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By L. W. Pommier, F. B. Brien

The Rheological properties of pulps are non-Newtonian in character and more than one viscosity parameter is necessary to describe their behavior, therefore, the single term 'apparent viscosity' which has been used in the past may be misleading. The study reported in this paper uses a dimensional analysis based on the Ostwald-de Waele shear stress-rate of shear model for non-Newtonian liquids to develop velocity and resistance equations for falling spheres. An electronic monitoring apparatus was assembled for determining the velocity of metallic bodies as they fall through opaque liquids and suspensions. By means of this apparatus the behavior of the viscosity parameters of the Ostwald-de Waele model and the applicability of the proposed equations were examined for a number of non-Newtonian liquids. The validity of the equations for these liquids was confirmed. Preliminary data collected using solid-liquid suspensions established the validity of the form of the basic equations for these systems. The differential movement of solid particles through solid-liquid pulps and suspensions is very important LO many branches of engineering, such as minerals processing, soil mechanics, ceramic slip processing, oil well drilling-mud technology, materials-handling in pipelines, and many others. There is a dearth of fundamental knowledge on the flow resistance encountered by immersed bodies moving through solid-liquid suspensions. The resistance offered by Newtonian liquids to the movement of free settling spheres is well described for laminar and turbulent conditions by Stokes' and Newton's Laws, respectively. However, problems are encountered when attempts are made to extrapolate these simple relationships into solid liquid suspensions. The rheological properties of pulps are such that they are non-Newtonian in character;'" that is, the applied shearing stress and resulting rate-of-shear are related by non-linear functions, and thus, in the simplest case two viscosity parameters are necessary to describe their rheological properties. For this reason the single term 'apparent viscosity' which has been commonly used to explain the flow resistance of suspensions and non-Newtonian liquids may be misleading. It is realized that a rigorous analysis of the rnechanisms of momentum transport of liquid-solid systems is complex indeed. There are many variables that affect the rheological properties of the systems such as density, size, shape, and surface energy of the suspended solid and density and viscosity of suspending liquid, as well as the solid to liquid ratio. However, it was felt that a useful contribution to the knowledge of the behavior of suspensions could be made by examining the systems in terms of the basic fundamentals of nowNewtonian flow. This has led to the development, by means of dimensional analysis, of velocity and resistance equations, using two viscosity parameters to describe the velocity of penetrating bodies and the flow resistance encountered by these bodies, as they pass through non-Newtonian systems. THEORY In order to examine the effects of the rheological properties of solid-liquid suspensions on the movement of immersed bodies it is appropriate to start with non-Newtonian liquids and develop equations, analogous to those of Stokes and Newton, for laminar and turbulent flow respectively, from which quantitative information may be obtained. Further investigation would then be directed at the complex suspension systems, and the effects of the many variables on the velocity and resistance equations. Liquids are classified on a basis of viscosity which may be defined as the relationship between applied shear stress and resulting rate of shear?-'* Pure single phase liquids composed of small light molecules behave as Newtonian liquids, having a single viscosity parameter since the shearing stress and rate-of-shear are related by a linear function. Bingham plastics are similar but have a yield stress. Of particular importance in our investigation are dilatant (shear thickening) and pseudoplastic (shear thinning) non-Newtonian liquids, with and without yield values.

Jan 1, 1968

By C. C. Harris, A. Jowett, S. K. Ghosh

An equation derived from first-order kinetics and accounting for return from froth to pulp has correlated continuous flotation data. The concentration of floatable material in the pulp can be altered either by changing the feed concentration or the feed rate. The latter does not affect the flotation rate constant, the froth to pulp return constant, and the concentration of non-floatable material in both the pulp and concentrate. Both the return constant and the concentration of non-floatable material in the pulp are directly proportional to the feed concentration, while the concentration of non-floatable material in the concentrate is related to the feed concentration. The investigation of the froth flotation process by continuous test methods, previously used by Brown and smith,1 Jowett and Safvi2 and Jowett and West,3 is being continued. Recent tests, primarily concerned with flotation cell design, have yielded kinetic data suitable for testing an equation proposed by Arbiter and Harris4 which postulates that a flotation process is defined by two rate constants: 1) the rate constant for mass transfer from pulp to froth. Previous workers have regarded this as the flotation rate constant. 2) the rate constant for mass transfer from froth to pulp, which has previously been ignored. THEORY Under continuous flow conditions at the steady state in Fig. 1 the equation developed4 is Symbols are defined in Table I. The air-liquid ratio terms4 have been omitted, since they are substantially constant for a given set of conditions. Also, for a system operating at the steady state Vf and V, remain constant and Eq. 1 can be written: Cp/Cc=b'/a,+Qc/a' [2]

Jan 1, 1963

By R. S. Olson

An analysis of the wash thickener-two stage filtration circuit was undertaken to quantitatively describe the circuit performance. On the basis of information developed in this study, the factors of major importance in reducing soluble loss are: filter wash, wash zone size, filter capacity, filter feed pulp dilution, blow back, filter cloth, water to repulp, water to primary wash, water to feed pulp and thickener underflow. The wash thickener-two stage filtration circuit has been used in many hydrometallurgical plants to separate solute from leach solids. As many as 20 to 30 plant operating variables determine the performance of the wash circuit and hence the soluble loss. The complex relationships of these variables, with each other and with soluble loss, make the evaluation of their effect on mill performance difficult. An analysis of this type of circuit was undertaken to quantitatively describe the circuit performance. THE CIRCUIT The diagram in Fig. 1 represents the operation of the wash thickener-two stage filter circuit. This circuit provides for counter current, cross current or for a combination of countercurrent-cross current operation. The feed pulp stream, J, is intended to include any solution or water, other than primary and secondary filtrate, which enters the wash thickener. Except for filter washing, the operations in the circuit are simple mixing operations which can be described by material balance. The concentration of solute in the filtrate and cake solution after application of wash liquor cannot be described by simple material balance. The displacement washing equation, derived by Rhodes1 and extended by Choundhury and Dahlstrom,2 appears to best describe this case of miscible displacement in porous media. In a useful form, it is

Jan 1, 1963

By H. H. Dreissen, F. J. Fontein

The operating principle of the classifying cyclone has been described often but some special aspects of the cyclone receive further clarification here. In addition, several uses of the classifiers are summarized and made clear by means of practical examples. In coal and ore washeries, the washing cyclone is widely used for the separation by specific gravity of sizes up to about 12 mm. This application has lately been extended to the separation by specific gravity of particles up to about 50 mm. This use makes special demands on the construction and wear resistance of the cyclone. The sieve bend, a development of the Dutch State Mines which is less well known than the hydrocy-clone, is dealt with at some length. The sieve bend is an apparatus designed for wet screening. Attention is given to the variables influencing the performance of the sieve bend. Hydrocyclones are now so widely applied that it would be difficult to find an industry not, directly or indirectly, using them or knowing how to use them since publications on this subject abound.1-3,5,9-11,13-15 However, because of the large number of variables influencing the operation of classifying cyclones, it is not entirely possible to calculate the results of this type of cyclone. Therefore, a number of lesser known variables will be discussed here along with some special applications of the classifying cyclone. FACTORS INFLUENCING CYCLONE CLASSIFICATION Shape of Particles: The shape of particles may cause a much coarser classification than the one expected, considering the sieve analysis and the cyclone dimensions chosen. This was clearly shown by feeding a mixture of spheres and disks in water into a cyclone. The spheres were 0.36 mm diam and the disks, 3 mm diam and 0.03 mm thick. These dimensions were chosen in order that the disks and spheres might have the same rates of fall under gravity. Both spheres and disks had a specific gravity of 1.05. The results obtained with these particles in a cyclone are summarized in Table I. Test No. 2 shows that the catch of spheres was

