Search Documents

By R. J. Charles

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

Jan 1, 1958

By W. P. Rawles

In the foreword by C. K. Leith, Chairman of The Mineral Inquiry, it is pointed out that the ordinary mineral production tables do not show the commercial control, and that some knowledge of the situation is desirable as a background for the consideration of problems involving mineral raw materials. The report consists principally of tables, accompanied by a brief text, giving the production and an analysis of the control, according to nationality, of 18 minerals: aluminum, chromite, copper, iron and steel, lead, manganese ore, mercury, molybdenum, nickel, nitrates, petroleum, potash, silver, sulfur, tin, tungsten, vanadium, and zinc. For the most part, the production figures for 1929 and the latest figures for reserves have been used. When feasible, the control has been shown at the various stages of production; mining, smelting and refining. American capital was dominant in the production of 10 mineral commodities, including six of the most important; British capital, in four instances; while Spanish, German, Chilean or Chinese interests cach led in the control of one. British, French, German, and Dutch capital occupied second place in the control of most of the important minerals. Between two-thirds and three-fourths of the world&apos;s mincral production is controlled by British and American capital.

Jan 1, 1934

By J. C. Fisher

C. S. Smith has described a method for measuring the relative values of different solid-solid and solid-liquid interfacial tensi0ns. When a polyphase alloy is held at an elevated temperature, individual particles of each phase adjust their shapes and minimize the interfacial energy. Wherever three interfaces meet, the dihedral angles are such that the three interfacial tensions, considered as forces, are in equilibrium. When the angles between three forces in equilibrium at a point are known, it is possible to determine any two in terms of the third. In this way ratios of interfacial tensions have been .obtained. The value of a given interfacial tension ratio was found to be independent of the alloy system from which it was determined. Smith also has employed the method when one of the phases is liquid. When equilibrium is reached with respect to In the course of work on grain growth in high purity aluminum a simple optical method was developed for detecting the presence or absence of preferred orientation in annealed specimens. The specimens were prepared by grinding, polishing and "deep etching." The etching reagent used for high purity aluminum has been described.* The resulting etch pits produced selective

Jan 1, 1949

By N. B. Hoffman

Much of the drill steel produced in America is manufactured into hollow rods. After all forging has been finished the entire bar should be thoroughly annealed and heat treated before the point is hardened and tempered, at least where the drill has heavy duty, such as working in deep holes and hard rock. A large number of tools of like character and doing work requiring similar properties are now being made of alloy steels; for instance a steel with a carbon content of 0.75 to 0.85 per cent., manganese 0.25 to 0.35, phosphorus under 0.020, sulfur under 0.030 and vanadium 0.18 to 0.23 has proved very satisfactory for chisels. A steel of this type properly manufactured will be far superior to the ordinary carbon steels, while at the same time is one whose price range should not prove prohibitive. Much of the cutting efficiency of a drill depends on proper heat treatment. This vanadium steel has a far greater safe hardening and forging range than ordinary carbon steels, making it more nearly foolproof. It will harden nicely at 1400" I?. but will also harden well and satisfactorily at 1550" F. retaining its quality of hardness and toughness in either case.

Jan 1, 1922

By F. C. Blake

THE test of the English cupellation furnace should be so supported that the cupeller can change readily the elevation of the test, and at the same time watch the litharge channel. It is also important to raise or lower either side, independently of the other, in me of uneven wear of the side walls or of the breast. If the refined silver is poured from the test, it is much better to control the lowering of the test from the front than to raise the back by screws or a lever. In order to enable the cupeller to manipulate the test with one hand, when the litharge is running, and to pour the refined silver from the test without aid, I have altered the common support to the test, as shown in the accompanying drawing. The common method of supporting the test is by four screws, working in cross-bar nuts beneath the test. The points of the screws set, into the test plate upon which the test rests. These screws are usually worked by pounding or pulling upon the heads, which may be either small pulleys or straight bars, as shown on the back screws in the drawing. The screws are also worked by turning a crank, which is

