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By A. H. Tousley

Current problems in the cement industry are discussed and suggestions for solving them by modernization are made. Cement facility modernization is discussed in considerable detail with examples illustrating before and after conditions. Itemized are the improvements realized in better working conditions, better efficiency, higher production, lower costs, and better community relations. These improvements are related to the overall profitability of the particular plant or facility.

Jan 1, 1972

By F. W. Bowdish

Analysis of data on the equilibrium exchange of sodium ions from salt solutions for calcium ions, from various fractions of an oxidized calcareous iron ore from Lorraine, France, strongly suggests that the calcium may be attached to the solid by only one of its bonds. Nearly equal values were found for the equilibrium expression from data covering concentration ranges of 1000 fold for the salt and 235 fold for the ion-exchangeable calcium. Differences indicated between the exchangeable calcium contents of the slime and the sandy portions of the ore, as well as the equilibrium relationship itself, are of importance in the flotation of the ore. During an experimental program on the flotation of oxidized calcareous iron ores from Lorraine, France, ion-exchangeable calcium was found in the ore. Because this source of calcium ions, if not controlled, could thwart all efforts at flotation, an extensive study was made of the phenomenon. The part of that study reported here was to obtain data on the equilibrium established between ore solids and solutions of sodium chloride, and to analyze the data to try to understand better the physical chemistry of the exchange. The ore contains oolites of goethite and quartz grains embedded in a matrix consisting of calcite and a brown cement believed to be the residue from oxidation of the silicate minerals found in fresh unoxidized ore. When ground, a substantial fraction of the ore becomes a fine slime in which is concentrated more than half of the alumina content of the ore. It is believed that the alumina occurs as unidentified clay minerals with which most of the ion-exchange capacity of the ore is associated. A preliminary experiment on the exchange of ions from the ore for sodium ions from solutions of NaCl showed that calcium was about ten times as abundant as magnesium in the exchange solutions. Thus calcium was the predominant ion in causing difficulties with flotation, and it was the only one for which data was obtained in this study. It is believed that the omission of magnesium ion exchange from consideration does not invalidate the results. It is possible, however, that inclusion of magnesium in the analyses and calculations or its prior elimination from the samples would have improved the consistency of the results. EXPERIMENTAL Data about the equilibrium exchange of sodium from solutions for calcium from the solids were obtained using two different samples of material. The solids

Jan 1, 1963

NEW MEMBERS. The following list comprises the names of those persons who became members during the month of April, 1913: BARNES, BLAKESLEE, Min. Engr Burrwood, La. BOYLSTON, HERBERT M., Cons. Met. Engr 26 Abbot Bldg., Cambridge, Mass. BUEHLER, HENRY A., State Geol Rolla, Mo. CASTO, WILLIAM H., JR., Mining Bonanza, Idaho. COHEN, MAXWELL B., Mill Operator Miami, Ariz. EVANS, MILTON R., Shop Draftsman 92 Division St., Kingston, Pa. HARPER, WALTER S., Asst. Treas 42 Broadway, New York, N. Y. JAMES. JAMES S.. Min. Engr Telluride. Colo.