Jan 1, 1963

By S. W. Nabbs, W. D. Bachman, A. W. Last

A study has been made of wet, autogenous grinding of disseminated copper ores, including testing of a large number of samples from. Kennecott Copper Corp.'s Chino mine. The grindability of the various samples was found to vary over an extremely wide range, even among samples taken from diflerent locations within the same ore body. These variations in grindability can be qualitatively correlated with the composition of the rock and the fracturing and alteration that had occurred. Because of the large-scale nonhomogeneity of disseminated copper ore bodies, extensive and careful testing of autogenous grinding is needed. An accurate correlation of the grinding data from various samples with the geology of the ore body and with mining plans will indicate if variations in grinding mill throughput can be avoided in practice by mixing or blending of mill feed and if, therefore, autogenous grinding can be applied successfully. In the past 15 years, comminution by primary autogenous grinding has been investigated and applied economically in the minerals industry, particularly in iron-ore processing. Successful application of primary grinding is described by A. A. Dor,l.' P. B. Dettmer,334 R. R. Turner, and W. F. McDermott." other authors describing the advantages of primary grinding include H. Hardinge,' R. T. Hukki,' D. S. Coyle" and F. C. Bond,"," to mention only a few. For the past several years, Kennecott Copper Corp.'s Metal Mining Div. Research Center has been investigating primary grinding of disseminated copper ores. Both fully autogenous and semi-autogenous grinding has been explored. Ores from three of Kennecott's western operating properties and from several development properties have been tested. Host rocks include diabase, schist, silicated and argillaceous limestones, shale, granite porphyry, quartzite, and granodiorite. The object of this paper is to supplement the general knowledge in the field of primary grinding by presenting information gained from the studies with the various disseminated copper ores. Data are presented which show that carefully considered test programs are required to determine the practicality of applying autogenous grinding to a specific mining-beneficiation operation. Particularly this is so if more than one rock type occurs within an ore body or if there are wide variations in the degree of rock alteration within a deposit. Extensive sampling and subsequent testing of the ores within a mine are required if serious pitfalls are to be avoided and good engineering data acquired. We hope that this presentation will stimulate studies to increase the understanding of the fracturing process applicable to large pieces of rock, a factor which is important in autogenous grinding. Test Facilities and Procedures Both pilot-scale and full-scale test facilities were used to investigate primary grinding characteristics of the disseminated copper ores. A 6-ft Hardinge Cascade mill, a 24-ft Hardinge Cascade mill, and a 5-ft Aerofall mill were used in the studies. The Cascade mills were operated wet, while the Aerofall mill was operated both wet and dry. The Cascade mills were operated both for fully autogenous and for semi-autogenous grinding; the Aerofall mill was operated only semi-autogenously. Fully autogenous grinding, as the term is used in this presentation, is defined as the direct grinding of coarsely crushed rock by the action of the rock mass. Semi-autogenous grinding is defined as the grinding of coarsely crushed rock with the rock mass supplemented by a steel ball charge. Most of the test work was done using the 6-ft Cascade mill, operated under fully autogenous grinding conditions. Only limited testing was conducted with the 5-ft Aerofall mill and only one ore was tested using the 24-ft Cascade mill. This presentation is concerned, therefore, primarily with fully autogenous, pilot-scale grinding in the Cascade mill. Fig. 1 presents a diagram of the test facilities used with the 6-ft Cascade mill. Principal test equipment consists of a 6-ft Cascade mill, an 18-in. spiral classifier, an elevator, a 2 x 9-ft belt feeder, a conventional integrating kilowatt-hour meter, and a recording wattmeter. In testing, feed charges, adjusted as to weight, were deposited as evenly as possible on the belt feeder every 15 min. The weight of each charge was adjusted to maintain a mill charge of 27 to 30% of mill volume. The classifier was adjusted to obtain the desired size-consist of the final product, generally at 20% + 100 mesh. After equilibrium was established in the circuit, the feed, mill discharge, classifier sand, and classifier overflow were sampled and their size distributions determined. During the sampling periods, the power drawn by the mill was measured to determine the energy consumed in the reduction of the size consist of the ore solids. Fully Autogenous Pilot Grinding Tests on Various Kennecott Ores Typical test results obtained in the 6-ft Cascade mill with samples from Kennecott's Ray Mines Div., Chino Mines Div., Utah Copper Div., and a development property designated as Mine A are presented in Table 1. As shown, the ores that were ground most easily in the pilot-scale mill were composite mine samples obtained

Jan 1, 1971

By J. W. Axelson, J. N. S. Kwong, J. T. Adams, E. L. Pire, J. F. Johnson

CRUSHING has always been a major operation in the chemical and metallurgical industries, yet little is known about the theory of crushing, and today, the design of crushers is still based almost entirely on empirical knowledge and accumulated practical experience. In view of the increasing national need for the economic working of poorer grades of ores, the lack of a fundamental understanding of this unit operation hardly presents a satisfactory situation. Basic investigations of crushing have been concerned mainly with three phases of the problem, 1—the mechanism of the fracture process itself, 2— the particle size distribution of the crushed product, and 3—the relationship between the energy input and the amount of new surface produced. Probably adequate information on these phases will be required for a comprehensive understanding of the process of crushing. A bibliography covering these phases will be given as well as a review of the work done in recent years at the University of Minnesota on the relationship between the energy input for crushing and the amount of new surface produced. Fracture of Solids This phase of the crushing problem is the most fundamental because it is concerned with the actual mechanism of fracture. The main problems in a study of the fracture process are concerned with the questions of why and how fracture occurs and why there is such a discrepancy between the actual and theoretical energies needed in a fracture process. In considering the how of fracture, Poncelet40 carried Out experiments On the crushing of glass under compression. Actual photographs were taken of the glass plates in various stages of fracture-From these experiments Poncelet was able to postulate a probable mechanism of fracture. Probably because of the quantitative nature of the problem, considerable effort has been expended to find an explanation for the low tensile strength of materials and the conversely high energy for crushing. Tensile strengths are often only 1/500 of the theoretical while the energy for crushing is usually at least 500 times the theoretical. A review of the work to explain the low strength of glass is given by Weyl,52 in which the work of Griffith," Joffe,32 and Powell and Preston " are discussed. In a recent paper Seitz46 holds that the presence of flaws and fissures, as originally expounded by Griffith, is the most probable reason for the low strength of metals. Since a mass of data has been accumulated on the fracture strength of materials, several investigators have attempted to correlate this data in the form of an equation. Glathart and Preston," Taylor,40 Ponce-let,40 Machlin and Norwich," and Frederickson and Eyring,20 have all considered this problem, and the final relationship has always been that the stress for fracture is proportional to the logarithm of time. Murgatroyd30 arrived at a very similar relationship by a different method. The study of the fracture process has used many methods. Among some of these are the thermody-namic approach used by Furth21 which was based on the work of BornxL and later used by Saibel,43 and the statistical method applied by Fisher and Hollo-mon.10 In recent years metallurgists have concerned themselves with the problem of brittle .fracture as opposed to the usual plastic failure of metals. The great amount of interest shown is reflected by the number of contributors to the recent symposium on the fracture of metals.' Repeated failures of welded ships during World War II have accelerated these Studies.31,50,34 The shifting of thought from an emphasis on the

