waves can exert a radiation pressure'," against any obstacle upon which they impinge. When a froth surface is subjected to the periodic puncturing of sound waves, the bubbles are broken. According to Rayleigh9 and Bergmann,12 the radiation pressure of sound, P, in dynes per sq cm is given as: P = 1/2 (r+1)i/v where r is the ratio of the specific heats of the medium through which sound is traveling and is equal to 1 on the basis of Boyle's law; i is the sound intensity in ergs per sec per sq cm, and v is the sound velocity in cm per sec. In this case, the accuracy of the formula is only approximate, because a perfect reflection can hardly result from a column of froth. In addition to the radiation pressure, the propagated sound waves cause the bubbles of the froth to have a resonant vibration.'" he vibratory motion of the bubbles causes collision and coalescence, thereby weakening if not breaking the bubble walls. Sonic wind and heat were also generated." The sonic wind can exert pressure on the froth surface, and the heat can evaporate the moisture content of the bubble walls as well as expand the enclosed air. Apparatus The defrothing apparatus, shown in Figs. 1 and 2, consists of a powerful high-frequency siren, a glass or stainless steel beaker of 2-liter capacity with 12.4 cm diam and 17.1 cm height, and a metal reflector. The beaker was placed 2 in. above the top point of the siren. The metal reflector was adjusted to reflect and focus the generated sound waves into the central part of the beaker. Fig. 2 shows the crystal probe microphone used to measure the acoustic intensity and the mandler bacteriological filter employed to introduce compressed air into the beaker for frothing. The apparatus was enclosed in a soundproof cabinet equipped with a glass window. The siren, shown in Fig. 3, consists of a rotor that interrupts the flow of air through the orifices in a stator. The rotor, a 6-in. diam disk with 100 equally spaced slots, is driven by a 2/3 hp, Dumore W2 motor at 133 rps. The frequency of the siren can be varied from 3 to 34 kc. The maximum chamber pressure is about 2 atm, yielding acoustic outputs of approximately 2 kw at an efficiency of about 20 pct. The siren itself is relatively small and can be operated in any orientation. A detailed description of the siren has been given by Allen and Rudnick.11 Collapse of Froth To study the sequence of the collapse of froth, the glass beaker was partially filled with 920 cc water, 100 g of —150 mesh bituminous coal, 0.3 cc petroleum light oil, 0.2 cc pine oil and 1.54 cc Pyrene foam compound. This mineral pulp was agitated for 5 min and then aerated through a mandler filter until the empty space of the beaker, approximately 9 cm high, was filled completely with min-

Jan 1, 1952

By William Lodding

Muscovite was the crystalline material used in the experiments discussed in this paper. It was both wet and dry ground for various periods of time. The effects (physical and chemical changes) produced in grinding are analyzed by use of thermal analysis. That grinding may change a crystalline material both in a physical and in a chemical sense has been shown by a number of authors in recent years. Mackenziel and Bartha2 reported the effects of careful grinding on muscovite, quartz, gypsum, dolomite, etc. Increase in specific surface produced by grinding implies increase in total energy of a system. Newly produced surfaces are chemically more reactive; dislocations may be introduced during grinding and, on the other hand, existing strain may be released by the same process, as shown by Holt, et a1.3 All these changes are easily detected by thermal analysis, but it is not easy to separate the multiplicity of effects registered and to arrive at quantitative interpretations. This paper is an attempt to analyze, by the use of thermal analysis, some effects produced in grinding. In differential thermal analysis (DTA) one measures the sum of all thermal changes occurring in a substance during heating or cooling; e.g., chemical changes, such as decompositions, synthesis, oxidation, reduction, etc., and physical changes such as phase transformations, changes in specific surface and thermal conductivity, strain release, etc. By thermogravimetric analysis (TGA), on the other hand, only chemical changes involving weight loss or gain are recorded. Similarly, gas evolution analysis (GEA) will register only reactions involving gas evolution. By performing two or all three of these methods of thermal analysis simultaneously and on the same specimen, one can separate the different effects registered and, by difference, evaluate their magnitude. The results of TGA are usually plotted as percent weight against furnace temp. When one differentiates weight against furnace temp, a rate of weight-change curve is obtained, and the resulting differential thermogravimetric (DTG) plots are similar in appearance to DTA thermograms for the same reaction. While the integrated area under a DTA peak represents enthalpy and can be expressed in calories per gram the area under the corresponding DTG peak represents the weight change which took place during a reaction. The similarity of DTA and DTG thermograms obtained from one material can be seen in Figs. 1 and 2. EXPERIMENTAL A Fisher mortar grinder and a porcelain mill with burundum balls were used for both dry and wet grinding. Muscovite was first carefully hand-filed and screened on 20 and 100 mesh. The middle fraction was considered essentially unaltered muscovite.

