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By J. E. Hilliard, J. W. Cahn

calculation has been made of the standard deviations to be expected in the measurement of volume fractions by areal analysis, lineal analysis and four point-counting Procedures. The effect of experimetztal errors is not included. Our conclusion is that a point count using a two-dimensional grid will be the most efficient method of volume fraction analvsis providing the grid spacing IS coarse enough. The predicted standard deviation for such an analysis is shown to he in good agreement with that determined experimentally. A metallurgist wishing to estimate a structural property by means of quantitative metallography is often faced with a choice between several different procedures. In such a case, he will naturally wish to know: a) Which procedure is the most efficient in the sense of requiring the least effort for a given precision? b) For a given procedure, what are the conditions for maximum efficiency? c) Under these conditions, how many measurements are required to attain a given precision? It is our aim in this paper to provide at least partial answers to these queries as they relate to the estimation of volume fractions from measurements on a random two-dimensional section of an opaque specimen. The commonly used techniques1,2 for volume-fraction analyses are based on one or more of the following principles: i) For an areal or Delesse3 analysis: That the areal fraction of a three-dimensional feature intercepted by a random plane provides an unbiased estimate of the volume fraction of that feature. ii) For a lineal or Rosiwal4 analysis: That the fractional intercept on a line passing at random through a two-or three-dimensional feature provides an unbiased estimate of, respectively, the areal or volume fraction of that feature. iii) For a point-count analysis: That the fractional number of randomly or regularly dispersed points falling within the boundaries of a two-dimensional feature on a plane, or within the boundaries of a three-dimensional feature in a volume, provides an unbiased estimate of, respectively, the areal or volume fraction of that feature. The absence of bias referred to in these principles does not, of course, imply that the results of an analysis will be free of error, but only that the expected result is equal to the true one. Application of the foregoing principles provide the following six possible experimental procedures: a) An Areal Analysis—This involves the measurement with a planimeter (or other means) of the area of a constitutent intercepted by the plane of polish b) A Two-Dimensional Random Point Count—Apos-sible experimental procedure for this analysis is to superimpose a sheet of transparent graph paper on a micrograph, and then use a table of random numbers to select coordinates for the points. c) A Two-Dimensiotuzl Systematic Point Count-Similar to b) except that the points are distributed in a prescribed manner, usually at the corners of a lattice superimposed on a micrograph or the screen of a projection microscope. d)A Lineal Analysis—A measurement of the fractional line length intercepted. It is usually performed by traversing the specimen under the cross hairs of a microscope and recording the distance travelled in each constituent. e) 4 One-Dimensional Random-Point Count— This could be performed by traversing the specimen with stops at random intervals to identify the constituent then present under the cross hairs. f) A One-Dimensionul Systematic Point Count— Similar to e) except that the traverse is stopped at prescribed (usually equal) intervals. It will be noted that the point-counting procedures b) and c) can be regarded as methods of estimating the areal fraction. Similarly, e) and f) are indirect methods of making a lineal analysis. All of the six procedures described above involve at least one stage of sampling. Thus, quite apart from any experimental errors, there will always be a statistical uncertainty associated with the final results. It is with the calculation of this uncertainty that we will be concerned. To avoid unnecessary repetition, the statistical relationships that will be used in the calculations are collected together in the appendix. For a fuller discussion reference should be made to one of the many textbooks5,6 on statistics. For symbols relating to the specimen structure we will follow as far as possible the terminology used by Smith and Guttman.7

Jan 1, 1962

By Keats, J. L.

IN THE literature on the elimination of metalloids in basic open-hearth practice, there are a great many heats recorded in which excellent data on changes in slag and metal composition during refining are given, but in almost all of these heats either temperature data or weights and analysis of charge are unrecorded and observations on the physical charac- teristics of the slag are almost always lacking. With these points in mind, a test heat was made in which as complete as data possible on all the factors that affect the elimination of metalloids were obtained.

