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By W. Philippoff

ALTHOUGH Gaudin1 and more recently Sutherland2 have calculated the probability of collision of a falling mineral particle with a rising bubble, there is no published information concerning the details of the mechanism of attachment of a collector-coated particle to a bubble. During the past year the writer has developed a theory for the mechanism of attachment, which has been substantiated experimentally. Funds for the investigation and for some of the equipment used have been supplied by the Mines Experiment Station of the University of Minnesota. Motion picture studies of the phenomena involved in the collision between mineral particles and bubbles, such as those of Spedden and Hannan," show that the contact can be completed within 0.3 millisec. Formulas developed for rigid bodies have hitherto been used' for the calculation of the motion of bubble and particle, but it is obvious that a bubble cannot be regarded as a rigid body. On the contrary, Spedden and Hannan's pictures show a great degree of deformation during the collision. The time of attachment was calculated as the time the particle drifted past the bubble. Time of Collision The theory presented in this paper enables calculation of the time of collision, using the concept that the bubble, or more generally, a liquid-air interface, acts as an elastic body. The elasticity, defined as the restoring force on a mechanical deformation, is caused by the surface tension and is the result of the principle of the minimum of free surface energy. It is well known that an elasticity together with a mass determines a frequency of vibration. The vibrations of jets and drops caused by the elasticity of the interface are known to comply exactly with the classical theory of capillarity.' However, the vibrations of isolated bubbles, as distinct from foams, have not been investigated previously. The following equation, presented elsewhere,' has been deduced for these frequencies: 3_____________________ fB = 9.20.vV.vn. (n-1).(n+2)/8 [I] in which fB is the frequency of a harmonic of the bubble in cycles per second, V the volume of the bubble in cc, n a number determining the order of the harmonic, and n = 2 the basic vibration. The first (basic) harmonic describes a change of the spherical bubble to an ellipsoidal bubble. The higher harmonics are more complicated, for the circumference of the bubble is divided approximately into as many parts as the order of the harmonic. As an example, Spedden and Hannan's published motion picture of a vibrating bubble corresponds to the sixth harmonic. Eq 1 shows that only the first and third harmonics are simple multiples (1 and 3), all the others being irrational fractions of the basic frequency. This means that the shape of the vibration can change with time and is in general unsym-metric in respect to the time axis. Such conditions prevail when there is a distributed elasticity or mass, as in the case of vibrating membranes or rods. The constant 9.20 is valid for water at room temperature, but a general solution involving the physical constants of the liquid has not been found. The case of the floating particle is much easier to treat than that of the bubble. It can be assumed that the elasticity is caused exclusively by the interface and that the mass is concentrated in the particle together with some adhering water. The following expression for the frequency of a system of one degree of freedom can be applied: fP = -1/2-vE/m [2] Here fp is the frequency of the particle vibration in cycles per second, E the elasticity in dynes per cm, and m the mass in grams. The classical theory of impact phenomena gives the time of collision during the striking of a spring (in this case the surface of the bubble) by a mass, as: t, = 2/f = nvm/E [3] It is now possible to develop an expression for the elasticity of a floating cylindrical particle. The force equilibrium of a cylinder floating end on at the air-liquid interface is given by the well-known equation (Poisson7 1831) P = /4 D2-pL-g-h + D.y sin a [4] which accounts for the buoyancy and the action of the surface tension where P is the force acting on the particle in dynes (weight-buoyancy), D the diameter of the cylinder in cm, PL the density of the liquid in grams per cc, g the acceleration of gravity = 981 cm per sec2, h the depression of the cylinder below the surface of the liquid in cm, y the surface tension in dynes per cm and a the supporting angles or the one required to insure equilibrium, a being smaller than the contact angle 0. Although demonstrated by Poisson, it has not

