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By W. A. Backofen, D. Lee

Titanium of commercial purity (RC-70) and two all-a (hcp) alloys (4Al-1/4O2 and 5Al-2.5Sn) were tested in sheet form under conditions of combined-stress loading. Plane-strain compression and plane -strain tension together with uniaxial compression and tension provided information for constructing the tension-tension and compression-compression quadvants of the plane-stress yield locus. Coordinate values were obtained from yield-strength measurements; the slope at each point was based on a plastic-strain ratio. The materials represented a wide range of plastic anisotropy, which was reflected in correspondingly varied departures of the yield locus from that for iso-tropy. The tension-tension and compression-compression quadrants were not identical. If the uniaxial yield strength is insensitive to direction and the sign of the applied stress, the Mises or perhaps the Tresca criterion is adequate for predicting the onset of yielding under combined-stress loading. The prediction is not so straightforward in plastically anisotropic material. Depending upon details of texture, combined-stress yielding resistance may be substantially different from that indicated by the usual criteria.' However. a continuum theory of yielding under such conditions is available for reasonably direct application.2,3 Whether or not it can be used successfully must, of course, depend upon how closely the conditions of the theory are satisfied in the material in question. In its present form the theory contains no provision for Bauschinger-type effects, nor does it allow for the consequences that might grow out of deformation by more than one mechanism, e.g., by slip and twinning.4 With those limitations, more importance must be attached to experimental information about the yield surface for anisotropic materials. Studies of the yield surface have generally been confined to states of plane stress (tension-tension and tension-compression) established in thin-wall tubes by externally applied forces and internal pressure. That approach would be entirely suitable for anisotropic materials if they were available in tube form or in sufficient bulk to be machined into test specimens. 6-9 It would not serve for the textured and anisotropic sheets of much current engineering interest, unless sheet could be formed into high-pressure tubing without structural change. Since there would seem to be little chance of the latter, practical alternatives are needed. One such alternative is the subject of this paper. It involves the use of a few selected but relatively simple uniaxial loading tests on sheet specimens. The underlying idea is presented here with some details relating to application and a few results bearing on how well it has worked. THE BASIS OF TESTING Conventional Measurements. Yielding for a general case of anisotropy is described by the plane-stress locus in Fig. 1. Reference directions in the sheet specimen are related to the stress coordinates as shown with the insert: x is the rolling direction, y the transverse direction, and z the through-thickness direction. The four reference-direction yield strengths (t, tension; c, compression), Xt, Xc, Yt, and Yc, are all different. Nine paths that can be followed in uniaxial loading experiments are identified. Paths 1, 2, 3, and 4 represent conventional tension and compression testing to establish Xt, Yt,.Xc, and Yc. Useful information also comes from the ratio of the transverse plastic-strain components associated with yielding and flow in conventional tension or compression. A condition to be satisfied in locus construction is that the plastic-strain vector be everywhere normal to the locus.10 The projection of the vector which would

Jan 1, 1967

By A. M. Sarem

For the performance prediction of multiphase oil recovery processes such as steam stimulation, there is an acute need for three-phase relative permeability data. No fast and simple experimental technique, such as the unsteady state method proposed by Welge for two-phase flow, is available for the three-phase flow. In this paper, an unsteady - state method is presented for obtaining three-phase relative permeability data; this method is as fast and easy as Welge's method for two - phase flow. Analytical expressions are derived by extension of the Buckley-Leverett theory to three-phase flow to express the saturation at the outflow face for all three phases in terms of the known parameters. It is assumed that the fractional flow and relative permeability of each phase are a function of the saturation of that phase. Other simplifying assumptions made include the neglect of capillary and gravity effects. The effect of saturation history upon relative permeability is acknowledged and attainment of similar saturation history in laboratory and field is recommended. The required experimental work and computations are simple to perform. The test core is presaturated with oil and water, then subjected to gas drive. During the test, required data are the rates of oil, water, and gas production, together with pressure drop and temperature. The ordinary gas-oil unsteady-state relative permeability apparatus can be readily modified to measure the required data. The proposed technique was applied to samples of a Berea and a reservoir core. The effect of saturation history upon relative permeability was studied on one Berea core. It was found that increase in initial water saturation has a similar effect upon three-pbase relative permeability as it does in two-phase flow. INTRODUCTION In the light of increasing demand for three-phase relative permeability data for predicting the performance of thermal and other multiphase-flow recovery processes, a simple and accurate method of experimental determination of such data is extremely desirable. Leverett and Lewis 1 described the simultaneous flow method of obtaining three-phase relative permeability data. However, Caudle et al.2 reported that this method is very time consuming and cumbersome. Corey3 proposed calculating the three-phase relative permeability from measured krg data. Corey's theory is based on simplified capillary pressure curves,4 assuming a straight line relationship between I/Pc2 and saturation. Also, Corey's method assumes a preferentially water-wet system. The simplest and quickest method of obtaining three-phase relative permeability data is the unsteady-state method where, for instance, oil and water are displaced by gas. However, in such a test the correlation of average saturation with relative permeability does not give a valid relationship because the rates of oil, water and gas flow in the sample change continuously from the upstream to downstream end. This difficulty in calculating valid relationships was solved by Welge for two-phase flow by deriving an expression for determining the outflow face saturation from Buckley and Leverett frontal advance equations.5,6 In this paper, relations are established to determine the outflow face saturation and relative permeability to all phases in a three-phase flow displacement experiment. PROPOSED METHOD The fundamentals established by Buckley and Leverett5 for two-phase flow were extended to three - phase flow and used as a basis for the derivation of saturation equations. This approach is comparable to Welge's6 use of Buckley and Leverett theory in arriving at expressions to determine the outflow face saturation of the displacing fluid in a two-phase flow system.

