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By Brahm Prakash, R. Schuhmann

Chemical conditions for flotation and nonflotation of cassiterite and fluorite with oleic acid as collector and with alizarin dyes as modifying agents were studied by means of small-scale, vacuum-flotation tests. Artificial cassiterite was prepared fot these tests by high-temperature methods, especially by crystallization from borax melts. FLOTATION test work on Bolivian tin ores some years ago led to the development of several workable schemes of selective soap flotation, but left unanswered many questions of soap-flotation chemistry.' Accordingly, the study of the activation and soap flotation of quartz just reported? was undertaken as a start toward the elucidation of some of the unanswered questions. The experimental work on quartz flotation consisted primarily of small-scale, vacuum-flotation tests in which activator and collector additions and pH were varied between wide limits. In the work to be described in this paper, the soap flotation of cassiterite and fluorite was studied by the vacuum-flotation technique developed in the previous study of quartz. Using oleic acid as collector, conditions for floating cassiterite and fluorite in the absence of modifying agents were first determined. Then the effects of barium, calcium, and alizarin dyes on the flotation of cassiterite, fluorite, and quartz were studied. Alizarin dyes were chosen for study because of the promise they have shown as selective modifying agents in the flotation of non-sulphide minerals.12,1 Also, they form a family of reagents in which there should be a systematic correlation of chemical properties with composition. As a preliminary to the study of cassiterite flotation, an investigation of the preparation of synthetic cassiterite and X ray studies of natural and synthetic cassiterite were undertaken. Experimental Methods The flotation technique and most of the reagent preparations were described fully in the previous paper.' In addition, for the present work it was necessary to prepare satisfactory stocks of clean cassiterite and fluorite and to obtain samples of alizarin dyes. Cassiterite: High-grade cassiterite from the Netherlands East Indies was crushed, sized, and cleaned

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 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 J. J. Strohl, H. J. Schwellenbach

This paper relates the results obtained by decreasing the size of feed to a rod mill screen circuit. As would be expected, added production was gained and a finer grind with no tonnage loss was made possible. THE MacIntyre mill of the National Lead Co. has four parallel sections in which magnetic and gravity separations are made. Ore from a 5000-ton bin is fed by Hardinge constant weight feeders to a 6x12-ft open-end Marcy rod mill in each section. Rod mill discharge is bucket elevated to two 4x10-ft Tyrock screens whose oversize is returned to the rod mill. Screen undersize is pumped to Crockett separators for magnetite removal, and the Crockett tailings are sized and tabled to make an ilmenite concentrate. Minus 200-mesh material, overflowed by the Crockett and Dorrco sizers is thickened, de-slimed, and concentrated by flotation.' By 1948, the development of a successful slime flotation process and numerous improvements in the gravity circuit of the mill had increased the capacity of the available concentrating equipment. At the same time, improvements in the operating techniques of the dry crushing plant and improved feeding of the crusher by the mining department had appreciably increased the production rate per operating hour in that plant. Therefore, it was decided to take advantage of the added crusher capacity to produce a finer rod mill feed and in that way increase grinding capacity. At approximately the same time, finer screens were installed in the rod mill circuits to give finer grind and thus improve liberation of the magnetite and ilmenite from the gangue and from one another. Prior to the first part of 1948, a 3/4-in. limiting screen was used for sizing rod mill feed. The first reduction in crushing plant screen size was to 1/2 in. With this screen, the circulating load in the tertiary crushing circuit was too high and plant capacity dropped below a practical hourly rate. A 9/16-in.-sq opening screen, installed next, proved satisfac-

Jan 1, 1951

By H. J. Schwellenbach, J. J. Strohl

This paper relates the results obtained by decreasing the size of feed to a rod mill screen circuit. As would be expected, added production was gained and a finer grind with no tonnage loss was made possible. THE MacIntyre mill of the National Lead Co. has four parallel sections in which magnetic and gravity separations are made. Ore from a 5000-ton bin is fed by Hardinge constant weight feeders to a 6x12-ft open-end Marcy rod mill in each section. Rod mill discharge is bucket elevated to two 4x10-ft Tyrock screens whose oversize is returned to the rod mill. Screen undersize is pumped to Crockett separators for magnetite removal, and the Crockett tailings are sized and tabled to make an ilmenite concentrate. Minus 200-mesh material, overflowed by the Crockett and Dorrco sizers is thickened, de-slimed, and concentrated by flotation.' By 1948, the development of a successful slime flotation process and numerous improvements in the gravity circuit of the mill had increased the capacity of the available concentrating equipment. At the same time, improvements in the operating techniques of the dry crushing plant and improved feeding of the crusher by the mining department had appreciably increased the production rate per operating hour in that plant. Therefore, it was decided to take advantage of the added crusher capacity to produce a finer rod mill feed and in that way increase grinding capacity. At approximately the same time, finer screens were installed in the rod mill circuits to give finer grind and thus improve liberation of the magnetite and ilmenite from the gangue and from one another. Prior to the first part of 1948, a 3/4-in. limiting screen was used for sizing rod mill feed. The first reduction in crushing plant screen size was to 1/2 in. With this screen, the circulating load in the tertiary crushing circuit was too high and plant capacity dropped below a practical hourly rate. A 9/16-in.-sq opening screen, installed next, proved satisfac-