Jan 1, 1968

By N. F. Schulz

The purpose of this investigation was to evaluate the effects of variables in equipment and procedure on tube test results. This information was then to be used to formulate specifications, preferably within the practical ranges of existing machines, for test procedures capable of yielding precise and meaningful data concerning the magnetic separation of any magnetite ore, regardless of its origin. A survey of current practice was conducted among laboratories using the Davis tube test. Many tube tests were performed to experimentally evaluate the variables most likely to affect test results. A simple method was then sought for adequately interpreting tube test results. The Davis magnetic tube concentrator is a laboratory machine designed to separate a small sample of pulverized magnetic iron ore into magnetic and non-magnetic fractions. It was developed in 1921 by mechanization of a test previously performed manually No significant changes have been made in the design of the apparatus since that time. The Davis magnetic tube test continues to serve as a practical basis for judging the amenability of an ore to magnetic separation and for controlling magnetic separation plant operations. The apparatus consists of an inclined cylindrical glass tube supported adjacent to closely spaced pointed poles of a powerful C-magnet. (Fig. 1). To conduct a tube test, a sample of suitably prepared ore is poured into the water-filled tube. With wash water flowing through, the tube is oscillated to gradually reject the non-magnetic and weakly magnetic ore particles until the desired degree of separation is attained. Both the magnetic concentrate and the tailings may be recovered for examination. MAGNETIC SEPARATION BY THE DAVIS TUBE Mechanical separation of a specified mineral component from an ore usually requires comminution to fine sizes for sufficient liberation. Some distinguish- ing property of the mineral is then exploited to sort the desired mineral particles from the gangue particles. The magnetic separation of iron ores is based on the fact that magnetite, Fe3O4, is strongly attracted by a magnetic field while the gangue minerals are not. Maghemite, ?-Fe2O3, which may occur in certain chemically processed ores, responds similarly to magnetite. The magnetic process is practical only when the loss of iron in the form of relatively nonmagnetic hematite, Fe2O3, goethite, Fe2O3.nH2O, or other iron mineral can be tolerated. In the Davis magnetic tube concentrator, magnetic attraction holds magnetically susceptible particles in a magnetic field. Forces due to gravity, inertia, and fluid-solid friction tend to remove the less susceptible particles from the field. The probability that a given middling particle will be rejected from the tube in a given period of time is an inverse function of its magnetite content, with some modification due to particle size and mineral specific gravities. The net result is that ore particles tend to be rejected in their order of increasing magnetite content, while the retained portion or magnetic concentrate increases in grade continuously during the process. MAGNETIC SEPARATION CHARACTERISTIC The magnetic separation characteristic or MSC of a magnetite ore is the correlation between concentrate

Jan 1, 1964

By J. N. Ong, J. P. Ratledge, J. H. Boyce

SINCE German operators opened the Tsumeb mine in the early 1900's, continuous operation has been interrupted only by enforced shutdowns during two world wars and the depression of the 1930's. Original metallurgical practice was blast furnace smelting. This was applicable only to low zinc ore, leaving large tonnages of high zinc ore to be stockpiled on the surface. A gravity concentrator using tables, buddles, and jigs operated for several years, but differential flotation of the ore did not get beyond the experimental stage. When the property was put up for sale by the South African Custodian of Enemy Property there was an estimated 434,000 tons of ore on surface dumps. The dump material, assaying 4.48 pct Cu, 15.8 pct Pb, and 10.9 pct Zn, had become highly oxidized during a stay of many years on the surface. But these dump ores had to be used in evaluating possible metallurgy because the shaft became flooded after the 1940 shutdown and underground ore was unavailable. Many companies examined Tsumeb but quickly lost enthusiasm because of the formidable metallurgical problems presented by the dump ore. However, on the basis of extensive test work, the present company decided that differential flotation would be successful and purchased the property after competitive bidding. Geology and Mineral Association is Complex The Tsumeb mine lies near the northern boundary of South West Africa at an altitude of 4200 ft. The village of Tsumeb is 335 air miles northeast of Wal-vis Bay, territorial port of entry. The orebody is a hydrothermal replacement deposit associated with an irregular intrusion of aplite cutting folded pre-Cambrian dolomite beds. In plan the deposit is a lens of 250x600 ft maximum dimensions. In section the orebody dips 55" south from the surface to 2000 ft, below which there is a reversal in dip to 75" north. Mineralization is localized in the aplite and in the adjoining brecciated dolomite. In the upper levels the ore is largely confined to a single lens, but below the 1890 level massive sulphide ore forms north and south lenses that partially enclose a pipelike body of medium to low grade disseminated ore, part of which is of too poor a grade to mine. Drilling below the 24th, or bottom level, has disclosed that a high percentage of the mineralization from the 3000 to 3300-ft horizons is comprised of copper and lead oxides. The deep oxidation may be local, since it appears due to circulating waters in a major fault cutting the orebody. Tsumeb ranks as one of the highest grade base metal deposits in the world. It is geologically and mineralogically famous for 41 copper, lead, zinc, vanadium, and germanium ore minerals, but its complex mineral assemblage is not attractive to metallurgists. In addition, there is a gradual change in oxidation intensity from the upper levels to the lowest level now operating, which is the 24th. This is well illustrated by the copper minerals. In the upper levels malachite and azurite are predominant, in the intermediate levels chalcocite, and in the lower levels tennantite. Throughout the mine there are sufficient heavy metal soluble salts to activate zinc, and large amounts of depressants are required even for so-called clean sulphide ores. When the same sulphide ore is exposed to prolonged oxidation aboveground, as was the case with the dump ores, reagent requirements become fantastic. Plant Construction First staff members arrived at Tsumeb in March 1947, and by May essential services had been restored and mine unwatering began. In 2 1/2 months company employees built a temporary jig and sorting plant for treating existing dumps to provide a saleable product during high metal prices. Meanwhile, concentrator design and construction was contracted to a South African firm, with subcon-