Jan 1, 1952

By C. C. Harris

An analytical solution of the integro-differential equation of batch grinding is proposed as a first appoximation to the xYt surface. The size distribution equation (xY plane) is a three parameter equation previously suggested. Possible refinements are outlined. Comminution kinetics research is presently following several related courses. Some are equivalent, in that they represent different ways of viewing the same facet of the problem, though the entire endeavor cannot be described as being completely integrated. The purpose of this note is to propose and discuss a framework into which the various approaches might be fitted. This must clearly be founded upon an analysis of the xYt surface.' (See also Fig. 1 of Reference 26.) The investigations referred to above comprise mainly researches into the following: (1) The kinetics of the creation of the finer sizes during relatively small grinding times. This is the Fahrenwald-Arbiter-Bhrany 2-3 approach which leads to equations equivalent to a special case of the charles4 relationship. It emerges that initial production of fines follow essentially zero order* kinetics. (2) Disappearance kinetics of the coarser fractions. This appears to be a first order relationship.5-6 (3) Prediction of the xYt surface via the selection and breakage functions utilizing computer-programmed or approximate solutions of the integro-differential equation of batch grinding.5,8-17 A recent discussion by Mika et al.5 references the relevant literature up to about 1966. In addition to these main-stream researches there is some work on the minor topic of extremely long grinding time considered as a limiting case.18-19 The field is supported by investigations into the size distribution of fragments produced by breakage processes, some of this work being most valuably statistical-mechanical in nature.20-25 Better fitting equations, however, are obtained by statistical and curve-fitting methods.26 This

Jan 1, 1969

By A. W. Asman

The problem of balanced design in a belt conveyor has been under constant study. Increased use of this method of transport in recent years has stimulated investigations. Conveyor belt, power transmission and other machinery should be adequate to perform the required service. All components of the belt conveyor should work as an efficient unit moving its load continuously between terminals. As part of a long term research project on belt conveyors, Hewitt-Robins established in 1954 a 2-year grant at Pennsylvania State University. Under terms of the grant, certain fundamental phenomena were to be studied. This work evolved a new concept in belt conveyor power determination based on the principle of belt tension. The Penn State contract furnished the foundation for later more detailed studies. From these most recent investigations, more specific factors were defined. In the final analysis, all of the data collected has been worthwhile in belt conveyor design. Units now operate over long distances at speeds of over 800 fpm. Long high lifts are commonplace. Where vertical or inclined shafts were the rule, belt conveyors receive first consideration. Although belt conveyors have moved forward rapidly, the future will see a tremendous gain in their use. The ideal test belt conveyor would be several thousand feet in length and have a maximum tension of at least 70,000 lb., Also, this conveyor should be horizontai and have a variable feed rate of more than one material. Data from such a field belt conveyor combined with laboratory information would permit accurate analysis. Since this type of conveyor was not available, many field locations were visited: An alternate would have been to erect a closed circuit system in the laboratory. Either method had limitations and the first was selected as having the best possibilities. Manufacturers of conveyor belting and machinery basically have been using the same horsepower formula. As more information became available from field installations, factors in the basic formula were modified. Practically all conveyors are designed today by adding together the horsepowers required to move the empty belt, move the load horizontally, and elevate the load. In selecting size of drive motor, the first two elements are relatively unimportant if the last is large. However, it is the combination of

Jan 1, 1961

By C. D. Thompson, D. C. Violetta, C. A. Czako

The mechanics of the continuous sintering process are briefly reviewed and the application of this process for the beneficiation of principal minerals used in making cement is shown. Pilot plant tests using pyrobeneficiation techniques were conducted with mixtures of limestone and shale in various ratios. Results are illustrated and show the percentage removal of carbon, carbonates, sulfur, alkalies, and volatiles as a function of the limestone-shale ratio. Tests with varying quantities of solid fwls, added to mixtures containing limestone and shale in a 4 to 1 ratio, were made to attain optimum elimination of the volatile constituents. Experimental results show that 90 pct of these constituents were removed during the calcination sintem'ng process. The advantages of using the beneficiated material for making cement are discussed with regard to prepam'ng, handling, and clinkering operations. A sintering process for treating raw materials or kiln waste products which contain high amounts of alkaline materials is described. Tests were performed with a high alkaline waste dust mixed in a 1 to 1 ratio with raw cement meal. The data from these tests and others using different halides for aiding alkali removal are evaluated by the alkali content of the cement clinker. Test results showed that the Dwight-Lloyd process could be applied with facility in beneficiating raw materials for cement making. Substantial quantities of deleterious volutile constituents were removed by calcining and sintering techniques. The continuous sintering process has been applied for a number of years as a means of beneficiating minerals for subsequent conversion to merchantable products. The process was developed and first used for nonferrous metallurgical applicatfons. However, it has risen to prominence for ferrous metallurgical applications where last year in the U.S. and Canada nearly 40 million tons of iron ore were treated by grate firing processes. Through the years of process development many investigators have realized the versatility of the sintering process and have directed experiments toward the use of it for applications with nonmetallic minerals. These have included calcining limestone, carbonizing coal, expanding shale, and burning cement raw meal. Today commercial sintering plants produce cement clinker from mixtures of limestone and shale, lightweight aggregate from shale or clay, and calcined products from phosphate shale. The mechanics of the downdraft sintering process have been presented by many authors. In general practice the materials to be agglomated are mixed as moistened fines with a solid fuel and this mixture is spread uniformly on the grates of the sintering machine. The charge is then momentarily directed under an ignition furnace. After ignition a continuous downdraft of air promotes combustion of the fuel and through heat transfer particles become partially fused into a coherent mass. This is cooled from continued draft induced after combustion. Many investigators have shown that distinct zones are formed during the process of sintering iron ores. At the midway point of the sintering process these are prominent and are, respectively, from the top of the bed to the bottom, comprised of a cooling zone of sintered material, a combustion zone of sinter formation, a calcination zone, a drying zone, and a zone of unreacted materials. Completion of sintering occurs near the discharge end of the machine where the firing zone approaches either the grates or grate dressing material called hearth layer. Here the peak draft temperature usually can be noted in the windboxes. The zonal pattern has been illustrated with the use of graphs which show thermal gradients as they progress through the bed of materials during sintering. Fig. 1 shows, in simplified form, thermal gradients existing when clinkering cement on a sintering machine. The thermal gradients illustrated are for periods of initiation, midway and completion of the clinkering process. The occurrence of these zones has importance for the beneficiation of cement raw materials. A research program was performed at the Dwight-

