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By G. C. Wallick, W. R. Foster, J. G. Savins

Inasmuch as the differentiation and integration methods represent different modes of rheological analyses, a dual scheme of analysis using both methods should lead to a generalized method of data analysis. A dual differentiation-integmtion method of analysis is applied here to the Poiseuille flow of a variety of ideal Generalized Newtonian and viscoplastic models. Using machine-processing techniques, the result is a spectrum of response patterns which are expressed in terms of certain derivative functions. It is shown that these characteristic functions form the basis of a highly-sensitive analytic technique for optimizing the selection of the most appropriate functional relationship between shear rate and shearing stress. INTRODUCTION In the first paper of this series, Savins, Wallick and Foster1 presented an historical review of the salient features of the differentiation method of rheological analysis in Poiseuille flow, and also indicated how the method could be applied to problems involving plane Poiseuille flow. It was shown that the differentiation and integration methods, although basically not incompatible, do represent different modes of rheological analysis. This suggests that valuable background information regarding the probable response characteristics of real data obtained with the differentiation method can be obtained from an integration method-differentiation method analysis of the response of a variety of ideal rheological models. The present paper describes how this dual method of analysis has been applied to suites of idealized models representing a wide variety of Generalized Newtonian and viscoplastic behavior which have received attention at various places in the literature.

BIRINGUCCIO was born in Siena in 1480, the son of Paolo and Lucrezia di Bartolommeo Biringuccio.* He was baptized on October 20 of that year with the given names Vannoccio Vincenzio Austino Luca. His father appears to have been an architect, for in 1504 he was paid 600 scudi for his work on the walls of the Communal Palace and at the same time he was superintendent of streets for the city. The course of Biringuccio's life followed closely the checkered fortunes of the Petrucci family of Siena. A warm supporter of Pandolfo Petrucci, Biringuccio did not falter in his allegiance to the family and their party during his lifetime. It was probably to the protection and patronage of this lord that he was indebted for the opportunity to travel widely through Italy and into Germany during his early years and so to lay the foundation for the extensive knowledge of the subjects he was to describe in the Pirotechnia. In 1507, as he himself indicates (p. 48), he was 'in Friuli and. Carnia in northern Italy after having traveled in Germany,, and he also visited the, brass, works in Milan. After returning to Siena; he was sent by Pandolfo to direct the iron mines in near-by Boccheggiano. When Pandolfo died in 1512 (in which year Biringuccio's s father also died), Biringuccio continued to support the Petrucci family in the person of Pandolfo's son, Borghese, who succeeded, to the rule. Under his patronage, Biringuccio was appointed to a post in: the Armoury of the Siena Commune in 1513. In ISIS a popular uprising forced Borghese and his followers, including Biringuccio, to flee from Siena. Biringuccio and the goldsmith Francesco Castori, head of the mint, were accused of having debased the coinage alloy with the knowledge and consent of Borghese. When he failed to appear in 1516 to answer these charges-which may well have been invented by the opposing political faction-Biringuccio was declared a rebel and was exiled as a traitor to the Republic. He then traveled about Italy, was in Rome and Naples, and visited Sicily in 1517.

