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By W. E. Keck, Paul Jasberg

THE flotative properties of the principal minerals in Michigan's potential iron ores have been investigated to develop methods of beneficiation for the ores. One of these minerals, magnetite, is of considerable importance as a source of iron. Study of its flotation was similar to that of hematite1, another iron mineral in these potential ores. The present research consisted essentially of: (1) a survey of the literature on magnetite flotation, (2) the preparation of pure magnetite, (3) the development of laboratory procedure and (4) flotation experimentation. Literature on Magnetite Flotation.-For the purpose of this discussion, the results of previous work on the flotation of magnetite can be summarized as follows. The mineral has been floated with pine oil2, and it has also been separated from synthetic mixtures with silicates by the use of the same reagent2. Magnetite and apatite in iron-ore slimes have been separated by flotation of apatite with sodium palmitate3. These data were utilized in the present investigation. Preparation of Magnetite.-The pure mineral was prepared from the magnetic-separator concentrate of an iron ore (obtained from the Witherbee- Sherman Corporation, Port Henry, N. Y.). This concentrate was slowly comminuted with laboratory rolls and pulverizer to pass 65-mesh and was then tabled several times. Tabling yielded a relatively coarse magnetite concentrate, tailing and slimes. The two latter materials were rejected insofar as the present work is concerned, and treatment of the magnetite (table concentrate) was continued by separating it into -65 + 200 and -200-mesh sizes. Separation of the sizes was made by first dry screening and then wet screening. The -200-mesh material was rejected to eliminate possible introduction of error into flotation This paper describes a part of a general investigation into the flotation of Michigan's potential iron ores. A comprehensive discussion of the status of these ores and of the reasons for research on their Rotation beneficiation is available in mimeographed form on application to the Michigan allege of Mining and Technology, Houghton, Michigan. Manuscript received at the office of the Institute Nov. 12, 1936. Printfed without author's corrections. Subject to revision.

Jan 1, 1937

By George A. Macready

Trinidad, British West Indies, is an island near the north coast of South America, situated between latitudes 10" and 11" N., and opposite the numerous outlets of the Orinoco River Delta. It is separated from Venezuela by the Gulf of Paria (salt water) and straits over 5 mi. (8 km.) wide. The area of the island is approximately 1750 sq. mi. (453,-250 hectares) and the population is approximately 400,000. The climate is tropical with an annual rainfall of from 45 to 60 in. (114 to 152 cm.). The oil fields consist of several units, or fields, located in the southern half of the island. Approximately 90 per cent. of the total production has been yielded by fields situated within 7 mi. (11.3 km.) of the famous asphalt lake and on the southwest peninsula. The most important producing fields, or units, are the following, which are shown on the accompanying map: Brighton, or Pitch Lake Field, operated by the Trinidad Lake Petroleum Co., Ltd., is situated beside the famous Pitch Lake; it even encroaches on the lake. Vessigny Field, operated by the Trinidad Lake Petroleum Co., Ltd., is situated 2 mi. (3.2 km.) south of Pitch Lake. Lot One Field, operated by the Petroleum Development Co., Ltd., the United British Oilfields of Trinidad, Ltd., and Stollmeyer, Ltd., is situated 3 mi. south of Pitch Lake upon Lot One of Morne 1'Enfer Forest Reserve and adjoining properties. Parry Lands Field, operated by the United British Oilfields of Trinidad, Ltd., and the Petroleum Development Co., Ltd., is situated 31/2 mi. south of Pitch Lake on Lot Three of Morne 1'Enfer Forest Reserve and adjoining properties. Point Fortin Field, operated by the United British Oilfields of Trinidad, Ltd., is situated at Point Fortin, 6 mi. southwest of Pitch Lake. Fyzabad Field, operated by Trinidad Leaseholds, Ltd., is situated several miles southwest of Fyzabad Village and 6 mi. south-southeast of Pitch Lake. Barracpore Field, operated by Trinidad Leaseholds, Ltd., is situated several miles south of San Fernando and 15 mi. (24.14 km.) east of Pitch Lake.