Jan 1, 1956

By O. E. Palasvirta

Several drum-type, low-intensity dry magnetic separators have recently been described 1,2,3,4 all of which share at least two generic similarities. The magnet consists of a multiplicity of poles of alternating polarity and, the speed of the drum shell, relatiw to the magnet, is such that the magnetics are agitated through rotation of the magnetic particles around their individual axes. The speed of the drum relative to the magnet (differential speed) determines the frequency of the field reversals. For effective agitation this frequency generally has to be above a specific value, which varies according to the mean particle size of the magnetics. With separators of small diameter, say less than 11/2 ft., a sufficient differential speed for treatment of fine magnetite can be attained only by rotating both the magnet and the drum separately; separators of large diameter may attain sufficiently high differential speeds with stationary magnets. Separators of large diameter thus have the advantage of simplicity of design. The capacity of a separator of this type is directly proportional to the speed of the shell. As the centrifugal force opposing the magnetic force increases at a slower rate than the peripheral speed of the shell when drum diameter is increased, large drums can be operated with higher peripheral speeds. Thus they have a higher capacity than smaller drums. Separation is also a statistical phenomenon, i.e. the grade of concentrate improves as the number of agitations or rotations of the magnetic particles per separation increases. As separators of large diameter have space for a large number of magnets they are best suited for production of optimum grade concentrate. The statements above are general clues For separator design. In the following an expression IS derived showing a more exact relationship between the pertinent separator variables. As both magnetic attraction and centrifugal forces are directly proportional to the volume of the affected bodies, complications in mathematical analysis, arising from variable particle size, are avoided by considering the force per unit volume of affected material. For the magnetic force per unit volume Runolinna (3) gives the following equation: V " 1 + N(ur, - 1) uo dr (1) where ur and uo stand for the relative permeability and the permeability of vacuum, respectively, N is the demagnetization factor, B the intensity of the magnetic field, and r the distance from the face of the magnetic pole. The permeability of a specific magnetite ore can generally be considered as a constant. For ground, liberated material N can also be treated as a constant, and the first simplification can be made by writing ur-1 1=k1. 1 + N(ur - 1) uD k1. Fig. 1 shows the field intensity curves for two U-magnets of different size, but of roughly similar geometry of cross-section as plotted against the distance from the plane of the pole faces. The curves

Jan 1, 1961

By Pablo Hadzeriga

Great Salt Lake brine was subjected, in laboratory scale, to conditions simulating solar evaporation. Solid phases and the variation in composition of the liquid phase throughout the potassium salts crystallization zone are presented. These experimental results are discussed and compare with stable equilibrium data of the quinary system Cl-, SO4, Na+, K+, Mg + + and H2O. The Great Salt Lake brine in Utah is a vast reserve of several potential chemicals which has attracted much attention in the recent past. From the standpoint of an ore reserve, it may be said that the lake contains a low grade ore which has to be concentrated by evaporation of water. Because of the fairly favorable weather conditions in the Great Salt Lake area, it seems reasonable to consider solar evaporation as an economical means of concentration. From the view of phase chemistry, the main constituents of Great Salt Lake brine make it belong to the five component system: C1-, SO4=, Na+, K+, Mg++ and H2O. Because of their low concentration, the presence of other elements may be regarded as having little effect on the equilibrium of the five main components. Equilibrium data for the quinary system of our interest has been available for many years. Using these data, it is possible to calculate how the brine of the lake will concentrate when subjected to solar evaporation. In practicing solar evaporation, the weather factor and supersaturation conditions cannot be ignored, but their introduction into calculations using equilibrium diagrams is almost an impossible task. With the experimental work presented in this paper, an attempt is made to compare the stable equilibrium data of the quinary system as applied to the case of the Great Salt Lake brine and the dynamic equilibrium when that brine is subjected to continuous solar evaporation. Sea water brine belongs to this quinary system when only the major constituents are considered. The study of this system has been carried on since the last decades of the nineteenth century. The reason for these intensive studies was to give a geological explanation to the underground potash deposits. AS a result, many theories were presented trying to relate the equilibrium data with the geological formation, paragenesis and metamorphism of these deposits. Two main approaches were followed for the equilibrium studies of this quinary system. One of them, and the best known to us, was the school started in Germany in the last century by J. H. Van't Hoff. The other one, which started about the same time, was the school of N. S. Kurnakov in Russia. Both approaches were different and as a consequence generated opposite theories about the geological formation of potash deposits. The Van't Hoff school studied the quinary system of sea water under careful laboratory control, resulting in stable phase diagrams. During these studies, Van't Hoff recognized the difficulties in crystallizing some double salts.' ". . . . we unexpectedly found that some compounds whose formation in the solutions under investigation was possible at 25°C, nevertheless totally failed to put in an appearance. These, not to mention the calcium salts, were leonite, MgSO4 . K2SO4 4 H2O; kainite, KC1-MgSO4 . 3 H2O; and kieserite, MgSO4 .H2O. Even exceedingly slow crystallization with the addition of the compounds themselves did not remove the condition of supersaturation in the case of these bodies." However, those salts (leonite, kainite, and kieserite) were included in the stable phase diagram at 25°C as shown in Fig. 1 using D'Ans data.3 The figure also shows the sequence of crystallization of the Great Salt Lake brine according to the stable diagram. In later studies by the Van't Hoff school, especially by D'Ans,3 Karsten,4 Autenrieth,5,6 attention

