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By P. D. Rao, H. B. Charmbury, D. R. Mitchell

As a result of a changing market pattern for anthracite, there is now an increasing demand for steam size and a decreasing demand for domestic sizes. To help the producer meet this new demand, the authors present the technical aspects of the problem of crushing domestic sizes to steam fineness and size. The market pattern for anthracite coal has changed considerably in recent years. The demand for domestic sizes has been gradually decreasing and the demand for the steam sizes has been increasing. The companies however aim for a maximum production of domestic sizes, since these sizes command premium prices. To meet the market demands, particularly in certain periods of the year, further size reduction of the coarse clean coal is necessary. The present practice of multistage crushing in toothed rolls leads to complicated flow arrangements and is high in cost. Data presented herein indicate that crushers with high reduction ratios could be used with a resulting simplification of crushing flows and an appreciable reduction of capital and operating costs. The different types of crushing equipment investigated included the rotary-type breaker, the jaw crusher, the impactor-type crusher, and the Aerofall mill. CURRENT PRACTICE The standard sizes of anthracite are presented in Table I and market specifications require that any given size be maintained with only a limited amount of oversize and undersize material. The 1958 prices of the various sizes also are presented, so it may be seen that size reduction is only performed when dictated by market demands. At the present time the general practice of crushing anthracite consists of removing the top size and crushing it in a toothed double roll crusher to the next largest size. Consequently, to reduce the domestic egg, stove, and nut sizes to steam sizes of pea, buck, rice, and barley, the original material must be screened to produce the three top sizes and each size must be crushed in three separate rolls to the next largest size. Each crushed product must then be rescreened to remove the oversize for re crush ing. Thus a typical operation would consist of scalping the egg size from a mixture, crushing it to stove size, and rescreening the product. This same cycle would be repeated for the stove and nut sizes requiring three screens and three crushers as well as conveying equipment to handle the crushed products. This results in an expensive series of operations to make a product which sells for a lower price. If the three top sizes are crushed in one operation to the smaller sizes then the yield of steam sizes is low and the production of Nos. 4 and 5 sizes is large. These sizes sell for lower prices than the steam sizes. A typical operation is presented in Fig. 1. From the figure it may be seen that the original cleaned anthracite contains 67.4 pet domestic sizes, 26.4 pct steam sizes, and 6.2 pct fines. After multistage crushing of the domestic to steam sizes the composition of the product is 0.6 pct domestic sizes, 89.6 pct steam sizes, and 9.8 pct fines. From a technical standpoint these results are reasonable but the handling and crushing costs are

Jan 1, 1961

By John F. Abel

"The most conservative persons I ever met are college undergraduates." Woodrow Wilson said that in 1905. No one is saying anything like it today. Chaos on the campus was a cliche of the sixties. Since 1905, education has expanded in every direction. Many more people are being educated for much longer periods of time. The school-leaving age has risen from 14 years to 20 years, on an average. Many are in school until after their 25th birthday. On the surface this situation appears all to the good. Our technical society needs a massive yearly infusion of semitrained (or educated, if you prefer) new blood. The efficiency of our economy and our standard of living are tied to high individual productivity which can be achieved only with an educated work force. Our democratic institutions are said to be founded on an educated electorate.

Jan 1, 1970

By George H. Deike

DURING the past year a survey was conducted by the Committee on the Promotion of Student Interest in Coal Mining to determine whether the program as laid down in past years was operating effectively. It is a source of satisfaction and pleasure to be able to report considerable headway among operating companies in putting cooperative scholarship plans into operation. In previous committee reports the pioneer work along this line by Eugene McAuliffe, president of the Union Pacific Coal Co., has been cited. That Company now has in its employ, in responsible positions, three men who received their education under such scholarship plans. One student under a similar plan is now studying at the Colorado School of Mines.

Jan 1, 1942

By M. A. Scheil

Austenitic stainless alloys are susceptible to stress-corrosion cracking which may occur under certain corrosion environments irrespective of their susceptibility to intergranular corrosion. Test samples are described for investigating stress-corrosion susceptibility of alloys for industrial equipment. A laboratory test using a solution of magnesium chloride boiling at 309 F. was found to produce transgranular cracks in several alloys investigated and in types 347 and 316 stainless steel tubing a residual stress of the order of 10,000 psi. was observed to initiate cracking. The susceptibility to stress-corrosion cracking as judged by the boiling magnesium chloride test indicates that alloys may be selected which will withstand a high stress in service Stressed specimens of stainless alloys included in a corrosion testing program will aid in determining the acceptibility of these fabricated alloys, when stressed, to the service conditions.

