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By H. F. Yancey, O. L. Furse

For several years the Bureau of Mines at its Northwest Experiment Station, in cooperation with the Mines Department. of the University of Washington, has been studying the breakage and degradation of coal. The first phase of the study was devoted to the determination of the friability of many coals of various ranks and comparison of various methods for estimating friability.' A study of the relative ease or difficulty with which various coals are reduced to the fine size required for use as pulverized fuel followed the completion of this work. Baltzer and Hudson2 list twelve research organizations in the United States, two in England, one in Germany and one in Canada that are reported to be engaged on this problem; showing the general appreciation of the need for a simple method of estimating the grindability of different coals. Hardgrove,3 ho has advanced a method for estimating grindability, points out that pulverizer tests of different coals are incomplete and unsatisfactory. He compares such tests to that of a boiler test made without knowledge of the calorific value of the coal. Frisch arid Holder4 also stress the same point. They state that,

Jan 1, 1934

By Charles S. Barrett, Robert F. Mehl, Dana W. Smith

The Widmanstatten figures found in the steels have been long recognized and in some aspects carefully studied,' especially as they occur in cast hypoeutectoid alloys. Aside from the practical importance of the structures obtained in the steels by various heat treatments, a study of the characteristics of these figures is interesting because of the rich opportunity the system affords to obtain new data on the mechanism of segregation from solid solutions. This opportunity is twofold: first, by changing composition within the austenite range the proeutectoid precipitate may be changed from that of ferrite to that of cementite, thus offering the same opportunity for changing the type of precipitate while maintaining the same basic lattice as that afforded by the Cu-Zn alloys;2 and second, the eutectoid inversion leads upon drastic quenching to the formation of martensite, a Widman-statten figure of unique interest from the crystallographic viewpoint, particularly in comparison with those formed on slow cooling.3 We have, therefore, two types of structure to study: that formed on slow cooling of hypoeutectoid and hypereutectoid alloys, and that formed on quenching hypoeutectoid, eutectoid, and hypereutectoid alloys. For each of these types of structure we require the crystallographic plane in the mother austenite along which the precipitate forms (we shall see that the precipitates in these alloys are invariably platelike in form), and also the orientation of the precipitate upon this plane. Some of these

Jan 1, 1933

By E. K. C. Williams, Nathaniel Arbiter

INTRODUCTION The surface processes involved in preparing ores for flotation and for operations depending on their flocculation/dispersion characteristics * vary widely in agitation dependence. Most of the reagents used for these purposes are added to grinding circuits, pump sumps, launders, or directly to flotation cells with the turbulent flow conditions usually adequate both for mixing reagents and for surface reactions without special conditioners. However, some reagent systems do require specific control of agitation intensities and reaction times, the more important of these being the following: 1. Activation of ZnS with CuSO4. With the usual conditions pH about 10, with collector added with the CuSO4, Cu 2+ is almost completely precipitated as basic compounds and as collector salt. As a result the levels of reagent in solution are extremely low which probably accounts for the need for separate conditioning. The agitation intensities are at about the 0.01 HP/ton level.** 2. Flocculation with natural or synthetic polymers. In this case the agitation problem is two-fold; first, to insure adequate initial mixing of the viscous stock solution of the

Jan 1, 1980

By W. F. Flanagan, D. H. Polonis, S. D. Dahlgren

Rotation diffraction patterns of Cu-4.84 wt pct Si polymystalline samples were taken during the course of isothel-ma1 affing of the suPersaturated a phase, a diffraction spots were obserzled to streak during the initial stages of aging, and this streaking was similar to the streaking of a spots observed earlier by Barvett with deformed super saturated samples of the same composition. Although it was suggested that stacking faults were the sole cause of styeaking in the deformed samples, the present study has shown that plates with one small crystallite dimension can also contribute to the streaking when there is lattice coherency across close-packed planes. THE decomposition of the supersaturated a phase in Cu-Si alloys has been reported to occur by means of both thermal and stress activation.1-4 According to the Cu-Si phase diagram,3 Fig. 1, the supersaturated a phase (fcc) is expected to transform during aging by the precipitation of the y phase. The results of earlier studies2,4 have indicated that metastable k phase (hcp with nearly ideal close packing) forms initially at temperatures below the eutectoid temperature, after which the k transforms to the a and y phases. Hof-mann et al.4 have proposed a metastable version of the phase diagram, showing the approximate boundaries for k formation below the eutectoid temperature. In view of the close-packed nature of both the a and k phases, it is essential to consider the role assumed by stacking faults in the transformation. Streaking effects have been reported by Barrett 1 in the rotating crystal X-ray patterns of strained Cu-Si alloys and were attributed to stacking faults rather than particle size effects. This deduction was based on the observation that streaks in the diffraction patterns did not occur tangent to the 220fee Debye ring. It is known that the atom movements involved in faulting leave some X-ray reflections unaffected while others are broadened,' and, in particular, it has been shown that faulting will not cause streaking of 220fee reflections tangent to the 220fee Debye ring as would be expected if all the reflections were broadened.' The formation