Jan 1, 1882

By W. L. Freyberger

In a study of the kinetics of flotation of coal, employing a single-cell continuous flotation system, Jowett and Safvi1 pointed out that it was experimentally impossible to float all of the coal which could be floated in a batch tests. On the other hand, deBruyn and Modi, in a discussion of their paper, suggested that under certain conditions the recovery of floatable material from a similar one-cell continuous system would have been 100%.2 Both of these pairs of authors make the assumption that a state of perfect mixing exist in the flotation cell. This assumption, usually made by investigators studying flotation kinetics in a continuous system, has been confirmed experimentally on several occasions. The work is summarized by Arbiter and Harris.3 It is the purpose of this note to demonstrate that, for conditions of perfect mixing, one of two conditions exist: 1) the recovery of floatable material is 100%, and the flotation is infinitely fast, or 2) the recovery of floatable material must be less than 100%. This theorem can be proved simply in the following manner: 1) If recovery, R, of the floatable material is 100%, the concentration in the tailing must be zero. This follows from the definition of recovery as

Jan 1, 1964

By John V. Beall

W hen the blasts went off on West 11th St., just off 5th Ave. in New York City, James Michaels, editor of Forbes magazine, was in his office a few doors away reviewing color layouts with his production manager. Having once been a reporter, he grabbed his trench coat and dashed for the street to be con- fronted by the demolished townhouse which had been turned into a bomb factory by youths. To Michaels, this shocking episode supplied the exclamation point to thoughts he was formulating that an era had ended and a new one was beginning in the economic and social climate of the U. S. "For twenty years corporate profits, the stock market, middle income pay have gone up and up. . . The illusions of twenty years are in confrontation today with changed needs," he said. "International omnipotence is economically beyond our means, . . The anti-pollution and community renewal people are not nuts in tennis shoes who will go away. . . That corporation presidents can report an increase in earnings every year is an illusion that will be dropped. . . There has been a $200 billion shrink in value of stocks and bonds since Nixon came into office" were some indicators Michaels mentioned.

Jan 1, 1970

By F. C. Blake

THE test of the English Cupellation furnace should be so supported that the cupeller can change readily the elevation of the test, and at the same time watch the litharge channel. It is also important to raise or lower either side, independently of the other, in case of uneven wear of the side walls or of the breast. If the refined silver is poured from the test, it is much better to control the lowering of the test from the front than to raise the back by screws or a lever. In order to. enable the cupeller to manipulate the test with one hand, when the litharge is running, and to pour the refined silver from the test without aid, I have altered the common support to the .test, as shown in the accompanying drawing. The common method of supporting the test is by four screws, working in cross-bar nuts beneath the test. The points of the screws set into the test plate upon which the test rests. These screws are usually worked by pounding or pulling upon the heads, which may be either small pulleys or straight bars, as shown on the back screws in the drawing. The screws are also worked by turning a crank, which is

Jan 1, 1882

By Maximo Monte-Flores

A PERUSAL of the most recent literature on the subject of hydrocarbons reveals that one point seems, to have been neglected by the various theories; that is, the influence of the bed-rock on the accumulation and distribution of oil and gas. This can be seen from the following statement of the principles of the most accepted theories. ANTICLINAL THEORY The anticlinal theory claims that the accumulation of the hydro-carbons in deposits of commercial importance was brought about by the gravity of the hydrocarbons, the oil and gas being forced to the top of the porous stratum by the difference of the specific gravity of the hydro-carbons and the water. The principal factors toward the accumulation were the general stratigraphic condition of the rocks, their texture and porosity, and their water content. This theory advocated the preexistence of structural deformation as the basis of the motion of gravity, thus implying the principle that the forces that have caused the deformation have had no influence on the movement of the hydrocarbons. STRUCTURAL THEORY According to the structural theory, the accumulation is due, chiefly, to the structure of the subsurface rocks and differs from the anticlinal theory, mainly, in not considering that the motion of the liquids have been caused by the force of gravity.

Jan 1, 1920

By Chu-Phay Yap

This is the first of a series of theoretical papers on the iron-carbon system. A simple critical analysis of the ordinary constitution diagram of the iron-carbon system yields valuable information regarding the nature of the equilibria in the liquid and solid states. It is shown, for example, that the solute in the melt is Fe3C, but in solid Fe (austenite) the solute is carbon. The thermodynamic laws of the depression in the freezing point of solid solutions have been developed and discussed. Using the usual method of plotting the logarithm value of the concentration of the solvent (in this case, the ratio of concentrations of the solvent in the liquid and solid phases) against 1/T, curves are obtained. A rigorous thermodynamic analysis of these curves has been shown to yield considerable information regarding the internal equilibria of the system, with which the phase rule does not deal altogether. In this way, it is shown again that the solute in the melt is Fe3C, but in the solid rFe the solute is carbon. Various heats of reaction (fusion and transition) and other thermal data have been derived: and discussed with a view to correlating the conflicting experimental data obtained by different investigators of the system.