Jan 1, 1945

By Frances Hurd

WHEN 60:40 brass is heated to 825° C., given a drastic quench to obtain the beta solid solution, and reheated, various changes take place in the structure. Reheating at 200' C. causes a fine, granular, sorbitic structure to appear which has been considered alpha solid solution. These particles coalesce at higher temperatures of reheating, and at 470° C., the alpha forms twins. A further study of these transformations was considered worth investigating.

Jan 1, 1927

By Samuel S. Wyer

Bethlehem Meeting, February, 1906 THE following abbreviations have been used in the text:¬ Am. MF. and Iron World. American Manufacturer and Iron World, Pittsburg, Pa. Can. Min. Rev. Canadian Mining Review, Ottawa, Can. Cass. Mag. Cassier's Magazine, New York, N. Y. Col. Eng. Colliery Engineer, London, Eng. Col. Guard. Colliery Guardian, London, Eng. Eng. and Min. Jour. Engineering and Mining Journal, New York, N. Y. Eng. News. Engineering News, New York, N. Y. Engr. Engineering, London, Eng. J. I. and S. I. Journal of the Iron and Steel Institute, Lon¬don, Eng. Jour. W Soc. of Engrs. Journal Western Society of Engineers, Chicago, Ill. Lond. Eng. The Engineer, London, Eng. Mines and Min. Mines and Minerals, Scranton, Pa. North of Eng. I. M. E. North of England Institute of Mining Engineers, Newcastle-on-Tyne, England. Oester Zeitsch f. Berg u. Hüt. Oesterrcichische Zeitschrift für Berg. und Hüttenwescn, Vienna, Austria. Pract. Engr. Practical Engineer, London, Eng. Proc. I. C. E. Proceedings Institution of Civil Engineers, London, Eng. Trans. A. I. M. E. Transactions American Institute of Mining Engineers, New York, N. Y. Trans. A. S. M. E. Transactions American Society Mechanical Engineers, New York, N Y Trans. Fed. I. M E. Transactions Federated Institute Mining Engineers, Newcastle-on-Tyne, England. Trans. I M E Transactions Institute Mining Engineers, Newcastle-on-Tyne, England.

Mar 1, 1906

By C. P. Proctor

WESTERN Pennsylvania, eastern Ohio, and Illinois are carrying out experiments wherein much more slate and other impurities are loaded with the coal in the mine and hauled to the surface preparation plant for removal. In general everything is sent to the cleaning plant although there may be some gobbing in the mine. No conclusions have been announced as to the effect of such a mining system on clean coal costs. Such factors as ability of the surface plant to handle the impurities, land and facilities for disposing of the impurities, and the transportation facilities underground should be considered.

Jan 1, 1942

By Emory J. Douglass

Mining companies are unique in that they extract mineral resources and must therefore deal with ecological disturbances and other special problems. Like most enterprises, however, their primary motive must be to make money. The problem of mining investment starts with the question of what "make money" means. This article proposes an answer consistent with what economists call the theory of the firm and then applies it to two of the common, and perhaps unrecognized, problems connected with min¬ing investment. In essence, the concepts presented here call for thinking to terms of the income change associated with a given change it outlays or operating procedures To illustrate. ABC Distributing Co. has just discovered the power of advertising. It has raised its annual advertising budget from $25,000 to $50,000, and sales have, zoomed from 250.000 to 350,000 units. The company buy, for 50e per unit and sells at $l. This move has produced $50,000 of operating income for $25.000 in additional advertising expense. This looks great, so the next year the advertising budget goes up to $100,000. Sales go to 440,000 units. With 90,000 more units at 50[c] per unit, ABC sales are up by $45.000. Its advertising costs, however, went up $50,000.