Jan 1, 1953

By R. L. Manegold

This paper outlines the reasons for and the application of suspended magnets above belt conveyors for the purpose of removing tramp iron to protect equipment. The design of a magnet strong enough to extract iron through a distance of 24 in. is described along with the proper method of application in the field. Advantages of the suspended magnet in contrast to the conventional magnetic pulley are also discussed. IN RECENT years there has been a decided trend toward bringing ores and coal out of open-pit and underground mines by long, sloping single-stage belt conveyors. Because the high investment cost of haulage conveyors dictates maximum speed and full loading for economy, conveyor belts are running faster than ever before, with a greater burden on the belts. In addition, larger blocks of ore are being mined and conveyed. Rougher use of large mining equipment generates more tramp iron; mechanical loading rejects nothing. Therefore the extraction of tramp iron and other deleterious materials for the protection of haulage conveyors at transfer points, chutes, and idlers is becoming an increasingly difficult job. In our experience, the best method of protecting long haulage conveyor belts is to extract the tramp iron, at least the large tramp iron, ahead of the main haulage conveyor or series of conveyors. It is most practical to collect the tramp iron at the earliest source possible, usually directly after the primary car unloading dump or after the primary crushers, which are ordinarily not affected by tramp iron, see Fig. 1. The coal or ore from its primary source is fed by chutes or feeders onto a buffer or shock belt conveyor, a short, ruggedly built conveyor system that can be considered somewhat expendable. Its primary function is to bring the ore up to speed for transmission to the haulage conveyor. There is no assured method of protecting this conveyor from tramp iron damage at its feed end. Likewise, there is a possibility, although remote if the magnet applied to this belt is installed correctly, that the tramp iron extraction process will damage the shock belt, which is, however, short and comparatively inexpensive. Magnetic head pulleys with their maximum effective range of about 8 or 10 in. cannot be considered for large installations, even though they are desirable because of the continuous and automatic tramp iron removal feature. Further, the most dangerous form of tramp iron with respect to potential damage to a haulage conveyor is the long rod, roof bolt, or rail segment, which is not extracted satisfactorily because of the limited tangential contact of such an iron shape with the magnet. Magnetic head pulleys are also undesirable because the dribble or fines from the head pulley discharge at the same point as the tramp iron. Screens must be used to separate the fines from the magnetics, resulting in additional expense and loss of head room. Magnetic detectors have been used with success, but they only indicate the presence of iron, and the conveyor belt must be stopped for its manual removal. The stoppage of any conveyor means that all preceding equipment must be stopped or a cascade of material on the idle conveyor will result. Occasionally combinations of detectors and magnetic head pulleys are used. The detector precedes the magnetic head pulley and detects only large pieces of tramp iron, while the magnetic pulley subsequently takes out the smaller ferrous metals. Suspended magnets overcome the disadvantages of magnetic head pulleys, detectors or a combination of both. There are several magnetic extraction problems involved in applying a suspended magnet at this

Jan 1, 1953

By R. L. Manegold

This paper outlines the reasons for and the application of suspended magnets above belt conveyors for the purpose of removing tramp iron to protect equipment. The design of a magnet strong enough to extract iron through a distance of 24 in. is described along with the proper method of application in the field. Advantages of the suspended magnet in contrast to the conventional magnetic pulley are also discussed. IN RECENT years there has been a decided trend toward bringing ores and coal out of open-pit and underground mines by long, sloping single-stage belt conveyors. Because the high investment cost of haulage conveyors dictates maximum speed and full loading for economy, conveyor belts are running faster than ever before, with a greater burden on the belts. In addition, larger blocks of ore are being mined and conveyed. Rougher use of large mining equipment generates more tramp iron; mechanical loading rejects nothing. Therefore the extraction of tramp iron and other deleterious materials for the protection of haulage conveyors at transfer points, chutes, and idlers is becoming an increasingly difficult job. In our experience, the best method of protecting long haulage conveyor belts is to extract the tramp iron, at least the large tramp iron, ahead of the main haulage conveyor or series of conveyors. It is most practical to collect the tramp iron at the earliest source possible, usually directly after the primary car unloading dump or after the primary crushers, which are ordinarily not affected by tramp iron, see Fig. 1. The coal or ore from its primary source is fed by chutes or feeders onto a buffer or shock belt conveyor, a short, ruggedly built conveyor system that can be considered somewhat expendable. Its primary function is to bring the ore up to speed for transmission to the haulage conveyor. There is no assured method of protecting this conveyor from tramp iron damage at its feed end. Likewise, there is a possibility, although remote if the magnet applied to this belt is installed correctly, that the tramp iron extraction process will damage the shock belt, which is, however, short and comparatively inexpensive. Magnetic head pulleys with their maximum effective range of about 8 or 10 in. cannot be considered for large installations, even though they are desirable because of the continuous and automatic tramp iron removal feature. Further, the most dangerous form of tramp iron with respect to potential damage to a haulage conveyor is the long rod, roof bolt, or rail segment, which is not extracted satisfactorily because of the limited tangential contact of such an iron shape with the magnet. Magnetic head pulleys are also undesirable because the dribble or fines from the head pulley discharge at the same point as the tramp iron. Screens must be used to separate the fines from the magnetics, resulting in additional expense and loss of head room. Magnetic detectors have been used with success, but they only indicate the presence of iron, and the conveyor belt must be stopped for its manual removal. The stoppage of any conveyor means that all preceding equipment must be stopped or a cascade of material on the idle conveyor will result. Occasionally combinations of detectors and magnetic head pulleys are used. The detector precedes the magnetic head pulley and detects only large pieces of tramp iron, while the magnetic pulley subsequently takes out the smaller ferrous metals. Suspended magnets overcome the disadvantages of magnetic head pulleys, detectors or a combination of both. There are several magnetic extraction problems involved in applying a suspended magnet at this

