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By T. G. Decker, A. F. Witt, A. M. Gaudin

The historical development of the concept of contact angle hysteresis is reviewed. The measurements of contact angles reported in literature have all been made under static conditions. For the measurement of dynamic advancing and receding contact angles, four methods are described together with an evaluation of their precision. Three of these methods were adapted from devices already used for the measurement of static contact angles. The fourth method uses a new principle and apparatus and is the most accurate. While the relationship between surface tensions and the contact angle was extablished as early as 1805 by T. Young,' it was only in 1890 that the existence of contact angle hysteresis was reported by Lord Rayleigh. His observations, however, remained almost unnoticed. With the invention of froth flotation, the contact angle and its behavior became the subject of investigation. In 1907, L. Sulman and collaborators investigated the cause of discrepancies between recorded values of contact angles. They found that certain variations existed in most cases, but that definite maximum and minimum values of contact angles are obtainable. The difference between the maximum and the minimum contact angle in a given system was termed "hysteresis" by Sulman. First attempts to explain hysteresis were made by E. Edser. In the following years extensive studies of contact angles in various three-phase systems

Jan 1, 1963

By J. E. House, J. L. Drobnick, R. R. Swanson, D. W. Agers

The paper describes an improved process for the recovery, purification, and concentration of copper values from acidic dump leach liquors. The process employs a new liquid ion exchange material (LIX® 64 reagent) capable of separating copper values from iron and other impurities common to dump leach liquors in the typical pH range of 1.4-3.0. Properties and performance of the reagent are discussed. Design scale-up information for both pilot plants and commercial installations, including preliminary economics, are presented. Economic considerations include the production of electrolytic copper from the purified copper aqueous concentrate. INTRODUCTION Since the commercial acceptance of the liquid ion exchange process in the mineral processing industry, it has been predicted that a wide selection of chemical reagents to efficiently and economically separate many metals in solution under a wide range of conditions would be commercially available. Several years ago, General Mills began a basic research and development program to determine if it were possible to develop a reagent to extract economically metallic ion from existing process streams. Progress toward reaching this objective was reported in late 1963, when development of quantities of LIX -63 reagent, a highly selective reagent for the extraction of copper, was introduced. The properties of this reagent are described in a previous paper.' The development work with this reagent indicated that perhaps the largest potential application for a copper extractant, the treatment of acidic dump leach liquors, would not be economically possible with LIX-63 because of limitations of the reagent to extract copper below a pH of 3.0. The relatively small pH adjustment required with LIX-63 would result in a significant processing cost and the undesirable precipitation of ferric hydroxide from the liquor. This pointed to the need for another copper extractant which would extract copper from dump leach liquors without pH adjustment. General Mills was successful in synthesizing a molecule which does not have the pH limitation of the LIX-63, yet possesses the selectivity-solubility properties required of a metallic extractant. The resulting LIX-64 reagent broadens the pH range from which copper can be effectively extracted and separated from other metallic impurities. Of special significance is the fact that the reagent, LIX-64 was developed by combining the technical requirements of a specific problem in hydro-metallurgy with theoretical organic and physical chemical principles.

Jan 1, 1967

By U. N. Bhrany, N. Arbiter

Over the last one hundred years the problem of assessing the efficiency of energy consumption in producing rock breakage has been studied by many investigators from a variety of viewpoints. Their contributions fall into three main categories: (1) those characterized by a priori assumptions of a relation between the energy required for fracture and the degree of fragmentation produced (e.g. Rittinged(l), Kick(2) Bond(3)); (2) those studying simple systems with controlled energy applications (Gross(4)?(5) ); (3) those treating operating data to develop practical relative measures of efficiency (Coghill(6), Taggart(7)). Closely involved in the efficiency problem is the characterization of size distributions produced by comminution. Unless an experimental size distribution can be approximated by a distribution function and its constants, it becomes difficult if not impossible to develop quantitative energy-particle size relationships. While many such functions have been proposed, none are both completely adequate and convenient. The simpler fonns usually describe only a part of the sizing data, while those which apply to a greater extent are cumbersome(8). The thesis underlying the study here reported can be stated as follows: Size reduction in a tumbling mill subjects ore particles to a relatively constant fracture-producing environment. The intensity of the forces is determined by such factors as the mass of the breaking bodies (rods, balls, rock), and the speed and dimensions of the shell. For a particular ore the extent of size reduction will depend both on the intensity and on the duration of exposure. The latter is the residence time in a batch mill, or is determined by the effective volume and the flow rate in a continuous mill. Size reduction can thus be regarded as a rate process in which the weight of material in size intervals varies as a function of grinding time. Although both the rates of disappearance of coarser sizes and