Jan 1, 1971

By J. R. Long, E. T. Hayes, R. S. Dean, F. S. Wartman

THE production of titanium in 15-1b. lots and with a purity sufficient to be consolidated into ductile metal, as described in a previous paper,1 has provided adequate material for a study of the : physical properties of titanium and a more thorough examination of its working qualities. Data on the physical properties reported in that paper were obtained on metal fabricated by a fixed procedure, standardized for the purpose of control of the reduction, and are representative only of material fabricated under those conditions. There are many possible variables in the working schedule, which will have significant effects on the properties of the finished material; and since the previous working methods were not necessarily the best, an investigation of the fabrication of titanium by other methods was undertaken. In this work the consolidation of the powder by pressing and sintering was conducted essentially as outlined in the report cited' and all efforts were centered on fabrication methods for those powders and the properties produced by them. Hardness, density, microstructure, and tensile properties were determined at various stages in the working and annealing; and resistivity measurements were made on a few bars and drawn wire. [ ] CONSOLIDATION OF THE POWDER The screen analysis of the available titanium powder is given in Table I. No attempt was made to alter the size distribution from that noted because this powder, although coarse by normal powder-metallurgy standards, produced acceptable compacts suitable for the present work. Because of their large specific surface, finer powders are more contaminated by oxygen and produce harder compacts, which are difficult to work. The powder as produced is soft, compresses in a normal fashion, and exhibits very little tendency to adhere to the die surfaces. Unlike aluminum and magnesium powders, it can be readily pressed without the use of die lubricants. When compacted at so tons per

Jan 1, 1946

By Donald A. Dahlstrom

In 1961 it became increasingly more evident that significant technological changes must be made in minerals beneficiation. The status quo in technology in today's competitive markets will not be tolerated. Higher productivity, greater recoveries and newer and better products must be sought and incorporated with lower operating costs. In other words, "when you build a new mill, don't build an old mill." Recommended reading for proof of the vital necessity of new methods and techniques is in the September 1961 issue of MINING ENGINEERING. The article by one of MBD's cherished and true veterans, E. H. Rose, is entitled "Iron Ore: The BIG Picture". Because of new beneficiation methods for iron ores, nearly 47 million tons of plus 60% iron concentrates will be produced and another 40.1 million tons of capacity will be under construction or committed. Thus in a relatively short period, 87 million tons of this high-grade iron concentrate with record low silica will be available. As Mr. Rose also points out, "in gross tons, without allowance for better grade, this is the equivalent of almost exactly two-thirds of all iron ore used for all purposes in the U.S. and Canada in the peak years of 1953 or 1957." Needless to say, improved mineral beneficiation methods have had far more reaching effects than just the production of higher grade iron concentrate.

Jan 2, 1962

By F. N. Rhines, A. S. Nemy

The mode of high-temperature tertiary creep of 523-0 aluminum alloy was found to be strongly stress dependent. The occurrence of necking and/or fissures during tertiary creep exhibited a sequence with varying stress, wherein fissures with no necking occur at a minimum stress and necking with no fissures occur at a maximum stress. At an intermediate stress, tertiary creep begins without necking but with fissures in a region just beneath the external surface, followed by necking and the development of fissures along the axis of the specimen. The results are interpreted in terms of grain boundary gliding and the hydrostatic stresses produced by restraints to grain boundary gliding. THERE appear to be two possible reasons for the existence of a period of accelerating elongation prior to rupture during high-temperature creep in metals; namely, 1) a change in the structure of the metal itself, leading to a change in its response to loading, and 2) a reduction in the cross section of the metal resulting in a higher unit loading. Howe,' by annealing and retesting broken low-temperature creep specimens, found that irreparable damage is done once a metal is subjected to creep. Andrade2 first pointed out the association between the reduction in cross section and the increase in creep rate. The present research was designed to investigate both of these factors by retesting specimens machined from material which had been subjected to high-temperature creep testing short of rupture. EXPERIMENTAL METHOD An aluminum alloy, 52s-0, was selected for these studies because it is constitutionally simple, is strong enough to be relatively insensitive to mechanical damage during machining,3 and undergoes accelerating creep in a convenient temperature range. This alloy is hardened by 2.6 wt pct Mg in solid solution and is not subject to overaging effects; it has a very small quantity of an insoluble impurity phase, Mg2Si, finely dispersed throughout its micro-structure. Creep specimens, similar in design to ASTM 0.252-in. tensile specimens, were machined from 3/4-in. round stock and the surfaces were electro-polished. A 24-hr anneal at 500°C was then applied to stabilize the grain size to an average diameier of 0.27 mm. Subsequent heating for as long as 700 hr at the intended test temperatures produced no change in the tensile properties, indicating a well-stabilized state of the material. Corresponding to each of the typical testing conditions listed in Table I, one creep specimen was tested to destruction and this test was employed as a guide in the selection of times for subsequent tests. Duplicate creep tests were then run to various points along the creep curve to produce specimens which were used to determine changes in mechanical properties and microstructures. The latter were examined at the midsections of the specimens. Other specimens were tested to various stages of tertiary creep, after which they were remachined to new cylindrical test specimens, electropolished and re-tested in creep. RESULTS The major findings of this investigation may be illustrated by a comparison of the results of three sets of creep tests. These were run at 400°C at three stress levels, namely 750, 1000, and 1500 psi. In presenting these results in Figs. 1, 5, and 8, the creep curves are given in pairs: That curve of each pair which is drawn through filled circles corresponds to the initial test, and the curve drawn through open circles (and designated by - R) represents the result of retesting the same specimen after machining to a new cylindrical surface. The load was readjusted to the original unit stress at the beginning of each retest.