Jan 1, 1942

By R. J. Schaefer, M. E. Glicksman

Direct, in situ observation of metallic alloys during solidification reveals that in some systems crystal multiplication occurs by means of a dendrite remelt-ing process, without the necessity of independent nu-cleation events. The solidification is observed on optically clean surfaces of supercooled molten alloys. In one system (Sn-3 wt pct Bi) , a fine-grained equi-axed structure is produced by the complete disintegration, via remelting, of transient initial dendrites. In contrast, several other metallic systems show little or no evidence of remelting activity. The behavior of these metallic systems is consistent with that expected on the basis of published observations of dendrite remelting in transparent organic alloy systems. It is concluded that dendrite remelting is an important crystal multiplication process in some metallic alloys, but is velatively unimportant in some other alloys. The detachment of dendrite branches from the primary stem by a remelting process has been observed by Jackson, Hunt, Uhlmann, and seward1 during the solidification of some transparent organic alloy systems. The branches released by this remelting process can drift free of the primary stem and serve as seeds for the formation of numerous independent crystals. This proliferation of new crystals does not require repeated independent nucleation events, but only modification of the initial solidification structure. The mechanism of dendrite remelting, as described by Jackson et a1.1 and by Tiller and O''Hara,2 is dependent on the transport of both heat and solute and is, therefore, expected to operate only in alloys, and not in pure substances. It was found in the transparent organic alloy systems that remelting occurred primarily in the constricted regions near the base of dendrite branches, where the branches had grown through the solute-rich liquid layer surrounding the primary dendrite stem. It was suggested that impure solid had formed in these constricted regions at a relatively low temperature and had later become unstable as further solidification of purer material raised the temperature. Jackson et al. proposed that the equiaxed zone of metal alloy castings originates from a similar remelting process, and they demonstrated the operation of this mechanism in "ingots" poured from saturated salt solutions. Although these substances were especially selected to show solidification behavior similar to that of metals,3 the remelting mechanism has, until now, been subject to the objection that its operation has not been directly observed in a metallic system. Considering the fact that thermal properties such as diffusivity may differ by as much as two or three orders of magnitude between metals and organic compounds, this objection was considered to be possibly serious. A method has now been developed by which it is possible to make direct optical observations of metals during solidification. This method has revealed transient solidification processes which would not be detected by metallographic examination of totally solidified specimens. In particular, a grain-refinement process in a metallic alloy has been observed to be a direct consequence of the total disintegration of an initial dendritic structure. The influence of an initial, transient solidification structure on the final solidification structure is demonstrated here for the first time in a metallic system. I) EXPERIMENTAL The technique of using a transparent flux to maintain an optically clean metal surface during solidification has been described by us elsewhere.* The

Jan 1, 1968

By J. C. Martin

Stmplified equations are developed for the flow of fluids in gas drive reservoirs in which the effects of gravity can be neglected. The results show that the pressure distribution is governed by a nonlinear heat flow type of equation, and the saturation distributions are related to the pressure by the same equations QS those developed by Muskat for the average pressure and saturations in gas drive reservoirs. Unrler certain conditions the equation for the pressure can be approximated by the linear form of the heat flow equatlon. This equation tk analogous to the equation for the pressure in single-phase compressible flow The analysis reveals that the equation for the pressure in n~ultiphase flows can be obtained directly from the equation for the pressure in slngle-phase flows by simply replacing the single-phase compressibility by the total compressibility and the single-phase mobility by the sum of the mobilities of all the fluids present. Perrine's method of pressure buildup analysis for multiphme flows is based on these same substitutions. Thus, the development presented in this paper constitutes a theoretical justification for Perrine's method of pressure buildup analysis. One of the most difficult problems associated with the production of oil is the determination of the flow of the fluids within the reservoirs. One purpose of this paper is to present the development of simplified equations for the flow in gas drive reservoirs. The other purpose is to present some of the needed theoretical foundation for the methods currently being used in the analysis of multiphase pressure buildup data. The analysis presented in this paper makes use of a partial linearization of the equations governing multiphase flows. It is felt that the process of linearizing or partially linearizing the nonlinear equations of multiphase flows can lead to useful results since this process has proved extremely valuable in the study of other fields of science and engineering where nonlinear equations are encountered. Pressure buildup data of shut-in wells have been used for many years to estimate the static reservoir pressure. These data have also been used in studying the aver- age permeability both away from and close to the well-bores. The majority of the buildup data are obtained from wells producing two or three fluids. As yet the theoretical foundations for the methods of buildup analysis used in connection with rnultiphase buildup data have not been established. A number of methods of analysis of pressure buildup data have been developed." Most of these methods apply only to single-phase flows, and almost all of the theoretical analysis is confined to single-phase flows. Perrine' developed a method of analysis for rnultiphase flows from the method for single-phase flows of Miller, Dyes, and Hutchinson.' He did this by simply replacing the single-phase compressibility by the multiphase compressibility and replacing the single-phase mobility by the sum of the mobilities of the fluids in the rnultiphase flows. Obviously, such a procedure lacks a certain amount of theoretical justification, and such practices can lead to erroneous results. Fortunately, Perrine's results have a theoretical justification, and this justification is presented in the following discussion. It is assumed that gravitational effects and the cornpressibility of the rock can be neglected. Under these assumptions the equations governing the simultaneous flow of gas, oil and water in porous media areo* The preceding equations can be expanded into the following expressions.