Jan 1, 1957

By G. Townsend Harley

STOPING methods in which shoveling plays an important part are gradually being replaced by other and cheaper methods. But there will always be considerable shoveling done underground in stopes as well as in drifts, tunnels, urinzes, and shafts. At the mines of the PhelpsDodge Corporation at Tyrone, N. M., the cost of shoveling in all stopes in 1917 amounted to 24c. per T. In the top-slice stopes for the same period, it cost 27 c. per T. or 16 per cent, of the total cost of these stopes. The tonnage for shovelers from all stoping was 9.3 T. per man, and for topslicing 8.2 T. per man. These stopes were not unduly hot, and there was not more than the usual amount of timber to interfere with the work of the men. The tonnages obtained per shoveler were considered low; first, because of a poor grade of Mexican labor, many of the men having come in from railroad grading camps; and second, because of a poor spacing of raises, especially in the top-slice stopes, where, in general, they were spaced 25 ft. by 66 ft. (7.6 by 20.1 m.) centers. The average wage per laborer shift was $2.67 during the year. It was thought, however, that even under these conditions the men were not producing the tonnage that they should, so, with the consent of the management, the writer undertook to determine how the general efficiency of the underground shoveling could be improved. No predetermined plan for conducting these experiments was arranged because we had no definite ideas as to the scope of the work or the number of elements into which the investigation would resolve itself, before all of its phases could be determined. We were sure, however, that any work that would thoroughly cover the ground would have to be in the nature of a systematic time study, combined with a course of instruction in correct shoveling methods and adequate and intelligent supervision of the work. Two or three companies in the Southwest have done some work to determine the proper shovel to be used undcrground, but so far as is known the work has been limited to equipping certain parts of their mines with a particular type and size of shovel and thereafter watching the cost and efficiency records. In each case it seems to have been the shovel that held the 21-lb. (9.5-kg.) load that gave the bcst results. Excepting personal communications from these companies, the only data available on scientific shoveling are contained in F. W. Taylor's book, "The Principles of Scientific Management," and D. J. Haucr's article, in The Contractor for March 29, 1918, "A Hundred Hints for Shovelers." This paper discusses and draws conclusions from several thousand time-study readings, taken both on the surface and in the mines for nearly a year. A sufficient number of readings were taken on each factor in the problem for the plotting of curves of the performances and to obtain accurate indices of the work to be expected from this class of labor. The work is not as complete in all of its details as we would like to havc it, because we were forced to stop the work temporarily, owing to the numbcr of men going into the National service and our inability to get others who could make time studies. The results obtained so far, however, have been of such a startling nature that we have decided to submit them at this time, subject to future modification. It is hoped, also, that a free discussion of this paper will lead to a disclosure of any errors that may have becn embodied and offer some valuable suggestions for the conduct of future work.

Jan 1, 1920

By J. B. Neale

FRom the beginning of its activities, the members of the National Production Committee have felt that the following points were essential to the success of its work: The operators must feel that their operations were not 100 per cent. efficient; that they should be courteous and fair in their treatment of their employees; and that they should set an example of hard work and patriotic interest in increased production. Every move made must appeal to the sense of fairness of all parties concerned. The men must feel that in working more faithfully, and consequently producing more coal, they are rendering a distinct service to their Government in the time of its great need. As the workers feel that greater efficiency on their part results only in greater profits to the operators, the advantage to the operator should be lost sight of, as far as possible, and the advantage to the Government in fighting the war emphasized. Both operators and workers should know that the Government considered increased production an obligation, and opportunity for service, resting on both parties and not on the operators or the workers alone, and that both parties could very much better the efficiency of the pre-war period. Had the committee intimated that it thought the coal shortage was due entirely to the idleness and inefficiency of the workers, its campaign would have failed, for the men would have resented the charge because only too frequently their efforts to produce more coal were thwarted by bad management; besides, the operators would have lacked stimulus to better effort. On the other hand, had the impression been given that the committee thought that the coal shortage was due entirely to bad management, the operators would have resented the charge because only too frequently their efforts to produce more coal were thwarted by the idleness and inefficiency of the workers; and the workers, having been thus indirectly pronounced 100 per cent. efficient and patriotic, would have lacked stimulus to better effort.

Jan 1, 1920

By AIME AIME

BEGINNING Thursday, July 16, the National Broadcasting Co. is broadcasting from 6:30 to 6:45 p.m., over its nationwide network and possibly also by short wave a series of eleven radio programs dealing with the contributions of engineers to the prosecution of the war. The series is being arranged and sponsored by a committee of representatives of the national engineering societies, R. L. Sackett, chairman. The committee began its deliberations before Pearl Harbor and had scripts under way on blackouts, bombs, and damage to structures. The declaration of war emphasized the importance of the proposed radio program. The National Broadcasting Co. and the Office of Civilian Defense enthusiastically endorsed the committee's proposal and have been generous in their help and approval of scripts so far submitted. Controversial matters are included in the broadcasts and changes will be made when requested by O.C.D. up to the minute that a program goes on the air. In this way the latest and authoritative information will be given.