Jan 5, 1913

By G. S. Baker, S. H. Carpenter

Langenecker has reported significant reduction in strength of high-strength metals during ultrasonic t'ibration. Decreases in static yield stress an order of magnitude greater than the calculated stress amplitude of vibrations were reported by him for a stainless steel and for tungsten. in the present work, attempts were nzadc to verify such large reductions in yield and flats stresses using resonant librations of measured amplitudes. The results show that both the soft metals (copper and aluminum) and the high-strength metals (sleels) hare reductions in yield and .flow stresses no larger than the stress amplitude of libration. BLAHA and Langenecker,' investigating the effect of vibratory stresses on the deformation of zinc and aluminum, found a decrease in the static yield and flow stresses approximately equal to the vibratory stress imposed. Langenecker later extending this work to high-strength metals such as stainless steels and tungsten2 found a much larger effect. In these metals the static yield and flow stresses decreased by an amount more than an order of magnitude greater than the calculated vibratory stresses. It was suggested that this phenomenon could be a serious hazard to high-strength structures in an acoustic environment, such as a large rocket at launch, or could be used advantageously in the working of hard-to-work materials such as the refractory metals. Langenecker and others3 have investigated the effect of high-amplitude vibrations on many metal-forming operations. The results have been quite favorable with usually a large decrease in the energy necessary for the forming operation. The processes, however, involve large frictional forces and it is not clear whether the decreases in forming forces are to be ascribed to decreased friction or to decreased flow stresses. The present paper reports an attempt to determine the effect of accurately known vibratory stresses on the static yield and flow stresses. I) EXPERIMENTAL TECHNIQUE The standard multicomponent resonator technique for measuring internal friction has been adapted to allow simultaneous high-amplitude vibration, internal-friction measurement, and tensile deformation. This has been described in detail elsewhere.4 Longitudinal oscillations of approximately 50 kc frequency are excited in a multicomponent resonator by a quartz transducer. A second transducer measures the amplitude of vibrations. Fig. 1 shows a schematic drawing of the resonator and grip arrangement and the displacement pattern produced. Since the centers of the dummy bars are at displacement nodes, they represent points where attachments will not materially affect the vibrations. The force is applied by a standard Instron tester. The sample may be deformed while simultaneously vibrating at up to 104 strain amplitude. 11) EXPERIMENTAL RESULTS The effect of high-amplitude vibrations on the yield and flow stresses of copper. aluminum, tantalum. a soft iron, and a stainless steel has been measured. In addition samples of tungsten vibrating at stress levels up to 10' dynes per sq cm have been subjected to static stresses near the static yield stress with no indication of macroscopic deformation. Fig. 2 gives typical results for 99.999 pct polycrys-talline copper. A vibratory stress of 7 x 107 dynes per sq cm is applied at points "a" and removed at points "h". The behavior of aluminum is identical. In agree-

Jan 1, 1967

By R. A., Pallanch

SO many variations of lead-zinc ores occur in nature that it is impossible to state any rules that will apply to the concentration of ores of this type. Some have lead and zinc in approximately equal amounts; others may have pre- dominant amounts of one or the other metal. There are gradations from all sulfide to completely oxidized minerals. Some such ores carry little pyrite, others contain much more pyrite than they do lead and zinc combined. The behavior of ores in flotation is largely a function of their lead-zinc ratios. their content of pyrite or pyrhotite, the nature of existing soluble salt conditions, the character of the gangue constituents: and the speed with which the minerals float. For the purposes of this paper only those lead-zinc ores handled commonly in present-day flotation practice will be considered. These are practically all-sulfide ores with relatively minor degrees of sulphatization or oxidation.

Jan 1, 1936

By L. W. Pommier, F. B. Brien, A. K. Bhasin

In the field of mineral processing, although many operations are applied to suspensions of ore particles in fluids, there is a lack of fundamental knowledge relative to the flow resistance encountered by immersed bodies moving through solid-liquid suspensions. Previously proposed equations, based on the Ostwald-de Waele (power-law) model for non-Newtonian fluids, are exam ined in the turbulent flow region relative to a number of pertinent variables and their effects on the movement of immersed bodies. As more knowledge is acquired in regard to the effects of suspension variables on the rheological properties, useful relationships may be proposed to allow predictions of conditions to achieve optimum results for engineering purposes. In the field of minerals processing, many operations are applied to suspensions of ore particles in fluids. The differential movement of solids of various sizes and densities in suspensions is of utmost importance to gravity concentration, wet classification, flotation, hydrometallurgy, and pipeline transport of solids. The subject is also of importance to other branches of engineering; for example, those involved with soil mechanics, ceramic slips, and oil-well drilling fluids. There is a lack of fundamental knowledge relative to the flow resistance encountered by immersed bodies moving through solid-liquid suspensions. The problems encountered in the direct application of the well-known Stokes and Newton's Laws to non-Newtonian systems have been examined in a previous paper.' Equations were proposed based on the Ostwald-de Waele (power-law) model for non-Newtonian fluids. This present paper examines these equations in the turbulent flow region relative to a number of pertinent variables and their effects on the movement of immersed bodies. It is thought that, as more knowledge is acquired as to the effects of suspension variables on the rheological properties, useful relationships may be proposed to allow prediction of conditions to achieve optimum results for engineering purposes. The purpose of this paper is to make an initial assessment of the nature and magnitude of pertinent suspension variables. In order to avoid too voluminous a document, the examination of kinetics and mechanisms will be omitted at this time. THEORY A Newtonian fluid is defined as a fluid in which the stress is proportional to the rate of strain, 2 i.e.: H = viscosity; see Table I. for list of symbols The following equations are conventionally used to assess the motion of spherical particles moving under laminar and turbulent flow conditions through Newtonian fluids: When these relationships are applied in practice to suspensions, the liquid density is substituted by a composite suspension density, and viscosity is usually taken as that of the suspending liquid or an approximated "apparent viscosity." However, suspensions are non-Newtonian in character3 and thus, more than one viscosity parameter is required to describe their behavior. A number of models have been proposed for non-Newtonian fluids;2,4 among these the simplest is the Ostwaldde Waele or power-law model for incompressible fluids which for one dimensional flow may be reduced to:

Jan 1, 1970

By Thomas, J. Elmer

WHEN the price of crude oil was advanced on July 26, 1928, with some 4,000,000 bbl. daily of potential production shut in under proration regulations, and with as much more new production shortly available from semi-proved undrilled reserves, students of the oil industry were made to realize that a new order of things now prevailed in petroleum economics. A new interpretation of the law of supply and demand had taken the place of the archaic method of influencing current production by changing crude price levels. Proration had caused the change. The long period of over-production just experienced, the prospects of a potential over-supply far into the future, had set up certain forces which brought about some fundamental changes. Their cause, effect and future influence can best be developed by a detailed study of the history of the period since war-time regulation

Jan 1, 1928

By L. E. Fish, G. S. Wyman

CHUQUICAMATA open-pit mine is capable of producing a total of 105,000 tons daily. When the sulphide plant is operating to capacity the distribution of this quantity will be approximately 30,000 tons sulphide ore, 30,000 tons oxide ore and 45,000 tons of waste. At that time the combined capacity of the oxide and sulphide plants will be about 540 million lb of copper per year. Twenty one benches have been opened to date and all are still active except the three top ones at the northeastern limit of the pit. These have been pushed back to final slope line. The pit is 8850 ft long, 3540 ft wide and 980 ft deep. Benches are not all developed to a standard height as the large development shovels used in cutting new benches have been of different size and range. At this time new benches 521 ft high are being developed with an' 11-yd shovel. Ore haulage through the greater part of the pit operation has been on down grades to the crushing plant. With the opening of bench F-4 in April 1944 the first adverse-grade ore haul was encountered. Of the total tonnage now being mined, 35 pct comes from the four benches that are below the level of the crushing plant yard. Waste had been dumped on the same or nearly the same level as the bench from which it was removed up to the opening of bench F-4. Waste from this and lower levels is hauled to the level of the crusher, yard where it must cross the flow of ore traffic to reach the only available dumping space to the east of the mine. The average ore haul is 3.13 miles one way shovel to crusher, and the average waste haul from that portion handled by railroad is 3.32 miles one way from shovel to waste dump. Waste that is being removed by truck haulage from the upper part of the -mine is hauled an average of 1 mile. Ore loaded by trucks is hauled 3/4 mile to a car loading ramp and then by rail to the crushing plant. Drilling and Blasting There are two types of development for blasting being used: One for opening new benches and the other for bank shooting. The former consists of 9a in. diam churn-drill holes drilled 11.8 ft center to center in rows 10.2 ft apart with the holes staggered in the rows thus giving an equilateral-triangle pattern of 11.8 ft on a side. After the first block, 492 ft long by 71.5 ft wide, is shot in the pattern described above, the cut is advanced by smaller shots consisting of four rows of holes spaced 23 ft center to center with the rows 23 ft apart. These shots are fired in conjunction with side shots in which the holes are drilled 33 ft center to center and 29.5 ft back from the toe, thus squaring up the bank for subsequent shooting. An average bank shot consists of about 60 holes drilled in two rows parallel to the face, 30 holes to

Jan 1, 1952

By S. S. Hsieh, J. R. Lehr

Bench scale beneficiation studies were made on Idaho dolomitic phosphate rock using the TVA carbonate flotation process. The process used diphosphonic acid as a phosphate mineral depressant and fatty acid as a carbonate mineral collector. Silica was subsequently rejected as float using an amine collector, with phosphate product recovered as the sink fraction. Two samples of prepared flotation feed from commercial operation were used. One contained 21% P205 and 3.2% MgO. The other contained 26% P205 and 1.8% MgO. The results indicate that concentrates containing 31% to 33% P205 and 1% or less MgO can be obtained, with about 80% P205 recovery.