Jan 1, 1951

By J. F. Myers, F. M. Lewis

The purpose of the mill tests reported herein, was to determine the relative power efficiency of fast and slow rod mill speeds on the ores of the Tennessee Copper Co. The tests were carried out at the Isabella Mill of the Tennessee Copper Co. under normal operating conditions. Every effort was made to keep the ore supply and other conditions constant, but it will be noted that some slight variation did occur. The open circuit 6 by 9 rod mill, and ore, used in these tests have been previously described.' Four motor drive pinions were available and the tests were performed in the following manner: each pinion was used to drive the mill for a period of one week. Constant sampling prevailed during the test run, and a composite sample for each speed test was made. Realizing that some slight liner wear took place during the four-week test-run, and that some slight variation of the ore may have taken place, a second and then a third series of four-week test-runs were made with the four different pinions. The screen analysis of each of the three-week run samples at the various speeds were composited and the results are shown in Table 2. The authors feel that the 22 weeks of operation consumed during these test-runs would represent fairly the effect of each mil1 speed. The data of line 37 show that within the error of sampling and plant operation, the tons of minus 65-mesh material generated per horsepower hour was the same at all four speeds. Obviously, rod and liner consumption could not be determined for each mill speed in so short a time. The rod load was maintained at a uniform level throughout the series of tests. The authors have operated rod mills at various speeds over the past several years, and it is their observation that rod consumption is directly proportional to the mill speed. Likewise, that the rod consumption per unit of work performed is a constant, providing that all other operating factors remain the same. It is a well known fact that the efficiency increases in a ball mill as the speed decreases. This is due to lateral segregation of the large and

Jan 1, 1950

By J. F. Myers, F. M. Lewis

C. G. McLACHLAN*-I have read this paper with considerable interest and wish to congratulate the authors on the care with which they carried out their experiments and for the detailed sizing data they have presented. 011 the other hand I do not feel that these data establish their contention that "with other factors the same, the work accomplished in a fine crushing rod mill is directly proportional to the rotating speed." My reason for making this statement is that their conclusion is based on the percentage of minus 65 mesh material produced at each of the speeds at which their tests were run. The rod mill is, however, not a fine grinding machine and therefore figures based on minus 65 mesh production are figures outside the range at which it operates to best advantage. Further, if rod mill performance is to be judged on the production of such material it should have been established that a rod mill will produce it as effectively as a ball mill. To check this last point I have gone over some of the rod and ball mill grind-ing figures for our Waite-Atnulet operation and find that the ball mill at that property produces more minus 65 mesh material per horsepower than the rod mill. Moreover, this comparison is even more favorable to the ball mill if it is limited to minus 100 mesh production. It therefore seems to me that the most satisfactory basis on which to try to com-pare the performance of the rod mill in the present case is by taking a weighted average of all the new surface produced per horsepower. W. H. Coghill3 has published data which can be applied to the sizing figures presented by the authors, and if this is done the units of new surface per horsepower produced in the Tennessee tests are as follows: Admittedly the increment of increase in new surface per horsepower shown in the foregoing figures is not great, but its trend is nevertheless definitely in favor of slower speed operation, for the conditions under which these particular tests were run. I also feel that some information regarding liner contour should have been given as I think it will be found that a mill which is equipped with liners which lift the rod load can be run at a slower speed than a mill in which the liners are comparatively smooth. J. F. MYERS and F. M. LEWIS (authors' reply)—The position taken by Mr. McLachlan is to be respected even though we are all aware of the faults of surface considerations. As he points out. the increment of increase is very small. It is so small in fact that for all practical purposes it does not conflict with the conclusions of the paper. The authors appreciate Mr. McLachlan's comprehensive study of the data.