Jan 1, 1921

By T. Reed Woodbridge

The object of this paper is to bring to notice a method in use at the Cedar Point laboratory of Witherbees, Sherman & Co., for determining the phosphorus in the ore mined at Mineville, N. Y. This ore is magnetite, with a gangue containing crystals of apatite. In 1886, Mr. H. F. Dawes, then head chemist at the works, suggested that as all the phosphorus seemed to be in the apatite, it could be obtained in solution by dilute nitric acid. After some experimenting the following method was adopted, and has proved invaluable for rapidity and ease; half a dozen determinations requiring very little more time or trouble than one. From + to 10 grammes of ore are weighed into a 150 c.c. beaker; 50 C.C. hot water and 10 c.c. strong nitric acid are added; the beaker is covered and the contents are boiled for 1/2 hour (10 minutes sometimes proves sufficient; but 4 hour is safer). The bumping which ensues if more than & gramme is used need cause no trouble. The hot solution is filtered into a 250 C.C. beaker. The filtration and washing (with hot water) proceed rapidly, as the magnetite itself is but slightly acted upon. After the addition of 15 C.C. ammonia and 15 c.c. nitric acid, the solution is cooled to 45' C., and from 15 to 40 C.C. of molybdic acid solution is added and stirred vigorously. In 5 minutes the precipitate will be down, and the determination can be finished by any good method. At Cedar Point the method more commonly used is weighing as yellow salt. Good washed filter-paper is used, No. 0 Swedish being preferred; and dozen 3 1/2-inch filters are numbered and dried and weighed at 110°C. These are always kept in stock. The yellow salt is filtered on one of these, washed with dilute nitric acid (2 per cent. by volume); dried for 1 hour at 110' C., and then weighed, 1.63 per cent. of weight being calculated as phosphorus. The filters vary in the two weighings from

Jan 1, 1889

By C. R. Dodson, W. T. Cardwell

This paper presents the results of a theoretical and experimental study of the effect of preperforated liners on well productivity. The analysis concerns the rectangular type of slot, either machine or torch cut, which is common in California. Muskatla treated this problem recently in a mathematical analysis of the flow of oil or gas from natural reservoirs into both gun-perforated and slotted liners. This paper presents additional and simplified analytical considerations and conclusions for the slotted liner, the solutions being applicable in the laboratory as well as in the field. An application of the analytical methods to permeability measurements on mounted core samples is given, to show the effects of sealing wax or other obstructions on the end faces of the cores. Results Fig. I 'Ompares the results of some theoretical calculations with the results of electrical analogy experiments performed in the Standard Oil Company of California's Production Technology Laboratory at La Habra, California. Fig. I indicates that the flux into short, "three-dimensional slots" of the relative dimensions encountered in practice is approximately equal to that into full-length, "two-dimensional slots" having the same open fraction of pipe. (The same numbers of slot rows, and the same radius ratio are also implied.) It can be seen from physical considerations that the closeness of this approximation must improve as the ratio of the external radius to the internal radius increases. Therefore, it is possible to calculate the flow into a slotted liner using a simple modification of the Darcy equation: where N is .the number of slot rows and O is the open fraction of the pipe. Fig. 2 shows the results of calculations . using Eq. 28. The most remarkable features of Fig. 2 are the high flux values for very small open fractions of pipe. For instance, with six slot rows and a radius ratio of 500, 74 per cent of the open-hole flux may be obtained with only o.I per cent of pipe Open. Fig. 2 shows that for a given open frac tion of pipe, the flux is greater, the greater