Jan 1, 1968

By R. J. Linney

Reserve Mining Co. produces 5 million tons of iron ore pellets per year. The finished product runs about 65.50 pct Fe, with 7.75 to 8.00 pct SiO2. Less than 12 pct arrives at the blast furnaces smaller than % in. This plant was originally designed to produce 3.75 tons annually—not 5 million. To handle the increased tonnage a fifth fine crushing line was added, and some very minor changes were made. When production can be stepped up 33 1/3 pct without extensive additions or changes—within the short period of a year—basic engineering has been sound. Operators of the plant consider it the best design job they have seen or heard of, and competent authorities have said that start-up was quicker and easier than for any previous large-scale minerals beneficiation plant. One big advantage is the elbow room allowed. Generally speaking, there is an eternal conflict between operator and designer over space. The designer has his costs per cubic foot, and he is keenly aware that if he permits the number of cubic feet to rise unnecessarily, total costs will be too high. But this was a new operation, and on a large scale. There were no proven standards to go by. Realizing this, Reserve's engineers provided ample and efficient access to machinery, allowing extra space for unanticipated situations. In three years of production this planning has paid off handsomely. Gravity Flow Saves Time and Money: This plant is on a rocky hillside, the car dumper about 270 ft above Lake Superior. In locating buildings and placing machinery the designers mad= good use of gravity flow, at considerable financial savings. In the concentrator building from rod mills to filters, gravity carries the material between all stages of the operation except one—the closed circuit pumping of concentrate between cone classifiers and ball mills. Since no machine is located directly above any other, an observer can stand on the truck ramp adjacent to the offices and laboratory and see practically every phase of activity in the huge building. The first mill section started in August 1955. After a day's run several modifications were made on auxiliary chutes and launders where spillage had occurred. This procedure was followed for the first

Jan 1, 1960

By Brahm Prakash, R. Schuhmann

Chemical conditions for flotation and nonflotation of quartz with oleic acid as collector and barium, calcium, aluminum, iron, and tin as activators were studied using a simple vacuum-flotation technique in glass-stoppered graduates. The detailed study of barium activation led to an interpretation based on ideal Langmuirian chemi-sorption. FLOTATION of quartz is of practical importance as something to be avoided in soap-floating many types of ores. Clean, unactivated quartz is not floated with fatty acids and soaps, such as oleic acid and sodium oleate, in the quantities normally used for flotation. However, data in the literature indicate that almost any multivalent cation will activate quartz if given an opportunity. Thus, a common problem is to prevent activation of quartz by the various inorganic cations inevitably present in flotation pulps. Wark and his coworkers1 have demonstrated the reversibility of the chemical reactions and adsorptions involved in the activation, depression, and collection of the common sulphide minerals. The procedure in much of their work was to bring a mineral surface to equilibrium with solutions of known pH, collector concentration, and activator concentration, and then to test the floatability of the mineral by contact-angle measurement. From the data, graphs were constructed with pH and reagent concentrations as coordinates. These graphs show fields of flotation and fields of nonflotation, separated by narrow transition regions whose locations are shown by so-called contact curves. From the shapes and locations of the contact curves, which roughly separate fields of flotation from fields of nonflotation, a quantitative understanding of the interaction of the reagents with each other and with the minerals often can be deduced. The study of quartz flotation to be described in this paper follows in broad lines the approach of Wark and coworkers. That is, pH, activator concentration, and collector concentration were varied to find equilibrium conditions of flotation and non- flotation, and the results are presented graphically by means of contact curves. However, instead of testing for floatability by measuring the contact angle on a polished surface, a simple vacuum flotation technique was developed and used. Purified oleic acid was the collector and terpineol the frother. Barium activation was studied in some detail, and exploratory studies were made of activation with calcium, aluminum, ferric iron, and stannic tin. Preparation of Materials Quartz: Large lumps of high-grade vein quartz were crushed dry in a cone crusher and rolls. The —20, +28-mesh portion was screened out and used in the subsequent steps. This material was passed through a high-intensity magnetic separator to discard iron, then leached twice with hot concentrated HCl and washed repeatedly with distilled water. The cleaned sand was then wet ground with porcelain balls in a porcelain pebble mill, deslimed repeatedly by settling and decantation to discard —800-mesh material, and again washed with hot HCl followed by distilled water. The resulting stock of quartz was stored under water. Chemical analysis gave 99.8 pct SiO2. Table I gives the size analysis of the quartz used for flotation tests. Calculations from these data, using shape factors given by Gaudin and Hukki9 indicate a specific surface of about 500 cm2 per g. Blank flotation tests in distilled water, and in water with added frother, showed the prepared quartz to be completely nonfloatable and thus indicated the absence of organic contamination. Oleic Acid: The preparation of oleic acid was based on fractional vacuum distillation of methyl oleate2,3 followed by regeneration of oleic acid, and finally fractional crystallization of oleic acid from acetone solutions at low temperatures." The pure oleic acid was stored in a refrigerator. The iodine number of the oleic acid was found to be 90.0 (theoretical 89.93). Oleic acid was used in the form of a dilute water solution of sodium oleate, after preliminary flotation tests showed no effects of form of addition and order of addition of reagents when an adequate conditioning time (that is, 30 min) was provided. Other Reagents: Sodium hydroxide solutions low in carbonate were prepared by first making 1:1