Jan 1, 1950

By S. R. B. Cooke, H. S. Choi, I. Iwasaki

Oleic acid is the chief ingredient of fatty acids used as collectors in nonsulfide flotation. With a few notable exceptions, the various quantities of saturated and other unsaturated acids comprising the remainder are usually unspecified. There have been occasional investigations to determine the collecting ability of these other acids and their effect on collection with oleic acid, but much remains to be done in this field. Hukki and Vartiainen, on the basis of tests using palmitic, oleic, and linoleic acids and an impure linolenic acid, concluded: "The collecting power of fatty acids used in flotation increases with increasing unsaturation of the hydrocarbon chain." ' Their work was concerned mainly with the response of ilmenite to the foregoing collectors, although tests were also made with magnetite, pyrite, hematite, and rutile. Cooke and Nummela, employing an almost identical technical procedure to evaluate flotation of hematite, magnetite, and goethite with various fatty acids, including oleic, linoleic, and linolenic acids of the highest purity obtainable, found: "The effectiveness of 18-carbon unsaturated fatty acids, as collectors for hematite, decreases with increase in the number of non-conjugated double bonds." 2 Vn the foregoing investigations, collector efficacy was measured on the basis of reagent addition in moles per liter. Sources of fatty acids which may be used as collectors are legion, but provided the oleic acid content is high enough, cost is normally the determining factor. Usually this restricts severely the purity of the collector in terms of its oleic acid content. Within the past year or so users of crude oleic acid have become somewhat more discriminating, apparently realizing that some of the organic acid impurities may exert deleterious effects upon certain separations. Marine fish oils have been used as collecting agents, particularly in the earlier days of froth flotation. Currently their use is restricted in this field to relatively minor applications, although they are cheap sources of fatty acids. In an effort to increase the range of uses for fish oils, the U. S. Fish and Wildlife Service has awarded contracts to study these materials as sources of new products suitable for commercial development. Funds for these investigations were provided by the Saltonstall-Ken-nedy Act of 1954. One such contract was awarded to the University of Minnesota School of Mines and Metallurgy for the purpose of investigating the use of fish oil fatty acids and their derivatives in ore flotation. Besides the esters of various saturated aliphatic acids and of palmitoleic and oleic acids, fish oil also contains esters of monoethenoid and polyethenoid acids with 20, 22, and 2 carbon atoms. The basic purpose of the investigation was to determine whether the longer-chained unsaturated acids possess collective properties superior to those of the C,, monoethenoid oleic acid, the C16 monoethenoid palmitoleic acid, or the saturated C,, stearic acid and its shorter chain homologues; whether highly unsaturated acids have merit as collectors; whether rela-

Jan 1, 1960

By M. Takeda, H. Majima

Pyrite has been subjected to xanthate adsorption experiments in order to determine the nature of adsorption. The identification of adsorbed species by means of IR spectroscopy, as well as UV, shows that the dixanthogen adsorption is undoubtedly predominant on pyrite surface. The rest potential measured in a xanthate solution coincides with the redox potential of the xanthate-dixanthogen couple. Considering all the factors together, the adsorption mechanism of dixanthogen on pyrite has been proposed as This mechanism is consistent with the "passive" character of pyrite. From the measurement of the redox potential of the xanthate-dixanthogen couple in the homologous series, a rule similar to that for surface tensions proposed by Traube is also applicable. The polarization experiments were conducted on pyrite in a solution containing xanthate. In the anodic polarization, xanthate is observed to oxidize to dix- anthogen, which depresses oxygen evolution on py rite at higher potential levels. In spite of the importance of the presence of pyrite in the flotation of sulfide minerals, not many studies have been made on the xanthate-pyrite system in the absence of an activator or a depressant. In an early study by Gaudin and Wilkinson,' it was pointed out that no ferric xanthate was formed on a pyrite surface, while in another study Gaudin and his collaborators2 proved the formation of a very small amount of ferric xanthate. Afterwards, Gaudin et al.3 studied the pyrite-xanthate system with a radiometric technique and found indications of the presence of adsorbed dixanthogen on pyrite surfaces. Mamiya4 studied the flotation behavior of the pyrite-xanthate system and also suggested the possibility of dixanthogen. Recently, Fuerstenau and his coworkers at The Colorado School of Mines5 studied the role of dixanthogen in the xanthate flotation of pyrite and discussed the problem in terms of such properties as oxidation potential, zeta potential, flotation recovery, pH of solution, etc. However, the mechanism of dixanthogen adsorption at the pyrite-water interface is not yet understood. This paper is concerned with an electrochemical in-vestigation through which the mechanism of dixanthogen adsorption on pyrite is interpreted. EXPERIMENTAL MATERIALS AND TECHNIQUES Pure potassium xanthates were synthesized by an