Jan 1, 1967

Jan 1, 1952

NEW MEMBERS The following list comprises the names of those persons who became members during the period of Mar. 10, 1917, to Apr. 10, 1917. ADKINS, HARVEY S Adkins & Denham, Engineers, Box 291,. Hazard, Ky. ANDERSON, ARTHUR P .... Leaser, Gibson Copper Co., Box 1978, Miami, Ariz. ARNOLD, EDWARD C... Min. Engr., Chief Engr., Federal Lead Co., Flat River, Mo. ASKIN, THOMAS B. H., Ball Mill Expert, Inspiration Cons. Copper Co., Miami, Ariz. BAIN, C. KREMER Butte & Superior Mining Co., Butte, Mont. BAKER, WILLIAM A.,.JR., Vice Pres. & Sales Mgr., The Georges Creek-Parker Coal Co., 306 North Gay St., Baltimore, Md. BOOTH, GEORGE H Mech. Engr., Inspiration Cons. Copper Co., Miami, Ariz. BRIDGMAN, G. TEMPLE, Asst. Consulting Mining Engr., Guggenheim Bros., 120 Broadway, New York, N. Y. BROOKS, CHARLES A Mine Surveyor, Homestake Min. Co., Lead, So. Dak. BUTCHER, FREDERIC E., Secretary, Missouri Metals Corpn., 1945 Railway Exchange Bldg., St. Louis, Mo.

Jan 5, 1917

By D. D. Donald

C. J. Barber (U. S. Smelting Refining & Mining Co., Salt Lake City)—In his paper Donald describes how New Jersey Zinc Co. made surveys for a connection between the Ivanhoe and Van Mater shafts at Austin-ville, Va. Except to say that the two faces had to meet "accurately" on line and grade, Donald does not indicate the required precision. Assuming that there were 24 angles in the 11/2-mile traverse and 15 in the one-mile traverse, it can be shown that if the average error in plumbing each shaft was 230" and the average error in measuring each traverse angle was 210". then the average error at the point of -connection would have been about ±1.9 ft normal to the line between the shafts. This calculation assumes that any errors in the triangulation would be negligible compared with the errors in the plumbings and traverses, and it also neglects taping errors. With no constant errors or blunders, the latter would be important only in lines normal to the line between the shafts. To make the average error at the connection less than 1.9 ft would, therefore, require either reducing the error in the plumbings to less than ±30", or that in the traverse angles to less than ±l0", or fewer stations, or a combination of these. Referring briefly to the triangulation, because of the problem of fitting a new triangulation into older surveys of the district the orientation deserved some mention, even though the connection could have been made with an assumed bearing. It would be interesting to know how many triangles were required and what the average summation error was before making any adjustments and without considering the algebraic signs. Perhaps this is referred to indirectly in the statement that the maximum angular error distributed was 2". Turning to the shaft plumbings, it would be helpful to know how many men were employed and how long each shaft was in use. Donald says that the surface positions of W-2 and W-3 were carefully surveyed from the collar position of W-1, without indicating how this was done. The length of the backsight would be particularly important. There must have been some error in setting W-1 vertically below the stations in the headframes. How immovable were the headframes, especially the Van Mater, which appears higher than the Ivanhoe and subject to more vibration because of skip hoisting? Donald does not say whether the plumbing wires had been previously restraightened to minimize spinning (otherwise they behave like weak helical springs). The use of light steel weights is most surprising because there seem to be excellent reasons for using heavier, nonmagnetic weights. Did the shafts contain no steel sets, pipes, power cables, etc., which might attract steel? The plumbing method described by Donald was designed for deep shafts in South Africa but differed from the South African practice in two important respects. As described by Browne,6 in South Africa the line between the wires was made parallel to the long axis of the shaft, whereas in the Ivanhoe shaft the lines between the wires were diagonally across the shaft. The main reason given for the South African practice is to insure that the gravitational attraction between the wires and the rock walls is the same on both wires, and therefore does not affect the bearing of the line between them. It seems probable, however, that the effect of air currents might be minimized in the South African procedure, and might be serious with the wires in the diagonal position at the Ivanhoe shaft. In the South African case cited by Donald the wires were swinging freely (although the plumb bobs were sheltered from air currents) but in the Ivanhoe case they were dampened with the plumb bobs set in water. In the discussion of Browne's paper R. St. J. Rowland said:' It has been the practice for a long time to damp the oscillations by immersing the bobs in oil or water. The time per oscillation is thus increased, thereby extending the time taken to complete the work. The longer the suspended wire the less there is to recommend the practice . . . The theoretical time for one swing of a simple pendulum 1050 ft long is approximately 36 sec, which would be increased by dampening the plumb bob in water. Hence very few complete swings would be observed in the 5 min intervals used at the Ivanhoe shaft. In the two South African cases described by Browne, the length of plumb line in one shaft was 5425 ft, the calculated period of swing was 81.6 sec, the average actual period was 76.6 sec, and 94 complete swings were observed in 2 hr. In the other case the length of plumb line was 3116 ft, the calculated period of swing was 61.8 sec, the average period was 63.5 sec, and 86 complete swings were observed in 1 hr 31 min. Browne concluded that observations of more than 30 swings are not likely to result in sufficient gain in accuracy to be justified. Returning to the Ivanhoe and Van Mater plumbings, an objection to the method used is that all four azimuths were taken from fixed points instead of swinging wires, and that each pair of observations would— barring blunders— check closely, and so perhaps give a false feeling of security. In fact, it seems that only two azimuths were obtained from one plumbing, and not four as stated by Donald. Nevertheless, the tying in of each pair of wires from both sides of the shaft has much to commend it. Donald's description leaves the impression that if each shaft was plumbed only once, the engineers were fortunate indeed if the average error in the underground orientation was as little as 30". Because the survey was done over a period of three years, it seems likely that the plumbings were repeated, perhaps more than once. The underground traverse angles were measured by conventional methods, but because the number of angles in the overlapping traverses was not given, the angular closure given by Donald does not indicate the accuracy with which this was done. Donald's description of a method of taping lines of irregular length is welcome. The literature on taping is usually confined to lines of about one tape length, generally 100 ft. Such lines are rare in metal mining because the time, trouble, and cost of setting points at 100-ft distances underground are not warranted. (Nevertheless civil engineers may go to this expense

