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By T. M. Morris

A SEARCH of the literature reveals that no measurements have been made of the forces acting between a small solid particle whose surface is hydrophobic, and an air bubble to which the solid adheres, both immersed in water. Analyses have been made of the forces acting to support a greased solid on the surface of water, and the forces acting to cause a solid, whose surface is hydrophobic, to adhere to an air bubble in water. The latter analysis T. M. MORRIS, Junior Member AIME, is in the Department of Metallurgical Engineering and Mineral Dressing, School of Mines and Metallurgy, Rolla, Mo. New York Meeting, February 1950. TP 2734 B. Discussion of this paper (2 copies) may be sent to Transactions AIME before Feb. 28, 1950. Manuscript received May 16, 1949. This paper is the result of work done for part of a doctor's thesis at the Missouri School of Mines and Metallurgy. is often incomplete, however, because the internal pressure of the bubble has been neglected. It will be demonstrated that the internal gas pressure is not a negligible factor when dealing with bubbles of the size encountered in flotation. A study of the forces acting between an air bubble attached to a large flat surface is informative. It must be borne in mind, however, that this is not the condition present in a flotation cell, where the particle is small compared to the size of the bubble. The bubble is allowed to spread to its maximum contact angle on a large flat surface in the first case, whereas in the second case, the spread of the bubble is limited to the surface of the small particle which is presented to the bubble. Kabanov and Frumkinl studied the forces acting to cause adhesion of bubbles of hydrogen to a large surface of mercury, which served as an electrode in a dilute sulphuric acid solution. The force acting to hold the bubble to the mercury surface was found to be the vertical component of the surface tension between hydrogen and the sulphuric acid solution. The forces tending to cause the bubble to separate from the mercury surface were found to be: (1) the force exerted due to the internal pressure of the bubble acting upon the area of contact between the bubble and the mercury surface, and (2) the buoyant force of the bubble minus the hydrostatic force acting at the base of the bubble. These investigators photographed bubbles that were just on the verge of separating from the mercury surface. From these photographs, they measured the contact angle between the mercury surface and the tangent to the hydrogen-solution interface at the point of contact between bubble and mercury surface. They calculated the volume of the bubble and the internal pressure of the bubble. The equivalence between the upward acting and downward acting forces was remarkable. Wark2 pursued an investigation similar to that of Kabanov and Frumkin, and at the same time. His deductions verified those of Kabanov and Frumkin. He also considered the conditions present in flotation and was aware of the effect of the internal pressure of the bubble. Further, he proposed several conditions under which a small solid particle would adhere to an air bubble in water. In 1922, Edser," an English physicist, made the following statement. "It must be remembered that no particle could float stably, but for the possibility of variation of the contact angle, for if this were a constant, a slight tilt would inevitably cause the particle to sink." Wark criticized this statement, maintaining that the contact angle does not vary. The experimental data to be presented indicates that Edser was correct. Experimental Procedure: Briefly, the experimental procedure was as follows. A bubble of air was generated in distilled water. A rod of known diameter, one end of which was water repellent, was attached to this bubble. The weight of the 'rod was measured. The internal pressure of the bubble was measured with a manometer. The hydrostatic head from the surface of the water to the bottom of the rod was measured. The angle between the horizontal projection of the end of the rod and the tangent to the bubble at the circle of contact be-

Jan 1, 1951

By T. M. Morris

G. L. Simard and D. J. Salley—The authors and ourselves" independently came to similar conclusions both as to the value of tracer methods for the study of flotation and the general nature of collector-mineral interaction. The dodecylamine-quartz system appears to be simpler than the dithiophosphate-galena one, and the results therefore appear clearer. It is evident from a comparison of the two papers, however, that care must be used in extending the results to other more complicated systems. In the case of dodecylamine-quartz, the possible influence of micelle formation is of interest. There is no a priori reason why complete monolayer formation should necessarily occur at the concentration for micelle formation, since sorption depends on the nature of the substrate as well as on the properties of the solute in solution which alone determine micelle formation. Indeed, the fact that the onset of increased adsorption, point B in fig. 2, occurs at a concentration one tenth the critical value for micelles might imply that micelle formation does not have an influence. Interestingly enough, the data may be handled by the methods used for multilayer adsorption of gases on surfaces. Thus, if the amount adsorbed is plotted versus concentration, a sigmoid type curve is obtained, similar in form to a so-called Type I1 isotherm13 generally attributed to multimolecular adsorption. A monolayer value of about 0.12 mg per g may be estimated from the knee of this isotherm. On the other hand, if a plot is made according to the multilayer gas equation for adsorption to an unrestricted number of layers, eq 38,13 assuming the critical micelle concentration as the saturation concentration, the data above 120 mg per liter fall on a straight line from which a monolayer adsorption of 0.3 mg per g results. These considerations suggest that the monolayer may occupy an area somewhat less than the geometric value of 0.4 mg per g, and that micelle formation may indeed be a factor in the adsorption. 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 T. M. Morris

G. L. Simard and D. J. Salley—The authors and ourselves" independently came to similar conclusions both as to the value of tracer methods for the study of flotation and the general nature of collector-mineral interaction. The dodecylamine-quartz system appears to be simpler than the dithiophosphate-galena one, and the results therefore appear clearer. It is evident from a comparison of the two papers, however, that care must be used in extending the results to other more complicated systems. In the case of dodecylamine-quartz, the possible influence of micelle formation is of interest. There is no a priori reason why complete monolayer formation should necessarily occur at the concentration for micelle formation, since sorption depends on the nature of the substrate as well as on the properties of the solute in solution which alone determine micelle formation. Indeed, the fact that the onset of increased adsorption, point B in fig. 2, occurs at a concentration one tenth the critical value for micelles might imply that micelle formation does not have an influence. Interestingly enough, the data may be handled by the methods used for multilayer adsorption of gases on surfaces. Thus, if the amount adsorbed is plotted versus concentration, a sigmoid type curve is obtained, similar in form to a so-called Type I1 isotherm13 generally attributed to multimolecular adsorption. A monolayer value of about 0.12 mg per g may be estimated from the knee of this isotherm. On the other hand, if a plot is made according to the multilayer gas equation for adsorption to an unrestricted number of layers, eq 38,13 assuming the critical micelle concentration as the saturation concentration, the data above 120 mg per liter fall on a straight line from which a monolayer adsorption of 0.3 mg per g results. These considerations suggest that the monolayer may occupy an area somewhat less than the geometric value of 0.4 mg per g, and that micelle formation may indeed be a factor in the adsorption. 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 A. M. Gaudin, J. H. Brown