Jan 1, 1945

By Frank Firmstone

The furnace from which the brick here referred to were taken, was lined under my supervision and blown-in in May, 1902. It was 75 ft. high and 18 ft. in greatest diameter, and used coke to smelt a lean magnetic iron-ore. The lining was put in as follows:—First, blocks 14 in. long by 6 in. thick; second, 2 in. of loam; third, 13.5 in. of 9-in. fire-brick (one-and-ahalf brick wall) laid in English bond; fourth, red brick to within 2 in. of the iron shell; and fifth, 2 in. of slag-wool between the red brick and the shell. The brand of brick used has been known to me for over 20 years, and in my observation had always proved very durable, notably when used in a small furnace 50 k. high which treated the same magnetic. ore. On revisiting and examining the furnace in March, 1903, it was found that the whole of the lining of 14in. blocks at the top, and for an unknown distance (more than 20 ft.) below, had completely disappeared; and a few weeks later the 13.5-in. lining and the red brick at the top likewise vanished, and the furnace was blown out. N~twithstanding the complete failure of the lining higher up, measurements taken after blowing-out showed no unusual wear in the lower part of the furnace. The exact position in the furnace of the piece of brick-work used in the analysis, given below, is not known; but it came from between 30 and 40 ft. above the bottom. It had formed part of the 13.5-in. wall (no 14-in. brick remaining at that level) and consisted of parts of several bricks so firmly sintered together that fracture occurred indifferently through the joints and through the body of the brick. The joints could, however, be traced by a close examination. The surface which had been in contact with the material in the furnace was covered with a yellowish, translucent glaze, somewhat vesicular, and from

Jan 1, 1904

At the meeting of the Board of Directors of the Institute on Jan. 26, 1917, the following actions were taken: Messrs. A. C. Clark, Lawrence Addicks and G. D. Van Arsdale were appointed Tellers to count ballots for Officers and Directors. Messrs. T. T. Read, V. S. Harper, and. E. J. Hall were appointed Tellers to count ballots on revised spelling. The Finance Committee's audit for the year 1916 was approved and ordered filed. The Report of the Finance Committee upon the method of raising this Institute's share of the deficit on the additions to the building was approved and accepted. Upon the recommendation of the Secretary, increases in the salaries of some of the employees were approved. The St. Louis Section received an appropriation of $200 for the year 1917. The Columbia Section received an appropriation of $150 for the year 1917. The Montana Section received an appropriation of $100 for the year 1917. The Colorado Section received an appropriation of $175 for the year 1917. The Utah Section received an appropriation of $125 for the year 1917. The Puget Sound Section received a set of Transactions in standard binding. The International Engineering Congress received a loan of $300 until the Congress can realize upon some of its assets.

Jan 3, 1917

By Edward I. Salkovitz

THE determination of the orientation of metal single crystals and the studies of plastic deformation are greatly facilitated by the use of the stereographic projection. To draw a standard projection of the crystal it is necessary to have a tabulation of the angles between the various crystal-lographic planes of the particular crystal studied. Bozorth' has published such a table for the cubic system which can be found in many reference books; such convenient tabulation for the hexagonal metals, however, does not appear to be in the literature, although scores of workers have calculated these angles. Therefore, Table I of angles for magnesium, zinc, and cadmium has been compiled. Since the c/a ratio is different for each of these metals, three separate calculations are necessary. The angles 4 between (HKIL) and (hkil) were calculated by means of the formula: Hh+Kk+½(Hk + hK)1+~3aLl cos The c/a ratios were calculated from data given in the 1948 edition of Metals Handbook. Fig. 1 is a typical (0001) standard projection of zinc. For all practical purposes, it serves for cadmium as well, as can be seen from the table. For magnesium, however, it is necessary to construct another net. R. M. Bozorth: Physical Review. (1925) 26, 390.