Jan 1, 1942

THE great development of the mines and metallurgical works of this country during the last few years, accompanied as it has been by the investment of enormous sums of money in purchasing lands, and in the erection of improvements, requires that advantage should be taken of the accumulated knowledge of engineers, superintendents, and' others, in mastering &he problems which are constantly presenting themselves for our action. Among those may be mentioned the consideration of more economical systems of mining in our coal and metal-liferous mines, improved methods of transportation above and below ground, unwatering and ventilating mines, the mechanical preparation of coal and other minerals, the various metallurgical processes, and, in fact, every question tending to the attainment of two great objects : 1st. The more economical production of the useful minerals and metals. 2d. The greater safety and welfare of those employed in these industries. In European countries, where the arts of mining and metallurgy have long been the subject of the most careful study, no means have been found so effectual in attaining the end above proposed as the free interchange of experience among those actually engaged in these industries, and this object has been accomplished, mainly, through the medium of institutes, associations or societies, composed of those engaged in these occupations, and by the periodical publication of essays or papers, communicated to such societies by their members. I t must be evident to all practical men that the interchange of the varied experience of those engaged in such occupation in this country could not fail to advance very materially the desired objects; it is, therefore, proposed to establish an American Institute of Mining Engineers, which will hold its meetings periodically in the great mining and metallurgical centers, where works of interest, such as mines, machine shops, furnaces, and other metallurgical works, can be inspected, and the members exchange their views, and consult for mutual advantage upon the difficulties encountered by each; these transactions or proceedings, when published, would form a most valuable and greatly-needed addition to our professional literature. I t is proposed that a meeting of those sympathizing with the object above mentioned shall be called for the purpose of organizing such an association, the place and time of meeting being Wilkes-Barre, Pa., and the month of April or May. Communications indicating the opinion and wishes of all, both as to these points, and also as to the organization and objects of the Institute, will be gladly received by any of the undersigned, and a notice of the date of meeting, which will be arranged to suit the greater number, will be duly communicated. Any

By W. H. Bassett

IN the commercial annealing of cartridge brass there are four points regarding which definite data are essential. They have to do with the correct interpretation of grain count in its relation to annealing temperature and, incidentally, to Brinell hardness. These points are: 1. The comparison of the grain sizes of two cartridge-brass mixtures: 69 copper, 31 zinc, 0.376-in. (9.5-min.) gage; and 68 copper, 32 zinc, 0.130-in. (3.3-mm.) gage. 2. The comparison of the grain sizes of annealed metal that had previously been reduced by rolling varying amounts; for instance, 20.0, 36.6, 50.9, and 59.1 per cent. 3. The determination of standards for grain sizes on annealed brass of the composition 68 per cent. copper, 32 per cent. zinc and 69 copper, 31 zinc. 4. The comparison of grain size with Brinell hardness on identical samples of annealed metal. In their comprehensive and thorough investigation of the recrystallization of cold-worked alpha brass on annealing,1 Mathewson and Phillips have discussed the relations between temperature of anneal, degree of deformation, and structural alteration in alpha brass. They have also shown certain comparisons between the ordinary physical properties and the grain size of annealed brass. The purpose of the present investigation is mainly concerned with the grain size of cartridge brass, its relation to Brinell hardness, and the publication of sufficient data to enable those engaged in the inspection of such material to have a correct foundation upon which to work.

Jan 1, 1919

An Engineers' Symposium was held Wednesday evening, Mar. 26, in the auditorium of the Engineering Societies Building, 29 West. 39th St., under the general auspices of the Local Sections of the American Institute of Mining and Metallurgical Engineers, American Society. of Mechanical Engineers, and the Society of Automotive Engineers. It was participated in by members of the American Institute of Electrical Engineers, American Society of Civil Engineers, American Chemical Society, American Electrochemical Society, American Institute of Chemical Engineers, American Society of Heating and Ventilating Engineers, American. Society of Refrigerating Engineers, New York Electrical Society, Brooklyn Engineers' Club, Illuminating Engineering Society, Institute of Radio Engineers, Municipal Engineers of the City of New York, Society de Chemie. Industrielle, Society of Chemical Industry, and the Society of Naval Architects and Marine Engineers. In opening the meeting the chairman, Gano Dunn,* said: The program calls this an engineers' symposium, which means a putting, together of things, and these things tonight are ideas of fundamental relations to the engineering profession and the engineering societies. Not only engineers, but all men nowadays are examining their views in respect to their relation to what we call Society. My conception of Society is that there is no such thing in the concrete sense of the word. It is an abstraction, and just in proportion as it is a generalization and broader in scope than the particulars from which it is drawn, so is it emptier of content. That does not mean that it is not important, but it does mean that we should be careful and not be led astray into a zeal for doing things for Society that we would not do for our fellow engineers and our brothers. The man who is unwilling to do something for his brother or fellow engineer and yet urges that same thing for Society-is thoroughly inconsistent and, in my opinion, wrong.