In a survey of the effects of heat treatment on the comminution of various rocks, it was found that unusual size distributions often characterize the broken products, and that this is related to a great increase in intergranular fracture1. It is the purpose of the present paper to contribute to an understanding of this effect. In a thesis by one of use, critical consideration was given to many mechanisms which could conceivably be responsible for the increased intergran-ular fracture. It was shown that neither gross chemical changes nor intergranular corrosion are required. Among non-chemical mechanisms the most likely appeared to be (1) Uneven expansion due to thermal gradients, giving spalling (2) In a manner similar to that prevailing in metals, the appearance at high temperature of intergranular weakness. (3) Unequal thermal expansion of adjacent grains. Experiments were designed and conducted to permit a choice among the many alternative mechanisms and in particular among the three listed here. EXPERIMENTAL MATERIALS Tests were made on the materials listed in Table 1. Of each material, only lumps similar in composition and grain size were used. The three marbles listed in Table 1 were analyzed to assure that their chemical compositions did not differ greatly (Table 2). On the basis of the chemical analyses, of differential thermal analyses, and of X-ray powder diffraction patterns, it appeared that the marbles were very similar except for their grain sizes.

Jan 1, 1961

By D. A. Elgillani, M. C. Fuerstenau

In this paper, oxidation potentials measured in the presence of various concentrations of cyanide, ferro-cyanide, and ferricyanide and ethyl xanthate at various values of pH are related to flotation response. Eh-pH diagrams are presented to show that the formation of surface ferric ferrocyanide is probably responsible for depression when cyanide is added. The influence of cyanide on the depression of pyrite with xanthates as collector has been the subject of a number of investigations,'-6 and several theories on the mechanism of depression have evolved from these studies. Wark and Cox7 and Gaudin8 have suggested that the depressing effect is due to a competition of cyanide ion with xanthate ion for the surface. Cook and his colleagues9-11 have explained this phenomenon in terms of competition between hydrocyanic acid and xanthic acid. Sutherland 12 has shown that although both of these theories accurately describe the relation between pH value and cyanide addition at constant collector addition, they fail to describe the relation between pH value and the amount of collector required to cause flotation. Taggart 13 suggested that depression in these systems is due to the formation of a reaction product between ferric ion at the pyrite surface and ferrocyanide ion derived from solution. Majumdar4,6 has attempted to prove this hypothesis by measuring the contact angles of pyrite in the presence of 25 mg per liter ethyl xanthate and different concentrations of potassium ferrocyanide and ferricyanide. In all cases the contact angles were quite high up to pH 10. These results indicate that pyrite should not be depressed by either potassium ferrocyanide or ferricyanide. In view of these facts, Majumdar has assumed that the compound Fe(CN)2 forms at the surface. Gründer and Bornl4 have stated that depression may be due to the formation of the compound K2Fe(II)Fe(CN)6 at the pyrite-solution interface. This compound is thought to be an interaction product between the K2Fe(CN)6-2 ion from solution and the Fe++ ion at the pyrite surface and, accordingly, K4Fe(CN)6 should depress pyrite at least as effectively as KCN. This was proven experimentally, but there was no simple relation between the depression of pyrite and the concentration of either KCN or K4Fe(CN)6 in solution. In view of the many mechanisms that have been proposed for pyrite depression by cyanide, it is apparent that a clear understanding of the phenomena occurring in these systems is lacking. One reason for this may be the fact that the species responsible for pyrite flotation in the presence of xanthate is not the xan-thate ion but rather dixanthogen.15 Since the oxidation of xanthate to dixanthogen is dependent on the oxidation potential of the solution, it would seem that knowledge of these potentials would be a requisite to understanding the pyrite-xanthate-cyanide system. It is the object of this paper to measure both the oxidation potential and pH of the pyrite systems in the presence of various concentrations of cyanide, ferrocyanide, and ferricyanide and xanthate and to relate these values to flotation response. EXPERIMENTAL MATERIALS AND 'TECHNIQUES In the experiments discussed here, pure potassium ethyl xanthate was used as collector, and reagent grade potassium cyanide, potassium ferrocyanide, and potassium ferricyanide were used as depressants. Reagent grade HC1 and KOH were added for pH adjustment. Conductivity water, made by passing distilled water through an ion exchange column, was used in all experimental work. Two natural samples of pyrite were used in the investigation. Sample preparation for flotation included dry grinding with a mortar and pestle and sizing the product to 100 x 200 mesh. Prior to flotation, a 0.75-gm sample of pyrite was added to a solution containing a known amount of depressant at the desired pH value, and the system was conditioned for 4 min. Following this, a known amount of collector was added and the system was conditioned for another 4 min. The pH — termed flotation pH - was measured; the pulp was transferred to a Hallimond cell, and flo-