Jan 1, 1961

By E. J. Roberts

Hydrometallurgical operations and many processes in the chemical industry require the separation of dissolved material from solids. One of the decisions which has to be made in designing a plant for such an operation is how this separation shall be accomplished. It is the purpose of this paper to set forth the general principles involved in such separations in order that the optimum flowsheet and equipment may be selected. Countercurrent Decantation with thickeners, or C.C.D. as it is generally known, is, of course, only one way of separating dissolved material from undis-solved. Other unit operations such as Countercurrent Filtration (C.C.F.) and Countercurrent Classification (C.C.C.) are widely used. The same principles may also be applied to centrifugally assisted decantation, as with nozzle or solid bowl type centrifugals, and to separations using screens, either gravity or centrifugal type. Another form of countercurrent washing applicable to granular materials is practiced in continuous ion exchange operations. All of these operations depend on two basic principles, or combinations of these principles. In C.C.D. type operations the solids are concentrated into the smallest possible volume of liquor in each step and the resulting pulp then mixed with a more dilute liquor and recon cen trated, the liquors separated from the more dilute stages being advanced to dilute the more concentrated liquor in a previous solids concentrate, as is shown in Fig. I. This will be termed the solids concentration-solution dilution principle, or, for short, solution dilution. countercurrent decantation- type circuits. The second principle used in washing solubles from solids is that of solids concentration-solution displacement. Here the solids are restrained from movement while wash solution is forced through the interstices in a counter-current fashion, as in Fig. 2. In the simplest application of this principle, once the "cake" has been formed, it is not disturbed until the operation is completed. In continuous filters, the cake is merely moved under the successive washes and the displaced filtrates removed as in Fig. 4. Often, however, after one or two displacement washes, a repulping step is introduced, the cake reformed and washed again. This procedure brings the solution dilution principle into play as well as the solution displacement principle. Merely thickening ahead of filtration, which is often operationally advantageous, does not hybridize he circuit. It still can be a pure solution displacement operation from the washing

Jan 1, 1961

By H. Tabachnick, N. Hedley

The extraction of gold and silver from ores with alkaline cyanide solutions is well known. Cyanide solutions are also good solvents for many base metal minerals, particularly most of the copper minerals. Leaver and Woolf,1 who determined the solubilities of copper minerals in 0.10 pct sodium cyanide solution, showed that malachite, cuprite, chalcocite, and bornite are readily soluble in cyanide; least soluble are chalcopyrite and chrysocolla. The Mining Chemicals Laboratory of American Cyanamid Co. has studied the possibilities of using cyanide solutions for leaching base metals. In this article the authors present the results of their experiments with cyanide leaching to reduce the copper content of a zinc concentrate from 0.050 pct to the desired specification of less than 0.02 pct. Zinc Ore Sample: The sample of commercial zinc ore used in this investigation to produce zinc concentrates was ball mill feed ranging from 1/2 in. to fines. The ore was crushed to —10 mesh and riffled into 600-g charges for zinc flotation. Analysis revealed 4.54 pct Zn and 0.005 pct Cu. Examined microscopically, the ore consisted essentially of cream-colored sphalerite and carbonate gangue. It contained a small amount of pyrite, partly tarnished. The only copper mineral identified was chalcopyrite, mostly smaller than 20µ, some of which occurred as attachments on sphalerite. Flotation Procedure: Batches of zinc concentrates were made as required according to the following general procedure. A 600-g charge of —10 mesh ore was ground for 4 min at 60 pct solids in a laboratory steel rod mill. Screen sizing showed it to be all —35 mesh with 42 pct —200 mesh. The pulp was transferred to a Fagergren laboratory flotation machine, diluted to 25 pct solids and conditioned for 5 min with 0.6 lb per ton CuSO4, . -5H2O. It was then conditioned with 0.10 lb per ton Sodium Aerofloat promoter and floated for 5 min with pine oil as frother and creosote as froth stiff-ener. The pH during flotation was 8.5. A typical analysis of zinc concentrate subjected to leaching is 44.41 pct Zn and 0.051 pct Cu. The ratio of concentration was close to 10 to 1. Leaching Procedure: Aero Brand cyanide, technical calcium cyanide analyzing 49.5 pet NaCN equivalent, was used for all cyanide leaching tests. For each test three rougher concentrates floated as described were combined (total weight close to 180 g) and the water content adjusted to 150 ml. The percent solids in the pulp was thus 55. After a weighed amount of cyanide flakes had been added, the pulp was agitated on rolls for a given period, then filtered and washed. Filtrate and washed concentrate were assayed for copper content. The procedure for ammonia leaching was similar to the cyanide process. A series of tests was run in which the effects of ammonia as a solvent for copper in the zinc rougher concentrate were investigated. In each test 180 g of zinc rougher concentrate was leached with 150 ml of ammonia solution. Various strengths of ammonia and times of leaching were investigated. The results are shown in Table I. It is apparent that ammonia was a poor solvent for copper in the zinc concentrate; 60 min of agitation with a relatively strong NH:, solution extracted only 2 pct of the copper. CYANIDE LEACHING TESTS Effect of Solution Strength: The solvent effects of 0.125, 0.187, and 0.250 pct NaCN equivalent solutions were compared for leaching periods of 15 min. Residue and filtrate were assayed for copper content. The copper content of the filtrate plus wash was calculated back to the original volume of cyanide solution (150 ml). The effects of cyanide strength are given in Table II, It will be noted that 15 min leaching with 0.25 pct NaCN equivalent solution extracted 74.6 pct of the copper in the zinc concentrate. The leached product assayed 0.013 pct Cu, appreciably below the required specification of 0.020 pct. Effect of Leaching Time: Portions of zinc concentrate were leached with 0.25 pct NaCN equivalent