Jan 1, 1953

By Norman F. Schulz, Emert W. Lindroos, Strathmore R. B. Cooke

DURING the course of an investigation of the effects of various starch products on hematite and quartz in regard to their separation by flotation, it was found that whereas most starches flocculated suspensions of hematite in water, they did not flocculate similar suspensions of quartz. However, a derivative of whole corn starch containing approximately one tenth aminoethyl group (-—CH,CH2NH2) per glucose unit proved to be an exception. This aminoethyl starch was a very good flocculant for both hematite and quartz, and also possessed the property of depressing both minerals in cationic flotation tests. In view of the widespread use of starch as a flocculating agent of solids in tailing water, pulps, and for coal slimes, ore and various other purposes in sulphide and nonsulphide flotation, attention is called to the effective surface activity of aminoethyl starch in flocculating suspensions of the two minerals investigated. Test Materials The starch products employed included Globe Pearl starch No. 144 and fresh aminoethyl starch, both supplied by the Corn Products Refining Co. Dr. A. L. Elder" has kindly furnished a description The minerals used in the various tests are listed in Table I. Their specific surfaces were determined by the air permeability method, which gave results reproducible to within plus or minus 3 pct. Surface areas obtained by krypton adsorption were greater than the air permeability values by a factor of 2.0 for quartz and 62.4 for hematite. Starch Adsorption on Mineral Surfaces Starch adsorption data were obtained by agitating for 1 hr measured volumes of neutral starch solutions of known concentrations with weighed quantities of finely divided mineral of measured specific surface. The mineral then was separated from the pulp liquor by centrifugation and the residual starch content determined by chemical analysis. The analytical procedure consisted of oxidizing the starch with an excess of dichromate in acid medium at elevated temperature and titrating the excess dichromate by the ferrous ammonium sulphate—potassium permanganate method. Analytical results were reproducible to within less than 1 pct. Adsorption data obtained in unbuffered solutions near the neutral point are plotted in Fig. 1. The adsorption on either mineral was far greater for the aminoethyl starch than for the Pearl starch. Flocculation The degree of flocculation was determined for a given pulp by measuring the time required for the supernatant liquid to reach a certain degree of clarity. This was accomplished by passing a standard light beam through the pulp, contained in a glass settling tube, and measuring the time required after agitation ceased for the intensity of the transmitted beam to reach a predetermined value. Starch reagent was added to each pulp in small uniform increments, and the settling time was determined after each such addition. Increase in pulp liquor volume due to the added starch reagent was ignored in these tests. Pulps were maintained at or near neutrality. of the preparation of the aminoethyl starch: "Three hundred and sixty grams of powdered unmodified corn starch was slurried in 3 liters of water and stirred during gelatinization. Eighty-six grams of ethylenimine was added slowly during reflux which was continued for 4 hr. The yellow solution set to a gel upon cooling. This was broken up and neutralized with HC1. The thick paste was dried on hot rolls. Adsorbed polyethylenimine and salts were removed from the yellowish products by washing first with acidified aqueous '60 per cent' alcohol. The white product contained nitrogen corresponding to about one aminoethoxy group per ten glucose residues." Only laboratory samples of this starch derivative have been prepared. The starch reagents for use in flocculation, flotation, and adsorption tests were made up by dispersing the appropriate quantities of air-dry starch in cold water, adding boiling water, and heating for 30 min at 120°C under pressure. When used ip adsorption tests, the starch solutions first were cleared of insoluble matter by centrifugation.