Jan 5, 1919

Executive FREDERICK M. BECKET, Chairman HOWARD N. EAVENSON J. V. W. REYNDERS H. A. GUESS WILLIAM WRAITH Finance HENRY KRUMB, Chairman PAUL H. MERCER H. G. MOULTON Admissions JOHN M. LOVEJOY, Chairman GEORGE D. BARRON DONALD M. LIDDELI. E. V. DAVELER W. D. B. MOTTER, JR. Alternates AMOR F. KEENE L. F. STROBEL SAM TOUR Membership LEWIS B. LINDEMUTH, Chairman EDWARD H. ROBIE, Secretary Executive Committee NELSON DICKERMAN FREDERICK LAIST FRED H. KAY THOMAS T. READ H. A. KURSELL A. T. SHURICK SAM TOUR

Jan 1, 1932

CONTENTS PAGE. WHITE, DAVID.-Environmental Conditions of Deposition of Coal. Discussed by E. C. Jeffrey, George H. Ashley, Reinhardt Thiessen, S. W. Parr, David B. Reger, Wilbur A. Nelson, James F. Kemp, E. S. Moore, Homer G. Turner, David White, A. C. Noé, W. A. I. M. van Waterschoot van der Gracht 2 THIESSEN, REINHARDT.-The Constitution of Coal. Discussed by Edward C. Jeffrey, Reinhardt Thiessen, Ralph H. Sweetser, David White 12 TURNER, HOMER G.-Microscopical Structure of Anthracite. Discussed by E. S. Moore, Edward C. Jeffrey, Reinhardt Thiessen, H. J. Rose, James F. Kemp, David White, Clarence A. Seyler, A. C. Noé 14 JEFFREY, EDWARD C.-Coal in Relation to Coke. Discussed by H. J. Rose, David White, E. S. Sinkinson, S. W. Parr, James F. Kemp, Edward C. Jeffrey, Reinhardt Thiessen, Chas. R. Fettke 17 FRANCIS, W., and WHEELER, R. V.-The Resolution of Coal by Oxidation. Discussed by Edward C. Jeffrey, S. W. Parr, E. S. Sinkinson, Reinhardt Thiessen, David White 23 TIDESWELL, F. V., and WHEELER, R. V.-The Constitution of Coal. Discussed by David White, A. C. Fieldner 24 JOLLY, J., and WHEELER, R. V.-Organic Sulfur Compounds in Coal. Discussed by S. W. Parr 25 SINNATT, F. S.-Selective Combustion in Coal. Discussed by J. D. Davis, A. C. Fieldner, Geo. S. Rice, W. M. Grant, H. J. Rose, S. W. Parr, David White 25 COBB, JOHN W.-Nitrogenous Constituents of Coal. Discussed by S. W. Parr, H. J. Rose, Reinhardt Thiessen 28 PARR, S. W., and HOBART, F. B.-Coal and Oxygen. Discussed by J. D. Davis, W. T. Thorm, Jr., S. W. Parr, H. J. Rose, A. C. Fieldner, F. F. Jorgensen, David White, W. M. Grant 30 FIELDNER, A. C., and DAVIS, J. D.-Modern Views of Chemistry of Coals of Different Ranks as Conglomerates. Discussed by S. W. Parr, David White, Reinhardt Thiessen, A. C. Fieldner, Clarence A. Seyler 32 EBY, J. BRIAN.-Contact Metamorphism of Some Colorado Coals. Discussed by Geo. C. McFarlane, W. T. Thom, Jr 35 WHITE, DAVID.-Progressive Regional Carbonization of Coals. Discussed by A. C. Fieldner, Homer G. Turner, W. A. J. M. van Waterschoot van der Gracht, A. C. Noé 37 THOM, W. T., JR.-Moisture as a Component of the Volatile Matter of Coal. Discussed by A. C. Fieldner, S. W. Parr, Clarence A. Seyler, W. T. Thom, Jr., R. D. Hall 39