Jan 1, 1969

By R. S. Kinasevich, D. D. Crabtree, D. W. Fuerstenau, T. P. Meloy, A. L. Mular

This paper presents details of the concept that size reduction in comminution machines takes place by three mechanisms; namely impact, abrasion, and chipping grinding. Experimental evidence is presented to show that each of these comminution mechanisms produces particles of a characteristic size distribution. The actual product from a comminution device has been postulated to be the result of a composite of these three types of mechanisms. Composite curves are demonstrated for a material following the Gaudin-Schuhmann, Gaudin-Meloy, and Rosin-Rammler size distributions. About forty years ago, Gaudin1 showed that grinding may be considered a combination of impact and attrition. Since that time, major efforts have been devoted to studies, both experimental and theoretical, of impact and compression fracture, while attrition has been almost wholly neglected, at least quantitatively. A significant attempt to distinguish between attrition and impact grinding is the work of Tanaka2 in Japan. By means of an instrumented abrasion grinder and a drop weight device, he determined coefficients relating the increase in surface area of various materials to the energy expended by the two methods of comminution. He showed that physical properties of a material determine its response to attrition and impact grinding. By extending his ideas to ball milling, he concluded that to a large extent the basic comminution process in a ball mill is due to the impact of falling media. Because Tanaka used a mass of particles in his drop weight device, however, he did not obtain pure impact size reduction. The purpose of this paper is to define basic mechanisms of size reduction, to verify that each has a characteristic and meaningful distribution curve, and to show how a combination of these mechanisms results in a size distribution very like that produced by grinding mills. DEFINITION OF COMMINUTION MECHANISMS The product from a grinding device will be considered to be the sum of the contributions resulting from the action of three basic mechanisms of size reduction which operate in a ball and rod mill. These are impact grinding and two forms of attrition, namely abrasion grinding and chipping grinding. Each is defined below. Impact Grinding: If a straight line is obtained when the cumulative weight fraction finer than a given size is plotted on log-log paper as a function of that size, the slope of the line is defined as the distribution modulus. A number of investigators 3,4,5 have shown that impact fracture of single specimens of different composition and shape results in a distribution of daughter particles that exhibit a distribution modulus of unity. This has also been true for materials broken in slow compression. Moreover, under slow compression or impact fracture conditions, theoretical distribution equations6*' which approximate the Gaudin-Schuhmann distribution when the distribution modulus is close to unity agree reasonably well with the experimentally obtained products. If one now considers a comminution process where many impact or compression fracture events are taking place, then any rational summation of the individual events yields, in the finer size range, a Gaudin-Schuhmann distribution whose distribution modulus is also unity. If the size distribution of the product from a mill has a distribution modulus of unity, it is implied that particles are fractured in a manner which results in a comminution event having a distribution like that obtained for the breakage of single specimens. These impact events would occur when a particle is smashed between balls or between a ball and the mill liner. Attrition, on the other hand, is that form of grinding which cannot be called impact grinding, and comprises both abrasion and chipping grinding. Abrasion Grinding: Abrasion is a form of surface wear resulting when particles rub against each other or against balls or the mill liner of a tumbling mill, somewhat like a piece of wood being rubbed over a piece of sandpaper. The surface wears at a more or

Jan 1, 1964

By R. S. Kinasevich, D. D. Crabtree, D. W. Fuerstenau, T. P. Meloy, A. L. Mular

The effect of such variables as feed size, particle shape, cleavage, and hardness on the relative proportion of impact, abrasion, and chipping events in a tumbling mill is demonstrated. The concept of an average event, which is a combination of the three comminution mechanisms, is introduced. It is postulated that the average event in a particular mill determines not only the size distribution but also the energy-size reduction relationship for the comminution process. Fragmentation of particles in tumbling mills appears to result from a combination of impact, abrasion, and chipping grinding.' The relative rates of size reduction attributable to any of the basic grinding mechanisms must depend upon a number of variables, such as feed size, particle shape, hardness, and the number and kind of particles in the mill. The purpose of this paper is to show experimentally how these variables in the properties of materials affect the size distributions obtained by grinding the material's in a laboratory tumbling mill. The resulting size distributions will be intetpreted in terms of a combination of three comminution mechanisms. METHODS AND MATERIALS In this study, minerals of widely differing properties were ground either separately or as mixtures in laboratory mills using rods or balls for grinding media. The materials used include quartz, Tuolomne, limestone (99.8% CaCO3), barite, corundum, galena, pyrite, glass beads, and crushed glass. The mill used was 8 in. in diam. and 9-1/4 in. long. For the ball milling tests, 17.6 kg of steel balls (36: 7/8 in. balls, 178: 1 in. balls, and 44: 1-1/8 to 1-1/4 in. balls) were used. For the rod milling experiments, 17.6 kg of steel rods 9-1/16 in. long (25: 5/8 in., 10: 3/4 in., and 5: 7/8 in. in diam.) were used. In each test, 1 kg of solids were ground wet at 60% solids at 77 rpm. In all cases except where otherwise specified, the feed to the mill was 4 x 8 mesh material. Size distributions of the ground products were determined by a wet-dry sieving procedure with Tyler series sieves. Size distributions of mixed products containing limestone were determined by dissolving the limestone with acid and sizing the residue. EXPERIMENTAL RESULTS AND DISCUSSION If the size distribution of the product from a tumbling mill depends upon the relative proportion of impact and attrition (abrasion and chipping) events, altering the grinding conditions may change these proportions and consequently alter the size distribution of the product. Data to illustrate this point can be taken from Gaudin's classic 1926 paper.2 In one series of experiments, Gaudin ground quartz of different initial sizes for four hours in a laboratory ball mill with 7/8-in. balls. In Fig. 1, his data are reproduced as the cumulative fraction finer than the stated size for the following initial feed sizes: 13.3 x 9.4 mm, 6.7 x 4.7 mm, 2.6 x 1.6 mm, and 0.83 x 0.59 mm. As the feed size was decreased, a dramatic change in the shape of the size distribution curves took place, even though the amount of minus 100-mesh