Jan 1, 1969

By J. M. W. Mackenzie

Recent successful applications of emulsion flotation suggested that a detailed study of some of the physicochemical aspects of the process was warranted. The objective of the current research was to provide general information on the electrokinetic properties of emulsion drops of the type commonly used in oxide mineral flotation. Combinations of the parafin oil Nujol and several long-chain reagents in water were studied with respect to the effect of pH on the surface and zeta potentials. It war concluded that for emulsion drops in the presence of a long-chain reagent but in the absence of any other electrolyte which is adsorbed at the oil-water interface, the surface potential will be some two to four times the value of the zeta potential. During the last decade there has been a revival of interest in the so-called agglomeration, or emulsion flotation (in this paper the term emulsion flotation will be used), process. In this flotation technique, a neutral hydrocarbon oil, together with longcnain reagents, usually of a polar-nonpolar structure, are added to the pulp to function as collectors for specific minerals. The combination of oil and longchain reagent is either emulsified prior to addition to the pulp, or in the pulp itself, and the resulting collector species is an oil-in-water emulsion of a neutral hydrocarbon oil emulsified by polar-nonpolar long-chain reagents. Emulsion flotation has been used successfully in the treatment of ores containing iron, manganese,' and titanium oxides. 2 Two other major and long established applications of emulsion flotation are the flotation of coal and Florida phosphate ores. In recent years, emulsion flotation has been particularly successful in the treatment of ores containing oxide minerals which slime readily and, consequently, are difficult to treat by conventional flotation processes. The recent successful

Jan 1, 1970

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

By I. C. Edwards, G. E. Agar

INTRODUCTION Many research efforts over the past years have been devoted to the study of energy consumption in comminution and the characteristics of the broken material. The old "laws" have been superseded by more general methods of analysis1,2,3 but these methods have not received much attention outside the laboratory. The work to be described here was done in order to obtain scale-up information on wet rod milling of sylvinite. EXPERIMENTAL A 30 x 51 in. Denver rod mill with a scoop feeder was used for these tests. Ore was fed from a variable speed screw conveyor into the feed box along with saturated brine. The mill was filled to approximately 45% of its volume with 2400 lbs of a mixed rod charge. The minimum possible feed rate was 2.5 tph and the practical maximum for this mill was 8 tph. Individual tests were run by setting the solid feed rate, then adjusting the brine flow rate to give the desired pulp density. After steady state, as evidenced by constant discharge pulp density, had been reached, samples of the discharge were taken at 15-minute intervals. These samples were filtered, washed with alcohol, dried, then screened on Tyler screens using a Ro-tap shaker. The sylvinite feed was regular plant feed that had been scalped at 20 mesh and was tapped from the coarse ore bins. It had been previously passed through a roll crusher set at 3 inches and after scalping was essentially minus 1 in. plus 20 mesh. RESULTS The screen analysis of samples from each series of tests was plotted on double logarithmic scale paper to determine the reliability of the series. In some cases, a faulty sample or screening procedure dictated that the results of one test be discarded. The criterion is a simple one — if the slope of one plot was noticeably different from the others in the series, it was discarded. The only cases that caused difficulty were those in which the brine was not thoroughly displaced from the solids. When this occurred agglomerates were easily identified on the screens and the whole of the sample was retained on 3 or 4 screens. There were no border line cases. The number N given in Table 1 is the number of size analyses that were pooled to form the data shown in Fig. 1. While examining the reliability of the sizing and sampling by plotting the data, it became apparent that there was no significant difference between grinds made at 50 and 60% solids. For the analysis given here, these tests were regarded