Jan 1, 1986

By A. T. Miesch, L. B. Riley

Distribution of minor elements in sandstone-type uranium deposits of the Colorado Plateau is being studied by the USGS on behalf of the A EC. A primary objective has been to provide basic data which could be useful in geo-chemical exploration for new deposits. The basic statistical measures — similar to those used in sedimentary petrology—are described. The underlying principle is that the frequency distributions fit or approach the log-normal form. Since 1952 the U. S. Geological Survey on behalf of the U. S. Atomic Energy Commission has conducted a study of the distribution of minor elements in sands tone-type uranium deposits of the Colorado Plateau. A primary objective in this study has been to provide basic data which could be useful in geo-chemical exploration for new deposits. Among the basic data considered important are estimates of the abundance and habit of each element in the ore and in the host rocks. It has been found that a few basic statistical techniques, and variations of these techniques, are useful in this type of study. Some of the basic techniques have been used to advantage by researchers in geochemistry and in other fields of geology, especially sedimentary petrology; others have been used to only a limited extent. Among the latter is the linear correlation coefficient, which has proved useful in assessing the element associations in a particular rock type without analysing individual mineral separates. In computing the basic statistical measures a scale has been used which is, in some ways, similar to the phi ($) scale used by sedimentary petrol-ogists in grain-size studies.' FREQUENCY DISTRIBUTIONS It has been recognized for some time that the results of analyses for a given minor element in a suite of samples of rocks or ores yield frequency distribution curves which are approximately normal when the curves are plotted on logarithmic or geometric scales. In other words, the analytical results give an approximate lognormal frequency distribution. A classical example is given by D. G. Krige2 in the study of the distribution of gold values from a mine on the Witwatersrand. Another example is shown in Fig. 1, the distribution of barium concentrations in samples of uranium ore from the Chinle formation. The geochemical data are analogous to grain-size data gathered by the sedimentary petrologist. Both types of data, after simple logarithmic transformations, may be treated by conventional statistical methods based on the normal distribution. This is not to say that other types of transformations may not serve equally well or better for particular element distributions.3 Spectrographers and other analysts are quite aware of the dependence of their precision on the concentration of the element present.4 For example, in the part per million range the variation may

Jan 1, 1961

By T. A. Rickard

"The chief aim in style ought to be absolute precision", said Flaubert. "There is only one noun that can express your idea, only one verb that can set that idea in motion, and only one adjective that is the proper epithet for that noun." Let this be your motto. The engineer tries to be exact in all his measurements; he should measure his language with similar exactness. The technical term is a word of precision. It is not only precise, it is a word-saver. To the unscientific the earth is "a ball slightly flattened at the poles, something like an orange". To the scientific it is "an oblate spheroid". A similar contrast between the precision of the technical term and the vagueness of common words is afforded by a conversation between Ivanhoe and Rebecca: "' What device does he bear on his shield?' asked Ivanhoe. 'Something resembling a bar of iron, and a padlock painted blue on a black shield.' 'A fetterlock and shacklebolt azure', said Ivanhoe "-using the technical terms of heraldry. It is good style in writing, however, to adapt your manner of expression to the intelligence and experience of the person or persons to whom the writing is addressed. The description of a mine should be worded differently according as it is intended to inform a mining engineer, a director, or a bishop. REMEMBER THE READER. It is as incorrect to write in a technical way for a non-technical reader as to write in a popular way for a technical or scientific reader. That style is best which enables the writer to place himself in the closest mental touch with his reader, to establish the maximum of sympathetic understanding. Let your precision be\ proportioned to your accuracy. You should not try to be precise in matters that do not admit of

Jan 1, 1931

AN announcement of the annual meeting to be held in New York, Feb. 14 to 17 inclusive is being mailed to all members. Particular attention is called to the necessity of asking for certificates when you purchase your ticket in order that all may secure reduced return fares.