Jan 1, 1951

By Brahm Prakash, R. Schuhmann

Chemical conditions for flotation and nonflotation of quartz with oleic acid as collector and barium, calcium, aluminum, iron, and tin as activators were studied using a simple vacuum-flotation technique in glass-stoppered graduates. The detailed study of barium activation led to an interpretation based on ideal Langmuirian chemi-sorption. FLOTATION of quartz is of practical importance as something to be avoided in soap-floating many types of ores. Clean, unactivated quartz is not floated with fatty acids and soaps, such as oleic acid and sodium oleate, in the quantities normally used for flotation. However, data in the literature indicate that almost any multivalent cation will activate quartz if given an opportunity. Thus, a common problem is to prevent activation of quartz by the various inorganic cations inevitably present in flotation pulps. Wark and his coworkers1 have demonstrated the reversibility of the chemical reactions and adsorptions involved in the activation, depression, and collection of the common sulphide minerals. The procedure in much of their work was to bring a mineral surface to equilibrium with solutions of known pH, collector concentration, and activator concentration, and then to test the floatability of the mineral by contact-angle measurement. From the data, graphs were constructed with pH and reagent concentrations as coordinates. These graphs show fields of flotation and fields of nonflotation, separated by narrow transition regions whose locations are shown by so-called contact curves. From the shapes and locations of the contact curves, which roughly separate fields of flotation from fields of nonflotation, a quantitative understanding of the interaction of the reagents with each other and with the minerals often can be deduced. The study of quartz flotation to be described in this paper follows in broad lines the approach of Wark and coworkers. That is, pH, activator concentration, and collector concentration were varied to find equilibrium conditions of flotation and non- flotation, and the results are presented graphically by means of contact curves. However, instead of testing for floatability by measuring the contact angle on a polished surface, a simple vacuum flotation technique was developed and used. Purified oleic acid was the collector and terpineol the frother. Barium activation was studied in some detail, and exploratory studies were made of activation with calcium, aluminum, ferric iron, and stannic tin. Preparation of Materials Quartz: Large lumps of high-grade vein quartz were crushed dry in a cone crusher and rolls. The —20, +28-mesh portion was screened out and used in the subsequent steps. This material was passed through a high-intensity magnetic separator to discard iron, then leached twice with hot concentrated HCl and washed repeatedly with distilled water. The cleaned sand was then wet ground with porcelain balls in a porcelain pebble mill, deslimed repeatedly by settling and decantation to discard —800-mesh material, and again washed with hot HCl followed by distilled water. The resulting stock of quartz was stored under water. Chemical analysis gave 99.8 pct SiO2. Table I gives the size analysis of the quartz used for flotation tests. Calculations from these data, using shape factors given by Gaudin and Hukki9 indicate a specific surface of about 500 cm2 per g. Blank flotation tests in distilled water, and in water with added frother, showed the prepared quartz to be completely nonfloatable and thus indicated the absence of organic contamination. Oleic Acid: The preparation of oleic acid was based on fractional vacuum distillation of methyl oleate2,3 followed by regeneration of oleic acid, and finally fractional crystallization of oleic acid from acetone solutions at low temperatures." The pure oleic acid was stored in a refrigerator. The iodine number of the oleic acid was found to be 90.0 (theoretical 89.93). Oleic acid was used in the form of a dilute water solution of sodium oleate, after preliminary flotation tests showed no effects of form of addition and order of addition of reagents when an adequate conditioning time (that is, 30 min) was provided. Other Reagents: Sodium hydroxide solutions low in carbonate were prepared by first making 1:1

Jan 1, 1951

By S. Korman, S. B. Tuwiner

THE purpose of this study is to investigate the effect of agitation upon the flotation of chal-cocite. It is believed that the concentration of collector which is required to produce a water-repellent surface upon the mineral is determined among other things by the rate of collector diffusion through an impeding film of more or less stagnant fluid. Its thickness depends upon the intensity of agitation. In the first part of this study a method is developed for determining the thickness of the fluid film upon a polished surface of synthetic chalcocite. The film thickness is then determined as precisely as possible under three readily reproducible condi-tions of agitation intensity. These determinations serve as a quantitative evaluation of agitation. In Part 2 it is demonstrated that in solutions of lime at PH 10.5 and in the absence of air or dissolved oxygen the concentration of collector required to develop water-repellency upon the surface in any given time is a function of the fluid film thickness, and that after about 10 min the relation becomes linear. This points to the possibility that the collector ions may be involved in a diffusional process through the fluid film. In Part 3 it is shown that where air is present more collector is required to produce water-repellency than for the case in which air is excluded. Next, it is shown that for the latter case the most minute amount of sodium sulphide suffices to preclude development of water-repellency. Both oxygen and sulphide are in a sense, therefore, depres- sants for chalcocite in a lime solution at PH 10.5. When oxygen and sulphide are present simultaneously there is a region of minimum critical collector concentration for water-repellency which is very markedly lower than the concentration where oxygen alone or where sulphide alone is present. Moreover, this minimum appears to be identical with the collector concentration which is required where sulphide and oxygen are both excluded. This would appear to indicate that in certain ranges of concentration of oxygen and sulphide, each cancels the effect of the other. The range of concentration of solution for this effect in solutions saturated with oxygen is a function of the agitation intensity. Thus we are led to believe that a chemical reaction involving sulphide and oxygen occurs at the surface of the chalcocite. Part 4 of this study is a further development of this idea and some of its consequences from an electrochemical standpoint, while in Part 5 the disappearance of sulphide from pulps of several minerals is noted with an indication that both dissolved oxygen and the mineral are necessary, the reaction being catalytic or pseudocatalytic. Part 1. Determination of Fluid Film Thickness The Fluid Film Concept: The hindrance to the diffusion of collector to the surface of the chalcocite is a barrier of stagnant fluid in the vicinity of the surface. It is the same barrier that limits the rate of transfer of heat, the rate of solution of dissolving crystals, or any of the other rates pertaining to chemical engineering unit operations in which the film resistance to diffusion plays a principal role.' Fluid films are present upon the surface to an extent which varies with the geometry and intensity of agitation. They result from the fact that in the region within the fluid near a surface, motion is entirely parallel to it. From the standpoint of transfer to or away from the interface the effect is as though the fluid were stagnant. Outside of the film, movement of the fluid may be streamline or turbu-