Jan 1, 1960

By T. C. Campbell

Copper is extracted from the Chuquicamata oxide ore by a hydro-metallurgical process. The ore is crushed to 3/8-in. sizing, and leached with a sulfuric acid electrolyte. Chlorine is precipitated. and the ferric iron reduced in the enriched electrolyte, after which the copper is recovered by electrolysis with insoluble Chilex and lead-antimony anodes, the spent electrolyte being returned to leaching. Cathodes are melted and refined in market furnaces and cast into commercial wire-bar and cake shapes. Sulfuric acid for the process is supplied by the brochantite in the ore. Water for washing the ore is advanced through the solution system and finally after cutting by electrolysis to from 6 to 16.0 grams per liter is completely stripped by the cuprous chloride method and run to waste. The cuprous chloride so obtained plus that resulting from precipitation of chlorine from strong solution is dissolved in ferrous chloride brine and the copper cemented on scrap iron. The cement so obtained is in part used to reduce ferric iron in electrolyte, and as it is of exceptional purity is also furnace refined and cast into an exceptional quality of fire-refined copper. Fig. 1 is flow sheet of the operation. The reduction plant is composed of seven divisions as follows: (1) crushing, (2) leaching, (3) tailings disposal, (4) dechloridizing, (5) sulfur dioxide treatment, (6) electrolytic tank house, (7) smelting and melting. A brief description of each of these divisions will be given. Crushing Ore that is frequently blocky and up to 5 ft. in section is crushed in four stages to 3/8-in. mesh. The first stage of crushing is called primary and the next three stages are known as secondary crushing. The first stage is accomplished with two 60-in. Superior McCully gyratory breakers by which the ore is broken to 9 in. The second coarse gyratory breakers crush the ore to 3-in. sizing. There are seven No. 10 McCully gyratories in this service, for one of which recently has been substituted a No. 7 cone crusher. The third and fourth stages of crushing are accomplished by fifty 48-in. disk crushers. In the third stage 14 disk crushers break the ore to 1 in., and in the last stage 36 disk crushers turn out the final product of 0.371-in. sizing. Reference to the flow sheets of Figs. 2 and 3

Jan 1, 1934

Escalating energy costs and tough environmental standards were two major factors affecting the minerals processing area in 1978 For the most part, new startups and research and development initiatives were directed toward improving process dynamics, investigating alternative processing strategy, and lowering unit costs. In the flotation area, the trend to larger machines continued. Scientific investigation of the modeling and process control of flotation was apparent, as was the research and development of new flotation reagents.