Jan 1, 1927

By BARONJUPTNER VON JONSTORFF, Andrew A. Blair, GUNNAR DILLNER

IT is a well-known fact that the results of different analysts, when operating on the same identical sample of steel or iron, are far from concordant, and it not infrequently happens that great annoyance and trouble in the commercial community are occasioned by these discrepancies. Attempts have been made at various times to investigate the causes of such differences and to obtain more reliable methods of analysis. The most important of these was made by the British Association in 1889: The following gentlemen, with Sir W. Roberts-Austen as Chairman, and Professor T. Turner as Secretary, were constituted as a committee to investigate the question, viz.: Sir F. A. Abel, Mr. Edward Riley, Mr. G. J. Snelus, Mr. John Spiller, Professor J. W. Langley, and Professor Tilden. Average .samples of steel were prepared in America under the superintendence of Professor J. W. Langley. The steels, in the form of turnings, were divided and distributed to sub-committees in Great Britain, America, France, Germany, and Sweden. In Sweden Professor Åkerman acted as Secretary to the Swedish committee. The Government Department of Tests was appointed in Germany; Mr. Ferd. Gautier in France; the British Association Committee in England; Messrs. William

Mar 1, 1905

By Herbert H. Kellogg

The chemistry of sulfide roasting is analyzed to show those aspects of performance which Thecan be predicted from considerations of thermodynamic equilibrium. It is concluded that equilibrium calculations can serve as a yardstick for prediction of roaster-gas composition and sulfate formation in the calcine for fluid-bed roasting practice. A method of calculation which combines the equilibrium and stoichiometric factors is outlined, and illustrated by an example from the roasting of Cu-Fe sulfides. ON first examination the roasting of sulfides would not seem to be a process to which equilibrium calculations could be applied to yield results of practical value. The burning of sulfides is an ex-tremely spontaneous reaction, excess air is always used to obtain rapid reaction, and in most traditional roaster designs (hearth roasting) the temperature and gas composition vary widely from point to point in the roaster. These are all conditions which promote a non-equilibrium state in the roasting process. However, the introduction of the fluid-bed roaster1 has brought to roasting practice new conditions of operation, so that equilibrium calculations can be used to predict certain limited aspects of practical operation. The fluid bed is characterized by uniformity of temperature, gas composition, and calcine composition from point to point throughout the bed. These relatively uniform properties of the bed make the meaningful calculation of the equilibrium state of certain reactions in roasting possible. It is the purpose of this paper to analyze roasting from an equilibrium viewpoint, to show where the method may be expected to yield valuable information, where it fails, and to outline methods of calculation. Main Roasting Reaction The reaction MS (s) + 3/2 0, = MO (s) + SO, [I] might well be called the main roasting reaction. It adequately accounts for the well known facts that metal sulfide and air are the main reactants, and metal oxide and SO, the main products. Deviations from this simple stoichiometry will be discussed under side reactions. For all metal sulfides, Reaction 1 is strongly exothermic and the equilibrium position is far to the right. Since the reaction is exothermic, the equilibrium shifts in the right-to-left direction as the temperature is raised. However, at all practical roaster temperatures (between 500" and 1200°C), the amount of this shift is small, and the equilibrium position remains far to the right. The main roasting reaction is essentially irreversible, and the application of equilibrium considerations to this reaction will not be! a fruitful field of investigation. A knowledge of the rate of this reaction. although not the proper subject of this paper, is of great importance to the roasting process. Analysis of the factors which influence this rate shows that: 1) The rate will increase rapidly with increased temperature. 2) The rate will be proportional to the partial pressure of oxygen at the surface of the reacting particle. Because of diffusion effects, the partial pressure of oxygen at the particle surface may be considerably less than in the bulk of the roaster gas. For this reason, intimate contact between gas and solid and high relative velocity between gas and solid, such as can be obtained in a fluid bed or flash roaster, will markedly increase the rate of reaction. 3) The rate will be proportional to the surface area of metal sulfide. Therefore, smaller particle size will permit a more rapid rate per unit of weight. To achieve practical rates of roasting the partial pressure of oxygen in the roaster gases must be maintained at a finite level at all times. Even where the gas-solid contact is very good, as in the fluid-bed roaster, the oxygen content of the gas must not be allowed to drop below some limiting value (perhaps 1 pct), or the rate of the main roasting reaction will become too small for practical operation. Side Reactions in the Gas Phase The gas phase during roasting of metallic sulfides contains the elements oxygen, sulfur, nitrogen, by-