Jan 1, 1953

By Strathmore R. B. Cooke, Emert W. Lindroos, Norman F. Schulz

DURING the course of an investigation of the effects of various starch products on hematite and quartz in regard to their separation by flotation, it was found that whereas most starches flocculated suspensions of hematite in water, they did not flocculate similar suspensions of quartz. However, a derivative of whole corn starch containing approximately one tenth aminoethyl group (-—CH,CH2NH2) per glucose unit proved to be an exception. This aminoethyl starch was a very good flocculant for both hematite and quartz, and also possessed the property of depressing both minerals in cationic flotation tests. In view of the widespread use of starch as a flocculating agent of solids in tailing water, pulps, and for coal slimes, ore and various other purposes in sulphide and nonsulphide flotation, attention is called to the effective surface activity of aminoethyl starch in flocculating suspensions of the two minerals investigated. Test Materials The starch products employed included Globe Pearl starch No. 144 and fresh aminoethyl starch, both supplied by the Corn Products Refining Co. Dr. A. L. Elder" has kindly furnished a description The minerals used in the various tests are listed in Table I. Their specific surfaces were determined by the air permeability method, which gave results reproducible to within plus or minus 3 pct. Surface areas obtained by krypton adsorption were greater than the air permeability values by a factor of 2.0 for quartz and 62.4 for hematite. Starch Adsorption on Mineral Surfaces Starch adsorption data were obtained by agitating for 1 hr measured volumes of neutral starch solutions of known concentrations with weighed quantities of finely divided mineral of measured specific surface. The mineral then was separated from the pulp liquor by centrifugation and the residual starch content determined by chemical analysis. The analytical procedure consisted of oxidizing the starch with an excess of dichromate in acid medium at elevated temperature and titrating the excess dichromate by the ferrous ammonium sulphate—potassium permanganate method. Analytical results were reproducible to within less than 1 pct. Adsorption data obtained in unbuffered solutions near the neutral point are plotted in Fig. 1. The adsorption on either mineral was far greater for the aminoethyl starch than for the Pearl starch. Flocculation The degree of flocculation was determined for a given pulp by measuring the time required for the supernatant liquid to reach a certain degree of clarity. This was accomplished by passing a standard light beam through the pulp, contained in a glass settling tube, and measuring the time required after agitation ceased for the intensity of the transmitted beam to reach a predetermined value. Starch reagent was added to each pulp in small uniform increments, and the settling time was determined after each such addition. Increase in pulp liquor volume due to the added starch reagent was ignored in these tests. Pulps were maintained at or near neutrality. of the preparation of the aminoethyl starch: "Three hundred and sixty grams of powdered unmodified corn starch was slurried in 3 liters of water and stirred during gelatinization. Eighty-six grams of ethylenimine was added slowly during reflux which was continued for 4 hr. The yellow solution set to a gel upon cooling. This was broken up and neutralized with HC1. The thick paste was dried on hot rolls. Adsorbed polyethylenimine and salts were removed from the yellowish products by washing first with acidified aqueous '60 per cent' alcohol. The white product contained nitrogen corresponding to about one aminoethoxy group per ten glucose residues." Only laboratory samples of this starch derivative have been prepared. The starch reagents for use in flocculation, flotation, and adsorption tests were made up by dispersing the appropriate quantities of air-dry starch in cold water, adding boiling water, and heating for 30 min at 120°C under pressure. When used ip adsorption tests, the starch solutions first were cleared of insoluble matter by centrifugation.

Jan 1, 1953

By Fred C. Bond

MOST investigators are aware of the present unsatisfactory investigatorsstate of information concerning the fundamentals of crushing and grinding. Considerable scattered empirical data exist, which andare useful for predicting machine performance and give acceptable accuracy when the installations and materials compared are quite similar. However, there is no widely accepted unifying principle or theory that can explain satisfactorily the actual energy input necessary canexplain commercial installations, or can greatly extend the range of empirical comparisons. Two mutually contradictory theories have long existed in the literature, the Rittinger and Kick. They were derived from different viewpoints and logically lead to different results. The Rittinger theory is the older and more widely accepted.'TheRittinger In its first form, as stated by P. R. Ritted.'tinger, it postulates that the useful work done in crushing and grinding is directly proportional to the new surface area produced and hence inversely proportional to the product diameter. In its second form it has been amplified and enlarged to include the concept of surface energy; in this form it was precisely stated by A. M. Gaudin' as follows: "The efficiency of a comminution operation is the ratio of the surface energy produced to the kinetic energy expended." According to the theory in its second form, measurements of the surface areas of the feed and product and determinations of the surface energy per unit of new surface area produced give the useful work accomplished. Computations using the best values of surface energy obtainable indicate that perhaps 99 pct of the work input in crushing and grinding is wasted. However, no method of comminution has yet been devised which results in a reasonably high mechanical efficiency under this definition. Laboratory tests have been reported- hat support the theory in its first form by indicating that the new surface produced in different grinds is proportional to the work input. However, most of these tests employ an unnatural feed consisting either of screened particles of one sieve size or a scalped feed which has had the fines removed. In these cases the proportion of work done on the finer product particles is greatly increased and distorted beyond that to be expected with a normal feed containing the natural fines. Tests on pure crystallized quartz are likely to be misleading, since it does not follow the regular breakage pattern of most materials but is regularrelativelybreakage harder to grind patternat the finer sizes, as will be shown later. This theory appears to be indefensible mathematically, since work is the product of force multiplied by distance, and the distance factor (particle deformation before breakage) is ignored. The Kick theory4 is based primarily upon the stress-strain diagram of cubes under compression, or the deformation factor. It states that the work required is proportional to the reduction in volume of the particles concerned. Where F represents the diameter of the feed particles and P is the diameter of the product particles, the reduction ratio Rr is F/P, and according to Kick the work input required for reduction to different sizes is proportional to log Rr /log 2." The Kick theory is mathematically more tenable than the Rittinger when cubes under compression are considered, but it obviously fails to assign a sufficient proportion of the total work in reduction to the production of fine particles. According to the Rittinger theory as demonstrated by the theoretical breakage of cubes the new surface produced, and consequently the useful work input, is proportional to Rr-l.V f a given reduction takes place in two or more stages, the overall reduction ratio is the product of the Rr values for each stage, and the sum of the work accomplished in all stages is proportional to the sum of each Rr-1 value multiplied by the relative surface area before each reduction stage. It appears that neither the Rittinger theory, which is concerned only with surface, nor the Kick theory, which is concerned only with volume, can be completely correct. Crushing and grinding are concerned both with surface and volume; the absorption of evenly applied stresses is proportional to the volume concerned, but breakage starts with a crack tip, usually on the surface, and the concentration of stresses on the surface motivates the formation of the crack tips. The evaluation of grinding results in terms of surface tons per kw-hr, based upon screen analysis, involves an assumption of the surface area of the subsieve product, which may cause important errors. The evaluation in terms of kw-hr per net ton of —200 mesh produced often leads to erroneous results when grinds of appreciably different fineness are compared, since the amount of —200 mesh material produced varies with the size distribution characteristics of the feed. This paper is concerned primarily with the development, proof, and application of a new Third Theory, which should eliminate the objections to the two old theories and serve as a practical unifying principle for comminution in all size ranges. Both of the old theories have been remarkably barren of practical results when applied to actual crushing and grinding installations. The need for a new satisfactory theory is more acute than those not directly concerned with crushing and grinding calculations can realize. In developing a new theory it is first necessary to re-examine critically the assumptions underlying