Jan 7, 1925

F. G. SMITH, Waterbury, Conn.-I would like to ask whether small amounts of iron give the maximum resistance at a low temperature, and if the large amounts of iron raise the temperature at which the maximum resistance occurs? That is, with a small amount of iron, will a maximum be at, say, 10°? F. E. BASH.-With the small amount of iron, the maximum is at a lower temperature, and with the increase of iron, the maximum increases; it seems to come to a maximum and then decrease; that is, increasing the iron up to a certain value increases the temperature at which there is a maximum of resistance, and any increase of iron beyond that value will start decreasing this temperature. With 2 per cent. of iron, the maximum is lower than for 1.5 per cent. which was the value that we found to be satisfactory. F. L. DRIVER,* Jr., Harrison, N. J.-I would like to ask what chance there is of the instrument companies getting together and deciding on standards for both manganin and constantan? We make both of these alloys in this country and we find that each one of the instrument com-panies who buy these materials require different standards of specific electrical resistance and thermal e.m.f. For instance, some of our cus-tomers require an electrical resistance in manganin or therlo of 240 ohms per circular mil foot and others require it with a specific electrical resist-ance of 270 ohms per circular mil foot. They buy these alloys in relatively small quantities so that it means much extra melting and supervision when making up small quantities for each consumer. If something could be. clone to eliminate this, it would be a benefit to the instrument com-panies, who could secure their material more cheaply, and to the manu-facturers, who would not have to spend so much time and effort in special manufacturing.

Jan 12, 1919

By David White

THE submission of carefully prepared estimates of the oil reserves of the United States calls for no apology or explanation. In this country, petroleum is a rapidly wasting asset and an occasional appraisal of the amount remaining in the ground is a simple business procedure to safe-guard the general welfare and the prosperity of the republic. The rumored danger of failure, in the near future, of the foreign supply on which we depend in constantly increasing amounts makes the immediate review of our available reserves the more imperative. The Director of the U. S. Geological Survey, in March, 1921, requested the American Association of Petroleum Geologists to cooperate in the preparation of new estimates of the oil remaining in the ground. With the members of this cooperative committee, state geologists, regional geologists, consulting specialists, and geologists and engineers attached to many companies worked both independently and through sub-committees. The reports for districts, counties, fields, etc., after review by local or state committees, were discussed by the joint cooperative committee in conferences that, in some instances, were attended by the original compilers of estimates for the states or smaller areas. Finally the data were reviewed and the figures revised by the joint cooperative committee, so that the totals given in Table 1 represent the opinion of the committee, which was composed of F. W. DeWolf, W. E. Wrather, Roswell H. Johnson, Wallace A. Pratt, Alexander W. McCoy, Carl H. Beal, C. T. Lupton, G. C. Matson, K. C. Heald, W. T. Thom, Jr., A. E. Fath, Kirtley F. Mather, R. C. Moore, and David White, chairman.

Jan 6, 1922

By Joseph Gurland

EVERAL carbide-cobalt compositions were pre-^-5 pared for the purpose of determining the transverse rupture strength of various carbide-binder systems. The binder content was held at 10 and 37 volume pct Co, so as to be representative of low and high bjnder compositions. The carbides used, WC, Tic, TaC, CbC, VC and ZrC, were selected on the basis of availability, knowledge of their properties, and small solid solubilities in the binder metal at room temperature. The methods of preparation and carbon analysis of the carbides are summarized in Table I. The carbides with cobalt added were ball milled, pressed, and sintered. vacuum sintering was used throughout, except for the WC-Cs alloys, which were sintered in hydrogen. The sintering temperatures ranged from 2500" to 2750°F for the low binder alloys and from 2300" to 2550°F for the high binder alloys. Compositions and properties of the sintered com- pacts are presented in Table 11. For the transverse rupture strength, the average and range of the five best samples of each alloy are listed. Discrepancies between the actual and theoretical densities are attributed to carbon deficiencies in some samples. The theoretical densities were calculated by assuming mixtures of carbides of stoichiometric compositions and cobalt. Representative microstructures are shown in Figs. 1 to 6. The porosity was A-2 or better' in all alloys except those with ZrC. A grain size of about 3 p was