Jan 1, 1961

By R. J. Brison, W. C. Bleimeister

The International Salt Company has long been interested in finding an efficient process for the removal of impurities from rock salt, and particularly from the rock salt produced at the Detroit mine. Methods which have been used previously at the Detroit mine included both hand sorting and differential crushing in a Bradford breaker with rejection of the oversize. Neither of these methods was adequately effective. The development of a new process for removal of impurities from rock salt has been described in the preceding article." Basically, the process consists of exposure of crude rock salt to radiant heating which selectively heats the impure particles. Subsequently the heated particles are removed by adhesion to a heat sensitive-coating on a conveyor belt. This method was found to be effective in improving both the quality and appearance of rock salt by the rejection of the dark, impure particles. The first commercial unit employing the new thermoadhesive method of dry separation of minerals was installed at the Detroit mine of International Salt Company in Detroit, Mich. (Fig. l). This unit was first put into operation in March 1957. The purpose of the Detroit installation was 1) to serve as a pilot plant for evaluating the process on a commercial scale and 2) to produce marketable quantities of rock salt of improved quality and ap- pearance. The design of this plant was based on the results and information obtained from a 1-tph pilot plant at Battelle Memorial Institute. DESCRIPTION OF PLANT Location: The separation plant was installed underground near the crushing and screening plant, for this was the most suitable location from the standpoint of material handling. Furthermore, ample space was availabe at this location. Because the process requires a relatively constant temperature, the uniform year-around temperature of the mine (57°F) gave an added advantage to an underground operation. Feeding: The rock salt is conveyed to a surge bin, from which it is fed to the heating unit by a conveyor. The feed-rate control consists simply of an adjustable gate at the bottom of the surge bin. The plant may be fed either No. 1 grade of rock salt (0.279 to 0.375 in.) or No. 2 grade (0.375 to 0.500 in.) with a maximum input capacity of 500 tons per 15-hour day. Heating Unit: The heating unit (Fig. 2) consists of a panel of infrared lamps suspended inside a low-speed revolving screen. The radiant-heat panel, which is curved for most effective utilization of the heat, holds 240 infrared lamps of standard industrial type, each rated at 500 watts. The position of the panel is adjustable so that it can be placed centrally over and to within 6 in. of the salt bed on the screen. The entire heat panel is suspended by rollers in ¦ R. J. Brison and O. F. Tangel: Development of a Thermo-adhesive Method for Dry Separation of Minerals.

Jan 1, 1961

By N. J. Sather

A detailed description is given of Bunker Hill's concentration process employed at the company's lead-zinc property in the Coeur d'Alene district, Idaho. The plant is equipped to process 3000 tpd of Pb-Zn ore. The history of the Bunker Hill mine dates back to Aug. 26, 1885, when Noah S. Kellogg found the outcrop of the Bunker Hill orebody on the hillside of Milo Gulch above the present town of Wardner, Idaho. A small concentrator was erected in 1886, and before the railroad came, the mine output was transported by mule teams to the head of navigation on Coeur d'Alene Lake. After ten years of production, an interest was purchased in the Tacoma smelter at Tacoma, Wash., to which the entire output was shipped. In 1916 and 1917, a modern lead smelting plant and refinery was erected, and a modern electrolytic zinc reduction plant was built in 1927-1928 by the Sullivan Mining Co. which was 50 pct owned (and now totally owned) by the Bunker Hill Co. The first concentrator, a 100-tpd capacity plant, was built in 1886 near the Reed Tunnel in Wardner. The treatment consisted simply of crushing ore to 2 in. and then to 1/2 in. through rolls in closed circuit with a bucket elevator and trommel screen. The undersize was further sized in trommels to 10 mm and 3 mm. Oversize from the latter was treated in Hartz jigs. The 3 mm undersize was classified in crude hydraulic classifiers furnishing sands to sand jigs, the overflow being dewatered in a long V tank which supplied sands to a Cornish buddle and to Frue vanners. The concentrates were of excellent grade, old records showing assays of 69 pct lead and 29 oz. of silver per ton. Tailings were high inasmuch as the provision for treating the slimes was inadequate. Since the erection of the first mill, the Bunker Hill plant has gone through many changes and improvements. In succeeding years, the flowsheet was enlarged somewhat with Huntington and Chilean mills, vanners, tables, ball mills, and flotation cells being progressively added. In the transition period to the present day practice, the object was not only to improve the equipment for better mechanical performance, but to add new equipment whenever practicable so as to improve both grade and recovery of the product at a lower cost. For the modern plant and flow-sheet, see Figs. 1 and 2. The history of flotation at Bunker Hill dates back to 1913 when experimental work was done in a cell in which the pulp was circulated through a centrifugal pump set outside the cell and discharged against a baffle in the cell. The cell was built with a spitzkasten, and the quiet zone in the latter tended to let the froth break down before it got to the overflow weir. To remedy this situation, a belt drag with light metal flights was arranged for drawing off the froth over a ramp in each cell. Recovery of lead was not as high as present day practice, but was so much better than the vanners that the cells were multiplied gradually to eight cell units. The mill men called them mud hens. Flow between the cells was controlled by a weir, which determined the pulp level in each cell. These early machines were called Bunker Hill machines. The tailings were later treated in pneumatic scavenger flotation machines in a series, producing concentrates for retreatment in the Bunker Hill cleaners as well as the final tailings. This system of flotation served with minor changes until the Fahrenwald machine was developed at Bunker Hill during the period from 1921 to 1925. In 1925, the Fahrenwald flotation machine gradually replaced the Bunker Hill machine, although the Hearing pneumatic scavengers for retreatment of the tailings from the Fahrenwald machines were retained in the lead section until 1928. The use of the Hearing pneumatic machine for cleaning the rougher concentrates was begun in 1924. In 1941, plans were made for remodeling and modernizing the concentrator, the goal being a modern concentrator employing the latest equipment and milling practices. The old wooden building was to be replaced by a steel and concrete structure. Shortly after preliminary work got under way, the United States entered World War II and the demands for metals increased. To meet this requirement, the management decided to increase the capacity of the concentrator to 1800 tpd. This was accomplished in record time by the construction and operation of a sink-float plant. Installation of this plant was the first step in the general plan for modernization. In 1947 the concentrator (including the sink-float plant) was enlarged to handle 3000 tpd. Milling operations today are at the rate of 2300 tpd, five days per week. During 1959, 453,000 tons of ore was beneficiated. The Bunker Hill concentrator is in three sections: the crushing plant, a 3000-ton capacity storage bin, and the concentrator building. The crushing plant is of wood design with a gunnite coating on the exterior.