Jan 1, 1953

By Fred C. Bond

MOST investigators are aware of the present unsatisfactory investigatorsstate of information concerning the fundamentals of crushing and grinding. Considerable scattered empirical data exist, which andare useful for predicting machine performance and give acceptable accuracy when the installations and materials compared are quite similar. However, there is no widely accepted unifying principle or theory that can explain satisfactorily the actual energy input necessary canexplain commercial installations, or can greatly extend the range of empirical comparisons. Two mutually contradictory theories have long existed in the literature, the Rittinger and Kick. They were derived from different viewpoints and logically lead to different results. The Rittinger theory is the older and more widely accepted.'TheRittinger In its first form, as stated by P. R. Ritted.'tinger, it postulates that the useful work done in crushing and grinding is directly proportional to the new surface area produced and hence inversely proportional to the product diameter. In its second form it has been amplified and enlarged to include the concept of surface energy; in this form it was precisely stated by A. M. Gaudin' as follows: "The efficiency of a comminution operation is the ratio of the surface energy produced to the kinetic energy expended." According to the theory in its second form, measurements of the surface areas of the feed and product and determinations of the surface energy per unit of new surface area produced give the useful work accomplished. Computations using the best values of surface energy obtainable indicate that perhaps 99 pct of the work input in crushing and grinding is wasted. However, no method of comminution has yet been devised which results in a reasonably high mechanical efficiency under this definition. Laboratory tests have been reported- hat support the theory in its first form by indicating that the new surface produced in different grinds is proportional to the work input. However, most of these tests employ an unnatural feed consisting either of screened particles of one sieve size or a scalped feed which has had the fines removed. In these cases the proportion of work done on the finer product particles is greatly increased and distorted beyond that to be expected with a normal feed containing the natural fines. Tests on pure crystallized quartz are likely to be misleading, since it does not follow the regular breakage pattern of most materials but is regularrelativelybreakage harder to grind patternat the finer sizes, as will be shown later. This theory appears to be indefensible mathematically, since work is the product of force multiplied by distance, and the distance factor (particle deformation before breakage) is ignored. The Kick theory4 is based primarily upon the stress-strain diagram of cubes under compression, or the deformation factor. It states that the work required is proportional to the reduction in volume of the particles concerned. Where F represents the diameter of the feed particles and P is the diameter of the product particles, the reduction ratio Rr is F/P, and according to Kick the work input required for reduction to different sizes is proportional to log Rr /log 2." The Kick theory is mathematically more tenable than the Rittinger when cubes under compression are considered, but it obviously fails to assign a sufficient proportion of the total work in reduction to the production of fine particles. According to the Rittinger theory as demonstrated by the theoretical breakage of cubes the new surface produced, and consequently the useful work input, is proportional to Rr-l.V f a given reduction takes place in two or more stages, the overall reduction ratio is the product of the Rr values for each stage, and the sum of the work accomplished in all stages is proportional to the sum of each Rr-1 value multiplied by the relative surface area before each reduction stage. It appears that neither the Rittinger theory, which is concerned only with surface, nor the Kick theory, which is concerned only with volume, can be completely correct. Crushing and grinding are concerned both with surface and volume; the absorption of evenly applied stresses is proportional to the volume concerned, but breakage starts with a crack tip, usually on the surface, and the concentration of stresses on the surface motivates the formation of the crack tips. The evaluation of grinding results in terms of surface tons per kw-hr, based upon screen analysis, involves an assumption of the surface area of the subsieve product, which may cause important errors. The evaluation in terms of kw-hr per net ton of —200 mesh produced often leads to erroneous results when grinds of appreciably different fineness are compared, since the amount of —200 mesh material produced varies with the size distribution characteristics of the feed. This paper is concerned primarily with the development, proof, and application of a new Third Theory, which should eliminate the objections to the two old theories and serve as a practical unifying principle for comminution in all size ranges. Both of the old theories have been remarkably barren of practical results when applied to actual crushing and grinding installations. The need for a new satisfactory theory is more acute than those not directly concerned with crushing and grinding calculations can realize. In developing a new theory it is first necessary to re-examine critically the assumptions underlying