Jan 1, 1964

By D. C. Seidel, M. C. Fuerstenau, R. J. Roman

The existence of a surface charge on the alkali halide salts is shown, and a flotation mechanism involving surface charge and collector solubility is developed. Data suggest that KC1 is positively charged and that NaCl is negatively charged in saturated brines, and that the neutral molecule RNH,Cl is the collector in the amine-KC1 system, RSO, is the collector in the sulfonate-KC1 system, and RCOONa) is the collector in the fatty acid-NaCl system. A number of hypotheses have been advanced to explain the mechanism of soluble salt flotation; one of these involves exchange between collector ions and surface cations. With this mechanism Gaudin1 suggested that the differences in flotability of halite and sylvite with primary amines are due to the ionic size of the RNH;, Kt, and Na t ions. Fuerstenau and Fuerstenau expanded this hypothesis to include many other alkali halide salts. Several exceptions to this hypothesis are known. That is, this model does not explain why salts containing the same cation, or why salts of different degrees of hydration, respond differently to flotation. For example, why NaI is floated with an amine whereas NaI .2H,O is not. Further, no correlation between ionic size and flotation response can be made with sulfonate or car-boxylate as collectors. In addition, this hypothesis does not explain the effect of magnesium or lead activation, nor does it offer any explanation of the role of temperature in salt flotation. Rogers and Schulman3 realized some of the inadequacies of the ion exchange mechanism and proposed another mechanism based on the heat of solution of the salts. They concluded that weakly hydrated salts can be floated with alkyl amines and sulfonates, that strongly hydrated salts can be floated with fatty acids, and that excessively hydrated salts cannot be floated at all. Their work was not limited to the al-

Jan 1, 1969

By D. C. Seidel, M. C. Fuerstenau, R. J. Roman

The role of surface charge in soluble salt flotation, which was developed in Part I, is extended to relate the theory to the specific phenomena of KCI-NaC1 separations. Temperature-collector solubility relationships, metal ion activation, and particle size effects are discussed. The initial paper in this series developed and presented the hypothesis that one of the mechanisms of soluble salt flotation may involve electrical attraction between the collector and mineral surface. This hypothesis was developed from a combination of experimental data and free energy calculations, and details of the logic are presented in this first paper.* The studies have indicated that KC1 has a positive surface charge and NaCl a negative charge. KC1 can therefore be floated with sulfonate ion (RSO;) or with an aqueous polar species such as the aqueous amine chloride, RNH3C1(,,). The chloride end of the RNH3C1(,,) molecular dipole is probably negative and will be attracted to the positive surface of the KC1 particles and absorb (actually probably fit into a vacant chloride site) on the mineral surface. The amine end of the collector molecule would extend into the solution phase and provide the air avid surface required for flotation. NaCl particles are floated by such collectors as aqueous molecules of fatty acid salt, RCOONa(,,), in which the positive inorganic end of the dipole is attracted to the negatively charged surface of the NaCl and, in this case, adsorb and probably fit into a vacant sodium site on the surface. The aminium cation, RNH~, should also be a collector for NaC1. For certain collectors, actual precipitates of the collector must be formed before a sufficient amount of the polar aqueous molecule is present to effect flotation. In a system of this type there is a three-way equilibrium between: Aqeous Molecular Solid Precipitate - A of the Collector (Not Dissociated) . Ionic Species (Dissociated). The controlling equilibrium is probably between the precipitated form of the reagent and the aqueous

Jan 1, 1969

By R. E. Pray, M. C. Fuerstenau, J. D. Miller, B. F. Perinne

Quartz cannot be floated with potassium amyl xanthate as collector at any pH. Complete flotation is achieved with certain minimal additions of amyl xanthate and Pb from pH 5.8 to 8.5 and with amyl xanthate and Zn from pH 7.5 to 8.1. The active species of these metal ions responsible for activation are shown to be PbOH and ZnOH No flotation was effected when Cu and Mg were added as activators. Previous work1,2,3,4,5,6,7 has shown that quartz may be floated in the presence of sulfonate or soap when the following two criteria are met: 1) some portion of the added metal ion has hydro-lyzed to its first hydroxy complex, and 2) a precipitate of the metal-collector has formed. Since sulfonate and soap, two substantially different anionic collectors, conform to these criteria, this phenomenon may well be expected to be of a general nature. In this view then, it would appear that any anionic collector, including xanthates, should also float quartz when these two criteria are met. The object of this paper is to demonstrate the conditions under which quartz will respond to flotation in the presence of potassium amyl xanthate. EXPERIMENTAL MATERIALS AND TECHNIQUES Quartz was prepared by leaching the sized sample (48 x 150 mesh) with HC1 until no iron could be detected in the leach liquor. Conductivity water, made by passing distilled water through an ion exchange column, was used in the investigation. Potassium amyl xanthate was selected as collector. Purification of this reagent was effected with the following method: 1) a laboratory sample of potassium amyl xanthate was dissolved to saturation in hot ethyl alcohol and filtered several times while still hot, 2) the filtrate was cooled, during which time potassium amyl xanthate crystallized out of solution; the xanthate was then separated from the solution by filtration, 3) the amyl xanthate was dissolved in fresh hot ethyl alcohol and filtered, 4) step (2) was repeated, 5) the crystalline potassium amyl xanthate was washed with ethyl ether five times, and 6) the xanthate was dried for 24 hours under continuous vacuum. Inorganic impurities are insoluble in hot ethyl alcohol whereas dixanthogen is soluble in ethyl ether. Five-gram charges of 48x150 mesh quartz were conditioned for 3 min in 125 cc of solution containing the reagents and were floated with the small-scale cell and procedure described in previous papers.478 Reagent grade HCl and NaOH were used for pH adjustment, while reagent n-amyl alcohol was added as frother. Frother addition is necessary with this technique, but it should be mentioned that data, similar to those shown in Fig. 2 for 1 x10-4 mole per liter Pb++ and 1 X 10-4 mole per liter AX-, were also obtained with a Hallimond cell in the absence of frother. EXPERIMENTAL RESULTS Clean quartz could not be floated with amyl xanthate at any pH. Flotation was achieved under certain conditions, however, when various metal ions were added to the system. The activating ions used were lead, zinc, copper and magnesium, added as reagent grade chloride salts. Lead as Activator: The effect of Pb++ as activator was examined at five different additions of amyl xanthate (Fig. 1, 2 and 3). When 1x 10-5 mole per liter xanthate was added in the presence of 1 x 10"4 mole per liter Pb ++, no flotation was obtained at pH 6.5 or below, while a recovery of about 60% was effected at pH 7. When the pH was increased to 7.8, no flotation was again obtained, Complete depression was noted from pH 7.8 to about 10, at which point a recovery of about 30% was achieved. At about pH 11, the precipitate of lead amyl xanthate which was present below this pH dissolved and complete depression occurred. When 2.5x 10-5 mole per liter xanthate was added with the same lead addition, no flotation was obtained at pH 5.8 and below, whereas a recovery of