Jan 1, 1961

By A. F. Colombo, R. T. Sorensen, D. W. Frommer

An analytical method has been developed and used in batch and continuous tests to provide initial insights into the effect of soluble calcium ion in anionic flotation of silica from iron ores. A deficiency or excess of calcium ion in pulps subjected to this type of flotation produces an impairment in flotation efficiency. Data developed in the investigation are from a single ore, but show that total calcium requirement is met from water, ore and reagent sources. In batch studies, starch additions were shown to exert no influence on the calcium level, but fatty acid and sodium hydroxide had subtractive effects. The investigation was next extended to continuous flotation testing where the general observations from batch testing were confirmed. Factorially designed experiments were performed showing that the relationship of calcium additions to flotation response was not a simple one, but tended to shift to higher additions with increased fatty acid. Nevertheless, the range of soluble calcium levels measured remained fairly constant in areas of good flotation response. It is concluded that techniques developed should be useful in removing empiricism from flotation operations in this and other systems requiring activation for success. Further development should aid in process control both through methods outlined and through investigations aimed at studying the effects of other soluble reagents. Of the major mineral commodities, iron ore was one of the last to succumb to flotation processing. Commenting on this fact, one of the speakers 1 at the convention celebrating the 50th Anniversary of flotation in the U.S.A., said ". . . in 1951 froth flotation as a means of beneficiating nonferrous minerals was a might giant and could be characterized by 'you name it, we float' - but not iron ore". This tardiness in applying flotation to iron ores was the result of a number of factors, including economics and ready availability of direct shipping ores. Even now, when the need for beneficiation can no longer be denied, proposals for flotation of iron ores are apt to be viewed with some misgivings. This disquiet results from knowledge that wide variability, which would necessitate corresponding adjustments in reagents, often exist within even a single ore deposit. Coupled with ore variability is the fact that, at present, there is no way of quickly and precisely anticipating the direction and magnitude of reagent changes required for uninterrupted production of acceptable concentrates. Despite the long delay, iron ore flotation is now practiced commercially, although the chief applications2-4 are to specular hematites having relatively coarse liberation and low slime content. In addition, the application of flotation in upgrading magnetic concentrates seems assured. However, these flotation methods do not appear applicable to substantial tonnages of fine grained, earthy, and frequently more complex semitaconites and nonmagnetic taconites. The U.S. Bureau of Mines, in devoting its attention to the semitaconite and nonmagnetic taconite class of materials, has demonstrated that anionic flotation of calcium-activated silica can be utilized with an expected high frequency of success.' Even so, it has been recognized that the flotation method is a complex one, and that the reagent suite must be carefully tailored to the feed. These conditions would be expected to offer difficulties in treating ores with the wide range of variability previously discussed. Accordingly, research was initiated to develop methods to remove much of the empiricism from the flotation operation by measuring the reagent variables within the pulp for a correlation with flotation response. A simple illustration of the technique sought would be in the well established use of pH meters to provide feedback control to reagent feeders and thereby limit acidity or alkalinity to a range producing optimum results. The first efforts in this area have been concerned with measurements of soluble calcium ion. Bureau experience in both laboratory and pilot plant over the past five years has proved that the amount of calcium

Jan 1, 1965

By D. L. Harris

Chemical upgrading testwork on Stillwater chomite concentrate shows that reduction roasting and leaching (sulfuric acid and/or ferric sulfate) can provide upgraded feed to ferrochromium furnaces for making upgraded ferrochromium. Two-stage reduction smelting in electric arc furnaces can make upgraded ferrochromium also. Sulfating roasts and leaching (acid and/or water) results using gaseous SO2—SO3 or solid ammonium sulfate were not satisfactory for upgrading chromite. Chemical upgrading of domestic Stillwater (Montana) chromite has been considered at various times1'2' to provide a material with higher chromium to iron ratio, more like foreign high grade ore, for the production of standard grade ferrochromium. Physical bene-ficiation of Stillwater chromite ore can provide a ratio, Cr/Fe, no higher than the ratio in the chromite mineral, which is approximately 1.7. For comparison the analyses of a foreign metallurgical grade chromite ore, a high grade electrostatic process Stillwater concentrate and a stockpile concentrate from the Stillwater ore are noted in Table I. Single stage smelting of the high grade foreign ore with a ratio, Cr/Fe, of 3.37 can provide a ferrochromium of over 65 pct chromium content. Similar smelting of the Stillwater concentrate with a ratio of 1.7 can provide a ferrochromium of 50 to 55 pct chromium content.' It has been demonstrated on a pilot plant scale that chemically upgraded Stillwater chromite having a ratio, Cr/Fe, of 3.0 also can be smelted to provide a ferrochromium containing over 65 pct chromium.5 Two major considerations for an upgrading process are the ratio, Cr/Fe, in the product and the chromium recovery. A minimum ratio, Cr/Fe, of 3.0 is required in the product but for economic reasons a higher ratio is desirable for blending purposes as long as the recovery is satisfactory. Data from different kinds of chemical upgrading testwork are presented in this report. Some of the testwork was conducted to make a product which was not intended to be feed for ferrochrome smelting, but the data are considered pertinent to chemical upgrading. Results reported by others are noted also for comparison. WORK REPORTED BY OTHERS The U. S. Bureau of Mines has contributed much to the literature on chemical upgrading of chromite and a summary is given in Table 11. Reduction roasting and acid leaching were reported by Boericke and Bangert,1 by Lloyd and Gorst, et a1,2 and by Boericke3 to demonstrate very good success on a laboratory scale and only fair success in pilot plant tests for Stillwater (Benbow) concentrates. This work included basic studies on thermodynamic properties to explain the reduction and leaching results. Canadian workers, Downes and Morgan,9 have reported experimental success in upgrading a low grade Bird River chromite, similar to Stillwater material by the same process. Russian workers1' have noted results on reduction tests of high grade chromite which may apply to low grade ores and which help in understanding the reduction process. The use of flux additives in the reduction process was an innovation of their work. The Canadian workers9 also reported other kinds of experiments, including autoclave leaching of the chromite in a limited amount of sulfuric acid. An insoluble basic chromium sulfate was formed and separated from soluble iron, magnesium, and aluminum sulfates to provide an upgraded material. U.S. Bureau of Mines workers, Lloyd, Rosenbzum, Home and Davis,' reported on autoclave leaching of Benbow concentrates as a means of obtaining chromium alum for electrolysis. This last work required selective crystallization of alum to separate iron from chromium. Chloridizing roasting of Benbow and Mouat concentrates has been reported by Hunter and Banning6 and others8 to show that the iron chloride could be volatilized from the chromite to provide upgraded residues.