By Moshe Sheinkin, Burke O. Trafton

This paper describes the use of a computer in analyzing the expected return on a mining venture. The computer program is designed to incorporate all aspects of a mining project, including the mine, mill, smelter, and refinery. Data input may consist of the operating variables in each phase such as the mining rate, grades, reserves at the mine, and the technical operating characteristics of the mine, mill, smelter, and refinery. Detailed tax computations are shown for a domestic operating company, for a foreign company and for a foreign subsidiary. In addition, the use of the various options that are available such as expense write-offs or deferments to create tax credits during preproduction years are considered, and its effect on the DCF. The program is also constructed to accommodate changes in metal prices, and escalation of capital requirements and operating costs. Output consists of profit and loss statements for entire projects using different methods of depreciation, cash flows, discounted cash flows, net present value and returns on investment. Returns on investment are computed for equity investment, total investment, and total investment less tax credits. Allowances are made for bank and guaranteed loans. Additional financial statements can be made for the following: a) A mine-mill segment with a concentrate selling schedule b) A mine-mill-smelter complex with a smelter product selling schedule c) Profitability of the smelter separately d) Profitability of the refinery separately

Jan 1, 1969

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Jan 1, 1907

By J. D. Prater, H. R. Spedden, E. E. Malouf

With the expansion of copper leaching of the various mine wastes at the Kennecott properties, additional copper recovery facilities have been required. A research and development program has been pursued to determine a suitable economic approach to the processing of the additional leach solutions contemplated. lnvestigations on laboratory and pilot plant scales covered electrowinning, solvent extraction, launder and vat type cells, activated launders, precipitation drums, and precipitation cones. This paper contains information on the development and use of a new precipitation-cone-type copper recovery plant, which provides many advantages over older systems. The application of research findings to the old art of leaching copper from copper-bearing mine waste has resulted in a significant contribution of copper to over-all copper production. For example, at the completion of the current expansion program at the Kennecott properties in the United States, copper produced from waste dump leaching will amount to about 25% of the total production. Formerly only 2% was derived from this source. This planned expansion of copper leaching focused attention on the problem of developing more efficient methods for the recovery of copper from greatly increased volumes of copper-bearing solutions.1 The detailed investigations which have been made in laboratory pilot plant and plant tests for the recovery of copper from copper-bearing solutions have included electrowinning, solvent extraction, ion exchange and cementation with iron in launders, precipitation drums, activated launders, and precipitation cones. The results of these investigations have led to the development of a new precipitation cone-type copper recovery system providing many advantages over older methods. ELECTROWINNING OF COPPER FROM COPPER-BEARING SOLUTIONS The direct electrowinning of copper from relatively dilute solutions of copper-bearing mine water, namely solutions containing 10 to 20 lbs of copper per 1000 gal, has always been an attractive possibility.2,3 By this method, high-purity copper powder can be recovered with a power consumption of 3.5 kwh per Ib of copper. However, once the solution strength de-

Jan 1, 1967

In the General Alphabetical and Analytical Index of A I M E Publications for the years 1926 through 1935, a complete list of the volumes covered is printed on page 5, but the dates of publication of the volumes are not given Therefore the following information regarding the volumes that were printed without numbers may be useful to users of the Index

Jan 1, 1937

By Edward L. Beutner, Robert M. Crump

Benson Mines low-grade iron ore reserve is a replacement deposit within the Grenville gneisses of the Adirondacks. The average grade of the crude ore is about 23 per cent iron. The iron minerals are principally magnetite and hematite disseminated throughout the gneisses as discrete grains about 1 mm in size. Both the ores that are beneficiated by magnetic means and the non-magnetic ores that are treated by a gravity method of concentration are found in stratigraphically different positions but are mined from one open pit, which is about 2.5 miles long and 800 feet wide and are treated separately. The gneisses are described and named according to the distinctive mineralogy of each. Recognition of the gneissic types permits the interpretation of the structure as a northward-plunging syncline overturned to the west. A large subsidiary anticline-syncline complex occurs on the east limb of the major syncline. Iron minerals in sufficient quantity to be considered ore are confined to areas where the footwall rock has been overturned to become the hanging wall.