Jan 1, 1960

By S. E. Bronisz, J. O. Brittain

Experiments have been carried out to study the effect of an applied stress on strain aging in steel. It was found that the stress-induced strain aging reaction proceeds rapidly in the temperature range of 0° to 60°C. The variation of stress-induced strain aging with plastic strain, aging time, and temperatures is reported. The activation energy for the stress-induced strain aging was found to be 10,000 cal per mol for the steel used in this investigation. VARIOUS observations1-5 have been made of the influence of an applied stress upon the yielding of iron and steel. However, there have been only cursory studies of the effect of an applied tensile stress upon strain aging in iron and steel1,2 The following represents the results of a preliminary study of strain aging as influenced by the application of an external tensile load during the aging process. For the most part, previous experimental work on strain aging can be classified into two parts. First, the experimental technique involved a direct determination of mechanical properties of a suitable specimen that has been plastically deformed to a constant strain and aged generally at a temperature of the order of 200°C, with the aging times varying from about 1/10 to 2 hr.6-8 The second classification of strain aging experiments involves an indirect determination of strain aging by means of physical property such as electrical resistivity or internal friction as a function of the aging time at a constant temperature and strain.9-12 The latter results have

Jan 1, 1961

THE metal iron has physical arid chemical properties which are some- what different from those of steels, but a knowledge of the pure metal is a useful starting point in studying the behavior of steels. Solid iron exists in two different crystalline forms, called alpha (a) and gamma (?) iron the former being the ordinary form at room temperature. When heated above the "A2 point," 769 C (1416 F), the metal becomes nonmagnetic, and at the "A3 point," 911 C (1672 F), it undergoes a change in crystalline form to become gamma iron. 111 the range 769 to 911 C, it is sometimes called beta (ß) iron to distinguish it from the magnetic alpha, but the two are identical in crystal structure. When gamma iron is further heated to 1392 C (2538 F), it changes into delta (d) iron, which is identical with beta or nonmagnetic alpha iron. Pure iron melts (in an inert atmosphere) at 1536 C (2797 F); the melting point is generally lowered by alloys or impurities. PHYSICAL AND THERMAL PROPERTIES OF IRON Many of the properties of iron undergo abrupt changes at the transition temperatures.1 For example, in heating through the A3 point, a sudden shrinkage in volume occurs. Similarly, melting is attended by sharp physical changes such as an increase in volume. Table 16-1 contains a summary of the measured physical properties of pure iron at several temperatures. Usually the properties change smoothly with the range of stability of a given form, but this is not always true. For ex- ample, the specific heat reaches a sharp maximum at the A2 point al- though no transformation occurs. (See Fig. 14-1.) Solvent Powers of Liquid Iron. Liquid iron is capable of dissolving most of the other metals and many nonmetallic elements as well. Of the metals that are liquid at the melting point of iron, only lead, silver, and bismuth refuse to dissolve to an appreciable extent. Table 16-2 contains a list of the common elements classified with respect to their solubility in liquid iron. Those which are very soluble or practically insoluble require no further discussion, but several of the nonmetals that are gases and exhibit limited solubility are of considerable importance to us and merit more detailed consideration.