Jan 1, 1964

By J. M. Steininger

The mechanism of flotation of sphalerite with sulthydryl compounds of different acidities has been interpreted in terms of chemisorption of unionized collector molecules on hydroxylated zinc surface sites. At a constant collector concentration of 1.5 x 10 -4 M, the upper pH limit of flotation has been found to be directly and closely related to the negative logarithm of the collector acidity constant, pKa The experimental results indicate that flotation is prevented when about 95% of the collector is ionized. At low pH, collector adsorption decreases because of the reduction in number of hydroxylated zinc surface sites. These two effects explain why sphalerite does not float with the more acidic sulfhydryl compounds. Typical anionic collectors for sulfide minerals are short chain xanthates or dithiophosphates which are nearly completely ionized in the generally alka- line flotation circuits.1,2 Flotation mechanisms have therefore been usually interpreted in terms of ionic collector adsorption and competition with ionic depressants of the same sign as the collector. A few attempts have been made, however, to consider adsorption of neutral collector molecules. Contact angle measurements obtained by Wark and cox3 have been interpreted by Cook and Nixon4 as representing adsorption of the free acid molecules on sulfide minerals such as pyrite, galena, chalcopyrite, and sphalerite. Cook and Nixon tried to show that the free acid concentration of the collector was substantially constant along the curves relating collector addition and minimum pH for bubble adherence. However, in a review of the subject,5 Sutherland presented new data on the flotation of pyrite with mercaptobenzothiazole which did not support the hypothesis of constant concentration of either collector ions or collector free molecules. He further showed that, with the assumption of constant occupation of surface sites, both theories lead to relations between pH and collector addition having similar mathematical expressions. In fact, with the more likely assumption of variable occupation of surface sites which results in more complex relationships, it appears impossible to

Jan 1, 1968

By F. X. Tartaron

The comparison of actual energy of comminution with theoretical surface energy presents a wide gap. On the other hand, Solid State Theory presents a viewpoint that places actual energy of breakage in understandable relationship with the theoretical strength of materials. Therefore the physical background of comminution theory favors Kick's Law. A11 discussions of comminution theory appear farfetched when comparison is made of the actual energy of crushing with the energy input called for by thermodynamic theory. Quoting Taggart:' "The work required to crush halite was of the general order of 0.10 kg cm per sq cm of new surface produced (based on air percolation) whereas the theoretical energy of this new surface, based on thermodynamic calculation by a number of investigators is 1 x 10'4 kg cm per sq cm or the work expended was 1000 times the new surface energy — an indicated crushing efficiency of 0.10 pct." It is frustrating to probe into comminution theory with the prospect that the energy one is measuring is 99.9 pct waste energy. Do the laws of comminution deal with energy consumed by mineral breakage or with waste heat energy? There seems to be something wrong. Solid State Theory may provide the answer. The following statement is particularly apt to the situation: "The fundamental fact about metals and indeed all materials, is that they are much weaker than they should be. By this, we mean that if the stress required to cause a given plane of atoms to slip past a neighboring plane is calculated from basic atomic and Solid State Theory, the resulting number is some 1000 times too large to be accounted for by errors in approximations or assumptions. We know now that this is due to dislocations, and we even have a fair understanding of the details of the process by which dislocations make a crystal weak. An intriguing possibility which suggests itself, results from the discovery of very minute metallic crystals which are apparently free of dislocations and which have a strength approaching the ideal value for a perfect crystal." Here we have an extraordinary reversal of the situation. The actual energy for breakage is only one-thousandth the theoretical instead of 1000 times as given by Taggart. But the theoretical energy presented by Solid State Theory is the binding energy between atoms (or ions) in a crystal lattice. This is the kind of energy envisaged by Kick's law. The surface energy or the other hand corresponds to Rittinger's law. Comparison of theoretical with actual, on the basis of surface or on the basis of Rittinger's law, seems to present an absurdity; yet Rittinger's law is confirmed by an impressive array of experimental evidence. Comparison of theoretical and actual on the basis of Solid State Theory or, in other words, on the basis of Kick's law seems reasonable; yet there is not a scrap of evidence to verify Kick's law. The situation appears paradoxical, but the developments in the next section of this paper show that the paradox is a hint to a strange turn of events. ENERGY-WEIGHT FRACTION FUNCTION charles3 has presented a final equation showing the relation of energy consumed in comminution to size of product n{-1) a-n + 1 E is energy, C is proportionality constant, a and n are constants and k is the coarsest size in the ground product (size modulus). In the course of study of a large amount of experimental evidence, Charles discovered that in the general case, a-n + 1 approximated zero. For some reason, a and n differed only by unity. But if a—n + 1 = 0 within experimental error, then it is obvious that Eq. 1 states that it requires an infinite amount of energy to grind any sample to any size. This is a case where nature gives an absurd answer to a man-made mathematical equation, hence something is wrong with the equation. An adjustment must be made to fit the equation with experience. TO reveal the nature of the adjustment, the differential equation preceding the second integration in Charles' group of equations is given When Charles integrated the quantity xa-n it was almost impossible for him to realize that he was dealing with a special case of integration and that

Jan 1, 1962

By M. V. Lowry

This paper outlines the economic considerations that led to the recent installation of a thickener at St. Joseph LeadCo.'s Balmat, N.Y. mill. To incorporate storage of concentrates, they decided upon a single, unusually deep tank to be used for both storage and thickening. The abnormally high rake lift required was achieved by the novel feature of having the entire drive platform raise and lower. Initial operating problems are described along with the satisfactory solutions. Total costs for concentrate handling before and after installation of the storage thickeners are compared. In Northern New York State, the St. Joseph Lead Co. conducts a 2100 tpd zinc mining and milling operation at its Balmat Plant. Conventional crushing, grinding, and flotation is used to produce a zinc concentrate. For 32 years, from 1930 through 1962, the plant operated with the concentrates going directly from flotation to the filtering, drying, and loading facilities. All of the concentrate handling equipment, therefore, had to operate 24 hrs per day. It also had to accommodate wide fluctuations in tonnage, due to variations in the grade of ore. Many problems were thereby encountered in filtering and drying, but it was never concluded that the cost could be justified for installing a conventional, large diameter thickener. Finally, in 1963, they installed an unconventional thickener that is unusual in several respects. The tank depth is 16 ft instead of the normal 8 ft. The rakes are raised and lowered by having the main drive gear located on a movable platform. Automatic controls are programmed to raise the drive platform and rakes during one shift of storage. During the next two shifts of withdrawal, the controls are programmed to lower the drive platform and rakes. After three years of operating this unique storage-thickener, the conclusion is that a correct choice was made from several alternative schemes for storing concentrates. The various considerations involved in the final selection will here be analyzed, and the design features and installation details will be de- scribed. Operating problems and modifications made to the equipment will next be considered, and finally the effects upon filtering, drying, and loading will be reported. SELECTION CONSIDERATIONS Even without a thickener, concentrate handling had become reasonably efficient at the Balmat Mill by the year 1962. A tonnage that varied between 6 and 25 tph was being handled fairly satisfactorily. The filter cake moisture of 8%% seemed quite respectable, except that two large filters were usually in service. Three filters often had to be operated in order to prevent excessive filter overflow with consequent loss of values. This situation occurred when zinc concentrates from flotation exceeded 20 tph and when filter cloth blinding developed. Over the years, numerous small improvements had been effected, such as: selection of a filter cloth with better flow characteristics; addition of flocculant to the filter feed; and, in 1953, the smallest of three drum filters was replaced by a five disc, 8' 10" diam filter with a bottom agitator and snap blow. As another example of fairly efficient operation, the oil-fired dryer was doing a seemingly satisfactory job of further reducing the moisture content to an average of 3%. However, there were often considerable dust losses when the tonnage suddenly dropped off to 6 tph. At high tonnage rates, the resulting high moistures of 4% and 5% caused difficulties due to concentrates sticking and freezing in chutes leading to the box car loaders. (Drying of concentrates is justified because of the high freight rate for the long shipping distance to the company owned smelter at Josephtown, Pa. near Pittsburgh.) It was long realized that installation of a thickener would permit the subsequent steps of concentrate handling to proceed more smoothly and would alleviate the problems existing in the filtering, drying, and loading operations. It was also realized that even a slightly lower filter cake moisture could mean considerable savings in fuel oil. However, all these factors were never quite sufficient to warrant the expense of a thickener until three more considerations were added to the picture. First, the advent of flocculants meant that a thickener of relatively small area could now be considered. Secondly, a complete renovation of the zinc flotation circuit was made between 1957 and 1961. The