Jan 1, 1961

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 Milton E. Wadsworth, Edward M. Eyring

BETTER understanding of solid surfaces and their associated adsorption products is of both academic and practical value. The study of detergents and their behavior in cleaning surfaces is fundamentally related to the nature of the products adsorbed and their ability to compete for certain surfaces. Similarly in flotation, the nature of the adsorbate before and after adsorption is basic to clear understanding of the process. The recently developed pellet technique1,2 employing infrared spectroscopy provides a powerful tool for the study of solid surfaces. Absorption bands, which are infrared-active, may be observed for adsorbed products. Also any changes in the surface substrate that occur as a result of adsorption may be detected by means of differential spectra. In applying the pellet technique to solids of large surface area, French and his coworkers3 have surveyed the adsorption of organic flocculants on clay minerals, oleic acid on fluorite, and ammonia on cracking catalysts. Recent work on application of differential infrared spectroscopy to the study of solid surfaces' has demonstrated that the difference between a sample and a reference can be obtained with double-beam instrumentation. In this way displacement of surface products, adsorption of new products, and differences in the substrate, if any, may be detected. Experimental Procedure: Potassium iodide pellets were used in this study, prepared from recrystallized analytical reagent grade KI. Grinding was carried out in a Fisher mechanical agate mortar. Two-gram plates containing the solid under study were pressed in a special evacuated die constructed in the laboratory at the University of Utah." Concentration depended on the solid in question. Zinc sulfide and willemite are sufficiently transpar- ent in the infrared region for concentrations as high as 20 mg of mineral in 2g of KI to be used. Zinc oxide is even more transparent, permitting concentrations as high as 60 mg in a 2-g plate. For non-differential operation, however, much lower concentrations (2 to 10mg/2g KI) had to be used. Spectra were obtained on a Per kin-Elmer 21 double-beam recording infrared spectrophotometer. A sodium chloride prism was used giving a spectral range of approximately 2 to 15 v wave length. For differential runs a resolution of 1000 was used and the scanning speed was controlled commensurate with instrument response. The response was checked continuously and each spectrum was repeated several times. For nondifferential runs a resolution of 927 was used. Zinc oxide used was analytical grade oxide fume. The zinc sulfide was precipitated from solution with analytical grade zinc sulfate and sodium sulfide. The precipitate was washed and centrifuged several times and dried. Before use the precipitate was washed in dilute HCl and then treated with saturated NH4Cl to remove any bulk oxides and sulfates. X-ray patterns of the precipitate were comparable to that of the natural mineral sphalerite. The precipitate was much more satisfactory than finely ground natural ZnS because of its very large surface

Jan 1, 1957

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 C. H. Wayman, D. W. Fuerstenau