Jan 1, 1953

By Fred C. Bond

DISCUSSION Milton C. Shaw and Donald R. Walker (Massachusetts Institute of Technology)—For many years the two empirical rules of comminution bearing the names of Rittinger and Kick have been applied to grinding processes to account for the energy required to crush brittle materials. The basis for Rittinger's rule was the thought that the energy to grind a substance went largely into supplying the additional energy associated with the new free surface, while Kick's law was prompted by the concept of dimensional similarity and is a special statement of the concept of constancy of strain energy to cause rupture. According to Rittinger the energy to grind a given volume varies as the change in the square of the mean particle size, v - A (D2), while according to Kick this energy varies

Jan 1, 1953

By Fred C. Bond

DISCUSSION Milton C. Shaw and Donald R. Walker (Massachusetts Institute of Technology)—For many years the two empirical rules of comminution bearing the names of Rittinger and Kick have been applied to grinding processes to account for the energy required to crush brittle materials. The basis for Rittinger's rule was the thought that the energy to grind a substance went largely into supplying the additional energy associated with the new free surface, while Kick's law was prompted by the concept of dimensional similarity and is a special statement of the concept of constancy of strain energy to cause rupture. According to Rittinger the energy to grind a given volume varies as the change in the square of the mean particle size, v - A (D2), while according to Kick this energy varies

Jan 1, 1953

By C. Cánepa

In the treatment of many problems related with the optimization of a given ore dressing process, microscopic studies can provide invaluable assistance. Such studies are generally carried out through mineralogical determinations both qualitatively and quantitatively. Frequently the solution of a specific problem requires the combination of these in adequate proportions. Often the nature? of the problem poses some conditions regarding the way the microscopic determinations are made in order to yield useful information. Most publications applied to mineral beneficiation show results of ore microscopy without mentioning the methodological details involved in the determinative work and therefore it is not possible to judge their reliability and/or their relevance. As methodology must necessarily change from case to case, it is very important for the microscopist to identify first the direct and indirect mineralogical information required to solve the problem. Without such guidelines selection of methods for the qualitative and/or quantitative determinations cannot be made.

Jan 1, 1981

By A. Balint

The Photometric Optical Separation process is introduced and examples of sorting machines are given. Applications of the process are outlined in general terms with reference to specific types of industrial installations. Brief description is given of the capabilities and limitations of available equipment, including cost estimates.

Jan 1, 1967

By Nathaniel Arbiter

There is a history in all men's lives, Figuring the nature of the times deceas'd, The which observ'd, a man may prophesy, With a near aim, of the main chance of things. W. Shakespeare, Henry IV; Part 2 Introduction This nation's first century embraced two stages of the Industrial Revolution. During one, what had been a colonial agricultural economy began to industrialize; water power, then steam after 1794, were the energy sources; coal and iron were the essential ingredients. The second stage started after 1850; aided by rich and diverse mineral resources, the country began its transition from the Iron Age to the Age of Metals. Early civilizations had been built on stone, and fairly high levels were sustained on iron. But the spectacular advances in the past century in communication, in construction, in transportation by sea, rail, land and air, and in much that characterizes modern civilization have depended increasingly on the use of the complete metallic and nonmetallic resources of the earth's crust. Thus it was appropriate to define the Industrial Revolution as “the period during which man's relationship to natural resources became utterly changed”, 1 with minerals playing a major and indispensable role. But we are now becoming aware that the relationship of man to natural resources must change again. On every hand the dangers inherent in the contamination of land, sea and air by the wastes of civilization are becoming apparent. And from the growing realization that mineral wealth is finite must eventually come other far reaching changes in mineral use and distribution. For on the scale of centuries we cannot continue to exploit mineral resources even at present rates, let alone at expanded rates, without eventual depletion of the more abundant resources, and early exhaustion of the less abundant. In the past our problems were relatively easily met by the development of new and improved machinery and processes. But the future will