Jan 1, 1952

By L. C. Brown, J. S. Kirkaldy

Measurements have been made of carbon diffuswn in the five ternary austenites Fe-C-Si, Fe-C-Ni, Fe-C-Co, Fe-C-Mn, and Fe-C-Cr in which the carbon (component 1) diffuses through interstitial sites and the ternary addition (component 2) diffuses substitutionally. Values of the diffusion-coefficient ratio, D12/D11 were determined for each system with finite couples using the transient equilibrium method. The effect of temperature and of concentrations of both the carbon and substitutional component upon D12/D was examined and was found to agree with the theoretical predictions. It is concluded that within an experimental uncertainty of 10 to 15 pct, it is possible to calculate the ratio D12/D11 from purely thermody-namic data. Difficulties of measuring the other off-diagonal coefficient, 4,, are discussed. Any quantitative attack on the fundamentals of the hardenability problem in steel must begin with the multicomponent diffusion formalism and with the accumulation of data pertaining thereto. In a recent paper Kirkaldy and purdy 1 employed the formalism derived from irreversible thermodynamics to treat the problem of diffusion in ternary austenites. In the latter solutions, carbon diffuses through interstitial sites and the substitutional component diffuses through the lattice. Examples were given of diffusion in the systems Fe-Mn-C and Fe-Si-C. In the present paper, we present new results on and discuss their agreement with the thermody-namic theory. Since the theory has been slightly modified from the original presentation of Kirkaldy and Purdy, their results on Fe-Si-C and Fe-Mn-C have been recalculated and are presented here for completeness. The flux of the interstitial component with respect to a fixed lattice framework can be written as a linear expansion in the independent concentration gradients, where X1 and X2 are the independent thermody-namic forces in the lattice fixed frame of reference. These forces can be obtained from the general statement for forces in a volume fixed frame2 if the partial molar volume of carbon atoms is set equal to zero and that of the substitutional component 2 is set equal to unity, viz where the are the chemical potentials and the N's are mole fractions. Introducing into [3] and [4] the function If, as suggested by statistical arguments, the off-diagonal interaction L12 is sufficiently small, [6] reduces to i.e., the coefficient ratio becomes purely thermo-dynamic. The activity of components 1 and 2 in a dilute ternary system (standard state at infinite dilution) may be represented by the expansion3

Jan 1, 1964

By O. W. Ellis

In view of the extensive use of the brasses and bronzes in engineering practice it is indeed surprising that so little scientific work has been done on the oxides in these alloys. Recognition of the ill effects of these compounds is universally accorded, both in foundry procedure and in such specifications as cover the melting of these useful mixtures. In the latter, limits, for example, are placed on the proportions of scrap metal In the charge, and clauses governing the use of fluxes are included, the addition of fluxes to the charge being made with the object of avoiding oxidation during the process of melting and of subducing and separating non-metal-lic matter from the melt.1 In the manufacture of brass it occasionally, though rarely, occurs that the virgin metals, copper and zinc, alone arc used. In the event of virgin metals being employed, that of the higher melting point is always melted first. If it is melted under suitable conditions, little or no oxidation will occur. Whether oxidation has occurred or not, however, can best be determined by microscopic examination of a sample taken from the melt. Avoidance of Oxidation in Furnace Practice When melting virgin copper in crucible practice, the avoidance of oxidation is not difficult, nor is it hard to forestall trouble in the electric furnace. In gas-fired furnaces of the barrel type, however, the avoidance of oxidation is almost impossible, no matter what the condition of the flame, the flux employed, or the amount of charcoal included in the charge. Copper melted in furnaces of this type is almost invariably so highly oxidized as to requirc very considerable additions of such deoxi-dizers as, for example, silicon copper to render it free from cuprous oxide. As a result,, the castings produced are decidedly inferior, on account of the. large amount of silica which is engendered in the metal as a result of the reaction, Cu2O + Si = SiO2 + 2Cu. The deoxidation of such oxidized copper could, of course, be effected by means of zinc with, however, even more disastrous results.