The effect of bubble size and concentration of certain reagents on the terminal velocity, shape, path, and drag coefficients of single air bubbles in distilled water has been investigated. Bubbles of a certain size range rise considerably faster than Reynolds number-drag coefficient relationships predict, whereas a small amount of frothing agent reduces their terminal velocity. The rapid velocity at which bubbles rise in distilled water appears to result from slip at the boundary and from circulation within the bubbles. Surface-active agents retard bubble motion through prevention of both circulation and slip at the boundary. A surface tension concentration gradient helps maintain bubble sphericity. HE gas phase is one of the indispensible in-gredients in flotation operations. Flotation depends on the collision of an air bubble and a mineral particle in a pulp and their ability to remain in contact long enough for adherence to take place. Before it is possible to understand the mechanics of air bubble-mineral particle encounter, it is necessary to learn more about the nature of bubbles themselves before collision with a mineral particle has taken place. To date, little work has been done on air bubbles in flotation systems. In 1945 Fahren-wald' presented a study of the role of frothers on air bubbles and on aeration in flotation, and recently Wark and Sutherland' discussed the work of Rosenberg- in relation to flotation. The research reported in this present article was undertaken to investigate systematically the effect of bubble size and the concentration of certain reagents on the terminal velocity, shape, path, and drag coefficient of single bubbles in distilled water. Most of the work is concerned with the effect of a-terpineol on bubble motion in water, but studies were made with potassium chloride, potassium hydroxide, potassium ethyl xanthate, and potassium amyl xanthate. Experimental Method and Materials: To obtain free bubble rise and reduce wall and surface effects, the investigators used a tank of 5½x5½x30-in. internal dimensions, filled with water to within 4 % in. of the top.' The tank was made of acrylic plastic so that the walls would have good optical properties. Distilled water, which was re-distilled in a block tin still and saturated with air before each test, was used in all the experiments. All solutions were made with reagent-grade chemicals. During each experiment the water was at room temperature, and during the course of an experiment the temperature did not fluctuate more than 0.5°C. Since the experiments were performed over a period of six months, the temperature varied between 25° and 27°C. The temperature at which each series of experiments was conducted is recorded with the data. The experimental apparatus is presented dia-grammatically in Fig. l. Individual air bubbles were generated from purified compressed air through a capillary of 0.003-cm internal diameter at a rate

Jan 1, 1959

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 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 R. E. Powers, E. H. Kinelski, H. A. Morrissey

A group of 17 American blast-furnace sinters, an American open-hearth sinter, an American iron ore, and a Swedish sinter were used to evaluate testing methods adapted to appraise sinter properties. Statistical calculations were performed on the data to determine correlation coefficients for several sets of sinter properties. Properties of strength and dusting were related to total porosity, slag ratio, and total slag. Reducibility was related to the degree of oxidation of the sinters. THIS report to the American iron and steel industry marks the completion of a 1949 survey of blast-furnace sinter practice sponsored by the Subcommittee on Agglomeration of Fines of the American Iron & Steel Institute. The use of sinter in blast furnaces, sinter properties, raw materials, and sinter plant operation have been reported recently.1,2 After preliminary research and study," test procedures were adapted to appraise the physical and chemical properties of sinter to determine what constitutes a good sinter. During the 1949 to 1950 plant survey each plant submitted a 400-lb grab sample to research personnel at Mellon Institute, Pittsburgh, Pa. A 400-lb sample was also submitted from Sweden. In addition, 2 tons of group 3 fines iron ore were obtained from a Pittsburgh steel plant. The following tests were performed on the iron ore sample and on the 19 sinter samples: chemical analysis; impact test for strength and dusting; reducibility test; surface area measurements, B.E.T. nitrogen adsorption method; S.K. porosity test; Davis tube magnetic analysis; X-ray diffraction analysis for magnetite and hematite; and microstructure. Results of these evaluations are discussed in this paper and supply a critical look at testing procedures used to determine sinter quality. Sinter Tests and Results Each 400-lb grab sample of sinter was secured at a time when it was believed to represent normal production practice at each plant. It was not possible to use the same sampling procedures throughout the survey; consequently samples were taken from blast-furnace bins, cooling tables, and railroad cars. These were very useful for evaluation of test methods, since they were obtained from plants with widely divergent operations. With the exception of Swedish sinter and sinter sample N, which were produced on the Greenawalt type of pans, all survey sinters were produced on the Dwight-Lloyd type of sintering machines. Sinters submitted for test were prepared in identical manner by crushing in a roll crusher (set at 1 in.), mixing, and quartering. To secure specific size fractions for tests, one quarter of the sample was crushed in a jaw crusher and hammer mill to obtain a —10 mesh size. The remainder was screened to obtain specific size fractions. The group 3 fines iron ore was dried and screened and samples were taken from selected screen sizes to be used for various tests. Prior to testing, each ore sample except the —100 mesh fraction was washed with water to remove all fine material and was then dried. This iron ore, a hematitic ore from the Lake Superior region, was used as a base line for comparing results of tests on sinters. The iron ore did not lend itself to impact testing, since it was compacted rather than crushed in the test, and no impact tests are reported. However, the iron ore was subjected to all remaining physical tests to be described. Chemical Analysis: Table I presents chemical analyses performed on the survey sinter samples. Included in this table are data obtained from determination of FeO and the slag relationships: CaO + MgO and total slag (CaO + MgO + SiO, SiO2 + Al2o3 + TiO2). The percentage of FeO was used as an indication of the percentage of magnetite in the sinter. It was believed that slag relationships could be correlated with sinter properties. During initial determination of FeO great disagreement arose among various laboratories, both as to the results and the methods of determining values. Table I lists the values of FeO resulting from the U. S. Steel Corp. method of chemical analysis,' which reports the total FeO soluble in hydrochloric and hydrofluoric acids (metallic iron not removed) with dry ice used to produce the protective atmosphere during digestion. Use of dry ice was a modification required to obtain reproducible results. In this method, the iron silicates and metallic iron are believed to go into solution and are therefore reported as FeO. This is important, for in the study of the microstructure of sinters, glassy constituents suspected of containing FeO as well as crystallized phases of undetermined identity which may also contain FeO have been observed. Strength Test by Impact: In evaluating sinter quality, one of the properties stressed most by blastfurnace operators is strength. This strength may be described as the resistance to breakage during handling of sinter between the sinter plant and the blast-furnace bins. It is also the strength necessary to withstand the burden in the blast-furnace. After