Jan 1, 1967

By J. Mizrahi, A. M. Baniel, A. Mitzmager, S. Star

This article gives an account of the latest developments in the use of TBE for sink-float separation of silicate minerals. A number of minerals for which the process has been tested and found suitable are reviewed. Specific examples are discussed in relation to the particular problems of sink-float separation and recovery of TBE as compared with non-silicate minerals. The economic aspects are outlined. Silica and silicates comprise the most common and abundant group of minerals, and since they are present in variable amounts in most ores, they constitute an appropriate subject for the review and discussion of the recent developments in the use of TBE for mineral concentration. The silicates considered as a group have an extremely wide range of chemical and physical properties. Some of these properties, which are common to all minerals, are of importance to concentration by TBE and are discussed in some detail in this paper, as well as the development of methods and apparatus for concentration and recovery of TBE and several examples of concentration of silicates. PROPERTIES OF MINERALS WITH RESPECT TO CONCENTRATION BY TBE The properties considered as most important to concentration by TBE are specific gravity, structure, surface and shape. The specific gravity of a mineral is a fundamental property and is constant between very close limits for the same species of different sources if particles are pure and free from cavities or cracks. In many species, however, solid inclusions and changes in chemical composition due to replacement of elements cause variations in the specific gravity. The plagio-clase series of feldspars between albite and anorthite illustrate this point (specific gravity from 2.60 to 2.77). Fig. 1 shows the specific gravity distribution of some of the common silicate minerals.' The highest specific gravity is about 4.7 (zircon) and the lowest is 2.0 (sepiolite), with most of them ranging between 2.6 and 3.5. Although most of the silicates given in Fig. 1 are found as constituents of rocks, those generally considered as rock making minerals are comparatively few. They include quartz, feldspars, nephelite, sodalite, leucite, mica, pyroxenes, amphiboles, chrysolite, kaolin, talc and serpentine. These minerals may appear in igneous rocks as coarse crystals in granites, syenites and diorites or as very fine grained dispersions in basalt and felsite. When the latter rocks occur in an ore, their specific gravities depend on the minerals present and structure. The same is true for the sedimentary and metamorphic rocks (sandstones, shales, gneiss, slate, schists). A comparison of specific gravities for the minerals listed in Fig. 1 with that of TBE (see Table I) shows that the important rock-forming minerals, with the exception of pyroxenes, amphiboles and chrysolite (olivine), lie in the specific gravity range of less than 2.96 and can therefore be separated by TBE. The ore structure is important both in determining the apparent specific gravity and the efficiency of TBE recovery. The structure can be compact (as in

Jan 1, 1963

By F. W. Bloecher, A. M. Gaudin

H. H. Kellogg—There is one point that the author has failed to emphasize sufficiently in his paper. What is commonly called the equilibrium contact-angle (the author's "maximum contact-angle") can have only one value on a smooth, flat, homogeneous surface under a given set of conditions. The equilibrium contact-angle is defined, for such a system, as the angle between the solid-liquid and liquid-gas interfaces, measured through the liquid. The value of the equilibrium contact-angle is uniquely determined by the value of the interfacial energies of the three intersecting interfaces and is independent of other forces in the system. When the liquid-gas interface intersects the solid at an edge—as was the case for all the experiments reported in this paper—the orientation of the solid-liquid interface is indeterminate or varies through 90" for a right-angle edge. Mr. Morris has called the angle between the horizontal and the liquid-gas interface for this edge condition a "static contact-angle." I feel that this term is unnecessarily misleading. In the first place, "static contact-angle" sounds too much like "equilibrium contact-angle." In the second place, the magnitude of the "static contact-angle," which I would prefer to call the "supporting angle," is determined by the forces in the system other than those derived from the interfacial energies, hence "contact angle" is misleading. If Mr. Morris had said that the "supporting-angle" is variable and depends on the weight of the particle and size of the bubble and that it has a maximum possible value equal to the equilibrium contact-angle, his discussion would have been more accurate. T. M. Morris (author's reply)—Mr. Kellogg puts forth a reasonable criticism of some of the terminology used in the paper. I agree that the term "static contact angle" may be misleading. Substitution of the term "supporting angle" or "vector angle" may be more suitable. F. X. Tartaron—In this paper the author presents a very interesting mathematical development of the forces present when a mineral particle adheres to an air bubble. Excellent concordance is obtained between mathematical formulation and experimental results. It is the writer's understanding that when the mineral surface presented to an air bubble is greater than the area of contact, the maximum contact angle is obtained. However, this contact angle represents distortion of the bubble, the normal shape of which is spherical or in cross-section, circular. This distortion produces a force that acts in opposition to the force of adhesion between the bubble and particle. Hence, at maximum contact angle, the force of adhesion between bubble and particle is at a minimum for static conditions. However, when the size of bubble is increased, the size of particle remaining the same (and all other conditions remaining the same), the contact angle decreases, the distortion of the bubble decreases and the force in opposition to adherence of bubble and particle also decreases. Thus, there is stronger attachment between bubble and particle. When this situation is applied to actual flotation conditions, it is doubtful that it has any significance. The reason is that the bubbles are normally so much larger than the particles, that in substantially all cases, it is probable that negligible distortion of the bubble takes place. In table IV, the author makes computations for bubbles from 0.50 to 2 mm diam. This is from 0.02 in. to 0.08 in. Certainly the bubbles generated in a flotation machine are far larger than this. The surfaces of the author's bubbles range from 0.79 to 12.6 sq mm. The area of contact of the glass rod (0.15 mm diam) is 0.017 sq mm. Thus, ratio of bubble surface to mineral area of contact ranges from 47 to 741 in round numbers. If we take a %-in. diam bubble and a 65-mesh (0.208 mm) particle of cubical shape, the ratio of bubble surface to mineral area of contact is 2931. Mineral particles do not readily become attached to air bubbles. Taggart has shown that in pneumatic flotation machines collector-coated particles are only temporarily attached to bubbles. They keep falling off and down in the froth but at a delayed rate as compared with gangue. Spedden and Hannan's motion pictures confirm the difficulty of attaching particles to air bubbles. In the agitation froth process, according to Taggart, air is precipitated from the water selectively on to the collector-coated particles and these