Jan 1, 1930

South Dakota State Geological and Natural History Survey, State University, Vermillion, S D. A list of publications will be sent upon request Many of the publications are out of print A series of Biennial Reports of the State Geologist will be sent upon receipt of three cents for postage on each, and are available as follows: 1918-20, 1920-22, 1922-24, 1924-26, 1926-28, 1928-30 Available Bulletins of greatest interest are: Bulletin 4, Pre¬liminary report of the geology of the Rosebud Reservation (1909), 10 cents; 10, Possibilities of oil in South Dakota (1922), 10 cents A series of Circulars (5 cents each) deals with the possibilities of oil and gas in various parts of the state, as follows¬ Circular 8, Eastern Pennington County (1921), 9, Western Dewey County (1922); 10, Northern Dewey County (1922), 12, Eastern Harding County (1923), 13, Northern Ziebach County (1923); 20, Western Ziebach County (1925), 23, Northeastern Meade County (1925); 27, Western Corson County Other Circulars (5 cents each) are: Circular 16, The natural resources of South Dakota (1924), 22, Structures ,in northern Haakon County (1925); 24, The Ragged Butte structure (1925), 25, The structure of western South Dakota (1925), 28, Structures in western Haakon and eastern Pennington counties (1926)

Jan 1, 1933

Minute of the Board of Directors, Jan. 26, 1917 In the name of all the members of the American Institute of Mining Engineers, this Board extends to. Mr. Herbert C. Hoover, an honored Vice-President of the Institute, on the occasion of his present temporary return to his native land, the cordial welcome of his colleagues, and their congratulations upon the noble work splendidly done by the Commission for Relief in Belgium of which he is the head. It is understood that a leading purpose of Mr. Hoover's visit to America at this time is the collection of additional funds, to be administered by his Commission in the care of the destitute children of Belgium. To this enterprise endorsed by both the belligerent parties, as well as inspired by the purest and tenderest sentiments of humanity, contributions are solicited from engineers, especially through an organization known as the "Belgian Kiddies Limited," which this Board, heartily approving its object and method, recommends to the consideration of the members of the Institute. On motion duly seconded it was unanimously VOTED.-That this minute be spread upon the record of the Board, and published in the Bulletin, and that a copy thereof be transmitted to Mr. Hoover, and to the San Francisco Section of the Institute.

Jan 3, 1917

By G. F. Jenkins

The word asbestos is a broad term that has been accepted and applied to a number of fibrous mineral silicates found in nature. They are incombustible and can be separated by mechanical means into fibers of various lengths and thicknesses, but differ in chemical composition and other properties. It is generally recognized that there are six varieties of asbestos; the finely fibrous form of serpentine known as chrysotile, and five minerals of the amphibole group, i.e., amosite (not fully recognized as a mineral species name but accepted in asbestos terminology), anthophyllite, crocidolite, tremolite and actinolite. (Figs 1-4.) Physical and Other Properties The structures of asbestos fibers have been studied intensely in recent years. X-ray diffraction patterns 1 to 15 have been used as a means of identification and classification. The amphibole group structures have been fairly well established while the serpentine group has been the subject of many investigations during the past six years. Low-angle X-ray scattering techniques5 have shown that the chrysotile fibrils are "hexagonally close packed" and parallel to each other, having cross-sectional diameters varying from 180Å* units to 300Å units, while the amphibole fibers are many times larger in cross section. The electron micrographs of chrysotile asbestos (Figs 1-4) have also indicated that the fibrils might be in the form of a hollow tube. This point has been the subject of considerable controversy by a number of investigators.7 to 16 Density measurements17 made on a sample of high quality Arizona fiber did not indicate that the fiber had a hollow tube structure; however, the so-called "sheet structure" of the fibril could be distorted in such a way that it gives the appearance of a hollow tube in the electron microscope. It is of interest to quote one investigator, F. L. Pundsack,17 in this connection: Although the empirical composition of chrysotile is 3MgO.2SiO2.2H20, the true unit cell[#] composition is best represented as Mg12(OH)16Si8O20. This cell has dimensions of a= 5.3Å, b = 9.2 Å, and c = 14.6 Å where the "a" direction is the fiber axis. The calculated density of this unit is 2.56 g/cc, a value in close agreement with experimentally determined density values for chrysotile. The exact manner in which the unit cells of asbestos are stacked together to build up a single fiber of chrysotile is not known, but from various