Jan 1, 1955

By F. Petkovich, M. P. Sudbury

Development of a new method of treating flotation concentrates for the preparation of feed suitable for direct charging to blast furnaces or converters is described. The method takes advantage of the fact that pyrrhotite contained in the concentrates can be made to undergo exothermic reactions which, under properly controlled conditions, result information of oxidation products that serve to cement the concentrate particles together. Thus green concentrates either in the form of pellets or briquettes containing 5 to 8 pct moisture not only were hardened, but also completely dried autogenously by continuous countercu,vrent shaft treatment with air. The process was developed through pilot plant operations ranging from 35 1b per hr to 2.5 tph, culminating in products evaluation tests on a railway-car scale. Falconbridge Nickel Mines Ltd., Falconbridge, Ont., have practised sintering, on a travelling grate machine, for many years to prepare a pyr-rhotite-bearing Cu-Ni sulfide flotation concentrate for blast furnace smelting. In recent years the development of new mines, and the construction of concentration plants some 40 miles from the smelter has increased the quantity of concentrate shipped, and encouraged the search for a method of producing dry, hard pellets or briquettes suitable for direct charging to a blast furnace or converter, and capable of withstanding considerable handling. The cementing properties of pyrrhotite oxidation products were discovered during a search for a suitable agglomeration method for sulfide concentrates, and were exploited in a process subsequently developed for autogenously drying and hardening pellets and briquettes of pyrrhotite-bearing Cu-Ni sulfide flotation concentrate. EARLY TEST WORK The production of hard, dry pellets of concentrate filter cake was attempted in the drying plant of one of the new concentrators. While soft pellets were produced containing 5 pct moisture, attempts at further drying resulted in disintegration of the pellets and intolerable dusting. The plant therefore was controlled to produce a concentrate containing about 6 pct moisture. The partially dried concentrate, which was shipped to Falconbridge for sintering, tended to heat spontaneously in transit. An at- tempt to briquette the moist concentrate at Falconbridge, in a plant incorporating a muller, a 20-in. roll briquetting press, and a steam-heated travelling grate oven, was more successful, although the equipment corroded rapidly due to the acid nature of the concentrate after spontaneous heating had occurred. LABORATORY STUDIES OF SPONTANEOUS HEATING OF CONCENTRATE The spontaneous heating of partially dried concentrate was studied in the laboratory. Moist concen-