Jan 1, 1964

By R. A. Harrington, H. R. Nelson

The: structure of anodic films formed on aluminum and other metals under varied conditions is not well known despite the wide use of such films both as protective coatings and as the dielectric medium in electrolytic condensers. The present work was undertaken as a survey of the possibilities of electron diffraction in the investigation of anodic films, especially in comparing the properties of anodic films formed under different sets of conditions and subjected to various subsequent treatments. In addition, an effort has been made to compare surface films formed on aluminum by anodic treatment with surface films formed by heating, immersion in chemicals, etc. The elcctron diffraction method in many cases has been successfully applied to the study of thin surface films. Its principal advantage is that it can be used without removing the films from the base material upon which they have been formed. The low penetrating power of electrons, in the "reflection" diffraction method which has been used in this work, prevents the appearance of diffraction patterns from substances at depths greater than about 100 Angstrom units (lop6 cm.). Different investigations of the structure of anodic films have showll widely varying results, depending on the methods used in preparing the films. Apparently under some conditions these films are crystalline and under other conditions they are amorphous, and it has been difficult to say which type of structure will be found in any particular case. Schmid and Wassermann's1 X-ray diffraction patterns of eloxal‡ films show two broad, diffuse bands, which these investigators attribute to finely divided cubic y-Al2O3.§ Burgers, Claassen, and Zernicke³ obtained sharp X-ray

Jan 1, 1940

By R. A. Harrington, H. R. Nelson

The: structure of anodic films formed on aluminum and other metals under varied conditions is not well known despite the wide use of such films both as protective coatings and as the dielectric medium in electrolytic condensers. The present work was undertaken as a survey of the possibilities of electron diffraction in the investigation of anodic films, especially in comparing the properties of anodic films formed under different sets of conditions and subjected to various subsequent treatments. In addition, an effort has been made to compare surface films formed on aluminum by anodic treatment with surface films formed by heating, immersion in chemicals, etc. The elcctron diffraction method in many cases has been successfully applied to the study of thin surface films. Its principal advantage is that it can be used without removing the films from the base material upon which they have been formed. The low penetrating power of electrons, in the "reflection" diffraction method which has been used in this work, prevents the appearance of diffraction patterns from substances at depths greater than about 100 Angstrom units (lop6 cm.). Different investigations of the structure of anodic films have showll widely varying results, depending on the methods used in preparing the films. Apparently under some conditions these films are crystalline and under other conditions they are amorphous, and it has been difficult to say which type of structure will be found in any particular case. Schmid and Wassermann's1 X-ray diffraction patterns of eloxal‡ films show two broad, diffuse bands, which these investigators attribute to finely divided cubic y-Al2O3.§ Burgers, Claassen, and Zernicke³ obtained sharp X-ray

Jan 1, 1940

Jan 1, 1957

By R. D. Vaughn

The limiting cases of non- Newtonian fluids flowing inside a concentric annular duct are developed without using a model of the fluid behavior. The solutions provide limits with which to test the various models of fluid behavior such as the power law and Bingham plastic models. The results of previous theoretical work are discussed in terms of limiting cases. This limiting case study also shows that experimental work on flow of non-Newtonian fluids in annular ducts should be confined to ducts for which the ratio of the radius of the inner wall to that of the outer wall is less than 0.3 and preferably less than 0.2. INTRODUCTION During the last 10 years the problem of laminar flow of non-Newtonian fluids in concentric annuli has received much attention large1y because of its application to the hydrodynamics of the wellbore. Recently solutions utilizing the power law1,2 and Bingham plasticl,3,4 models have been published. In this paper the method of limiting cases, which has been successfully applied to laminar-flow heat transfer516 will be applied to the problem of flow of non-time dependent, non-Newtonian fluids through annuli. This method permits solutions for the limiting cases to be made without using a model of unknown validity. The solutions, therefore, provide limits with which to test the various models which have been or will be proposed. A pertinent conclusion concerning the region of experimental work is also provided. DEVELOPMENT OF LIMITING CASES The limiting cases for the axial flow of fluids in concentric annuli may be defined with reference to Fig. 1. It is possible to define two limiting cases which pertain to the physical dimensions of the annulus. First, the annulus must degenerate to a circular pipe as the radius of the inner wall decreases or, as k = (k R/R) ? 0. Second, the annulus must approach the limit of parallel plates of infinite extent as the spacing between the inner and outer tubes becomes small in comparison with the radius R of the annulus, or as k?1. It is also possible to ascertain three limiting cases which pertain to fluid behavior. With reference to Fig. 2, as a fluid becomes progressively more pseudoplastic, the shear stress-shear rate relationship progressively approaches the indicated horizontal line more closely. At this limit the shear stress becomes independent of the shear rate. At the other extreme of increasingly dilatant behavior, the vertical asymptote is approached. Intermediate between these two limiting cases lies the case of the Newtonian fluid. Fluids which exhibit a yield shear stress also approach the limiting case of "infinite" pseudoplastic behavior. The remainder of the theoretical development is concerned with the description of and the solutions