Jan 1, 1967

By P. L. De Bruyn, R. J. Charles

THE transfer of kinetic energy of translation into other forms of energy by impact is a fundamental process in most crushing and grinding operations. During and after the impact process the original source energy may be accounted for in any of the following possible forms: 1) Kinetic energy of translation of both the impacted and impacting objects. 2) Kinetic energy of vibration of the components of the impact system. 3) Potential energy as strain energy of the components of the system or in the form of residual stresses. 4) Heat generated by internal friction during plastic deformation or during damping of elastic waves. 5) New surface energy of fractured materials. At any instant during the impact process only the strain energy of the components of the system can contribute directly to the brittle fracture process. If fracture is the desired result, as in comminution, it would seem advantageous to choose or arrange the conditions of impact so that a maximum amount of the original kinetic energy could be converted to strain energy at some moment during a single impact. The present work deals with determination of these desirable conditions for a simple case of impact and application of the principles involved to general cases of impact. Experimental Method: Longitudinal impact of a rod with a fixed end was chosen as the impact system for investigation. The rod was mounted horizontally and the fixed end was formed by butting one end of the rod against a rigidly mounted steel anvil. The rod, of pyrex glass, was 10 in. long by 1 in. diam with both ends rounded to a 6 in. radius. The rounded ends permitted reproducible impacts on the free end of the rod and assured a symmetrical fixed end. Pyrex was selected as the rod material because of the marked elastic properties of such glass and the similarity of fracture between pyrex and many materials encountered in crushing and grinding operations. The frequency of natural longitudinal oscillation of the rod was 10 kc, and thus simple electronic equipment could be used for observation of strain changes occurring in the rod at this frequency. As shown in Fig. 1, impacts on the free end of the rod were obtained either by a pendulum device or by a spring-loaded gun. Relatively heavy hammers (100 to 600 g) of mild steel were used in the pendu- lum impacts, while fairly light projectiles (20 to 80 g) were fired from the spring-loaded gun. One of the main objects of the experimental work was to obtain the strain-time history of the rod as a function of the mass and kinetic energy of the impacting hammers. For this purpose a technique involving wire resistance strain gages and a recording oscilloscope was employed. Five gages were applied at equidistant sections along the rod, and by means of a switching arrangement the strain-time history at any section, and for any impact, could be obtained in the form of an oscillograph with a time base. The equation relating strain and voltage change across a strain gage through which a constant current is flowing is as follows: e = ?v/iRF [1] ? = strain, ?v = voltage change, i = gage current, R = gage resistance, and F = gage factor (from manufacturer's data — SRA type, Baldwin Lima Corp.). With the above equation an oscillograph depicting voltage change vs time on a single trace can be converted directly to a strain-time diagram if a calibration of the vertical response on the oscilloscope screen for specific voltage inputs is available. In the present case the calibration was obtained by photographing precisely known audio frequency voltages on the same oscillograph as that on which a voltage-time trace from a strain gage had been made. Synchronization of the beginning of the single trace with the beginning of the impact was accomplished by permitting contact of the impacting objects to close an electrical circuit from which a voltage pulse, sufficient to initiate the trace, was obtained. The struck end of the rod was lightly silvered for purposes of electrical conduction so that it would form one of the electrical contacts. Markers every 100 micro-seconds on the traces served for a time base calibration. Determinations of the kinetic energies of translation prior to impact were made in the case of the pendulum hammers by measuring the height of fall of the hammer and in the case of the projectiles by measuring the exit velocity from the gun barrel by means of an electrical circuit employing light sources, slits, and phototubes.' During the experimental work it became evident that the time of contact between the impacting object and the rod was an important variable in the impact process. Measurements of the times of contact were made, therefore, for every impact for which a strain-time record was obtained. The time of contact was determined by permitting the impacting components, when in contact, to act as a closed switch and discharge a condenser at relatively constant voltage. The discharge was observed and photographed with a time base on the oscilloscope screen.