Jan 1, 1961

By H. Kahata, I. Iwasaki, Y. Takahasi

A combined process of segregation roasting-flota-tion or magnetic separation was developed to recover nickel from lateritic iron ores and oxidized nickel ores. An ore was mixed with a halide, such as sodium or calcium chloride, and a solid reductant, and roasted, whereby the nickel content was segregated out as discrete metallic particles. Either by magnetic separation, or by flotation using a sulfhydryl collector together with a heavy metal salt as an activator, the metallic nickel could be concentrated, Effects of such variables as the types and amounts of the halide and solid reductant addition and of the roasting conditions were extensively investigated. The concentration results on several types of ores from Japan, the Philippines, and New Caledonia are presented. Laterite is a residual product of rock decay in tropical and subtropical regions, and consists mainly of hydrated oxides of iron and alumina. Those derived from serpentine sometimes become enriched in nickel, cobalt, and chromium contents. Oxidized nickel ores are of the similar origin, but their nickel as well as silica contents are higher due to gamierite-type silicates. Apparently, nickel enrichment is more pronounced in the transition region between the surface layer of iron laterite and the underlying serpentine. Iron laterites often contain over 50% iron, and their reserve is reported to exceed 22 billion tons, corresponding approximately to 20% of the world iron ore reserve.1 It is readily apparent, therefore, why the iron laterites have attracted much attention of the steel industry as a potential source of iron ores. Numerous attempts to remove nickel and chromium as byproducts, have been reported in literature.' Worldwide discoveries of high-grade iron ore deposits in recent years have inevitably lessened the interests in iron laterites. However, in view of the tremendous potential for their gross value and supplies of nickel, cobalt, chromium, and alumina along with iron, the problem remains as a challenge. Much of the chromium in laterites is present in the form of relatively coarse particles of chromite, and various classification methods have successfully been applied for its removal.2,3 The nickel, however, is intimately associated with limonite, and ordinary concentration techniques are totally ineffective. Much attention has, therefore, been given to hydro-metallurgical or pyrometallurgical means. Yet, all the known processes appear to have limitations either economically or for the use of products as iron raw materials due to a high residual content of nickel. Some attempts have been made to pre-roast laterites or oxidized nickel ores, particularly with sulfidizing agents, and to remove nickel either by magnetic separation,' or by flotation.4 It is apparent that any such concentration process would require grain growth of nickel during roasting for effective separation. Oxidized copper ores are reported to be concentrated by the segregation roasting-flotation process,5 in which the ores are roasted with a chloridizing agent and a carbonaceous reductant in order to promote the growth of metallic copper through repeated cycles of copper chloride volatilization and its reduction on the solid reductant surfaces. Examination of a vapor pressure-temperature diagram of various metal chlorides indicates that a separation of nickel from iron may be effected by a similar process. In fact, the segregation roasting of laterites was reported to increase the extraction of nickel by the ammonia leach process, as compared to the ordinary reduction roasting.6 In the present article some of the preliminary experimental results of the segregation roasting, followed by either flotation or magnetic separation, on laterites and oxidized nickel ores are reported. The effects of various parameters in the roasting as well as in the concentration steps are discussed. MATERIALS AND METHODS An oxidized nickel ore from Thio, New Caledonia, and three laterites from Homonhon, the Philippines, Wakasa and Miyagawa, Japan, were selected for the

Jan 1, 1967

By J. M. W. Mackenzie, M. H. Buckenam

Flotation experiments using stearic, oleic, linoleic, linolenic, and ricinoleic acids and naturally occuring products rich in these acids as collectors for calcite are described. The results confirm the validity of the rule of Hukki and Vartiainen relating the collecting power and unsaturation of the C18 acids. Reasons for this relationship are discussed and a close relationship between mineral depression and critical micelle concentration is reported. It has long been recognized that the unsaturated fatty acids are in general superior flotation collectors to their saturated homologues. Whereas earlier workers concentrated on saturated and monoethe-noid acids, recent investigations have centered on oleic, linoleic, linolenic, and the substituted mono-ethenoid acid: ricinoleic. From studies of the collecting properties of palmitic, oleic, linoleic, and linolenic acids on ilmenite, rutile, hematite, and magnetite, Hukki and Vartiai-nenl concluded that the collecting power of fatty acids increased with unsaturation of the hydrocarbon chain. Sun, Snow, and Purcel12 investigated the collecting properties of unsaturated fatty acids as collectors for phosphate ores and concluded that the collecting power increased with increasing unsaturation of the hydrocarbon chain up to two double bonds and that further unsaturation decreased the collecting power. More recently Sun3 studied the collecting power of the C18 fatty acids stearic, oleic, linoleic, and linolenic on 37 minerals. The results of these experiments with a few exceptions showed that the collecting power of the acids increased in the order stearic, oleic, linoleic, and linolenic. The relative collecting powers of linoleic and linolenic acids were in many cases altered by the cleanliness of the mineral surface prior to flotation. Sun concluded that linolenic acid may become oxidized by atmospheric oxygen during flotation, a reaction which would reduce its effectiveness as a collector. This deduction is supported by Gaudin and Cole4 who concluded that oleic and linoleic acids do not undergo appreciable oxidation of the double bonds during flotation but that the linolenic acid double bonds are measurably affected. The most complete investigation on the influence of hydrocarbon chain unsaturation on the collecting properties of fatty acids is that of Kivalo and Lehm~svaara.~ These workers using linolenic acid of a higher purity than Hukki and Vartiainen showed that this acid was superior to oleic and linoleic acids as a collector for magnetite. They also found that ricinoleic acid was a more effective collector for this mineral than the other acids investigated, an observation particularly apparent at high collector concentrations. Seeking to explain the superiority of the unsaturated acids these authors considered the effects of critical micelle concentration, surface activity, hydrolysis, and cross sectional area of the hydrocarbon chain in relation to unsaturation. Using what, according to the results of Caviere are erroneous surface tensions of the soap solutions of these acids, they concluded that the surface activity decreases and the critical micelle concentration increases with increasing unsaturation. In view of the data of Cavier, whose results show that surface activity of these soaps increases with unsaturation, the deductions of Kivalo and Lehmusvaara are open to criticism. The degree of hydrolysis of the soap solutions as measured by Kivalo and Lehmusvaara decreases as the unsaturation of the fatty acid increases, a result which helps to explain the superiority of unsaturated acids as collectors. In view of the superiority of unsaturated acids as collectors for many minerals, attention has been directed towards the utilization of fatty acid raw materials such as tall oils and linseed oils which contain considerable quantities of these acids. This paper describes test work to determine the effect of unsaturation of the hydrocarbon chain on the collecting properties of fatty acids on calcite, and includes comparable test work using natural products rich in unsaturated acids. TEST WORK Reagents: The pure fatty acids used were oleic, linoleic, and linolenic. Of these, oleic was supplied by British Drug Houses Ltd. and the others were produced by the Hormel Inst. When not in use these