Jan 1, 1951

By S. Korman, S. B. Tuwiner

THE purpose of this study is to investigate the effect of agitation upon the flotation of chal-cocite. It is believed that the concentration of collector which is required to produce a water-repellent surface upon the mineral is determined among other things by the rate of collector diffusion through an impeding film of more or less stagnant fluid. Its thickness depends upon the intensity of agitation. In the first part of this study a method is developed for determining the thickness of the fluid film upon a polished surface of synthetic chalcocite. The film thickness is then determined as precisely as possible under three readily reproducible condi-tions of agitation intensity. These determinations serve as a quantitative evaluation of agitation. In Part 2 it is demonstrated that in solutions of lime at PH 10.5 and in the absence of air or dissolved oxygen the concentration of collector required to develop water-repellency upon the surface in any given time is a function of the fluid film thickness, and that after about 10 min the relation becomes linear. This points to the possibility that the collector ions may be involved in a diffusional process through the fluid film. In Part 3 it is shown that where air is present more collector is required to produce water-repellency than for the case in which air is excluded. Next, it is shown that for the latter case the most minute amount of sodium sulphide suffices to preclude development of water-repellency. Both oxygen and sulphide are in a sense, therefore, depres- sants for chalcocite in a lime solution at PH 10.5. When oxygen and sulphide are present simultaneously there is a region of minimum critical collector concentration for water-repellency which is very markedly lower than the concentration where oxygen alone or where sulphide alone is present. Moreover, this minimum appears to be identical with the collector concentration which is required where sulphide and oxygen are both excluded. This would appear to indicate that in certain ranges of concentration of oxygen and sulphide, each cancels the effect of the other. The range of concentration of solution for this effect in solutions saturated with oxygen is a function of the agitation intensity. Thus we are led to believe that a chemical reaction involving sulphide and oxygen occurs at the surface of the chalcocite. Part 4 of this study is a further development of this idea and some of its consequences from an electrochemical standpoint, while in Part 5 the disappearance of sulphide from pulps of several minerals is noted with an indication that both dissolved oxygen and the mineral are necessary, the reaction being catalytic or pseudocatalytic. Part 1. Determination of Fluid Film Thickness The Fluid Film Concept: The hindrance to the diffusion of collector to the surface of the chalcocite is a barrier of stagnant fluid in the vicinity of the surface. It is the same barrier that limits the rate of transfer of heat, the rate of solution of dissolving crystals, or any of the other rates pertaining to chemical engineering unit operations in which the film resistance to diffusion plays a principal role.' Fluid films are present upon the surface to an extent which varies with the geometry and intensity of agitation. They result from the fact that in the region within the fluid near a surface, motion is entirely parallel to it. From the standpoint of transfer to or away from the interface the effect is as though the fluid were stagnant. Outside of the film, movement of the fluid may be streamline or turbu-

Jan 1, 1951

By M. E. Volin, D. W. Fuerstenau, A. L. Mular

This paper presents the results of an investigation of the effect of feed size on the integral rate at which feed material is dry ground in a laboratory rod mill. The data are interpreted in terms of the Gaudin-Meloy distribution equation. The equation, Mo — Mt/t = Aoxo r-1, is found to hold for feed sizes smaller than some critical size or for grinding times larger than some critical time. It is shown that a feed grindability is related to this critical size, which appears to be the transition between predominately impact and predominately attrition grinding. Detailed research on feed size effects in comminution has been rather limited. Gaudin1 ground single-sieve fractions of quartz for extended time periods (four hours) in a laboratory ball mill. His work, which was designed to study the nature of size distributions, showed that there is a critical feed size above which comminution occurs primarily by attrition. For his system, the critical size was about 2-mm when using 22-mm balls. In a more recent investigation2 single-sieve fractions of quartz were ground in a laboratory rod mill for constant time periods (15 min) to determine how feed size affects the grindability of the material. This work showed that grindability is essentially independent of feed size in the rod mill after this moderately long grinding period. To further clarify this observation, a study in which feed size and grinding times are varied over a fairly wide range, and particularly, a study of the dependence of the integral rate of grinding on feed size during the initial stages of rod milling is necessary. For an analysis of such data, it is desirable to use a parameter which is very sensitive to change during the initial grinding period when reduction ratios are