Jan 1, 1931

By Robert E. Tally

The ore reserves of the United Verde Copper Co. in 1907 were estimated at 4,500,000 tons, averaging about 7 per cent copper. Seventy-five per cent of this tonnage was confined to the so-called fire stopes and the remainder was virgin ore. The fire area was being operated at a maximum capacity of 150 tons per day, and the other workings furnished the remainder of the ore, approximately 600 tons per day. The mine was developed to a depth of 900 ft. and the lower levels were considered lean and unpromising. The smelter had been built directly over the ore-bodies. Its site was congested, the ground was settling and maintenance costs were excessive. The major needs of the United Verde obviously were 1. Additional ore reserves. 2. A new and modern smeltery. 3. A method for the mining of the fire-stope ores commensurate with the tonnage and values involved. It is the method specified in point, 3 with which this paper is chiefly concerned. Such a method required the removal of the old smelter, and additional ore reserves were essential not only for the maintenance of production but for the investment necessary for the building of a new smelter.

Jan 1, 1932

By M. C. Fuerstenau

Each year during the AIME Annual Meeting, the MBD Division has its Business Meeting. Because many members cannot attend, it has be- come policy for the secretary of the Division to present highlights of the business conducted at the Meeting in Fine Grind. This year the Meeting was held on March 1 in the Americana Hotel. Five major items of business were brought up for discussion. These were: (1) the proposed name change for the Division, (2) institution of the Taggart Award, (3) a name change for a Unit Committee, (4) MBD funding of scholarships, and (5) authorship of Fine Grind articles. The Matter of What We Should Call Ourselves A lively discussion was held on the issue of a name change for the Division. Two names have been proposed: (1) Mineral Processing Division, and (2) Mineral Engineering Division. A number of strong reasons for changing the name from Minerals Beneficiation Division have been pointed out. Perhaps the most important of these is that the term "beneficiation" does not describe all of the functions that engineers in our Division perform. Further, there are inherent problems associated in the term, in that beneficiation is a long word which has the twofold disadvantage of being both difficult to pronounce and difficult to spell.

Jan 1, 1971

ARTHUR KNAPP, Ardmore, Pa. (communication to the Secretary*). -The author has failed to consider the point which in my mind is the most convincing in advocating some sort of a bureau for the collection of well logs. I venture to say that 90 per cent. of the logs as taken today are absolutely worthless to any one but the one who has taken the log. This is largely due to the careless use of nomenclature. The author says on page 289, "He must ascertain which of the many factors might account for the dry hole in question and often only careful examination of well logs will convey this information." I believe that even a most careful examination of the average log reveals nothing. I have at hand a book on petroleum, by a well-known author. This book has a number of logs from fields all over the world, from which I shall illustrate. In a well log from Kansas I find "Soft gray shale" and in one from Humble I find "Hard blue shale." As a matter of fact the shale from Humble is softer than the shale from the Kansas well. The difference is that the drillers in Kansas, being used to limestone and

Jan 5, 1917

By John V. Beall

It is difficult to understand why they did it. It was a demonstration of total commitment which sent chills of mixed admiration and fear up and down your spine. The scene was the bodega in Section A, 2660 Level on the 12 to 8 shift. The jefe was patiently waiting for the tea leaves to settle in a large metal cup. His attention was distracted by the appearance of a miner who had a problem. The long and short of it was that the miner believed the branch raise he was driving was unsafe and he wanted the jefe to come and see it. After lunch the jefe went around. First cautiously shining his light to peer up the raise from outside the chute, he then scrambled inside and swiftly climbed the cribs to the face. No question, it was hairy; about 4 crib sets were needed to catch up to the face. The unsupported raise was slabbing. It didn&apos;t take the jefe more than a few seconds to ascertain this situation and to slide back down. As he came out of the chute, a small avalanche arrived on his heels and provided a sort of exclamation point to his order; "cerrado!" In other words, shut &apos;er down.