Jan 1, 1961

By H. R. Cooper

Beginning from the point of view that process control of ore flotation can be approached by on-line analysis of processing behavior, an equation was developed which has characteristics useful for a multi-variable feedback loop. The application of this equation to optimizing control with a data acquisition system will be discussed in Part 11. OBJECTIVE OF CONTROL The purpose of developing a feedback method for concentrator control is to provide a means for determining ore processing behavior in order that data describing the ore can be used to make appropriate changes in control conditions while the ore continues to flow through the flotation circuit. In absence of simple linear relationships between pairs of variables in the flotation process, attention is directed to the need for a generalized relationship which possibly would incorporate all pertinent variables. It would be possible to apply such an equation to the control of variables in a concentrator in real time according to operational requirements as ore gradually changes in quality and processing behavior. To meet this objective, it is necessary to define relationships describing flotation performance in terms of performance variables capable of being measured on-line, either with on-line instruments and analyzers or with manual methods lending themselves to quick determination of meaningful information. Relationships derived to meet this objective form a model for the flotation process. The evaluation of flotation parameters of the ore and the execution of control on the basis of the derived information while the ore is continuing through the process would constitute a feedback control system. Data for the following control and performance variables can be made available: 1) ore feed rate, 2) collector addition rate, 3) lime addition rate, 4) pulp density, 5) assay or multiple assays in feed, tails, or concentrate sufficient for material balancing, 6) particle size distribution in flotation feed, 7) froth height, and 8) frother addition rate. Other process variables, such as flotation air input and mechanical agitation intensity, are usually not considered as control variables and were not taken into account in this analysis. Other data, such as that describing the ore, would be useful for concentrator process control. However, information of this type (such as ore hardness, grain size of the mineral, chemical species of the mineral, and ore surface properties) being not presently measurable in the on-line sense, has the effect of causing disturbances in the system which can be detected only indirectly. The process control system being sought must recognize disturbances by their effect on measured performance followed by determining control changes to compensate for them in meeting the objectives of improved performance (perhaps higher throughput, maximum return, etc.). A suitable model for the process having capability of recognizing the effects of ore disturbances should provide the means for introducing proper compensation through control changes. This would be done by processing on-line data with the model to calculate coefficients reflecting ore characteristics. This procedure can only be applied in a typical flotation system when on-line data can be processed at faster rates than the usual rate at which the ore in flotation feed takes on significantly different characteristics. For example, material balance data can be accumulated in approximately 5-min intervals using on-line X-ray fluorescence analysis. The flotation system time constant might be 15 min including grinding. Ore changes having time constants longer than 1 hr could be accommodated using on-line feedback control by this procedure. FORM OF A FLOTATION MODEL A suitable form for mathematical expression of the flotation process is an equation involving rates, when each of the components entering into the separation can be treated independently by a rate equation. A first-order, kinetic rate equation can be written on