Jan 1, 1964

By S. R. Mitchell, M. C. Fuerstenau, A. M. Gaudin

The two principal attributes of a thickener pulp are its settling rate and the ultimate pulp density of the thickened mud. Testing for evaluation of thickening attributes of a pulp has usually been done batch-wise by placing the pulp in a one-liter glass graduated cylinder and noting the position of the boundary between clear liquor and mud as a function of time. Refinements in testing have included repulping a thickened mud to various dilutions and evaluating the settling rate on these various repulped muds. This is considered to make possible an estimate of the settling rate as a function of pulp density and therefore to pinpoint the slowest settling pulp which ought to be critical from the standpoint of thickener plant design. Finally, tests are sometimes made with model-size continuous thickeners of arbitrary size. In batch tests it is generally accepted that the behavior of a pulp is described by a curve such as the one shown in Fig. 1, in which the position of the boundary between clear liquor and mud (the mudline) is plotted against time. It has also been assumed that the initial settling rate (the slope of the line segment AB) is descriptive of the pulp and independent of the size and shape of the container. Where the settling rate is slower and clearly a function of time (portion CD of the settling curve), it has been assumed that the data are not of much use because of the intrusion of compacting phenomena. The next important datum is the height. PE, which is a measure of the so-called ultimate pulp density. This quantity is assumed to be characteristic of the pulp and independent of the container. When actual data are recorded, results are rarely exactly according to this theory and numerous deviations may be noted. For example, some pulps seem to require an appreciable delay before beginning to settle, as in line AF. This is spoken of as representing the need for an induction time for flocculation. It has seemed desirable to explore thickener data with a more sensitive charting tool than is afforded by the coordinates of Fig. 1. Instead of relating the position of the mudline to time, it has seemed desirable to relate the rate of descent of the mudline to time. This, in effect, amounts to charting the slope of the line in Fig. 1, or the derivative of its ordinates, against the same abscissas. Fig. 2 shows the new chart for the curve ABCDE of Fig. 1. When this new tool was applied to data obtained, for example, with sized clay pulps, astonishing differences appeared. Apparently the traditional tool conceals differences instead of revealing them, whereas the new method emphasizes them. It seems, also, that both charting methods have their uses. In this article attention is focused on the effects of pulp density and container height as they affect the settling behavior of flocculated suspensions of a sized kaolin. The thesis by M. C. Fuerstenau' gives more details than this summary, as well as some information about the effect of other variables. Sized fractions of kaolin were used, supplied through the courtesy of S. C. Lyons of the Georgia Kaolin Co. Large batches were made by agitation in a flotation machine and in a glass jar equipped with a mixer. The settling vessels were 2, 4, and 6-in. diam glass cylinders of various heights. Pulp Dilution: The effects of pulp dilution on sedimentation behavior are shown in Figs. 3, 4, and 5. Fig. 3 shows data on pulps ranging from 2.44 to 16.7 pct solids initial pulp density, flocculated with Separan and charted in the traditional manner. At least two of the lines appear nearly straight in their early sections, but neither of the others does. Each of the curves in this figure includes a region labeled

Jan 1, 1960

By F. A. Forward, A. H. Ross, J. Halpern

IN treating carnotite ores by carbonate leaching it is often necessary to subject the ore to a prior roast. Among the advantages that may result from roasting are: 1) improvement in settling and filtering characteristics of the ore; 2) destruction of carbonaceous impurities that would otherwise contaminate the leach solution and consume carbonate reagent; and 3) substantial increase in extraction of vanadium, which is usually low when the un-roasted ore is leached. Recovery of vanadium may be an important factor in processing carnotite ores, and the fact that vanadium is usually recovered in good yield by acid leaching has often been an economic advantage over results obtained with carbonate leaching. It has been found that response of an ore to carbonate leaching, following roasting, depends primarily on its composition and on the conditions of the prior roast treatment, particularly with regard to the roasting temperature, the atmosphere maintained above the charge during roasting and cooling, and the presence of certain reagents. These factors, especially the last, virtually determine the extractions of uranium and vanadium attainable by carbonate leaching, as well as the reagent consumption on leaching, whereas adjustment of the leaching conditions has only a limited influence. These variables were examined systematically to elucidate roasting and carbonate leaching of carnotite ores and to establish a treatment yielding high recoveries of both uranium and vanadium. Tests were conducted on samples of four different Colorado Plateau ores, described in Table I. Roasting Procedure: The roasting tests were conducted in an electrically heated furnace in which the temperature was controlled to +15oC. The ore (usually a 500-g charge) was ground to —100 mesh, mixed with the desired reagent, and spread in a silica tray to a bed depth of about 1/2 in. During the roast the charge was rabbled at intervals of 15 min. To provide free access of air the furnace was usually ventilated; however, in a few experiments a controlled atmosphere such as carbon dioxide or hydrogen was maintained above the charge. Leaching Procedure: The pulp, generally comprising 500 g of ore and a 2000-cc solution containing 80 g per liter of Na2CO3 and 20 g per liter of NaHCO3, was agitated in an autoclave at 120°C, under 30 psi O2. Samples were withdrawn periodically, and the solution and ore residue were analyzed. Under the conditions employed, maximum attainable extractions were generally achieved in 4

Jan 1, 1958

By Brahm Prakash, R. Schuhmann

Maurice Rey—It may be interesting to note that depressing effects can also be obtained from cyclic compounds other than dyes. One such compound which is a dispersing agent for carbon, pigments and other compounds is known in France by the trade name "dispergine" and in the United States by the name of Lomar P W (Jacques Wolf & Co.) Dr. Rey admits that the compound is not very selective and is similar in its action to starch and dextrin.

Jan 1, 1951

By Brahm Prakash, R. Schuhmann

Maurice Rey—It may be interesting to note that depressing effects can also be obtained from cyclic compounds other than dyes. One such compound which is a dispersing agent for carbon, pigments and other compounds is known in France by the trade name "dispergine" and in the United States by the name of Lomar P W (Jacques Wolf & Co.) Dr. Rey admits that the compound is not very selective and is similar in its action to starch and dextrin.