Jan 1, 1970

By F. H. Buchella

When Duval Sulphur & Potash Co. awarded pre- mining stripping and early mining at Esperanza to an independent contractor, it was agreed that monthly payments for excavation were to be made on a truck count. At six-month intervals, however, adjustments must be made on the basis of actual excavation or cut from the pit area. It was estimated that it would be three times more expensive to have the pit sectioned by chain and transit survey than to use photogrammetry, since it would take two crews of three men approximately two weeks to do the field work, another two weeks to plot the sections, and additional time to establish a control network. Therefore it was agreed to have the mine area mapped by photogrammetry for both the premined surface and for semi-annual check surveys necessary for intermediate settlements. A triangulation net was established with a maximum distance of 900 ft between control points. In about 30 working days a two-man survey crew, using a theodolite, set up and triangulated 30 stations and calculated their results. For ease in spotting on the photographs, control stations were marked on the ground with white-painted tires centered over the survey pins.

Jan 6, 1960

MELTING in a hearth and in a basket is almost the same thing; charcoal and bellows are used for both. These are made large or small according to the quantity that you wish to melt, and more or less force of the bellows is applied according to the need. The hearth, bowl, or refinery, as the masters call it, is made with bricks and clay like a forge; opposite the middle of the tuyère a round hole is made like a wash- basin, wide at the mouth and narrow at the bottom where there is a hole for emptying it. A little iron plug is put in this so that it may be closed when necessary, or a piece of brick that is cut and pointed. Now, when this has been well covered all over with ashes, and the tuyère has been arranged so that the wind strikes the center, it is first filled with charcoal and baked very well so that the metal may be kept hot once it has been melted. When it has been baked, it is again filled with charcoal, fire is applied, and it is left to inflame gradually by itself. Then put one or

Jan 1, 1942

By C. Jackson, J. J. Harrington

The pH control system at Kennecott Copper Corporation&apos;s Nevada Mines Division concentrator consists of two independent systems, lime dilution and lime addition. Lime dilution is accomplished in a mixing tank where slaked lime and water are introduced proportionately. The desired dilution of the milk of lime is determined by the electrical inputs provided by eight pH probes, one per grinding section. The inputs are averaged and applied to a time base generator. The summation output of the time base generator determines the proportion of lime and water that are to be mixed and applies this input to a voltage sensitive switching device. The switching device provides a signal to one of two relays which will add either slaked lime or water, dependent upon the summation output. The entire cycle is based on a 2-min repetition rate to allow for sufficient mix time. Responsivity is controlled by maintaing a limited maximum solution level in the mix tank. Lime addition is controlled independently within each grinding section. The electrical input from the pH probe in a given section controls the solenoid valves which provide lime to each of the ball mills. The valves remain open within a time range capable of maintaining the pH of flotation feed at a given set point.

Jan 1, 1978

(Butte Meeting, August, 1913.) IN metallurgical circle it is. known widely, but somewhat vaguely, that the ease of reduction of metallic .oxides. depends largely on the way they have been prepared. It is likewise known that. different forms of carbon have different and greatly varying reducing powers. It is the purpose of, this paper to show somewhat more definitely and scientifically these facts. Sonic years ago the writer published an account of pyrometric determinations of the reduction temperature of zinc oxides variously prepared and of several kinds.1 In said paper it was shown that the temperature at which zinc oxide evolves zinc according to the equation, ZnO+C? Zn+CO depends upon the nature of -the two reacting bodies. The determinations bad a range of accuracy of from 2°to 6°C.,whereas differences were found to, amount to an extreme of 90° C. So the differences are real ones and must have a definite cause. The equation of boiling water, (H2 O)4 = 4 (H20) has a fixed temperature for? equilibrium of 100° C. at 760 mm. pressure. In general, all equations reacting in the liquid or the gaseous phase have well-defined constant physical conditions which govern the equilibrium point and reaction velocities.