Jan 1, 1971

By R. W. Smith

Living and killed organisms, particularly microorganisms, and extracellular products derived from the organisms are increasingly finding use in minerals engineering. Goals include both enhancement of mineral processing/11.ydrometallurgica,l operations and remediation of mineral industry wastes. Some of the applications, such as biologically assisted leaching of ?sulfide ores and bioxidation of refractory gold ores, are well established commercial ?processes used around the world. Others, such as the use. of organisms for the removal of heavy metal ions from dilute aqueous streams, are nearing commercial application. Many other uses of microorganisms and. their derivatives are potentially possible. These include use of microorganisms in flocculation or flotation of minerals., remediation of organics potentially discharged from mineral engineering operations, degradation of cyanide, the recovery of bitumen from heavy oil reservoirs and tar sands and the solubilisation of lignites and low rank coals. In order to fully exploit these many possible uses of organisms and their derivatives, extensive fundamental .and .applied research work exploring the fundamentals, potential and practicality of the various possible uses of microorganisms in mineral engineering should be vigorously pursued. ?

Jan 1, 1991

By William E. Hughes, Roderick K. Davey

The objective of this chapter is to review and discuss interpolation techniques commonly in use in the mining Industry today, including simple examples. This chapter will not attempt to compare the relative accuracy of each technique as this subject has adequately been covered by several authors (Knudsen and Kim, 1967; David, 1974; and Barnes, 1979) When appropriate, methods will be compared relative to the results of simple examples and computational ease. The examples presented are based on metallic deposits. The techniques, however, are not restricted to metallic deposits and can generally be applied to nonmetallic ones. The purpose of interpolation, as applied to a mineralized deposit, 1s to extend the knowledge of the grade and geology of localized samples to an estimate of the grade and mineralogy of a larger block of ground or even an entire deposit. The word interpolation means to compute values between given values and is limited to that region between the known values. The distinction between interpolation and extrapolation is important and must be adhered to in the application of these techniques in general, the interpolation must be limited to the area enclosed by verified samples. The methods being discussed can be broadly broken into three categories. ( 1 ) geometrical methods, (2) distance weighting methods, and (3) geostatistical techniques.

Jan 1, 1979

By Marvin P. Barnes

Definition The term mineral inventory is a relatively new designation, born of the computer age and grown to common usage with the development of computer techniques for extending drill-hole sample values to regularly gridded data blocks representing in situ mineral values. The term has been generally accepted by geologists and engineers because it has a precise meaning which avoids many of the ambiguities of ore reserve. A mineral inventory is an estimated inventory of mineral in place and is usually achieved by dividing the deposit into regularly spaced gridded blocks to which are assigned estimated values using various extension techniques. A mineral Inventory makes no presumptions about the minability of the blocks or their cutoff grade. A mineral inventory estimate may be good or poor according to how much is known about the deposit, how extensively it has been sampled, and what techniques have been employed to assign estimated grade to the blocks Such an inventory, however, does not change with time, economic conditions, or mining technology, but only with new and better data and methods. Thus, the mineral Inventory is an excellent designation for describing mineral value distributron within a deposit's geological setting

Jan 1, 1979

By Bruce T. Stanley

A key point in the design and operation of a modern mining operation is the construction of what is called an ore-body model or block model. This model is a representation of reality constructed from predicted information. The blocks involved are merely subsets of the overall model which allows manipulation of the contained information on a local scale. In general, block models enable mine planners to effectively select the most promising means of extracting the ore both physically and economically. The uses of a block model can be quite diversified, but one must realize that a single model that satisfies all curiosities and forms of expertise is difficult to construct.

Jan 1, 1979

By Won C. Park

Experiments showed changes in the mineral content of dolomitic oil shale at temperatures and exposure times which bracket conditions encountered during in situ retorting. Laboratory results correlate with cores from a spent in situ retort at Occidental's Logan Wash test site at Garfield County, Colorado. Dolomite, CaMg(CO3)2, decomposes rapidly to form periclase, MgO, calcite, CaCO3, and CO . Both calcite and periclase are intermediate products that can be stabilized by CO atmosphere at lower temperatures, while steam accelerates the formation 2 of silicates. The decarbonation of calcite appears to involve a direct reaction with both quartz and periclase in forming these silicates. Decarbonation preceeds the formation of akermanite, Ca2 MgSi 207, and diopside, CaMgSi 206, within several hours of heating and is followed by the nucleation of forsterite Mg2SiO4, and monticellite, CaMgSiO4. Under in situ retorting conditions, akermanite and diposide are the major minerals above 800°C. Equilibrium is not attained within 200-300 hours. In situ retorting temperatures above 800°C for extended periods of time should reduce potential ground water leaching by the formation of silicate minerals. These silicates are less soluble than free lime, magnesium or alkali oxides. There is a corresponding decrease in the natural pH of these silicates from approximately 12 down to 7.5 to 9:

Jan 1, 1981

Mineral Changes that Occur During Coal Gasification

Sep 13, 2010

By I. Moreno-Ventas, G. Ríos, J. C. Fernández-Caliani, M. Bacedoni

"This paper delves into the constraints on the nature, origin and thermal evolution of the accretions formed in the uptake shaft of the flash smelting furnace operated by Atlantic Copper in Huelva, Spain, outlining recommended practices for preventing accretion buildup. The accretions were investigated using quantitative electron probe microanalysis, X-ray diffraction and digital imaging techniques, and the experimental data on mineral composition, crystal chemistry and textural relationships were interpreted in terms of thermodynamic phase equilibrium in the SiO2-Fe-O-S system. The results suggest that two distinct types of accretions were formed by the fractional crystallization of two coexisting immiscible melts, under changing conditions of oxygen partial pressure (pO2). The type I accretion of magnetite + delafossite ± cuprite ± tridymite ± metallic copper crystallized from a fractionating copper-rich melt at pO2 above about 10-5 atm, while the type II accretion of magnetite + fayalite + metallic copper + chalcocite derived from a melt with lower copper concentration when pO2 levels dropped below that critical level. Phase compositions and textures were consistent with a cooling history of both compositionally contrasting liquids from about 1,250 °C, the liquidus temperature of magnetite, to eutectic or near-eutectic temperatures of around 1,100 °C. The maintenance of appropriate temperatures — above the liquidus temperature of magnetite — and oxygen partial pressure levels may be critical for the prevention of accretion buildup. IntroductionCopper flash smelting with oxygen-enriched air, an autothermal process developed half a century ago by Outotec (Espoo, Finland), formerly Outokumpu, currently accounts for about 50 percent of the world’s primary sulfide-based copper (Schlesinger et al., 2011). The partial reaction of copper sulfide concentrates produces two separate molten streams, copper-iron-sulfide matte and iron oxide-rich slag, and releases sulfur dioxide (SO2) gas. The matte is sent to converters to remove the remaining iron and sulfur, leaving blister copper with grade of about 99.5 percent copper (Cu), which is cast into anodes for electrolytic refining.The SO2-rich gas generated by the oxidation of sulfide feed particles contains a significant proportion of dust that is entrained in the process off-gas. The gas from smelting is transferred into a waste heat recovery boiler, where it is cleared of dust and cooled before it is converted into sulfuric acid. If the process is not operated properly, the dust-bearing gas may form accretions between the uptake shaft of the flash smelting furnace and the waste heat recovery boiler, causing severe problems in the gas handling system (Swinbourne, Simak and Yazawa, 2002; Miettinen, 2008; Stefanova et al., 2012). Removing the dust accretions usually requires a greal deal of time, effort and resources. Understanding the buildup of accretion may help in reducing the problems and optimizing the process"

Jan 1, 2017

By A Larsson, K Niiranen

The Palaeoproterozoic Leveäniemi iron oxide apatite (IOA) deposit of the so-called Kiruna type is currently mined by Luossavaara-Kiirunavaara AB (publ.), commonly known as LKAB. The mineralogy of iron oxides, ie magnetite, hematite, maghemite, and goethite is more complicated compared to the neighbouring and more famous IOA deposits of Kiirunavaara and Malmberget. Furthermore, the mineral chemistry of the iron oxides in the Leveäniemi deposit is also slightly different. Especially, the information about the deportment of titanium and vanadium in iron oxides and distribution in the deposit is essential since they can have an impact in the steelmaking process. For this study 50 samples were selected from exploration drill cores and investigated by optical microscopy, FE-SEM-EDS and EPMA at LKAB and the Geological Survey of Finland. Investigations revealed that magnetite is the predominant iron oxide mineral with secondary hematite being the second most abundant mineral. Primary hematite, maghemite, and goethite seem to be less abundant. It should be noted, however, that this investigation focused on magnetite which currently is the only mineral with economic value. Vanadium occurs as a substitution element in the crystal lattice of iron oxide minerals in the Leveäniemi deposit and not as discrete stochiometric vanadium minerals. In the investigated samples vanadium concentration in magnetite ranges from 0.12 to 0.32 wt per cent V2O3 with higher concentration in the southern part of the deposit. Contrary, titanium does not substitute for iron in the crystal lattice of magnetite or secondary hematite (less than 0.018 wt per cent TiO2). It either occurs as tiny inclusions of titanium oxide minerals or as exsolution lamellae of ilmenite in magnetite. The spatial distribution for titanium in the deposit, however, remains unknown. Furthermore, results of this study indicate that alteration of primary magnetite to secondary hematite has had no significant effect on the trace element chemistry of these minerals in the Leveäniemi deposit.

Nov 8, 2021