By T. M. Morris

A SEARCH of the literature reveals that no measurements have been made of the forces acting between a small solid particle whose surface is hydrophobic, and an air bubble to which the solid adheres, both immersed in water. Analyses have been made of the forces acting to support a greased solid on the surface of water, and the forces acting to cause a solid, whose surface is hydrophobic, to adhere to an air bubble in water. The latter analysis T. M. MORRIS, Junior Member AIME, is in the Department of Metallurgical Engineering and Mineral Dressing, School of Mines and Metallurgy, Rolla, Mo. New York Meeting, February 1950. TP 2734 B. Discussion of this paper (2 copies) may be sent to Transactions AIME before Feb. 28, 1950. Manuscript received May 16, 1949. This paper is the result of work done for part of a doctor's thesis at the Missouri School of Mines and Metallurgy. is often incomplete, however, because the internal pressure of the bubble has been neglected. It will be demonstrated that the internal gas pressure is not a negligible factor when dealing with bubbles of the size encountered in flotation. A study of the forces acting between an air bubble attached to a large flat surface is informative. It must be borne in mind, however, that this is not the condition present in a flotation cell, where the particle is small compared to the size of the bubble. The bubble is allowed to spread to its maximum contact angle on a large flat surface in the first case, whereas in the second case, the spread of the bubble is limited to the surface of the small particle which is presented to the bubble. Kabanov and Frumkinl studied the forces acting to cause adhesion of bubbles of hydrogen to a large surface of mercury, which served as an electrode in a dilute sulphuric acid solution. The force acting to hold the bubble to the mercury surface was found to be the vertical component of the surface tension between hydrogen and the sulphuric acid solution. The forces tending to cause the bubble to separate from the mercury surface were found to be: (1) the force exerted due to the internal pressure of the bubble acting upon the area of contact between the bubble and the mercury surface, and (2) the buoyant force of the bubble minus the hydrostatic force acting at the base of the bubble. These investigators photographed bubbles that were just on the verge of separating from the mercury surface. From these photographs, they measured the contact angle between the mercury surface and the tangent to the hydrogen-solution interface at the point of contact between bubble and mercury surface. They calculated the volume of the bubble and the internal pressure of the bubble. The equivalence between the upward acting and downward acting forces was remarkable. Wark2 pursued an investigation similar to that of Kabanov and Frumkin, and at the same time. His deductions verified those of Kabanov and Frumkin. He also considered the conditions present in flotation and was aware of the effect of the internal pressure of the bubble. Further, he proposed several conditions under which a small solid particle would adhere to an air bubble in water. In 1922, Edser," an English physicist, made the following statement. "It must be remembered that no particle could float stably, but for the possibility of variation of the contact angle, for if this were a constant, a slight tilt would inevitably cause the particle to sink." Wark criticized this statement, maintaining that the contact angle does not vary. The experimental data to be presented indicates that Edser was correct. Experimental Procedure: Briefly, the experimental procedure was as follows. A bubble of air was generated in distilled water. A rod of known diameter, one end of which was water repellent, was attached to this bubble. The weight of the 'rod was measured. The internal pressure of the bubble was measured with a manometer. The hydrostatic head from the surface of the water to the bottom of the rod was measured. The angle between the horizontal projection of the end of the rod and the tangent to the bubble at the circle of contact be-