Jan 1, 1960

ALABAMA Altoona -Cain, J Anniston -Cowie, L K Heimrod, A A White, H E Bessemer-Abbott, C C Ball, E M Mitchell, F R Thompson, N E Birmingham -Adler, T E Aldrich T H Aldrich, T H, Jr Blackburn, A R Bush, 117 W Clark, G H Cowin, P G Crane, W R Crawford, G G Crockard, F H Darnelspn, G E Davis, C B

Jan 1, 1923

By W. L. Saunders

When work was begun in September, 1910, on the rock excavation for the foundation of the gigantic dam at Valhalla, N. Y., which is to convert Kensico lake into an important storage reservoir of the Catskill Aqueduct system, one of the first steps taken by the contractor, H. S. Kerbaugh, Inc., was the development of a quarry to supply the stone needed in the

Jan 1, 1915

By L. J. W. JONES, B. H. Bennetts

THE removal and disposition of large quantities of slag from blast-furnaces is a question of great importance in the design of works, and various methods have been devised, from time to time, in order to take the best advantage of local conditions. In blast-furnaces treating copper-ores or lead-ores, it is necessary to use a fore-hearth, or matte-settler, in order to collect, if possible, every particle of valuable matte which, otherwise, would be carried away with the out-flowing slag. In all of these cases, the slag overflowing from the fore-hearth is caught in pots and then conveyed to the dump. If the slag is of no value and the necessary water-supply, grade and dumping-space be available, the disposal of the slag by granulation is by far the cheapest and best method. It involves a minimum of labor, both at the furnace and at the dump; and it permits a continuous outflow of slag from the furnace- or settling-pot, thereby avoiding frequent tapping and plugging. When the conditions of water-supply, grade and dump-area will not permit slag-granulation, there are three other methods in common use. Large steel or cast-iron pots, or ladles, supported by trunnions on heavy cars which are moved by steam-, air-, or electric locomotives; some type of mechanical conveyor; and small pots or buggies moved by hand. The pots on the slag-cars are generally circular or oval in shape, and each one contains from 15 to 40 or more en. ft. of molten material. The mechanism for tipping them is more or less elaborate; and, as a general rule, the slag is dumped alongside, and quite close to, the track. They are more or less costly to construct and to keep in repair, and, in order to use them to best advantage, it is necessary to have a good elevation of track above the dumping-ground; furthermore, the rails must be of heavy weight, and well-supported on heavy ties. Other disadvantages of the slag-pots are-1, that the slag cannot be removed continuously

Mar 1, 1905

By J. D. Miller, R. L. Atwood

The structure, properties, and composition of commercial chelating-type copper extractants are examined. Characterization of these extractants was accomplished using organic separation techniques and analytical tools such as NMR and infrared spectroscopy. Results indicate that only the trans isomer of the diphenylhydroxyoxime (LIX 64N) is capable of copper chelation. The effects of structural modification of the extractants on the extraction and stripping reactions are discussed.

Jan 1, 1974

Arizona ROBERT E. TALLY, Chairman CARL E. ~IILLS, Secretary-treasurer, P. 0. Box 1462, Jerome. Ariz. W. S. BOYD THOMAS H. 0. O'BRIEN F. W. MACLENNAN Boston Meets first Monday each winter month GAL~N H. CLEVENG~, Chairman HOLCOMB J. BROWN, Vice-chairman F. I,EROY FOSTER Secretary-treasurer Room 8-219, Mass. lnst: of Tech., Cambridge Mass. A. E. WELLS H. A. WENTWORTH

Jan 1, 1928

William Kent, Montclair, N. J. (communication to the Secretary*):—The authors say, "The factor which determines the completeness of combustion of tlie volatile matter, after it has bee11 mixed with a certain amount of air, is the length of time the mixture is allowed to remain in the combustion-space; but this length of time depends on the extent of the space itself."