Jan 1, 1968

By R. A. Deju, R. B. Bhappu

The theory of electrophoresis is briefly outlined and an apparatus which may be used for electrophoretic studies is explained. The results obtained using this apparatus are in agreement with those obtained by other investigators. How to solve some of the complications which occur in the measurement of zero charge and zeta potential is explained. It is believed that the apparatus described in this paper will allow rapid measurements of zeta potential, zero point of charge, electrophoretic mobility and zeta coefficient. For many years the phenomenon of electrophoresis has been studied, and much work has been done in designing an apparatus for better measurements of mobility, zeta potential and zero charge of minerals. Up to the present, most electrophoresis experiments have involved cumbersome equipment and tedious microscopic observation. The modified cell proposed in this paper obviates these drawbacks by using a Rayoscope together with a special system of lenses and filters. It therefore allows a faster and more accurate measurement of zero charge and particle velocity. THEORY Most authors currently regard zeta potential as the potential difference in an otherwise uniform medium between a point some large distance from the surface of the mineral and a point on the plane of shear. Fuerstenau,1 Miaw,2 and Gaudin and sun3 have performed some calculations of zeta potential using Henry's equation.4 Their results show wide discrepancies, probably due to differences in the past histories of the minerals used. The authors have also noticed this difference on determining the zero point of charge of quartz as shown on Table I.

Jan 1, 1967

Jan 1, 1929

By R. M. Caitlin

QUITE a number of years ago in looking for basic facts, it seemed obvious, in view of an unquestion-able supply of raw material and an extensive requirement probable in the near future, that the funda-mental requirement of any shale-oil industry was mass production 'by a continuous process. This decision greatly simplified matters, as it eliminated all considera-tion of externally-heated retorts, and all batch processes, which only utilize a part of the capacity of the interior space because, unless the ashes are removed as rapidly as formed, the space occupied by them is dead, instead of being occupied either by shale in active distillation or in drying out and heating up preparatory thereto. A second imperative and basic necessity soon appeared as a natural sequence, namely, the fixed carbon of the spent shale must be utilized to supply the heat for the eduction of the oil. PRODUCTION OF THE CRUDE As the production of the crude oil is the first and most important step in the utilization of oil-shale, being the only source from which the multitude of possible by-products can come, each by a special treatment of the crude oil, I will devote the time allotted to me to the subject of crude oil production-its cost expressed in terms of tons treated per man per shift. The costs of mining the shale and refining the crude shale oil vary with local conditions and are not specially influenced by the source of the crude. But the cost of distilling the shale in terms of tons per man shift seems to be the basis of any proper comparison of costs. After considerable experimenting, ranging from laboratory tests up to and including quantities of fifteen to twenty tons, it was evident that a plant might be made up of an indefinite number of units operating in concert. The economic size of the units, however, would .have to be determined by experiment. The general theory of our process contemplates a regulated combus-tion of the fixed carbon in the spent shale, in its incan-descent condition after all the oil has been driven out of it; and a transfer of the resultant heat to the mass of raw shale above.

Jan 1, 1927

By Richard H. Olson, Lawrence A. Roe

Talc, when it can be isolated as a pure mineral, has a composition of 63.36% Si02, 31.89% MgO, and 4.75% H20. However, as an industrial commodity, talc rarely approaches theoretical purity. Nevertheless, the impure talc products of commerce find a multitude of uses and few substitutes in many industrial applications. Minerals commonly associated with and sold together in talcose mixtures are tremolite, chlorite, dolomite, mica, and magnesite. Steatite was originally a mineralogical name applied to pure talc. In today's commerce steatite generally refers to the massive variety of talc suitable for electrical insulator manufacture. Block steatite ore can be machined into various shapes. Impure varieties of massive or block talc are still commonly referred to as soapstone. Soft massive talc, suitable for crayon manufacture, has been referred to as French chalk. It has been common practice to discuss talc, soapstone, and pyrophyllite under the same general heading. In the case of soapstone and talc, this is a natural thing since many different types of platy, soft minerals exhibiting a high degree of lubricity (commonly referred to as "slip") have been grouped together and called soapstone or talc. Further, there is a mineralogical relationship of pyrophyllite to montmorillonite and talc to hectorite. Thus, talc and pyrophyllite are sometimes referred to as clay minerals. When finely divided talc or pyrophyllite are combined with water in proportions to make a slurry, the end product does have the appearance of a clay-water mixture. Soapstone for utensils and ornaments was mined by prehistoric Indians on Santa Catalina Island, CA. In the mid-1800s, soapstone from deposits along the western foothills of the Sierra Nevada mountains was used by white settlers for building and ornamental stone and in the linings and foundations of furnaces (Anon. 1956). Previous to 1916, the annual recorded production in California did not exceed 2000 tons. In the period 1912 to 1918, output rose sharply when the Talc City, Western, and Silver Lake mines were put into operation. From 1916 to 1935, the state's annual output of talc was in the range of 9,000 to 20,000 tons. In the mid-1930s, the use of talc in wall tile grew rapidly. In California, the production of talc grew to 63,000 stpy in 1943. The post-war building boom helped California production to grow to 120,000 tons in 1951. In 1968, production was 165,000 tons, 1969 was 145,000 tons, 1970 was 185,000 tons, and 1972 was 155,000 tons. Talc mining in New York state dates to about 1878 when a Colonel Palmer and associates opened the first commercial talc mine on the Nelson Freeman farm near Talcville, New York. In 1893, this operation was sold to the International Pulp Co. which changed its name to the International Talc Co. in 1944. The company was acquired by R.T. Vanderbilt Co., Inc. in 1974. A new talc operation, the Gouverneur Talc Co. owned by the R.T. Vanderbilt Co., began operations near Balmat, NY, in 1948. The initial capacity of the processing plant was 200 stpd (Gillingham, 1950). Subsequent expansions have increased capacity to over 600 stpd. The Vermont talc industry began just after the start of the 20th century. Talc was discovered in the area of the present Johnson, VT, talc mine in 1902. The American Minerals Co. initiated plant operations at Johnson in 1904. The Magnesia Talc Co. opened a plant at Waterbury, VT, in 1913 (Burmeister, 1963; Trauffer, 1964) and acquired American Minerals Co. in 1923. The Waterbury mine has a long history as a producer of talc crayons. The Eastern Magnesia Talc Co. was formed in 1924 by a merger of the Eastern Talc, Co.