Jan 1, 1965

By Frank T. Weems

The basic operating properties of the DorrClone are discussed and certain metallurgical applications which exploit these properties are presented. An effective method of controlling the consistency of the DorrClone underflow is described. THIS paper presents in a general manner some of the applications of the DorrClone (Dutch States Mines cyclone) in the metallurgical and heavy chemical fields. Technical or mathematical analyses of the design factors and of the mechanism whereby the cyclone effects its separation have been capably treated in a series of previous papers.'-' Engineering and operational aspects of a few installations and laboratory tests have been chosen to emphasize the unique classification characteristics of the DorrClone and to illustrate its utility in certain difficult situations. Its use in coal washing and heavy-media operations are not considered. Some 25 or more industrial installations and applications of the DorrClone in the metallurgical fields are operating at present, ranging from single trial units to complete batteries composed of a multiplicity of units. The data were obtained in part from some of these, and in part from operations of units at the Westport Mill, the laboratories and testing plant of the Dorr Co. at Westport, Conn. The DorrClone was developed, in principle, by the research dept. of the State Mines, Limburg, Holland, during World War 11. Its first use was to dewater a —50 micron sand used as a dense medium in coal washing. The metallurgical wet cyclone was first publicized by Driessen and Yancey and Geer.6 ince then the cyclone has been studied as a means of de-watering, heavy media concentration, and fine size classification. The DorrClone is shown in Figs. 1 and 2. pulp to be treated is pumped through the feed nozzle, A, into the feed cylinder, B. The feed nozzle is of rectangular cross-section, the outermost edge being tangent to the feed cylinder walls. Feed shims, C, may be attached to the innermost walls to adjust the open area of the feed nozzle available to entering pulp. The tangential injection of feed under pressure supports the vortex action of the pulp that has been detained in the cyclone; the centrifugal forces of this vortex throw the coarse particles to the walls of the cone, D, where they collect and pass downward and out through the adjustable apex opening, E. The fine particles contained in most of the water that entered with the feed pulp move to the inner spiral of the vortex and flow out through the vortex finder, F, contained in the orifice plate, G, which forms the top of cyclone chamber. The overflow pulp may then spray freely into a spray chamber, H, surmounting the cyclone or pass directly into a 90' elbow, I, of somewhat larger diameter than the vortex finder. Installation Where more than one cyclone is to be installed, best overall efficiency and ease of control are obtained with equal distribution of both pulp volume and weight of solids among the cyclones, and with the same pressure being maintained at each cyclone feed nozzle. Fig. 3 is a suggested arrangement for feeding two or more cyclones in parallel. Feed pressure control: Under normal operating conditions it is not unusual for some surge to exist in the feed that is to be sent to the cyclone. As will be discussed later, surges in the solids content of the pulp are usually not of great operational consequence, but surges in feed volume are a problem. Several systems have been devised for absorbing surges in feed volume, each involving a surge tank. If the surges are small and fairly rhythmical, a tank of sufficient size might be installed to dampen out

Jan 1, 1952

By J. R. Johanson

With the continuing development of automatic operations, it is important that reliable discharge rates through hoppers and bins be obtained for bulk solids. In most applications a feeder is used to control the feed rate. The selection of this feeder size is usually based on the rated ability of the feeder to move material without regard to the capability of the material to flow through the opening in the hopper onto the feeder. The dis charge rate through a given hopper opening may vary from zero to a theoretical maximum depending on the flow properties of the material. This paper presents an equation for the maximum discharge rate for a bulk material as a function of the hopper shape, the opening size and the flow properties of the material. Discharge-rate tests on various materials indicate good agreement with calculated values for opening sizes from a fraction of an inch to several feet. As part of a program to develop improved design criteria for bulk storage and handling facilities, a specific study of the methods involved in calculating the rate of discharge of bulk solids from hoppers and bins has been made. This study is closely related to earlier work done on the prevention of flow problems through the choice of proper design geometry of hoppers and bins1. The present paper is an extension of this earlier work, and therefore many of the concepts previously derived and explained will be used without explanation. Two types of flow will be considered: plane-strain flow in a wedge-shaped hopper and axial-symmetry flow in a conical hopper. The literature contains many studies on discharge rate for regular-shaped dry particles2*3 such as glass beads, lead shot and coarse dry sand. However, the work is empirical in nature, and it is difficult to extrapolate the given information to apply to moist, sticky materials typical of many industries. Some studies4 have shown a decrease in discharge rate with an increased moisture content of the material. However, no attempt was made to correlate the discharge rate with moisture. The method of calculating discharge rate presented in this paper was derived analytically from the basic knowledge of the flow of frictional, cohesive, granular solids, The equation includes the effect of material cohesion (stickiness), hopper configuration, opening size and bulk density of the material. THEORETICAL WORK The basic assumptions made in deriving the discharge rate equation are as follows: 1) The material is a frictional, cohesive, granular solid. 2) The flow is considered continuous and without significant density change. 3) The material at the hopper opening forms a continuously failing arch that is in dynamic equilibrium. 4) The strength of the material in the arch, which must be overcome for the arch to fail, is caused by the pressure in the flowing mass near the hopper opening. 5) This pressure at the hopper opening can be calculated5. If we consider the dynamic equilibrium of an arch of uniform thickness such as that shown in Fig. 1,