Jan 1, 1958

By W. Philippoff

ALTHOUGH Gaudin1 and more recently Sutherland2 have calculated the probability of collision of a falling mineral particle with a rising bubble, there is no published information concerning the details of the mechanism of attachment of a collector-coated particle to a bubble. During the past year the writer has developed a theory for the mechanism of attachment, which has been substantiated experimentally. Funds for the investigation and for some of the equipment used have been supplied by the Mines Experiment Station of the University of Minnesota. Motion picture studies of the phenomena involved in the collision between mineral particles and bubbles, such as those of Spedden and Hannan," show that the contact can be completed within 0.3 millisec. Formulas developed for rigid bodies have hitherto been used' for the calculation of the motion of bubble and particle, but it is obvious that a bubble cannot be regarded as a rigid body. On the contrary, Spedden and Hannan's pictures show a great degree of deformation during the collision. The time of attachment was calculated as the time the particle drifted past the bubble. Time of Collision The theory presented in this paper enables calculation of the time of collision, using the concept that the bubble, or more generally, a liquid-air interface, acts as an elastic body. The elasticity, defined as the restoring force on a mechanical deformation, is caused by the surface tension and is the result of the principle of the minimum of free surface energy. It is well known that an elasticity together with a mass determines a frequency of vibration. The vibrations of jets and drops caused by the elasticity of the interface are known to comply exactly with the classical theory of capillarity.' However, the vibrations of isolated bubbles, as distinct from foams, have not been investigated previously. The following equation, presented elsewhere,' has been deduced for these frequencies: 3_____________________ fB = 9.20.vV.vn. (n-1).(n+2)/8 [I] in which fB is the frequency of a harmonic of the bubble in cycles per second, V the volume of the bubble in cc, n a number determining the order of the harmonic, and n = 2 the basic vibration. The first (basic) harmonic describes a change of the spherical bubble to an ellipsoidal bubble. The higher harmonics are more complicated, for the circumference of the bubble is divided approximately into as many parts as the order of the harmonic. As an example, Spedden and Hannan's published motion picture of a vibrating bubble corresponds to the sixth harmonic. Eq 1 shows that only the first and third harmonics are simple multiples (1 and 3), all the others being irrational fractions of the basic frequency. This means that the shape of the vibration can change with time and is in general unsym-metric in respect to the time axis. Such conditions prevail when there is a distributed elasticity or mass, as in the case of vibrating membranes or rods. The constant 9.20 is valid for water at room temperature, but a general solution involving the physical constants of the liquid has not been found. The case of the floating particle is much easier to treat than that of the bubble. It can be assumed that the elasticity is caused exclusively by the interface and that the mass is concentrated in the particle together with some adhering water. The following expression for the frequency of a system of one degree of freedom can be applied: fP = -1/2-vE/m [2] Here fp is the frequency of the particle vibration in cycles per second, E the elasticity in dynes per cm, and m the mass in grams. The classical theory of impact phenomena gives the time of collision during the striking of a spring (in this case the surface of the bubble) by a mass, as: t, = 2/f = nvm/E [3] It is now possible to develop an expression for the elasticity of a floating cylindrical particle. The force equilibrium of a cylinder floating end on at the air-liquid interface is given by the well-known equation (Poisson7 1831) P = /4 D2-pL-g-h + D.y sin a [4] which accounts for the buoyancy and the action of the surface tension where P is the force acting on the particle in dynes (weight-buoyancy), D the diameter of the cylinder in cm, PL the density of the liquid in grams per cc, g the acceleration of gravity = 981 cm per sec2, h the depression of the cylinder below the surface of the liquid in cm, y the surface tension in dynes per cm and a the supporting angles or the one required to insure equilibrium, a being smaller than the contact angle 0. Although demonstrated by Poisson, it has not

Jan 1, 1953

By W. Philippoff

ALTHOUGH Gaudin1 and more recently Sutherland2 have calculated the probability of collision of a falling mineral particle with a rising bubble, there is no published information concerning the details of the mechanism of attachment of a collector-coated particle to a bubble. During the past year the writer has developed a theory for the mechanism of attachment, which has been substantiated experimentally. Funds for the investigation and for some of the equipment used have been supplied by the Mines Experiment Station of the University of Minnesota. Motion picture studies of the phenomena involved in the collision between mineral particles and bubbles, such as those of Spedden and Hannan," show that the contact can be completed within 0.3 millisec. Formulas developed for rigid bodies have hitherto been used' for the calculation of the motion of bubble and particle, but it is obvious that a bubble cannot be regarded as a rigid body. On the contrary, Spedden and Hannan's pictures show a great degree of deformation during the collision. The time of attachment was calculated as the time the particle drifted past the bubble. Time of Collision The theory presented in this paper enables calculation of the time of collision, using the concept that the bubble, or more generally, a liquid-air interface, acts as an elastic body. The elasticity, defined as the restoring force on a mechanical deformation, is caused by the surface tension and is the result of the principle of the minimum of free surface energy. It is well known that an elasticity together with a mass determines a frequency of vibration. The vibrations of jets and drops caused by the elasticity of the interface are known to comply exactly with the classical theory of capillarity.' However, the vibrations of isolated bubbles, as distinct from foams, have not been investigated previously. The following equation, presented elsewhere,' has been deduced for these frequencies: 3_____________________ fB = 9.20.vV.vn. (n-1).(n+2)/8 [I] in which fB is the frequency of a harmonic of the bubble in cycles per second, V the volume of the bubble in cc, n a number determining the order of the harmonic, and n = 2 the basic vibration. The first (basic) harmonic describes a change of the spherical bubble to an ellipsoidal bubble. The higher harmonics are more complicated, for the circumference of the bubble is divided approximately into as many parts as the order of the harmonic. As an example, Spedden and Hannan's published motion picture of a vibrating bubble corresponds to the sixth harmonic. Eq 1 shows that only the first and third harmonics are simple multiples (1 and 3), all the others being irrational fractions of the basic frequency. This means that the shape of the vibration can change with time and is in general unsym-metric in respect to the time axis. Such conditions prevail when there is a distributed elasticity or mass, as in the case of vibrating membranes or rods. The constant 9.20 is valid for water at room temperature, but a general solution involving the physical constants of the liquid has not been found. The case of the floating particle is much easier to treat than that of the bubble. It can be assumed that the elasticity is caused exclusively by the interface and that the mass is concentrated in the particle together with some adhering water. The following expression for the frequency of a system of one degree of freedom can be applied: fP = -1/2-vE/m [2] Here fp is the frequency of the particle vibration in cycles per second, E the elasticity in dynes per cm, and m the mass in grams. The classical theory of impact phenomena gives the time of collision during the striking of a spring (in this case the surface of the bubble) by a mass, as: t, = 2/f = nvm/E [3] It is now possible to develop an expression for the elasticity of a floating cylindrical particle. The force equilibrium of a cylinder floating end on at the air-liquid interface is given by the well-known equation (Poisson7 1831) P = /4 D2-pL-g-h + D.y sin a [4] which accounts for the buoyancy and the action of the surface tension where P is the force acting on the particle in dynes (weight-buoyancy), D the diameter of the cylinder in cm, PL the density of the liquid in grams per cc, g the acceleration of gravity = 981 cm per sec2, h the depression of the cylinder below the surface of the liquid in cm, y the surface tension in dynes per cm and a the supporting angles or the one required to insure equilibrium, a being smaller than the contact angle 0. Although demonstrated by Poisson, it has not