Jan 1, 1967

By R. T. Hukki

IT is no great exaggeration to say that present grinding practice and economics are largely determined by lining design. A record of outstanding liner wear can be achieved with any liner surface pattern that will positively lock the outer layer or layers of grinding media. With no slippage, lining wear is bound to be slight. At the same time, popular practice calls for tumbling loads of about 50 pct of mill volume to obtain maximum grinding capacity. Innumerable parallel grinding investigations have verified that optimum speed for such a mill lies within 70 to 85 pct of theoretical critical speed. If the mill is speeded up to 100 pct of critical, little or no grinding can be accomplished. Earlier Work on Supercritical Grinding: First investigations concerning grinding at supercritical speeds seem to be very old. Remarkable work on the subject has been performed by White,&apos; and his experiments have been described and summarized by Richards.&apos; White&apos;s contributions seem to have passed unnoticed by Fahrenwald,2,3 whose extensive experiments have been well presented, yet apparently very little appreciated. Additional work on grinding at supercritical speed has been reported, e.g., by Lewenson and Tscherny,&apos; USSR; Anselm and Grunder,&apos;, Germany: and Rose and Evans." Great Britain. Subcritical and Supercritical Speeds: In the formula of the critical speed given in the textbooks of mineral dressing, no factor indicating the coefficient of friction is generally included. If this factor = 1.0, which is equivalent to grinding conditions in a mill provided with heavily ribbed lining, the formula of the critical speed holds as such and grinding is possible at subcritical speeds only. In a mill equipped with a smooth or relatively smooth lining, the numerical value of the friction factor in the denominator of the formula becomes <1.0, indicating that grinding at supercritical speeds should be possible in such mills. It has been recently shown by the author&apos; that a wide supercritical speed range will become available for grinding—and especially for fine grinding—if the basic conditions within the mill have been selected properly. Mathematical analysis of mill dynamics at supercritical speeds&apos; has indicated that the mill speed may be increased if: 1) total mass of grinding medium decreases, 2) mass of the individual grinding piece increases, and 3) the coefficient of friction between the outer layer of medium and the mill lining decreases. It is obvious that the mass of the individual grinding piece will be affected by its shape and by its specific gravity. The coefficient of friction decreases with: 1) increasing smoothness of liner surface, 2) increasing roundness of the grinding piece, 3) increasing fineness of material to be ground, 4) decreasing pulp density, and 5) decreasing hardness (abrasiveness) of the mineral to be ground. In a mill equipped with heavily ribbed lining, practically no size reduction will take place between the lining and the outer layer of tumbling medium, because slippage is prevented. In the overwhelming majority of today&apos;s mills the grinding accomplished is by virtue of cataracting and/or cascading media with some action within the tumbling charge. Sub-critical speeds only can be applied. In grate-type or peripheral discharge mills equipped with a smooth lining a tumbling load of any kind of common medium occupying about 50 pct of mill volume will behave in such a way that practically no slippage will take place. This has been verified in experiments run by the author in the laboratory and in pilot plant mills&apos; equipped with smooth lining. Again, the operation is limited to the subcritical range. In a mill with a smooth lining, grinding will be possible either at subcritical speeds or within a wide supercritical speed range as soon as the basic requirements for a desired speed are fulfilled. In a mill operated at supercritical speed, any point on the liner surface proceeds at a speed greater than that indicated by the formula of the critical speed, while any grinding piece situated in the outer layer of the medium against the lining proceeds in the same direction at a speed less than that indicated by the critical speed. This speed difference produces a very effective attrition grinding zone between the liner surface and the outer layer of the medium. The share of attrition grinding of the total grinding accomplished increases rapidly with increasing speed in the supercritical speed range. The smooth surface of the mill lining may be well illustrated by the surface of a bucking board. The outer ball layer may be similarly represented by the lower surface of a muller. If the bucking board, the material to be ground, and the muller all proceed in the same direction at the same speed, no grinding will result. This is the general situation in the mills of today. If, however, the muller is pulled with respect to the board, moving or stationary, grinding will be accomplished effectively. Although grinding in today&apos;s mills is primarily the result of cataracting and/or cascading media, the principal place of grinding at high supercritical speeds will be the attrition zone.&apos; In the mineral dressing laboratory of the State Institute for Technical Research. Helsinki, Finland, large quantities of different ores have been ground in a pilot plant ball mill (3x3 ft) at a top speed about 230 pct of the critical. With the same mill, theoretical investigations concerning the grinding characteristics of ball mills equipped with a smooth lining have been carried out up to the speed of 313 pct&apos; of the critical. With a smaller mill, the grinding characteristics with a variety of grinding media have been investigated at speeds up to 2000 pct of the

Jan 1, 1959