Jan 1, 1957

By J. P. Zannaras

Referring to the article by R. J. Charles and P. L. de Bruyn, let us assume that W = weight of glass bar; P = weight of hammer; e = total deformation; K = unit of deformation; K = potential stress energy; E = modulus of elasticity; L = length of the bar; 7 = coefficient of inertia; h = height, ft; V = velocity, fps; and a = cross section area. The portion of kinetic energy which is effective in producing stress energy in a fixed bar struck horizontally is given by the formula" 1 + 1/3 W/P K =1+1/3w/p/(1+1/2w/p)2 P.V2/2g = Ph where 1 + 1/3 W/P ? (1 + 3W/P/(1=1/2w/p)2 [8] Putting e e = W/P =------------ From the above equation it can be seen that the maximum transfer of kinetic energy to stress energy is when e = 0 or W/P = 0 which indicates that the weight of the hammer must be very large as compared with the weight of the impacted rod. Eq. 8 diametrically opposes the conclusions reached by the authors of this article. In fact, if their suggestions were followed to the extreme when e = co when P = 0, there would be no transfer of kinetic energy to stress energy at all, as 7, becomes zero. Eq. 8 presumes that the velocity with which the stress is propagated through the bar is infinite, whereas the authors claim that the compression waves reflected are reaching the struck end of the bar prior to the complete transfer of the kinetic energy to cause such modification of the conditions there as to make them reach the reverse conclusions demonstrated by the above formula. That such interference exists is unquestionably demonstrated by the authors and others. However, if my observations are correct, such interference for this specific experiment and also for practical comminu- tion is insignificant, and the conclusions of the authors are in error and must be reversed to comply with Eq. 8. Eq. 5, w. = AE 2/2, given by the authors on page 51, is derived from the following equation (Eq. 9): K = 1/2Pe, where P = Sa, S = ?E, e = EL, and L = 1. The above formula, Eq. 9, cannot be applied in this case. This formula is applicable for static loads where the load increases from zero up to its final value, P, in such a way that the deformation at different instants is proportional to the loads acting at those instants and actually represents the area of a right triangle in the strain load diagram of base e and height P. The typical photographs shown in Figs. 3 and 4 represent the familiar strain load diagrams, and since the line of the wave marks the existence and intensity of the strain with the unquestionable conclusion that such strain has been caused by the action of a load acting continuously all along the wave until it reached the horizontal axis, the work stored at this point is represented by the area under the wave line and the horizontal axis and not by the area of the fictitious triangle given by the authors. Then if this is correct, even visual estimation of these areas at gage stations given in the typical photographs of Figs. 3 and 4 suffice to contradict the authors' calculation given in Figs. 6a and 6b and Figs. 7a and 7b. The typical photographs presented by Charles and de Bruyn show a considerable variation of the intensity of the strain at different stations but very small variation of areas which actually represent the stress energy at the corresponding stations. And, apparently, by squaring the small quantities, the authors magnified their error tenfold. J. M. Frankland's paperV iscusses the relative strain intensity and not the total energy for different types of impact loading. He states in his paper, "The reader is explicitly warned not to confuse the results in this report with those obtained when the load is applied by a blow as from a hammer. In this case the peak load rises to very large but mostly unknown values. The accompanying large deflections and stresses are the result of high values of P, not of the dynamic load factor n. According to Frankland "the dynamic load factor" is the numerical maximum of the response factor. It therefore appears that the authors followed the same procedure in obtaining the relative strain energy ab-

Jan 1, 1957

By G. E. Agar

The energy required for dry grinding of phosphate rock in ball and roller mills has been analyzed by the method suggested by Charles and others. The findings are not wholly in agreement with Charles' predictions; but, nevertheless, the method of analysis is shown to be sound. Some of the deviation is probably attributable to the characteristics of a dry grinding system. Many laboratory and pilot plant scale experiments have been made to determine the energy requirements for size reduction. This topic was recently reviewed by Agar and Brown' and it was apparent that very little if any data exists in the literature which permits one to apply the Charles 2-Holmes3 analysis to industrial size systems. More recently, the idea has been put forward that the postulate of comminution by impact used by Charles and others was not sufficient to explain size-reduction throughout the grinding operation. The opportunity exists in the grinding operations of International Minerals and Chemical Corp. (IMC) to analyze the energy-size relationship for dry grinding phosphate rock in both ball and roller mills. This situation arises because the mills are used for custom grinding and make products from 50% to 85% minus 200 mesh. BACKGROUND A correlation of particle size in a comminuted material with the energy expended in size reduction was proposed by charles2 to be of the form

Jan 1, 1965

By S. R. Mitchell, M. Weissman, J. H. Brown

It has been demonstrated that for fine grinding operations, the energy input (E) and the product size modulus (k) are related by an equation of the form E = Ak1-n (1) where "A " and "n" are constants.(1) Also, it was suggested that "A" is determined by the comminuting device and that "n" depends primarily on the rock. It was the purpose of this investigation to study these constants by determining the form of an energy-size reduction relationship over an extreme range of energy inputs, and at the same time, to evaluate the minimum particle size produced during grinding. The comminution system consisted of a stainless steel laboratory ball mill in which quartz was ground at 60% solids for times ranging from 1 minute to 700 hours. The mill which measured 10" diameter by 12" long was loaded with about 60 pounds of balls ranging in diameter from 3/8" to 1-1/8" and was driven at 55 r.p.m. Quartz was selected for the tests because it is a brittle material for which size distribution data were expected to show a constant distribution coefficient regardless of product size.(1) This permitted specification of product size by a size modulus alone. The quantities measured were the time of grind (measure of energy input) and the specific surfaces of the products. Since no accurate method is available yet for determining particle size directly in the very fine size ranges specific surface data were used for this purpose. The relationship between these two quantities may be expressed as where Cis a constant which includes a shape factor, p is the specific gravity of the solid,_S is the specific surface and D is an equivalent particle diameter. For a material in which the distribution coefficient does not change with size the term (l/S) may be substituted for k in equation L if the proportionality constant "A" is changed correspondingly. This substitution was made in this work but in addition, screen analyses were made on several products to verify the equivalence of the two methods of size specification. EXPERIMENTAL DETAIL QUARTZ Quartz from two sources was tested. One series of tests was made on a clear, high purity crystalline quartz from Brazil and Arkansas, and another series was run on massive quartz fromNewHampshire. Grinding charges of the high purity material consisted of 2000 gram samples of -3-8 mesh particles, while the charges of the New Hampshire quartz were 500 gram samples of a -35+48 mesh screen fraction. The difference in the sizes of these two series of charges was not significant in view of the extreme size reduction accomplished, and the New Hampshire samples were smaller to permit ginding to finer sizes in shorter times than required for 2000 gram lots. SAMPLING AND ANALYSIS Separate charges were ground for all tests in which the grinding times were less than one hour and for all tests on New Hampshire quartz since these products were difficult to sample accurately without affecting the entire charge. During the long time grinding tests the mill was