Jan 1, 1953

By Renato G. Bautista, David C. Lindholm

The results of scale-up studies on a continuous, multistage horizontal mixer-settler extractor are presented. The chemical and mechanical system involves the separation of lanthanum from a mixture of rare earth chlorides using di(2-ethylhexyl) phosphoric acid as the solvent and dilute HCl as a scrub solution in a bench scale extractor. Each stage has a hold-up of 2.6 l. A single stage unit is utilized for scale- up studies. Results are obtained on four sizes of geometrically similar units, the largest being six times the volume of the original bench size. A unit operations technique is chosen so that mixing and settling can be examined independently. Variables examined include type of continuous phase, flow rate of inlet streams, and power input to the mixer. Inlet flow-rate ratios are kept constant for all tests. TWO potential methods of unbaffled pump-mixer scale-up are explored; the maintenance of constant impeller tip speed and constant power input. For the settler, the previously successful method of basing design on constant flow-rate per unit cross- sectional area is used.

Jan 1, 1977

By Dean, R. S.

THE numerous theories of hardening which have been advanced in recent years are all satisfactory in accounting for some of the phenomena observed in hardening metals, but none so far presented account for all of the facts observed. Some years ago one of the authors, R. S. Dean,' presented a theory to account for some of the properties accompanying work hardening. The present paper develops this theory further in the light of recent experimental work and extends it to other forms of hardening. Many of the ideas included have come from the writings and personally communicated thoughts of others. We have attempted to give proper credit in every case, but it is possible that we have not always done so. As an historical basis it is desirable here to review very briefly the hardening theories which have been current. The first comprehensive theory of work-hardening phenomena was due to Sir George Beilby.2 He contributed the idea that with cold work part of the structure of the metal was rendered amorphous and that-it was to this amorphous material that the cold-worked metal owed its difference in properties. According to Beilby's theory this amorphous material was a supercooled liquid and, therefore, had the characteristics of a vitreous material. That such a theory is not capable of explaining the property changes in metals has been repeatedly pointed out. This theory also allowed a slip to take place only once on a given plane, which, as has been pointed out by Jeffries and Archer13 is not consistent with the observed length of an, individual slip and the amount of elongation which can be obtained by wire drawing. The modifications, which have been proposed to this hypothesis to make it coincide with the experimental facts, have to a considerable extent robbed the theory of its clean-cut characteristics. The commonest of these modifications replaces the amorphous phase with an

Jan 1, 1927

By ALBERT C. RUBEL

RECENT developments in the use of the core barrel in rotary drilling have led to its wide application in all types of development. Its use is essential to the wild-catter and a valuable guide and check even in the most closely developed areas. A perfect core would be an unbroken sample of formation whose length is equal to the amount of hole made by the core barrel, whose diameter is great enough to show the lithologic character, texture and attitude of the material encountered, whose formation is so unaltered in character and so free of contamination from outside sources that it represents a true and complete sample of the formation penetrated. From such a core it would be possible to determine the lithologic character and economic importance of the formation, whether it is oil bearing or barren, the nature and attitude of the sands and shale bodies, valuable fossil evidence and other points which would assist in the correlation or in the selection of suitable points for water shut off or production.