Jan 1, 1983

By Harold E. Rowen

Sintering is accomplished at a temperature of more than 2000°F. For the purpose of this discussion it will be defined as the art of burning a solid fuel with 90 to 95 pct ash content. Think of the problems of combustion involved in keeping a home furnace burning properly with 12 to 20 pct ash in the fuel and remember that the amount of fuel involved in the 5 to 10 pct combustion loss represented by the definition has to be just about right or nothing is going to happen. Our forefathers discovered that many ores containing metals csscntial to the steadily rising standards of living were associated with other minerals, sulfur and arsenic, for example, which had to be removed before ultimate refining. They did this by utilizing the solid fuels they had available-the sulfur or other readily combustible components- to create roasting heat.

Apr 1, 1956

By J. D. Prater, H. R. Spedden, E. E. Malouf

Application of research findings to the old art of leaching copper from copper-bearing mine waste has resulted in a significant contribution of copper to over-all copper production. For example, at the completion of the current expansion program at the Kennecott properties in the United States, copper produced from waste dump leaching will amount to about 25% of the total production, whereas formerly only 2% was derived from this source. This planned expansion of copper leaching focused attention on the problem of developing more efficient methods for the recovery of copper from greatly increased volumes of copper-bearing so1utions.l Detailed investigations made in laboratory pilot plant and plant tests for the recovery of copper from copper-bearing solutions have included electrowinning, solvent extraction, ion exchange and cementation with iron in launders, precipitation drums, activated launders, and precipitation cones. The results of these investigations have led to the development of a precipitation cone-type recovery system having advantages over older methods.

Jan 4, 1966

By A. L. Holley

The general usage of engineers, manufacturers, and merchants, is gradually, bat surely, fixing the answer to this question. In every country rails, boiler-plates, and machinery bars, whether hard or soft, are almost universally called steel, when they are made from cast ingots. Other names for the softer steels, such as " homogeneous metal,'' "Bessemer iron," " Martin iron," and the like, have failed to obtain general recognition. The meaning of the term steel, before it was enlarged to cover newly developing varieties, has been traced, by a recent writer, down through Percy, Shakspeare, and the Bible, in a most interesting manner, from an archœological point of view. Undoubtedly, it did characterize hardness arid other qualities imparted by carbon. It is within the memory of most of us, that all steels were tool steels, and that the soft, structural varieties were introduced—varieties which harden but little, which bend cold, and which, in many physical properties, are akin rather to wrought-iron than to tool-steel. But, since both the hard and the soft steels are made by the same processes, and have their great, distinguishing structural feature in common, viz., homogeneity resulting from fluidity, it has come to pass, despite every other proposed nomenclature, that all the compounds of iron which have been cast in malleable masses, are called steel, the term wrought-iron being still confined to malleable iron made from pasty masses, and hence laminated in structure. No inconvenience has been found, so far, in distinguishing between the more or less carburized products, in general, by the terms " highsteel," "low-steel," "tool-steel," etc., and, in particular, by prefixing the percentage of carbon and other ingredients, to the terra steel. Steels which contain distinguishing ingredients other than carbon, are called "chrome-steel," "titanium-steel," and the like, just as variously compounded bronzes are called " phosphor bronze," " aluminium bronze," etc. Thus the combination of several words or symbols, and figures, may completely disclose the characters of the metal, in terms that are subject to no misunderstanding. But inasmuch as several high metallurgical authorities and clever writers have of late proposed to disturb this natural and somewhat settled nomenclature, it seems important to consider the claims of the various classifications. I shall attempt, in this paper, to show