Jan 1, 1965

By Oscar Johnson

The industry has been canvassed for information on methods of handling grinding steel at milling plants, an important subject overlooked in most descriptive articles on milling plant arrangements. The data collected are offered in this paper as a guide to designers and planners who have loading and storage problems to solve. WITH capacities of milling plants expanding from a few hundred tons per day to many thousand, replenishment of grinding media is an important phase of mill operation. Information on this aspect of milling procedure, solicited from several mining companies, is summarized here. At International Nickel's Copper Cliff concentrator the normally strenuous job of changing rods is considerably simplified by the use of the Garrow rod charging machine, Fig. 1. The overhead crane, Fig. 2, brings a bundle of rods, weighing four to a ton, to the loading platform of the machine, positioned in front of the mill. The rods roll one by one down the slight incline of the platform onto a conveyor which sends them into the mill. A modified version of the Garrow machine, Fig. 3, is used at the Federal mill of St. Joseph Lead Co. An overhead crane places the portable steel structure in position in front of the discharge end of any one of the five 9x12-ft rod mills. It then raises a bundle of about twenty 3-in. rods to the discharge platform of the charging machine. The rods are 11 ft 7 in. long and weigh about 278 lb. By tripping a lever the operator allows one rod at a time to roll onto the inclined rollers. A slight push by the operator sends the rod smoothly into the mill. The Union Miniére du Haut Katanga rod charging machine, Fig. 4, is mounted on a pair of wheels at the forward end with swiveling castors at the back for steering it to position for use or storage. Wheels are equipped with locking brakes to maintain the machine in position while it delivers rods to the mill. The device is made in two parts. The first consists of the base, which carries the supporting wheels, grooved rollers, and drive. The other part serves as the rod deck, which can carry up to six 3-in. x 12-ft rods. A short boom built integral with the base reaches through the mill trunnion and delivers the rods into the mill barrel. Three grooved guide rollers ,are provided to receive the rods from the sloping charging deck. One rod at a time is fed to the rollers and thus delivered into the mill. Two of the rollers are driven by 11/2-hp motor through a V-belt drive. The third roller is driven off the first by a single V belt in a groove below the rod groove and on the same center line. Rods are delivered to the charger by an overhead crane in bundles of three to six as needed. The power is supplied by cables plugged into power outlets, suitably located near the rod mill discharge end. The Oliver Iron Mining Co. uses a rod charger, Fig. 5, suspended from a monorail by cables. It is constructed .of structural steel and has two decks, each capable of carrying five rods of 4-in. maximum diameter. The rods ride in grooved free-turning rollers. Legs extending down from the mill end of the mechanism act as supports when the unit is ex-

Jan 1, 1955

By Robert R. Walden, LeMont West

K ENTUCKY'S first acid-grade fluorspar flotation Kmill, shown in Fig. 1, was placed in operation Aug. 1, 1952, by the Pennsylvania Salt Manufacturing Co. at Mexico, Ky. During 1951 a critical shortage of acid-grade fluorspar developed and it became necessary for the company to produce part of its fluorspar requirements. In 1951 the company purchased the Crider and Lennen metallurgical fluorspar mill and an adjacent stockpile of tailing at Mexico, Ky. The tailing, assaying about 26 pct calcium fluoride, originated from log washer and jig mill concentrators in the area. As the mill did not have a fluorspar dryer or convenient rail facilities, the company leased the Burleson concentrator at Marion, Ky., where these facilities were available. At Marion, Ky., on the Illinois Central Railroad, dry acid-grade fluorspar is transported direct to the company's Calvert City, Ky., hydrofluoric acid plant. The Mexico flotation plant was reconditioned and designed to produce acid-grade fluorspar from the jig tailing stockpile. The new plant flowsheet is shown in Fig. 2. The ore feed, old tailing, which contains 10 pct of waste rock and coarse gravel assaying approximately 8 pct CaF,, is bound together by sticky clay

Jan 1, 1955

By S. C. Sun

With the aid of emulsifiers, intense high-frequency sound waves are capable of emulsifying any collector in water. The data show also that ultrasonically emulsified collectors are more effective in floating minerals than the nonemulsified collectors. THE use of ultrasonics in forming emulsions is not new. As early as 1927 Wood and Loomis reported preparation of emulsions with ultrasonics. In 1935 Rschevkin and OstrawskyV escribed the use of great ultrasonic power in producing fine emulsions of various oils and paraffin in water. Recently Oyama and Tanaka3 employed ultra-emulsification to increase the effectiveness of sodium ethyl xanthate in flotation of chalcopyrite and galena. An emulsion is a two-phase system consisting of two incompletely miscible liquids, the one being dispersed as finite droplets In the other. The dispersed liquld is known as the internal or discontinuous phase, and the surrounding liquid is termed the external or continuous phase. There are two types of emulsions; one is oil-in-water (O/W) and the other water-in-oil (W/O). The word oil refers to the liquid other than water. Circumstances exist in which the emulsion type is not clearly defined, and the internal and external phases both contain portions of the opposite phase. This is said to be a dual emulsion. Among the many hypotheses, 5a, B proposed for the formation of emulsions, the Bancroft's adsorbed film or double interfacial tension theory is widely accepted. Bancroft 7, 8 deduced that in the process of emulsification the interfacial tension between oil and water is lowered by the formation of an emulsifying film, which contains the adsorbed molecules and/or ions from the emulsifying agent and the two liquids. This film has two interfacial tensions, one with the water and the other with the oil, which are not necessarily equal. The difference in interfacial tension between the two surfaces of the film is chiefly responsible for forming different types of emulsions. For example, if the interfacial tension between water and film is less than that between oil and film, the film will become convex on the water side, thereby tending to form an oil-in-water emulsion. On the other hand, if the interfacial tension between water and film is greater than that between oil and film, the film will become concave on the water side, thereby tending to make a water-in-oil emulsion. In line with this theory, emulsifying agents soluble in water have the tendency to form oil-in-water emulsions, while those soluble in oil form emulsions of the reverse type. Apparatus and Experimental Procedure: The ultrasonic apparatus shown in Fig. 1 consisted of a hypersonic generator (A), Brush Development Co. model Bu-204; a hypersonic transducer bowl (B) whose resonant frequency is 400 kc per sec; and a round-bottomed glass tube (C) of 2.2 cm ID and 21 cm in length. The acoustical output power of the hypersonic transducer bowl was standardized with a Hewlett Packard vacuum tube voltmeter, model 41 0B, across the hypersonic generator output. The glass tube, containing the materials to be emulsified, was placed 1 cm above the central surface of the transducer bowl, which was filled with water as shown in Fig. 2. Ultrasonic emulsification was performed in three steps, although a one-step method has been used: 1) emulsifying the predetermined amounts of col-