Jan 1, 1951

By T. M. Morris

A SEARCH of the literature reveals that no measurements have been made of the forces acting between a small solid particle whose surface is hydrophobic, and an air bubble to which the solid adheres, both immersed in water. Analyses have been made of the forces acting to support a greased solid on the surface of water, and the forces acting to cause a solid, whose surface is hydrophobic, to adhere to an air bubble in water. The latter analysis T. M. MORRIS, Junior Member AIME, is in the Department of Metallurgical Engineering and Mineral Dressing, School of Mines and Metallurgy, Rolla, Mo. New York Meeting, February 1950. TP 2734 B. Discussion of this paper (2 copies) may be sent to Transactions AIME before Feb. 28, 1950. Manuscript received May 16, 1949. This paper is the result of work done for part of a doctor's thesis at the Missouri School of Mines and Metallurgy. is often incomplete, however, because the internal pressure of the bubble has been neglected. It will be demonstrated that the internal gas pressure is not a negligible factor when dealing with bubbles of the size encountered in flotation. A study of the forces acting between an air bubble attached to a large flat surface is informative. It must be borne in mind, however, that this is not the condition present in a flotation cell, where the particle is small compared to the size of the bubble. The bubble is allowed to spread to its maximum contact angle on a large flat surface in the first case, whereas in the second case, the spread of the bubble is limited to the surface of the small particle which is presented to the bubble. Kabanov and Frumkinl studied the forces acting to cause adhesion of bubbles of hydrogen to a large surface of mercury, which served as an electrode in a dilute sulphuric acid solution. The force acting to hold the bubble to the mercury surface was found to be the vertical component of the surface tension between hydrogen and the sulphuric acid solution. The forces tending to cause the bubble to separate from the mercury surface were found to be: (1) the force exerted due to the internal pressure of the bubble acting upon the area of contact between the bubble and the mercury surface, and (2) the buoyant force of the bubble minus the hydrostatic force acting at the base of the bubble. These investigators photographed bubbles that were just on the verge of separating from the mercury surface. From these photographs, they measured the contact angle between the mercury surface and the tangent to the hydrogen-solution interface at the point of contact between bubble and mercury surface. They calculated the volume of the bubble and the internal pressure of the bubble. The equivalence between the upward acting and downward acting forces was remarkable. Wark2 pursued an investigation similar to that of Kabanov and Frumkin, and at the same time. His deductions verified those of Kabanov and Frumkin. He also considered the conditions present in flotation and was aware of the effect of the internal pressure of the bubble. Further, he proposed several conditions under which a small solid particle would adhere to an air bubble in water. In 1922, Edser," an English physicist, made the following statement. "It must be remembered that no particle could float stably, but for the possibility of variation of the contact angle, for if this were a constant, a slight tilt would inevitably cause the particle to sink." Wark criticized this statement, maintaining that the contact angle does not vary. The experimental data to be presented indicates that Edser was correct. Experimental Procedure: Briefly, the experimental procedure was as follows. A bubble of air was generated in distilled water. A rod of known diameter, one end of which was water repellent, was attached to this bubble. The weight of the 'rod was measured. The internal pressure of the bubble was measured with a manometer. The hydrostatic head from the surface of the water to the bottom of the rod was measured. The angle between the horizontal projection of the end of the rod and the tangent to the bubble at the circle of contact be-

Jan 1, 1951

By C. E. Shoenfelt

Jan 1, 1942

By C. E. Shoenfelt

Jan 1, 1942

By Rossiter W. Raymond

The manufacture of ferromanganese in the blast furnace having been the subject of considerable attention in the Institute, I beg to put on record a contribution to the discussion from a quarter hitherto not directly represented, namely, the St. Louis furnaces, near Marseilles in France, belonging to a company of which M. Jordan, a member of the Institute, is Managing Director. These furnaces commenced in 1862 to manufacture specular pig (fontes facettes) containing from three to six per cent. of manganese. In 1864 the regular production of spiegeleisen (fontes miroitantes), containing seven to ten per cent. of manganese, was inaugurated. At that time the Rhine was the only locality of this manufacture, and the Bessemer works of England and France obtained from Gernlany all their spiegel. From 1864 to the present time, the St. Louis furnaces have been advancing steadily the percentage of manganese in their product. From ferromanganese of thirty per cent. they had arrived, about two years ago, at a product containing seventy to seventy-five per cent., and for some time past they have been turning out what, as M. Jordan remarks, may fairly be Termed fonte de manganese, or manganese pig, instead of iron, since the percentage of iron it contains is not more than 8.5, while the percentage of manganese is 85, or ten times as great. This very high grade material has a peculiar appearance, entirely different from that of ordinary cast iron or spiegel. It is granular, and steely gray in color. The following analyses, communicated to the Sociètè des Ingenieurs Civils, by M. Jordan, show the composition of various products of the St. Louis furnaces:

Jan 1, 1879

By P. Duwez, C. B. Jordan

The phenomenon of the change of volume of pressed powder compacts upon sintering is well known in the field of powder metallurgy. Depending upon the metal or metals involved and the pressure used in forming, a compact may, in the course of time of sintering at a given temperature, expand mono-tonically, contract monotonically, or first show a volume change of one sign followed by a change of the opposite sign. It is clearly desirable to have accurate knowledge of the magnitude and sign of the change in dimensions to be expected in any given case, both from the point of view of direct usefulness in the fabrication of parts by powder metallurgy, and from the longer range viewpoint of elucidating the fundamental mechanism of metallic sintering. The present study was therefore undertaken as a first step in acquiring systematic and reasonably quantitative knowledge of the change in density of metal powder compacts during sintering. For practical reasons, copper was selected as the material to be studied first, and its densification followed as a function of temperature and time of sintering in hydrogen and in vacuum. Experimental Procedure The copper powder used was that designated by the manufacturer (Metals Disintegrating Co., Elizabeth, N. J.) as MD-151. This powder was sifted through Tyler standard screens to separate the fraction having particle size range between 200 mesh and 325 mesh, and this fraction was used in all the subsequent work. Compacts weighing about 10 g were then pressed in a 1 in. diam round die, using a pressure of 20,000 psi throughout. Sintering was carried out in commercially built electric furnaces in which the resistance windings are so disposed as to produce a nearly uniform temperature along the axis of the furnace for a length of about 18 in. centrally located. In order to be able to sinter in a controlled atmosphere, a 2 in. stainless steel tubing was inserted in the furnace. Each end of the tube was cooled by a water jacket about 7 in. long, and closed with a rubber stopper. The hydrogen used for one series of specimens was purified as described in Ref. 1. For the other set, a pressure of about 0.5 mm Hg was maintained during sintering by a Welch Duo-Seal Pump. The specimens were heated on square trays made of stainless steel. In placing specimens in the trays, a thin even layer of powdered aluminum oxide was first sprinkled on the bottom of the tray. A copper guard disk about half the thickness of the specimen was then placed in the tray and covered with a second layer of alumina. The actual specimen was then set on the guard disk, and a final coat of alumina sprinkled over the specimen. This technique was evolved for sintering the specimens in such a way as to reduce the influence of unknown extraneous factors to a minimum. If the specimen is placed directly on the tray and sintered, it is found that the resulting shape is that of a frustum of a cone, rather than a section of a right circular cylinder, since friction with the tray prevents the bottom of the specimen from contracting at the same rate as the top. In the arrangement used in these experiments, the guard disk provided a support which shrank at the same rate as the specimen, and the alumina powder reduced to a minimum friction between guard disk and tray, and between specimen and guard disk. The procedure followed in sintering consisted of bringing the furnace to the required temperature, and then inserting the specimen into the central heated portion of the furnace tube in one of the two atmospheres used. At the end of the heating period, the specimen was cooled by bringing it into a portion of the furnace surrounded by a water jacket. These manipulations were carried out without opening the furnace, by means of rods which were attached to the trays and operated through a sliding seal in the rubber stopper. The progress of densification of the copper compacts was studied at 1300, 1400, 1500, 1600, 1700, and 1800°F. At each of these temperatures, a specimen was allowed to sinter for each of the following time intervals: M, 1, 2, 4, 8, 16, 32, and 64 hr. The thickness and diameter of each specimen were measured with micrometers before and after sintering, and each was weighed on an analytical balance after sintering. Results The techniques described in the preceding section were found to give satisfactory results. The specimens were not detectibly warped after sintering, and were usually of uniform diameter (that is, truly round) to within 0.001 in., a very few showing a variation in diameter of ±0.002 in. All specimens were found to have the same diameter

Jan 1, 1950

Jan 1, 1959

By Murray F. Hawkins, W. J. Ainsworth

In all types of subsurface pressure gauges the extension which occurs in the pressure-sensitive element is a function of the difference between the external (well or calibration) pressure and the internal pressure within the gauge, rather than a function of the external pressure only. The internal pressure is near atmospheric and depends upon (a) the quantity of air sealed within the gauge at the time of calibration or measurement, (b) the quantity of moisture (liquid water), if any, sealed within the gauge, and (c) the temperature at which the calibration or well measurement is made. Part of this correction for the change of internal pressure with temperature is taken care of by the customary temperature coefficient of the gauge. However, part of it is not, and while this portion may be only a few psi, it is nevertheless predictable or preventable, and should be considered in precision measurements. ERROR NO. 1 If air is sealed in the gauge at the same temperature and pressure for both the calibration and the well measurements, the usual temperature correction will take care of any difference between calibration and well measurement temperatures. However, if air is sealed within the gauge at temperature T1 and pressure P1 at calibration but at temperature T2 and pressure P2 for a well measurement, because different amounts of air are sealed within the gauge in each case, the internal pressure at. or corrected to, calibration temperature Tr will he different by where all temperatures and pressures are absolute. The calibration temperature is used, and not the well measurement temperature, because the usual temperature correction reduces the well measurements to calibration temperature. The correction term as calculated by the above equation is separate from. and in addition to, the usual temperature correction. Example: T, = 540°R, sealing temperature at calibration P, = 14.7 psia, sealing pressure at calibration T2 = 460°R, sealing temperature at well P2 = 14.7 psia, sealing pressure at well Tr = 660°R, calibration temperature AP = 660 [14.7/460 — 14.7/540] = 3.1 psi While this error is small even under these somewhat maximal conditions, it nevertheless represents a practical situation which did occur, and which as a matter of fact gave rise to this note. Where AP is positive, as above, the correction is added to the measured pressure; where negative, subtracted from the measured pressure. This correction should also be considered in successive calibration runs where the gauge, for example, may be warm from a previous calibration at an elevated temperature. ERROR NO. 2 Where a small quantity of moisture (liquid water) is sealed within the gauge at atmospheric conditions, the increased vapor pressure of the water at higher well or calibration temperatures will cause an increase in internal pressure. This moisture will come presumably from condensation within the gauge following temperature changes, from moisture on the operator's hands, and from atmospheric moisture (rain, mist, fog, etc.). Calculation shows that approximately 0.2 cc of water (three to four drops) is sufficient to saturate the air within an Amerada RPG-3 Gauge at 160°F, at which temperature the vapor pressure of water is about 5 psia. As the vaporization occurs in a sealed volume, the increase in internal pressure will be in excess of this 5 psi. At higher temperatures the pressures will be higher; however more water will be required to saturate the air within the gauge. Some experimental work was carried out with an Amerada RPG-3 Gauge at 200°F fitted with a 1,000 psi element, both with a dry recording chamber and with a small amount of water added. The results directly proved the existence of the error due to the presence of moisture, and, it is felt, indirectly, due to the differences in sealing temperatures and pressures, as both effects may be ascribed simply to an increase in the moles of gas within the recording chamber. SUMMARY In precision measurements the error introduced by sealing the gauge during a well test at a different temperature and pressure from that of calibration may be corrected for by using the equation presented, or it may be prevented by taking care always to seal the gauge at near calibration conditions. The error introduced by sealing moisture in the gauge may be prevented by taking care to keep moisture out of the gauge, or by removing the moisture by either warming or evacuating the gauge. Both of these errors are independent of the range of pressure measurement and the type of gauge, and are in addition to the usual temperature correction. ACKNOWLEDGMENT Appreciation is expressed to W. B. Kendall, Geophysical Research Corp., Tulsa, Okla., who pointed out the error from differences in sealing temperatures during some winter work in Canada. ***