Jan 5, 1979

By Paul F. Kerr

The uranium-producing areas near Marysvale, Utah provide an unusual group of veins and replacement deposits associated with a Pliocene-Oligocene intrusive and extrusive igneous complex. Aside from several scattered occurrences in older volcanics, uranium-bearing veins occur in intrusive quartz monzonite or granite and in nearby rhyolite. The veins in general trend within a few degrees of N55-65°E, are more or less vertical, and are found along the western margins of a quartz monzonite intrusive. The replacement deposits are found in rhyolite intrusives and also in the lower portions of rhyolite flows close to places where veins forming solutions rising through quartz monzonite came into contact with the rhyolite. At least 14 veins have been mined since uranium mining operations began at Marysvale some 16 years ago, while ore has been extracted through about 10 miles of underground workings. The active mmmg area is approximately 3000 feet long and in the central portion 1500 feet wide. Ores have been found over a vertical spread of almost 2000 feet, between the highest occurrence on Jungfrau Hill ( ca. 7200 feet) and the deepest discovery of ore in a drill hole near the Prospector Mine (ca. 5200 feet). Under existing mining and marketing conditions, mining along the veins in the main area appears to have reached an economic limit at about 500-600 feet below the surface. However, orebodies in the rhyolite and in the upper portions of veins close to the rhyolite are subject to active mining. Isotopic dates indicate that the uraninitebearing veins and replacements are late Miocene or Pliocene (ca. 10-13 m.y.), the rhyolite is Miocene (avg. 17.5 m.y.), and the quartz monzonite and granite intrusives are late Oligocene (23.6 to 26.0 m.y.). The older Bullion Canyon Volcanic Series which encircles the area is Oligocene (28 to 31.1 m.y.). Two generations of alteration occur: ( 1) Earlier alunitic veins and replacement bodies are found in the Bullion Canyon Volcanic Series, none of which have produced uranium; (2) Later argillic alteration associated with the introduction of uranium is found along veins, replacing glassy rhyolite dikes and replacing phases of the rhyolite.

Jan 1, 1968

By Maurice Magee

The Ducktown ore deposits have been known, explored, and mined for 120 years. Eight massive sulfide ore bodies occur in highly folded and metamorphosed graywacke, graywacke conglomerate, mica schist, chloritegarnet schist, and staurolite schist of Precambrian age. The ore deposits are tabular bodies that have been extensively folded, generally conform to the enclosing rocks, but show local complex differences. The ore deposits, ranging in size from 250,000 tons to over 20 million tons, are composed principally of the minerals pyrrhotite, pyrite, chalcopyrite, sphalerite, and magnetite. Gangue minerals are quartz, calcite, actinolite, tremolite, hornblende, garnet, and masses of schistose wall- rock. Three fault systems are present that have influenced ore control and ore body configuration. Hydrothermal effects are evident in wall-rock alteration. Evidence of retrograde metamorphism is extensive in the wall and ore associated rock. Preliminary isotopic age dates have indicated four possible metamorphic events during the Paleozoic Era. Ore genesis is considered to be hydrothermal replacement of receptive beds, predominantly highly calcareous zones, quartzitic zones, and brecciated shear zones. Ore deposition is thought to have occurred during the Devonian Period, with later mobilization and recrystallization of the ore and gangue during Middle and Late Paleozoic times.

Jan 1, 1968

By NEWTON B. KNOX

THE war has forced the principal industrial nations of the' world into the strait jacket of a closely controlled economy; taxes have been heaped upon all enterprises in order to maintain the armed forces and to deprive the people of the ability to bid for goods now unavailable. These restrictions, controls, and taxes are unlikely to disappear entirely after the war has been won, for debts will remain to be paid with a long period of difficult readjustment. Although the new economy will doubtless offer plentiful opportunities for the advantageous use of capital, no investor can ignore the favorable conditions offered by industry in Latin America, where taxes are relatively low and the restrictions on free enterprise comparatively mild. In mining in South America, the great international corporations have

Jan 1, 1944

CHICAGO SECTION CHARLES H. MACDOWELL, Chairman, LUTHER V. RICE, Vice-chairman, HENRY W. NICHOLS, Secretary-Treasurer, Field Museum of Natural History, Chicago, Ill. ALEXANDER K. HAMILTON, G. P. HULST, HENRY P. HOWLAND, FREDERICK T. SNYDER. A meeting of the Chicago Section was held at the Chicago Engineers' Club on the evening of March 30, 1918, on the occasion of the visit of the President, Vice-president. and Secretary of the Institute. The meeting was called to order by Henry W. Nichols, Secretary of the Chicago Section. The first speaker of the evening was Mr. Allen, Deputy Fuel Administrator for the State: of Illinois, who spoke on the problems and difficulties encountered by the Fuel Administration during the past -winter, He paid high tribute to the spirit of cooperation shown by the