Jan 1, 1956

By A. Vifian, I. lwasaki

Several samples of copper-nickel ore from the Duluth Gabbro were studied to relate their mineral-ogical characteristics with their amenability to concentration by flotation. The most common rocks in the samples were norites, gabbros, and troctolites. The texture of the rocks varied from coarse pegma-titic to very fine. The copper contents ranged from 0.2-0.7% and the nickel contents from 0.07-0.15%. The ore minerals were chalcopyrite, cubanite, pyrrhotite, and pentlandite. Most of the ore minerals occurred in interstices between laths of plagioclase, but some were included in the gangue grains. The samples responded readily to xanthate flotation. After a 65 to 100-mesh grind about 95% of the copper and 85% of the nickel were recovered in a bulk sulfide concentrate. Such recoveries remained constant even with grinds as fine as 270 mesh due to the extremely fine inclusions of sulfides in the silicate gangue. A finer grind than 270 mesh was necessary to free the copper-iron sulfides from the nickel-iron sulfides. A combination of time and British gum* was quite effective in producing concentrates analyzing 25-30% copper. The nickel concentrate averaged 1.5% nickel. Most of the nickel lost in the tailing was present as un-liberated sulfides and not as nickel in the olivine structure. The nickel content of the olivine was only about 0.05 or 0.08%. Western world nickel usage in 1967 is expected to be the second highest on record, amounting to 825 million lb. Despite a rise in mine production, however, demand is expected to exceed supply in 1968. ' Hence, exploration, development, and production expansion projects are being accelerated on a world scale. In Minnesota the copper-nickel bearing Duluth Gabbro is receiving much attention. During the past year 11 companies have been granted leases in the region, and the 1967 Minnesota legislature enacted a tax law designed to encourage the development of a copper-nickel industry. Although it is only during the past few years that mining companies have shown an active interest in the Minnesota copper-nickel deposit, copper-nickel minerals have been known to exist in northeastern Minnesota since 1899.3 At the 28th Mining Symposium, Dr. P. K. Sims, from the Geological Survey of Minnesota, gave a review of copper-nickel exploration in northeastern Minnesota,4 in which he emphasized that the potential of the Duluth Gabbro complex is large. Tests on samples from the Kawishiwi River area were reported by the United States Bureau of Mines in 1955.' In 1964, the Mines Experiment Station described tests on samples from the Gunflint Trail: and in 1966 the Minnesota Geological Survey published a geological map of the Gabbro Lake Quadrangle. The Mines Experiment Station published a study of the concentration of a Minnesota copper-nickel ore in 1967.7 The present paper is divided into three parts. The first describes the mineralogy of some rock samples from the Kawishiwi River area of northeastern Minnesota; the second summarizes the results of numerous flotation tests that were made on the samples, and the third explains the loss of nickel in the flotation tailing. MINERALOGY OF KAWlSHlWl ROCKS Recently five samples of mineralized gabbro from the Kawishiwi River area, a few miles east of Ely, were received at the Mines Experiment Station. One of the samples was a 175-lb composite, which was designated Ore 1556. The other four samples were 7-lb grab samples that had been obtained from four different exploration pits. They were designated Ore 1626, Lots 1 through 4. Basic Mineralogy: Many authors have reported that the rocks of the so-called gabbro of the Duluth Intrusion vary widely in composition.8-9 The samples on which our studies were based also contained a wide range of rocks. A gabbro, olivine-gabbro, anorthosite-gabbro, norite, and a troctolite were represented. The essential minerals in the samples were plagio-clase, pyroxene, and olivine, in variable proportions.