Jan 1, 1951

By W. Mitchell, B. H. Bergstorm, C. L. Sollenberger

A unique compression testing machine was constructed to load individual 1/8 to I-in. spheres of glass, etc., at rates from 100 to 100,000 lb per min. During loading the applied load was continuously plotted us the deformation of the sphere-platen system. The load-deformation curve conforms to the theory of elasticity. The spheres were surrounded by steel retaining rings or by gelatin (to prevent secondary fracture). The product size modulus was determined from screen analyses. The data shows: 1) Energy input per unit mass is inversely proportional to the product size modulus (or directly proportional to the surface area per unit mass). 2) Increased loading rates slightly increase the energy input per unit mass required for fracture without affecting the preceding relationship. Theory and experiments show that much of the input strain energy is transformed into kinetic energy of fragments at fracture, this being a reason efficiencies based on "surface energies" are exceedingly small. This large kinetic energy component is usually dissipated as heat but may be partially reclaimed because impact of fragments against the surface of steel retaining rings causes additional comminution. There are currently several theories of crushing, all of which can be derived from the general energy equation of Gillilandl as was pointed out by Mitchellet al in 1954'and more recently by Rose and Sullivan. If the exponent of the equation dE-x-"dx is assigned values of 2,1, or 3/2, one obtains by intergration between suitable limits, the equations of Rittinger, kick,' and Bond,' respectively. Other investigators prefer to let the exponent be a variable parameter. To help resolve the controversy, the Allis-Chal-mers Research Laboratories set up a series of carefully controlled experiments in which the level of energy input required to induce the comminution of a single particle by slow compression loading was very accurately measured. The energy input requirement, in conjunction with the size analysis of the fragments produced at fracture, yielded an accurate energy-product size relationship for the conditions studied. APPARATUS The experimental apparatus was designed to apply a compressive load on opposite sides of an "ideal particle." Spherical shapes were chosen, because point contact loading is typical of the mechanics of conventional crushers. The bulk of the experimental data was obtained with glass spheres because glass is a fairly homogeneous, brittle material for which the properties follow definite statistical distributions. The spheres ranged from 1/8 to 1-in. diam. The compressive load was applied to the specimen at a uniform rate by a loading mechanism (Fig. 1) which acted through a system of levers. The uniform rates, ranging from 100 to 100,000 lb per min, were obtained by metering water into a bucket suspended at the end of the secondary level. Point contact was made with the sphere through tungsten-carbide platens. This latter material is extremely hard and has a high modulus of elasticity, thereby having a minimum of distortion when loaded. The actual load on the sphere was measured independently of the lever system by a load cell, Fig. 2, which was designed so that the voltage output of the load cell would be proportional to load. The deformation of the specimen was indirectly measured by a pair of transformers which were attached to opposite edges of the upper platen. The cores of the transformers, which were attached to the lower platen, moved relative to the transformer so that the voltage output was proportional to the deformation of the sphere-platen system. The load was plotted against the deformation on an X-Y recorder. The area under the curve, as shown on Fig. 3, was proportional to the energy input of the

Jan 1, 1961

By R. Schuhmann

Distribution of material in the fine sizes of a comminution product generally is well represented by the empirical equation' y = 100 (x/k)a [1] in which y — cumulative percent finer, x = particle size, a -= distribution modulus, and k = size modulus. Charles3 found that the energy consumption in comminution is usefully expressed by another empirical relation, E = Ak(1-D) [2] in which E = energy input per unit volume of material, A = a constant, k = size modulus based on Eq. 1, and n = a constant; (1-n) is the slope of a plot of log E vs log k. Holmes3 has presented energy equations similar to Eq. 2. The constants a and n in Eqs. 1 and 2 have been shown to depend both on the nature of the material and on the comminuting device. Moreover, Charles showed that within experimental error a and n are a — n+1 = 0 [3] Combining Eqs. 2 and 3, E = A k-a [4] In the first sections of this article it is shown that the energy equation, Eq. 4, can be derived directly from the size distribution equation for the fine sizes, Eq. 1. The derivations are made without assuming any of the specific relationships between energy and particle size which have been common in previous literature. For comminution processes in which Eqs. 1 and 4 adequately represent the experimental data, the constant A in Eq. 4 is found to be a simple and useful inverse measure of grindability. That is, A is the energy consumption per unit volume of comminution product finer than unit size as determined from the straight line portion of the log-log plot of the size distribution. These considerations all lead to a unifying hypothesis of comminution mechanism from which both Eq. 1 and Eq. 4 can be derived. Finally, it is pointed out that this hypothesis raises serious questions as to the significance of the Rittinger hypothesis, the Kick hypothesis, and other theories in which energy numbers are systematically assigned to various size fractions of comminution products in order to calculate theoretical energy consumptions. Derivation of the Energy Equation from the Size Distribution Equation: For simplicity, consider the comminution of 100 volumes of a feed material of relatively uniform particle size. The comminution process may be considered as the summation of many individual and independent comminution events. The extent of comminution is most easily expressed as the number of comminution events, z. In the first derivation, the key assumption is that the characteristics of the comminution events in a given crushing or grinding process are substantially constant and do not vary with the progress of the comminution process. Accordingly the characteristics of an average comminution event may be defined. In one such event, a quantity of energy $E is applied to a single particle of size f and volume $v. The crushing of this particle produces fine particles with a size distribution similar to that given by Eq. 1: yw=100(x/ka)a0 [51 In this equation yo, a0, and k0 are used to characterize the product of an individual comminution event rather than the product of the comminution process as a whole. In using Eq. 5, we will not be concerned with values of x close to the feed size f and will therefore assume only that the equation is applicable to the finest sizes of the material. In 100 volumes of total product, the actual volume of product finer than x from a single comminution event, or dy, is given by The total volume of material below size x, resulting from z events, is then given by y = z(dy) =z(dv) (x/ka)a0 =" Eq. 7 reduces to Eq. 1 when we let a, = a and [8a] z =100/dv (ka/k )1 or k = ka (zdv/100)-1/a [8b] Eq. 8a shows that the distribution modulus of the comminution product is the same as for the product of an individual comminution event. Eq. 8b shows how the size modulus of the comminution product k varies with the extent of comminution as measured by the number of events, z, or as measured by the fraction of the feed actually subjected to com- minution1 zdv/100. The energy input to 100 volumes of total feed, or 100E, is the sum of the energy inputs for all the comminution events: 100E =z (dE) [9]

Jan 1, 1961