Jan 1, 1911

[EDMUND M. WISE, Chairman ROBERT H. LEACH, Past-Chairman D. K. CRAMPTON, Vice-Chairman CARL E. SWARTZ, Vice-Chairman W. M. CORSE, Treasurer LOUIS JORDAN, Secretary 29 West 39th St., New York, N. Y. Executive Committee 1941 1942 E. A. ANDERSON FRANCES H. CLARK D. L. COLWELL W. L. FINK W. P. SYKES J. T. NORTON 1943ERIC R. JETTE LOUIS W. KEMPF GEORGE SACHS]

Jan 1, 1940

By Nathaniel Arbiter

THE separation of minerals by flotation can be regarded as a rate process, with the extraction of any one mineral determined by its flotation rate, and the grade of concentrate by the relative rates for all the minerals. So regarded, the significant variables for the process are those that control the rates. These variables are of two types, the first describing the ore and its physical and chemical treatment prior to flotation and the second characterizing the separation process in the cells. This paper will examine the variation in rates for a group of separations, will show that a simple rate law appears to govern, and will consider the relation of the control variables to the rates. The use of rate constants for evaluation of performance and efficiency will be discussed. Flotation involves the selective levitation of mineral and its transfer from cell to launder. The flotation rate is the rate of this transfer. It may be defined by the slope of a recovery-time curve for any cell in a bank, or at any time in batch operation. The objective in flotation rate study is an equation expressing the rate in terms of some measurable property of the pulp. This can be either the concentration of floatable mineral in weight per unit volume1,2 or a relative concentration, which will be a function of the recovery." A rate equation for an actual flotation pulp will contain at least two constants, both to be determined from the data. One of these, the initial concentration or proportion of floatable mineral, is not necessarily equal to the feed assay because of nonfloatable oversize or locked particles." The other, a rate constant, is a measure of proportionality between the rate and the pulp property on which the rate depends. The value of the rate constant will be determined by the values of all variables which control the process and will be changed by significant changes in any of them. It is, therefore, a direct measure of performance. Where recovery or grade change continuously with flotation time, the rate constant will be independent of time and will characterize the entire course of the separation. Development of Rate Equations Rate equations can be developed either by analysis of the mechanism of the process or by direct fitting of equations to recovery-time data. Sutherland's attempt by the first method' suggests that the effect of particle size variation on the rate complicates the derivation of a simple equation applicable to an ore pulp. A further problem with an ore is the concentrate grade requirement, which usually involves a variable rate of froth removal. Thus the final rate for any cell may depend on the froth character and froth height, as well as on the pulp composition. This does not imply that each cell cannot reach a steady state2 in which the rate will depend ultimately on pulp composition. The second method is the fitting of rate equations consistent with the necessary boundary conditions* to experimental recovery-time curves. On the assumption that under constant operating conditions the flotation rate is proportional to the actual or relative concentration of floatable mineral in the pulp, a generalized rate equation may be expressed as follows: Rate = Kcn [I] where K is the rate constant, c is some measure of the quantity of floatable mineral in the pulp at time t, and n is a positive number. In previous rate studies, the value of n has been taken as 1, either by direct assumption," or as a result of the hypothesis that bubble-particle collision is rate determining.' A first order equation results, which after integration in terms of cumulative recovery R, leads to Loge A/A-R = Kt [2] The quantity A is the maximum possible recovery with prolonged time under the conditions used. No conclusive proof for the validity of this equation in flotation has been advanced. The evidence cited in its support consists entirely in the demonstration that it appears to apply to a limited number of recovery-time curves."' It will be shown subsequently that this procedure is not sufficient to establish the order of a flotation rate equation. The possibility that the equation may be of higher order therefore requires examination. If, in particular, the exponent in eq 1 is assumed to be 2, then after integration there results R = A2Kt/1 + AKt [3] with K again a rate constant and A the maximum proportion of recoverable mineral. Eq 3 may be

Jan 1, 1952