Jan 1, 1924

PRESIDENT SAMUEL A TAYLOR, District 3 PITTSBURGH, PA PAST PRESIDENTS WILLIAM KELLY, District 5 IRON MOUNTAIN, MICH J V W. REYNDERS, District 0 NEW YORK, N Y FIRST VICE-PRESIDENT E DEGOLYER, NEW YORK, N Y TREASURER CHARLES F RAND. . . NEW YORK, N Y

Jan 1, 1923

By M. Duclos, A. Sawatzky

A simple model has been developed which describes the steady-state solute distribution in Ti-H type systems above the eutectoid temperature in the presence of a temperature gradient. The solute distribution is dependent on the shape of the phase boundaries. An interesting result, and one that is not observed at steady state in thermal diffusion below the eutectoid temperature, is the existence of a two-phase region. The heat of transport for hydrogen in a titanium, Q*a, over the temperature range 275" to 650.C is determined to be 4500 * 230 cal per mole. The heat of transport for hydrogen in B titanium, QB* over the temperature range 320" to 590.C is found to be 630 ± 200 cal per mole. It is also shown that thermal diffusion provides a method by which phase bounduries above the eutectoid may be determined in Ti-H type systems. IN modern technology materials are being used at constantly increasing temperatures under greater temperature gradients. Thus atomic migration in metal alloys due to a temperature gradient (thermal diffusion) may in some cases occur to an observable extent. The thermal diffusion of hydrogen in zirconium has in recent years received considerable attention1-' because of the use of zirconium alloys in nuclear power reactors. The thermal diffusion kinetics below the eutectoid (547°C) are fairly well understood. At steady state the solid solution, a, and hydride, 6, phases are completely separated with the hydride precipitating at the lower temperatures. No experimental work has been carried out in the a + B region although Droege4 suggested that a complete separation of the two phases, as observed at temperatures below the eutectoid, might not always occur. In the present investigation a simple model has been used to determine the steady-state solute distribution under a temperature gradient in Zr-H type systems heated above the eutectoid temperature. The solute distribution is shown to be dependent on the shape of the phase boundaries in the constitutional diagrams and several typical cases are discussed. The model has been applied to Ti-H. This system was chosen in preference to Zr-H because of its much lower eutectoid temperature (-300°C as compared with 547.C), thereby reducing experimental errors due to oxidation and hydriding. The heats of transport for hydrogen in the a and B phases of titanium also have been determined since they were required to compare the proposed thermal diffusion model with experiment. THEORY In the presence of a temperature gradient the atomic flux in a single-phase region of a two-com-ponent system of which the atoms of only one component are diffusing is given by:' J = - U\dx + RT3 dx) which can be written as: j-D(dn/dt +Q*n/RT2)dt/dx [11 J - -D\dT + RT2)dx [1] where D = diffusion coefficient, n = solute concentration, T = absolute temperature, R = gas constant, dT/dx = temperature gradient, and Q* = heat of transport. At steady state (J = 0) Eq. [I] leads to the solute distribution: n = noexp Q*/RT where no = a constant depending on total solute content. The heat of transport Q* can be experimentally determined from the steady-state distribution. In the present paper we shall determine the solute distribution in systems having the constitutional diagram exemplified by Ti-H shown in Fig. l.' As shown, N,(T) and NB(T) are the equilibrium solute concentrations in the a and 0 phases at temperature T. Lines AA' and CC' define the region of interest to us. The following assumptions are made: 1) Steady-state conditions prevail. 2) In a single-phase region all points on an isotherm have the same thermodynamic potential so that the composition over an isotherm is uniform. If a two-phase region exists, thermodynamic equilibrium is found only at phase interfaces. However, we assume the component of the concentration gradient along an isotherm to be small so that the composition in each phase is approximately the same as at the interface and is given by the constitutional diagram, Fig. 1. 3) There is appreciable diffusion of only one component. 4) We shall consider only the case where Qa*, QB*, and Qg*, the heats of transport for solute diffusion in the a, B, and 6 phases, respectively, are positive. This has been observed for the thermal diffusion of hydrogen in zirconium3 and titanium.10 We will show that the steady-state solute distribution above the eutectoid is primarily determined by the heats of transport and the temperature dependence of Na(T) and Np(T). It may be quite different from the steady-state distribution below the eutectoid. For example, we will see that, under certain conditions,

Jan 1, 1970