By J. Jay Jacobsen

A dynamic regional coal development model is constructed for the Eastern Powder River Basin of Wyoming. Using this model, alternative development schedules from a recent environmental impact statement submitted to the Department of the Interior are simulated (Ref. 1). These alternatives include different mixes of export capacity, different coal conversion techniques within the region, as well as various levels of coal production. Exportation of 70 to 80 percent of an ultimate coal production of 180 million tons (163.3 x l09 kg) per year and the careful phasing of additional public services with population growth effectively reduce the social and environmental impacts of coal development. The alternative involving the addition of 43,000 megawatts of electrical generation capacity has very significant adverse social and environmental impacts on the region.

Jan 1, 1977

By James W. Neill

The occurrence of minerals of nickel and cobalt at Mine La Motte is probably known to every mineralogist. I will not attempt to describe these minerals, but, before entering on my subject, will briefly mention the ores, etc., which call for metallurgical treatment and enter into the composition of our mattes. Our staple lead-ore, the dressed galena, is the chief source of nickel and cobalt. It carries but a small percentage of these metals, viz.: 0.2 to 0.3 percent. usually, though when much copper pyrites is contained in the gangue, the amount of nickel and cobalt may be as great as 1.0 to 1.5 per cent. Next in importance is the ((middle product" of the dressingworks, consisting of the sulphides of iron (and copper) with gangue and galena. This usually carries 20 to 23 per cent. of lead, 0.5 to 1.0 per cent. of copper and 2.5 to 3.5 per cent. of nickel and cobalt. A larger percentage of copper always carries with it an increase of nickel and cobalt. In some few cases 12 to 15 per cent. of copper gives 6.5 to 8.0 per cent of these metals. Resides these products of the dressing-works, there is a small quantity of true nickel-cobalt-ore

Jan 1, 1885

By E. H. Rose

The present symposium on flotation machines provides a unique opportunity for group reappraisal of standard or habitual viewpoints. A symposium is by definition a trading post- for observations that might prove complementary when put together, thus leading to useful thoughts that might not have been evident from the original observations individually. The present paper, pertaining to power consumption in flotation, is deliberately an experiment of that kind. Data were solicited from the operating superintendents of several of the major flotation plants on this continent. The information received, covering a total of 14 separate operations in seven plants, has been collated in terms of power intensity; that is, the total power input per cubic foot of cell volume. This departs somewhat from the conventional expression of power per ton of ore treated, though the latter figure is also given for the plants concerned. Because of wartime restrictions, particularly in Canada, identifying names of plants and machines are withheld. Not as a firm conclusion, but as a tender for symposium discussion, the following points are made: 1. That flotation is a power operation in much the same sense as ball milling. 2. That contact time is the complement of power intensity and may be decreased as the latter is increased. 3. That a decrease in flotation power per ton of ore can result from an increase in power intensity. Analogy with Grinding In grinding, it has become axiomatic that the more the power put into a given operation, the greater the work performance. The analogous view is now proposed that the effectiveness of any flotation operation will be related to the mechanical energy usefully applied to that operation. Under this view, each increment of properly directed input energy should give either an increase in unit tonnage or an improvement in the metallurgical separation (concentrate grade or tailing grade), until either the theoretical limit imposed by mineral constitution or surface condition is reached, or until further increments of power become uneconomic under the law of diminishing returns. Thus, as in grinding, there are two forms of output that greater power input or improved utilization of power can produce. As for the law of diminishing returns, lower unit cost of power through improved generating efficiency in the past decade has pushed the limit back. Over and above this, however, there is strong indication in the operationg data herein presented that higher power intensity results in an actual economy of over-all power consumption. Like crushing and grinding, flotation accomplishes a rupture of the forces of molecular attraction, by taking particles from the common environment and placing them in the two separate environments of

Jan 1, 1947

Jan 1, 1932