Jan 5, 1918

By J. E. Strassner

Oilfield emulsions are stabilized primarily by film-forming asphaltenes and resins containing organic acids and bases. Adding inorganic acids and bases radically changes the physical properties of these films and their emulsion-stabilizing properties. Interfacial films show one of three different physical characteristics when retracted in pendent drop tests. These compressed films have rigid, soap-type or minimum film properties depending on the quantity of asphaltenes and resins in the crude oil and on the pH and composition of the brine. There exists for each crude oil-brine system an optimum pH range over which the adsorbed film exhibits minimum contracted filtn properties. In this range, intmfacial tension is high — frequently near its maximum value — indicating the absence of highly surface-active specier; crude oil-brine emulsions generally show minimum stability; and surfactant requirements for breaking these emulsions are significantly reduced — sometimes no surfactant is needed. About two-thirds of the world's crude oil is produced as emulsions that must be treated (demulsified) to be marketed.' Approximately three-fourths of all domestic crude oil produced must be treated. The percentage of crude requiring treatment increases as fields become older and more water is produced. Demulsification most frequently is attained through use of surfactants, heat and electric treaters. It is estimated that over 75 percent of all oilfield emulsions are broken by chemicals generally containing alkylene oxide condensates. Although acids and bases are known to affect emulsion stability:-' they rarely are used in the oil field except in batch treatment of the most severe emulsions. Nevertheless, pH adjustment by using acids or bases in demulsification has some advantages over other methods. Mainly, it is cheaper. Acids and bases frequently are cheaper to use than surfactants, or can appreciably reduce the amount of surfactant required for demulsification. Secondary advantages are that less oil is lost by emulsi-fication into the aqueous phase, and that less corrosion is encountered when the optimum pH is basic. Limitations to the use of pH include (1) use in brines containing high concentrations of reactive ions, (2) closer supervision for pH control than is required for surfactants and (3) need for corrosion protection when the optimum pH is sufficiently acidic. These factors indicate that the economics of pH con trol in demulsification will be maximized when relatively large treating facilities are needed, when relatively large surfactant concentrations are required to break an emulsion, when a relatively low concentration of the aqueous phase is emulsified in the oil and when the emulsified aqueous phase contains relatively low concentrations of reactive ions. Because there are no broad guide lines for using pH control in breaking oillield emulsions (and because the limited guides available are highly specific and frequently contradictory), this paper will attempt to clarify the principles involved in using acids and bases to break emulsions. These principles also should be useful in refinery separations and in other oilfield applications where stable or unstable petroleum emulsions are involved. Principles of Emulsion Stability Oilfield emulsions generally occur as water droplets dispersed in oil (w/o) and occasionally as oil droplets in water (o/w). These emulsion droplets are usually in the 0.1- to 10-micron range. However, more coarsely dispersed water droplets frequently are present in the emulsion. Pure hydrocarbons and water will not form stable emulsii except in extreme dilutions where the large distance brtween droplets inhibits coalescence. An emulsion breaks because interfacial tension acts to minimize the surface area of the dispersed drops by coalescence. However, emulsions can be stablized for long periods of time by the presence of a third phase that adsorbs at the oil-water interface and inhibits coalescence of the dispersed phase."' Emulsions generally are stabilized by (1) repulsive charges on the surfaces of the dispersed phase and (2) adsorbed films that, being preferentially wetted by the continuous phase, act as a physical barrier to inhibit contact between the dispersed droplets. Both these factors generally are important in stabilizing and in breaking o/w emulsions. However, repulsive charges are less effective in stabilizing w/o emulsions which generally are stabilized by adsorbed films.V or this reason the nature and importance of these films at oil-water interfaces were examined closely; as will be shown, pH changes were found to affect the films significantly, and this work led to laboratory tests of pH- adjustment in emulsion breaking. This paper will present evidence to show that emulsions are stabilized primarily by films that form around droplets