Jan 1, 1951

By F. W. Bloecher, A. M. Gaudin

H. H. Kellogg—There is one point that the author has failed to emphasize sufficiently in his paper. What is commonly called the equilibrium contact-angle (the author's "maximum contact-angle") can have only one value on a smooth, flat, homogeneous surface under a given set of conditions. The equilibrium contact-angle is defined, for such a system, as the angle between the solid-liquid and liquid-gas interfaces, measured through the liquid. The value of the equilibrium contact-angle is uniquely determined by the value of the interfacial energies of the three intersecting interfaces and is independent of other forces in the system. When the liquid-gas interface intersects the solid at an edge—as was the case for all the experiments reported in this paper—the orientation of the solid-liquid interface is indeterminate or varies through 90" for a right-angle edge. Mr. Morris has called the angle between the horizontal and the liquid-gas interface for this edge condition a "static contact-angle." I feel that this term is unnecessarily misleading. In the first place, "static contact-angle" sounds too much like "equilibrium contact-angle." In the second place, the magnitude of the "static contact-angle," which I would prefer to call the "supporting angle," is determined by the forces in the system other than those derived from the interfacial energies, hence "contact angle" is misleading. If Mr. Morris had said that the "supporting-angle" is variable and depends on the weight of the particle and size of the bubble and that it has a maximum possible value equal to the equilibrium contact-angle, his discussion would have been more accurate. T. M. Morris (author's reply)—Mr. Kellogg puts forth a reasonable criticism of some of the terminology used in the paper. I agree that the term "static contact angle" may be misleading. Substitution of the term "supporting angle" or "vector angle" may be more suitable. F. X. Tartaron—In this paper the author presents a very interesting mathematical development of the forces present when a mineral particle adheres to an air bubble. Excellent concordance is obtained between mathematical formulation and experimental results. It is the writer's understanding that when the mineral surface presented to an air bubble is greater than the area of contact, the maximum contact angle is obtained. However, this contact angle represents distortion of the bubble, the normal shape of which is spherical or in cross-section, circular. This distortion produces a force that acts in opposition to the force of adhesion between the bubble and particle. Hence, at maximum contact angle, the force of adhesion between bubble and particle is at a minimum for static conditions. However, when the size of bubble is increased, the size of particle remaining the same (and all other conditions remaining the same), the contact angle decreases, the distortion of the bubble decreases and the force in opposition to adherence of bubble and particle also decreases. Thus, there is stronger attachment between bubble and particle. When this situation is applied to actual flotation conditions, it is doubtful that it has any significance. The reason is that the bubbles are normally so much larger than the particles, that in substantially all cases, it is probable that negligible distortion of the bubble takes place. In table IV, the author makes computations for bubbles from 0.50 to 2 mm diam. This is from 0.02 in. to 0.08 in. Certainly the bubbles generated in a flotation machine are far larger than this. The surfaces of the author's bubbles range from 0.79 to 12.6 sq mm. The area of contact of the glass rod (0.15 mm diam) is 0.017 sq mm. Thus, ratio of bubble surface to mineral area of contact ranges from 47 to 741 in round numbers. If we take a %-in. diam bubble and a 65-mesh (0.208 mm) particle of cubical shape, the ratio of bubble surface to mineral area of contact is 2931. Mineral particles do not readily become attached to air bubbles. Taggart has shown that in pneumatic flotation machines collector-coated particles are only temporarily attached to bubbles. They keep falling off and down in the froth but at a delayed rate as compared with gangue. Spedden and Hannan's motion pictures confirm the difficulty of attaching particles to air bubbles. In the agitation froth process, according to Taggart, air is precipitated from the water selectively on to the collector-coated particles and these

Jan 1, 1951

By F. C. Bond

Since the Third Theory of Comminution was presented eight years ago (I) it has found increasing use in crushing and grinding problems. The practical utility of its wok index equation is quite generally acknowledged (2). However, its theoretical basis has been questioned in at least three technical articles (3) (4) ('). The purpose of this paper is to present experimental proof that it is scientifically correct. Particles under compressive stress are strained and deformed. They absorb strain energy, and when this locally exceeds the breaking strength, a crack tip forms. The surrounding strain energy flows to the crack tip, which rapidly extends and splits the rock, releasing the strain energy as heat. The initial energy flow causes additional crack tips in highly strained areas. If the compression is rapidly applied by impact, crack tips may form before the strain energy has reached equilibrium in the particle, thus decreasing the total work input required for breakage. The energy necessary to break is essentially the energy necessary to produce crack tips, since the energy necessary to extend the cracks to breakage is already present as strain energy in the deformed particles. After breakage nearly all of this energy appears as heat. The crack length cannot be measured directly. However, in particles of regular and similar shape the crack tip length is considered as equal to the crack depth, or crack extension necessary to break, so that the crack length equals the square root of one-half of the surface area. The Third Theory states that the useful work done in crushing and grinding is directly proportional to the total length of the new cracks formed. It can be confirmed by showing that a constant work input produces a constant length of new cracks when reducing the same material to different product sizes. This is done in the present paper on a wide variety of material. The constant work input was supplied by one revolution of the 12" x 12" laboratory ball mill used in making grindability tests by the Allis-Chalmers method (12) (13) The new crack lengths produced per mill revolution were measured from all available grindability test results at 28, 35, 48, 65, and 100 mesh on fifteen different ores, and were found to remain substantially constant for each ore at all mesh sizes. A new technique is used for the measurement of crack lengths. Size distribution plots of the mill feed and product are made by the Third Theory method (9) and the crack lengths are obtained from these plots by the procedure described in the present paper. The energy input required to produce a unit length is of fundamental importance in the size reduction of brittle solids. The crack length Cr is expressed in centimeters per cubic centimeter of solid material. It bears a definite relationship to the external surface area of the crushed or ground solid. A uniform particle shape must be assumed before the surface area and crack length can be evaluated. In this paper it is assumed that the relationship between the surface area and the particle volume of a particle d microns in diameter is the same as that of cube d microns on a side. The external surface areas of particles with a cubical breakage probably agree approximately with this rule, and correction factors can be applied when physical measurements of the surface areas are available for comparison. However, the assumption of equivalent cubes has been found satisfactory for most calculation purposes. Assuming equivalent cubes, one cubic centimeter of particles d microns in diameter will have a crack length Cr of v30.000/d centimeters, and a surface area of 60,000/d square centimeters. The specific crack length is thus equal to the square root of one-half the specific surface area. Where Sa is the surface area in square centimeters per gram and Sg is the specific gravity of the ground solid, then Cr = vSg . Sa/2 = 173.2/ vd (1)

Jan 1, 1961