Jan 1, 1957

By D. W. Fuerstenau

In 1940 Schuhmann1 showed that the size distribution of a comminuted material can be expressed by the following empirical relationship: y = 100 (|f [i] where y is the cumulative percentage of material finer than size x, k is a size modulus, and a is a distribution modulus which is constant for a given material and machine. During the past few years, considerable emphasis has been given to the investigation of the extent of size reduction resulting from the expenditure of mechanical energy in crushing and grinding. Recently Schuhmann' presented a derivation of the energy-size reduction relationship by postulating that comminution in a device such as a ball mill can be considered to be the summation of many single comminution events, each of which yields a size distribution of particles following the Schuhmann size distribution equation. By grinding

Jan 1, 1961

By Sherwin F. Kelly

SINCE we used Chief Buehler's name last year to give our annual report a semblance of respectability, we can follow the good precedent thus established by telling of the work his Missouri State organization has been carrying on, as reported by H. S. McQueen. Considerable value is set upon their magrletorneter working which has covered over 13,000 sq. mi.), for the indications it gives of the major structural features of the region. Numerous geological problems have been tackled Ly resistivity techniques, among which are the locating and outlining of filled sink deposits of sulphides, of iron ore, and of fire clay; tracing of faults and solution channels; mapping of the preglacial structural pattern; measurement of depth of overburden; and

Jan 1, 1937

By Carroll Forbes

INTRODUCTION MANY different shapes of drill bits are in use with hammer drills, but little definite information is available whereby to judge which one of these shapes is the best. The following investigation was undertaken in order to determine what effect, if any, the shape of the cutting edge has on the cutting speed and wearing qualities of drill bits. The bits tested were those in common use, namely, the 4-point or cross bit, the 6-point bit, the Z bit and the "Carr" bit. The rock in which the tests were made was the red granite from southeast Missouri. It is a coarse crystalline granite containing an unusually large amount of quartz and is extremely hard, and on account of its uniform texture is admirably adapted to this work. While tests in other rocks might show somewhat different results, nevertheless it is the opinion of the authors that the relative cutting quality inherent in the shape of the bits would be the same in all rocks. Other qualities, such as mudding freely, freedom from fitchering, etc., might make one bit more desirable than another in softer rocks. DESCRIPTION OF BITS TESTED The 4-point bits were the usual shaped bits commonly made on the Leyner sharpener with 14° taper on the wings and a 90° angle between cutting edges. Some tests were run at 85 lb. pressure with a 4-point bit made with a 5° taper on the wings. This was made by using the Carr bit die. The 6-point bits were the usual shaped hits made on, the Leyner sharpener. The Carr bits were made with a 5° taper and an angle of 100° between cutting edges.

Jan 8, 1917

By John A. Mathews

D R. CHARLES W. ELIOT, the great educator and philosopher-he of the five-foot book shelf-recently gave expression to a thought I had long been cherishing as a private opinion, when he said: "It is obvious that standardization has become a dangerous adversary of progress in both education and industry." This idea must have been more widespread than either of us knew, for some five years ago a writer of verse for one of the comic papers dealt with it at great length. I will quote only a few of his stanzas to illustrate his understanding of "A Standardized Existence" : A visitor at large, I stand Beneath a standard sky- Where everything is standardized To please the standard eye. Each tree is of a standard height, Each building is the same; Each man is uniform in height, And has a standard name. Above there is a standard star Beside a standard cloud, And a standard weather here prevails To please a standard crowd. With standard joy, and standard gain, The standard people live; And if there is one bit of pain T?is such as standards give.

Jan 1, 1926

By R. A. Wood, R. I. Jaffee, H. R. Ogden, D. N. Williams

Strain-induced porosity has been found to occur in titanium and other materials at tensile strains greater than the uniform elongation of the material. Porosity in titanium increases with increasing strain and temperature, being most severe at 300° to 800°F. Strain-induced porosity is believed to be a normal part of the mechanism of deformation in ductile materials. DURING the past few years there have been numerous references to the occurrence of voids in laboratory test specimens of metals subjected to strain.l-7 These voids have been referred to as intercrystalline cracking, strain-induced porosity, intergranular cav-itation, voids, and porosity. They appear to occur at grain boundaries or interfaces, and are generally associated with large amounts of strain and have been found mostly in creep specimens and to a lesser extent in tensile specimens. Because the phenomenon does not occur unless the material has been strained,

Jan 1, 1960

By C. C. Harris

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

Jan 1, 1969