Jan 1, 1969

(Members are urged to send in for this column any notes of interest concerning themselves or their fellow-members.) Members and guests who registered at Institute headquarters during the period Feb. 10 to Mar. 10, 1915: W. R. Van Liew, Batoum, Russia. Edward S. Jones, Scranton, Pa. Olof Wenstrom, Boston, Mass. Scott Turner, Tromso, Norway. D. G. Miller, Denver, Colo. A. H. Boyd, Denver, Colo. E. E. Olcott, New York, N. Y. M. M. Thompson, Morsemere, N. J. Francis R. Pyne, Elizabeth, N. J. F. C. Merry, Brooklyn, N. Y. Charles W. Goodale, Butte, Mont. Charles A. Filteau has been appointed General Manager for the Inca Mining & Development Co., Province of Carabaya, Department of Puno, Peru. Charles T. Kruse has been appointed Superintendent of the Jones & r, Loughlin mines in the Marquette and Menominee ranges.

Jan 4, 1915

By R. W. Heckel, R. A. Tanzilli

Treatment of the finite, diffusion-controlled, two-phase, moving-interface homogenization problem has been carried out by numerical methods for a wide range of input parameters. Solutions have been obtained for planar, cylindrical, and spherical diffusion geometries. The effects of parameters such as the interdiffusion coefficients (concentration-independent) of- both phases, the concentrations (time-independent) of each phase at the interlace, mean composition, initial size of the dissolving- phase, and initial composition of- the two phases are considered. The results are displayed to show both the position of the interjace and the degree of homogenization (expressed in terms of concentration at the matrix phase symmetry boundary) as a function of diffusion time. Typical exaw~ples to which the results may be applied are discussed. A limited number of exact, closed-form solutions to the multiphase, diffusion-controlled, moving-interface problem exists in the literature, e.g., Refs. 1 to 7. The exact, closed-form solutions generally consider the outermost phases to be infinite in extent and also assume an interfacial velocity function. It is through use of such boundary conditions that closed-form solutions are readily obtained. An extensive literature also exists on numerical solutions to the mathematically analogous solidification problem, e.g., Refs. 8 to 12. In addition, a numerical solution involving mass transfer with spherical interfaces and infinite boundaries has recently been carried out.13 A practically important class of diffusion problems exists, however, in which the boundaries of each phase away from the interface are finite. For example the finite boundary condition arises when one sets up a model for analyzing the homogenization behavior of two-component powder compacts in two-phase systems or for studying the solution behavior of precipitates. Although exact, closed-form solutions have as yet not been found to this class of problems, solutions are possible using numerical methods. The purpose of this paper is twofold: 1) to describe a numerical method for treating the two-phase, diffusion-controlled, moving-interface problem involving finite boundaries with planar, cylindrical, and spherical interfaces; 2) to present the results of a parametric study which identifies the role played by each variable appearing in the analytical model. R. A. TANZlLLI,Student MemberAIME,onleaveofabsence from the General Electric Co., Re-entry Systems Department and A. W. HECKEL, Member AIME, are Graduate Student in Materials Engineering, and Professor, Department of Metallurgical Engineering, respectively, Drexel Institute of Technology, Philadelphia, Pa. Manuscript submitted May 6. 1968. IMD MATHEMATICAL MODEL The three geometries analyzed are shown in Fig. 1. For each configuration a symmetry element is shown, across whose boundaries the mass transfer is zero. Mean composition, C, and the characteristic solute-rich phase half-thickness (or radius), 1/2, are the independent variables while the characteristic symmetry element half-thickness, L/2 (measured from solute-rich phase center to the matrix phase plane of zero mass transfer), is a dependent variable. The symmetry element for a planar interface accurately represents a real diffusion situation involving the stacking of symmetry elements of constant size. Because cylindrical and spherical symmetry elements of constant size cannot be stacked to fill space, the meaning of the dimension, L/2, for these situations may be considered in terms of the following approximations: and where NA is the number of parallel cylindrical elements per unit area on a surface normal to the cylinder axes and Nv is the number of spherical elements per unit volume. The model consists of a solute-rich phase matrix phase composite of limited mutual solubility. The concentrations at the interface are assumed constant with time; no assumption of local equilibrium at the interface is necessary except for the case where the

Jan 1, 1969