Jan 1, 1956

By R. L. Schmidt, J. D. Verhoeven

The diffusion coefficients and electrotralzsport mobilities of aluminum, gallium, and arsenic have been determined in molten germanium with the capillary reservoir technique. The diffusion coefficients are slightly higher than those determined by the solidification technique of Brirton et a1.1 It was found that aluminium and gallium migrate to the cathode in molten germanium) whereas arsenic migrates to the anode under an electric field. A possible technique for producing p-n junctions by means of electric field freezing is discussed in view of the experimental data. In the past decade or so the literature has abounded with articles concerning the solid-state properties of the semiconducting elements germanium and silicon. It is surprising by comparison how little has been published concerning the liquid-state properties of these materials. In the production of doped germanium or silicon the diffusion coefficient of the dopant in liquid germanium or silicon is an important quantity. Yet, to the best of our knowledge, no one has ever made a direct measurement of the diffusion coefficient of solutes in either molten germanium or silicon. A number of authors'-4 have determined some diffusion coefficients by the indirect technique developed by Burton et al.1 This technique appears to give numbers of the correct order of magnitude but it does depend upon a number of assumptions in the analysis and also requires prior knowledge of the viscosity of the melt. In the present work a more direct measure of the diffusion coefficients of arsenic, gallium: and aluminum in molten germanium has been made. It has been shown independently by two groups of authors5, 6 that, when an electric current is passed through the interface of a solidifying metal containing an impurity, the resulting electrotransport in the liquid boundary layer at the interface offers a mechanism for control over the redistribution of the impurity accompanying the solidification. These authors show that the degree of control is proportional to the mobility, U of the impurity atoms in the liquid boundary layer, where the mobility is defined as the drift velocity relative to the solvent per unit electric field. In principle the results apply to the solidification of a doped semiconductor and offer an interesting technique for control of the doping of a semiconductor. In the present work the mobilities of aluminum, gallium, and arsenic were determined in molten germanium in order to evaluate the potential usefulness of electro-transport as a technique for solute control when applied to the solidification of doped germanium. EXPERIMENTAL PROCEDURE Both the diffusion coefficients and the mobilities were measured using high-purity alumina capillaries and a resistivity technique for analysis. A schematic diagram of the electrotransport apparatus is shown in Fig. 1 and the details of the cell design are shown in Fig. 2. For the mobility experiments electrical contact with the bottom of the capillary was made with graphite, as shown in Fig. 2. In order to prevent electrical contact with the melt the graphite was coated with a thin layer of alumina using a plasma spray torch. The cell assembly, a graphite electrode, and another assembly containing two blank capillaries were fastened to the lavite disk shown in Fig. 1. To make a run the system was evacuated and the doped germanium was outgassed at the operating temperature of 1030°C. The cell and blank capillaries were then submerged beneath the melt and a slightly positive pressure of helium was introduced to fill them. After passing current through the cell for a given time the cell and blank capillaries were raised from the melt and the furnace was shut off. The temperature of the cells dropped below the freezing point of germanium within 1 to 2 min after the furnace was shut off.

Jan 1, 1968