Jan 1, 1961

By R. J. Charles

SEARCH for a consistent theory to explain the relationship between energy input and size reduction in a comminution process has accumulated, over the years, an enormous amount of plant and laboratory data. Although some correlation of these data has been possible for purposes of engineering design and for the advancement of research in fracture, there is still great need of a means of predicting behaviour of a solid when it is reduced in size by mechanical forces. The best known hypotheses proposed to describe the energy-size reduction relationships in crushing and grinding stem from a common origin. The present article analyzes problems of comminution in the light of the precepts of this origin. Its object is to reconcile points of difference between these well known hypotheses and to present relationships more widely applicable to comminution studies. Theoretical Considerations: Most existing relationships between energy and size reduction of a brittle solid stem from a single, simple, empirical proposition.&apos; Although this proposition can be demonstrated by observation and experiment, no theoretical derivation is yet possible. Mathematically, the proposition may be stated as follows: dE = -Cdx/xn [1] where dE = infinitesimal energy change, C = a constant, dx = infinitesimal size change, x = object size, and n = a constant. Eq. 1 states that the energy required to make a small change in the size of an object is proportional to the size change and inversely proportional to the object size to some power n. No stipulations are placed on the exponent n in either magnitude or sign. In 1867 Rittinger2 postulated that the energy required for size reduction of a solid would be proportional to the new surface area created during the size reduction. As far as can be determined there is as yet no physical basis for Rittinger&apos;s hypothesis. Rittinger&apos;s hypothesis can be stated mathematically as follows: E, = K(oa-a-0 . [2] Er = energy input per unit volume, K = a constant, <ti = initial specific surface, and o2 = final specific surface. In the size reduction of particles of size x, to particles of another smaller size, x2, Eq. 2 becomes the well known relation: ET = K&apos; {l/x2-l/xx) [3] where K&apos; is a constant. Eq. 3 may be arrived at from the proposition given in Eq. 1 by integrating and by assigning a value of 2 to the exponent n. J dE = J - C dx/x2 E = Kt (1x - 1x) where K&apos; = C. In 1885 Kick3 proposed the theory that equivalent amounts of energy should result in equivalent geometrical changes in the sizes of the pieces of a solid. For example, if one unit of energy reduced a number of equal-sized particles to particles of one half the size, then the same amount of energy applied to the particles resulting from the first test should result again in a size reduction of one half or a final size one quarter the original size. The Kick concept may be expressed as follows: Ek = K" log x1/x2 [41 K" = a constant and E, = energy per unit volume. The expression for Kick&apos;s law may be arrived at by again integrating Eq. 1 and in this case assigning a value of 1 to the exponent n. dE= J - C dx/x Eh = - C In {x/x2) = K" log (x,/x,) where K" = 2.3 C. Application of Kick&apos;s and Rittinger&apos;s laws to comminution has met with varied success. Gross and Zimmerley4 and Piret5 have shown that Rittinger&apos;s equation applies under certain conditions of experimentation. Walker and Shaw6 express the belief that in metal turning and shaping and in grinding of both metals and minerals the production of very fine particles (less than lP) follows Kick&apos;s hypothesis, whereas Rittinger&apos;s concept is valid for the size reduction of coarse particles. For the practical case of crushing and grinding, however, neither of the above hypotheses has received general acceptance. Bond&apos; has lately proposed that since neither Kick&apos;s nor Rittinger&apos;s hypotheses seem correct for plant design work, an energy-size reduction relationship somewhere between the two would be more applicable. The fundamental statement of Bond&apos;s work