Jan 1, 1969

By R. L. Bleifuss

The object of this study was to evaluate the oxidized taconites of the western Mesabi iron range and to establish a correlation between the various basic taconite types and their concentratability. The initial work included a study of the original mineralogical and stratigraphic facies of the fresh taconite and traced the oxidation and leaching patterns developed during the conversion of this material to oxidized taconite. Subsequent studies have extended this work to include the semitaconites and also the wash and heavy media ore types widely developed in the area. Each basic original mineralogical facies or taconite type produces during alteration an equivalent secondary oxidized facies which has a unique mineralogical composition and texture. These control the concentratability of the oxidized taconites. Actually the influence of the original mineralogical composition of the iron formation extends even further and determines whether the most likely product of oxidation and leaching will be a wash ore or a heavy media ore and even to the direct shipping ores where the ratio of hematite to goethite is largely determined by the original taconite type. The relationship between original taconite, oxidized taconite, semitaconites, and wash and heavy media ores is briefly summarized in Table I. The terms are not precise and in some instances tend to overlap. The table is intended to point out only the essential differences between the various materials. The original taconite was dominantly composed of mixtures of magnetite, iron carbonate, iron silicate, and quartz (chert). In a few thin stratigraphic units, hematite was present as an original constituent. The alteration of the original taconite to oxidized taconite has resulted from the circulation of ground waters through an initial fracture system related to minor structures in the iron formation. The chemical reactions have involved the oxidation and decomposition of original minerals such as magnetite, iron carbonate, and iron silicates to hematite or goethite. The alteration at this early stage is characterized by pseudomorphic replacement of the original minerals by oxidation products although retaining the major textural features of the original taconite. There was very little secondary migration of iron at this stage and the total iron content of the rock has been only slightly increased. Further alteration of this material to form a semi-taconite, a wash or a heavy media ore, involves extensive removal of silica in solution and significant redistribution of iron units. Wash and heavy media ores are developed by the growth of coarse secondary iron layers, dominantly goethite, coupled with the removal of silica in solution and decomposition of the cherty layers. This paper is concerned primarily with the materials classified as oxidized taconites which are characterized by oxidation of the original mineral constituents with little secondary enrichment. The area studied, shown on the index map, Fig. 1, extends some 30 miles along the strike of the Biwabik formation roughly from Hibbing to Coleraine. This study was greatly facilitated by the basic stratigraphic and mineralogical studies of Gruner1 and white2. The bulk of the material in this presentation represents a portion of the author's contribution to a study sponsored by the Great Northern Railway on the oxidized taconites of the western Mesabi.3 METHOD OF APPROACH A total of 106 drill holes, representing some 30,000 ft of drilling, were examined and sampled. The drill holes were logged and some 1500 composite samples were prepared for chemical analysis and bench scale metallurgical tests. These samples were analyzed for total iron and ferrous iron; and magnetite iron was determined by a standard Davis tube test at minus 200 mesh. Standard reduction roast tests using 150-gram samples of minus 10 mesh material were made on these 1500 composite samples with a mixture of H2, CO2, N2, and H2O at a temperature of 650°C. This roasted material was pulverized through 150 mesh and concentrated in the Davis tube. The iron recoveries and concentrate grades obtained on the roasted products were used to assess the concentratability of the oxidized taconites. Detailed mineralogical work was done on thin sec-

Jan 1, 1964

By A. M. Gaudin, T. P. Meloy

Based on the equation for single fracture, a formula has been obtained for repeated fracture. Solution of this equation is obtainable analytically for a few examples and numerically for all others. Graphs of the size distribution equations have been obtained; they agree broadly with the experiments of others. In another paper1 we have considered a model and a comminution distribution equation for single fracture of brittle materials. Most comminuting devices, however, depend on the occurrence of repeated fracture. This is especially true of continuous cylindrical mills of the ball, tube, or rod type. But even in primary crushers there is some repetition of the breaking process, so that this paper should be of interest in connection with all comminuting devices. HALF LIFE AND PROBABILITY OF FRACTURE To facilitate the study of fracture it is useful to introduce the concept of the half life of a particle, In the ball mill, for example, we may start with 10,000 feed particles. The time, 7, by which one half of these particles have been broken is the half life of the feed under the prevailing experimental conditions. The probability of breakage bears an inverse relationship to the half life. In a ball mill, for instance, it can be shown that the

Jan 1, 1962

By A. M. Gaudin, T. P. Meloy

This paper presents the theoretical derivation of the distribution equation for single fracture. The equation is shown to accord with experiment. Several empirical size-distribution equations have been proposed to describe the size of broken materials. Among them are the Gaudin-Schuhmann equation and the Rosin-Rammler equation.3*4 The Gaudin-Schuhmann equation relates the relative fraction of undersize to relative size —. In this relationship Mo is the total weight of crushed sample, M(x) the weight of undersize contained, x the size considered, K a quantity called the size modulus, which together with the slope parameter, m, characterizes the product. The slope parameter is usually close to unity. The Rosin-Rammler equation relates the same relative fraction of undersize to the relative size modulus by an equation of different form In this relationship, e is the base of natural logarithms. In the fine size-range when m is unity both equations give Gilvarry and Berstrom have sought a size distribution equation having a sound theoretical basis. They have come to an equation taking into account the effect of volume, surface and edge flaws in fragmentation. If the effect of the volume and surface flaws is neglected, the equation taking only edge flaws into account has the form of the Rosin-Rammler equation. In the present paper, a theoretical size-distribution

Jan 1, 1962

By H. E. Lee, D. Ingvoldstad

AT Bunker Hill the original charge storage and preparation system was installed in 1917 to accommodate lead-silver gravity mill products. Only minor tonnages of wet fines such as vanner and flotation concentrates were received. Charge flux and diluent requirements were provided by an ample supply of siderite middlings and coarse lime-rock. While oversize material was crushed through %-in., the use of roll crushers in series resulted in a more or less granular, free-running charge of adequate porosity. Under such conditions, receipts could be proportioned directly from receiving bins, and suitable blending was obtained by passing the resultant layered composite through a small Stedman disintegrator. This elementary system served well for production and smelting of an extremely lead-rich sinter, in the low column blast furnace. Here sinter physical quality is less critical, and appreciable quantities of raw flux and oxidized ore may be charged directly to the blast furnace without seriously impairing furnace capacity. Prior to 1938 the relative proportions of zinc receipts were low and extraneous flux requirements at a minimum. However, subsequent war-inflated zinc demands brought marked increase in fine concentrate and slimy zinc leach residue receipts and an abrupt introduction to smelting a more refractory zinciferous charge. The higher temperature demands of the more refractory zinciferous charge required a higher smelting column and the higher column, in turn, rendered the blast furnace less receptive to improperly prepared feed. Inadequate presinter processing facilities prevented the production of acceptable sinter, and blast furnace production declined to 50 pct of former capacity. In view of a prevailing contention among lead metallurgists as to the deleterious action of high zinc slag on blast furnace capacity, it was natural to overstress this factor and to concentrate on possible changes in furnace design. Another interpretation was that primary correction should be sought through expanded sintering facilities. This divergence of opinion, together with the extreme material shortages of the 1940's, delayed corrective

Jan 1, 1957