Jan 7, 1913

By G. K. Burgess

§ 22. THe results published in Professor Howe&apos;s paper10 of our determinations on the Ac3 and Ar3 points for a series of commercial carbon steels " containing manganese in varying proportion, represent the average temperatures found by taking several (4 or 5) heating and cooling curves. The accompanying curves, Figs. 6 and 7, are, for each steel, the first heating and cooling curves as obtained by the inverse-rate method of Osmond, using a cylindrical chronograph sensitive to 0.1 sec. for recording time. Simultaneous observations were also taken by the differential method with a platinum neutral and plotted by Rosenhain&apos;s derived differential method and gave substantially the same results, the curves having sensibly the same contours in both cases.12 The observations were taken in vacuo on cylinders 5 by 1 in. in length bored to center with a 1/8-in. hole to receive porcelain insulated thermo-couple, and inclosed in an out- and in-glazed Berlin porcelain tube heated electrically by platinum foil wound on the tube. The vacuum was usually better than 0.1 mm. The heating and cooling of the furnace was automatically controlled by a salt-water rheostat with shaped electrodes, giving a uniform rate of heating and cooling.

Jan 1, 1914

By R. Schuhmann, J. Th. Overbeek, P. L. De Bruyn

THE technique of concentrating valuable minerals from lean ores by flotation depends upon the creation of a finite contact angle at the three-phase contact, mineral-water-air. If the mineral is completely wetted by the water phase, contact angle zero, there is no tendency for air bubbles to attach themselves to the mineral. However, when the contact angle is finite, the surface free energy of the system, water-air bubble-mineral particle, can be diminished by contact between the bubble and the particle, and if not too heavy the mineral will be levitated in the froth. With a few exceptions, all clean minerals are completely wetted by pure water. Thus the art of flotation consists in adding substances to the water to make a finite contact angle with the mineral to be floated, but to leave the other minerals with a zero contact angle. The contact angle concept and experimental measurements of contact angles have played important roles in flotation research for several decades.&apos;-" Nevertheless, there remain unanswered some basic questions as to the scientific significance of the contact angle and the nature of the processes by which flotation reagents affect contact angles. The contact angle is a complex quantity because the properties of three different phases, or rather of three different interfaces, control its magnitude. Considering the interfaces close to the region of ternary contact to be plane, the relation among the contact angle and the three binary interfacial tensions is easily derived. The condition for equilibrium among the three surface tensions, Fig. 1, or the requirement of minimum total surface free energy leads to Young&apos;s equation, Eq. I: ysa — ysl = yLA cos 0 [1] According to this equation, the contact angle has one well-defined value. Actually it is found in many experiments that the value of the contact angle depends on whether the air is replacing liquid over the solid (receding angle) or the liquid is replacing air (advancing angle). The receding angle is always the smaller of the two.4 Two explanations have been offered for this experimental fact. According to some investigators,5-8 roughness of the surface causes apparent contact angles that are different for the receding and the advancing cases although the actual local contact angle may be completely determined by Eq. 1. The other explanation involves the hypothesis that the solid-air interface after the liquid has just receded is different from the same interface when no liquid has previously covered it.1,4 Adsorption of constituents of the air or liquid might play a role here. In this discussion the difference between advancing and receding contact angle will be neglected and plane surfaces where Eq. 1 describes the situation will be considered. But there is still a fundamental obstacle to the application of Young&apos;s equation. The surface tension of the liquid (rla) can easily be determined, but the two surface tensions of the solid (rsa and ySL) cannot be measured directly. Eq. 1, however, is not without value. By contact angle measurements it is possible to establish how ysl — ysl varies with the addition of solutes to the liquid phase. Also, Eq. 1 affords a convenient starting point for calculating net forces and energy changes involved in the process of bubble-particle attachment.1,2 . If for the moment surface tension of the liquid (yLa) is considered a constant, an increase in ysa — ysL, will tend to decrease the contact angle. A decrease in ySA — ysl, corresponds to an increase of the contact angle. In cases where ySA — ySL > yLa the contact angle is zero; it will only reach finite values when ysa — ysa has been decreased below YLA. Thus on the basis of Young&apos;s equation and contact angle measurements alone, it can be learned how flotation reagents affect the difference Ysa — ysl, but no conclusions can be drawn as to the effects of reagents on the individual surface tensions ysa, and ysL, not even as to signs or directions of the surface tension changes resulting from reagent additions. A quantitative relationship between the surface tension or interfacial tension and the adsorption occurring at a surface or an interface is given by the Gibbs equation, which for constant temperature and pressure reads dy = — 2 T, du, [2] where dy is the infinitesimal change in surface tension accompanying a change in chemical potential

Jan 1, 1955