Jan 1, 1958

By J. Leja, A. Pomianowski

This paper deals with equimolar solutions of xanthate and alkyl trimethyl ammonium bromide adsorption on copper, nickel and sphalerite powders. After an exposition of the experimental methods used and the results obtained, a thorough discussion leads to the conclusion that some molecular association between xanthates and CnTAB&apos;s does take place in the bulk of the solution as well as at the air/liquid interface. A spectrophotometric study of xanthate solutions alone and their mixtures with equimolar amounts of alkyl trimethyl ammonium bromide (CnTAB) has established the additivity of ultraviolet spectra (190 to 400 mµ) for potassium ethyl xanthate (KEtX) and C12TAB. No obvious effect of C12TAB addition on the decomposition rate of KEtX was observed, the half life of which was established as 29±3 days at 22°C and pH ~ 6. In mixed solutions of longer xanthate homologues (e.g. hexyl and nonyl) and equimolar CnTAB, colloidal precipitates are gradually formed which contain primarily the corresponding xanthate molecules. The kinetics of collector abstraction by copper, nickel and sphalerite powders were studied in 10-5 to 10"3 M solutions of KEtX alone and in equimolar mixtures of KEtX and CI2TAB. Presence of C12TAB caused a two to three fold increase in the amounts of xanthate (equivalent to many monolayers) abstracted by copper and nickel powders (and in their rates of abstraction) but had no effect on the abstraction of xanthate by unactivated sphalerite (equivalent to less than a monolayer). The adsorption of C12TAB itself from the mixed solutions was very low, at most one monolayer only, and was not influenced by the nature of the solid powder used. A change in the rates of abstraction, observed with copper powder, was interpreted as a completion of a multilayer coating (completely enveloping the grains of powder) following which the rate of reaction between solution and substrate becomes controlled by diffusion through this coating. Work of Buckenham and Schulmanl on molecular associations between different collectors has shown unusual synergistic effects in flotation of individual minerals using mixtures of xanthates and alkyl trimethyl ammonium bromides. The objectives of the present work were: 1) to determine whether these molecular associations between the two types of collectors (indicated by strong surface tension lowering in Buckenham and Schulman&apos;s work) take place at the air/liquid interface only or in the bulk of solution as well 2) to establish whether different solids adsorb any species from the mixture of these amphipatic molecules preferentially or as molecular complexes 3) to establish whether there are any differences in the kinetics of adsorption. Metallic copper and sphalerite powder were chosen as adsorbents since they represent two extremes since copper readily adsorbs multilayers of xanthate (and is easily floated with ethyl xanthate) while unactivated sphalerite does not appreciably adsorb xanthate but is known to be readily floated by the amine type collectors. Metallic nickel was included because the infrared spectroscopic work2 on xanthate

Jan 1, 1964

By A. Sutulov

The segregation process, an alternative to benefi-ciation of oxidized and mixed sulfide-oxide copper ores, is studied here with particular emphasis placed on time, temperature, and coke and salt percentage factors. The results show that in a segregated charge, the copper assay of the coarsest fractions normally is of the same order as the copper assay of the tails obtained from grinding and flotation of the same charge. This observation suggests the possibility of limiting or even eliminating the grinding step from the flowsheet of a segregation plant. The segregation process, which offers an alternative to beneficiation of oxidized and mixed sulfide-oxide copper ores, was discovered in 1923 by Moulden and Taplin1,2 who were attempting to apply the Perkins process3&apos;4 to a Chilean ore from the Sagasca mine. After a number of investigations and pilot plant tests,&apos;-&apos; the segregation process became a successful industrial operation.&apos;r9 The process aroused considerable interest in Chile because of the existance of large reserves of oxidized copper minerals which could not be treated by conventional hydrometallurgical methods because of the high consumption and prohibitive cost of sulfuric acid. During the last two years, the Mineral Dressing Dept. of the Institute de Investigaciones Tecnology cas of University of concepci6n (Chile) has carried out a test program on 23 different ore samples representative of the national territory. These tests were carried out on a semi-continuous and batch scale with a rotary, automatically controlled and gas-fired furnace (supplied by Bartlett and Snow, Fig. 1). The results of these tests indicate that out of the 23 samples 20 can be successfully treated by this process with recoveries of copper ranging from 85 to 95%.10,11 The purpose of this paper is to treat some specific problems related to the segregation process. TIME AND TEMPERATURE FACTORS Time and temperature of calcination play an important role in the segregation process. When moderate salt and coke conditions were maintained (each of reagents was added in the quantity of 1 — % wt), systematic testing easily demonstrated the influence of these two factors on segregation and flotation recovery. The pertinent results are summarized in Fig. 2. To determine what specific changes the segregation process made on the ore, the samples, segregated at 700°C for different periods of time and under standard conditions, were granulometrically analysed and

Jan 1, 1963