Jan 1, 1967

By C. J. Bier, J. F. O?Keefe

THIS study was carried out with copper because it represents the simplest form of sintering, in that but one metal is involved and all reactions occur in the solid state. [ ] The present work will cover three variables affecting the sintering process; namely, briquetting pressure, sintering temperature and time in hot zone. Although strength and dimensional changes were observed, this is primarily a metallographic study of the sintering process in copper. The term "sintering" should be understood to mean the process by which the metal powder particles of the compact become united into one body. MATERIAL USED The copper powder used was made from reduced copper oxide, and is typical of a grade used for the mass production of parts formed of metal powders. The screen analysis of the powder was as follows: [ ] The minus 325-mesh analysis was made by using a Roller Air Analyzer.1,2 The apparent density is here defined as the weight per cubic centimeter of the [ ] loose, unpacked powder as measured with the Hall flowmeter. The value for the powder used was 2.57 grams per cubic centimeter.

Jan 1, 1944

By Henry Rawdon

Cold-working is generally considered as a process of hardening metals. Diamet-rically opposite statements concerning the applicability of the scratch-hardness method in the testing of cold-worked metals, particularly after severe deformation, which exist in the technical literature led to the study of the results which are summarized in this paper. A series of metals, of which copper, iron and tin are used as illustrations here, were cold rolled to a definite degree without any intermediate annealing and the hardness determined by both the scratch and Brinell methods. The results indicate that the metal hardens rapidly during the initial stages of deformation; however, after a certain stage, which corresponds to a rather definite microstructure, the metal becomes softer and in its final form may be softer than the metal in its initial stage. As part of the study of the scratch-hardness method for metals and alloys in cooperation with one of the technical committees of the American Society for Testing Materials, the authors devoted considerable time to the study of the changes in hardness of metals when cold rolled. Various seemingly contradictory statements in the technical literature concerning the applicability of the scratch-hardness method to such cold-rolled materials were among the principal reasons for the investigation, the results of which are in part presented here. The effect of cold deformation, at least in moderate degrees, on the hardness as measured by the Brinell and other common methods is so well known that further reference is unnecessary. Concerning the scratch hardness of cold-worked metals, Martens and Heyn state' that hardness, whether measured by the ball-pressure method (Kugeldruck) or by the scratch method (Ritzverfahren), will be increased by cold deformation. Jeffries and Archer give a seemingly diametrically opposite view. They state,2 that "the sclerometer (indicating scratch

Jan 1, 1924

By D. L. Wood

INTERNAL oxidation of alloys has been investigated by Rhinesl,2 and by Meijering and Druy-vesteyn. Rhines showed that dilute Cu-A1 alloys can be internally oxidized without forming an external scale by annealing in an oxygen partial pressure equal to the decomposition pressure of Cu2O. The oxygen is supplied at the outside surface at a rate sufficient to maintain saturation of the surface with respect to oxygen. Oxygen diffuses inward and, at the interface between the subscale and the alloy, oxygen meets the solute and reacts to precipitate its

Jan 1, 1957

INTRODUCTION This chapter summarizes characteristics of porphyry copper deposits within the Cordilleran orogen east of the Coast Range plutonic complex of the Yukon and British Columbia and south to the Columbia River plateau and the Idaho batholith. Porphyry copper deposits in this area reflect a geologic environment different from that found for mineralized intrusions elsewhere in the Cordilleran orogen, both to the south in the United States and Mexico and to the west in Alaska. A section on the Tertiary Cascade porphyry copper province is included herein. The Cascade province is considered separately because its deposits display a unique mineralogy and age of mineralization. That portion of the Cordilleran orogen described in this chapter is shown in Fig. 32, with the Cascades shown in Fig. 39 (see p. 114). The regional geology of this area has been described by Monger, et al. (1972), Hollister (1974), Wolfhard and Ney (1974), Field, et al. (1974), and Stacey (1974). Each offer slightly differing views on the post-Mississippian evolution of the geology in this porphyry copper province. The descriptive geology in this chapter has benefited from many discussions with J. E. Armstrong and J. W. H. Monger. Two separate petrologic models have been used popularly to categorize porphyry copper deposits in this area, a diorite and a quartz monzonite model. The diorite model, which involves a mineralized quartz-free pluton, has also been called the alkalic type (CZM Special Volume 15, 1976, and Soregaroli, 1975) and the syenite suite (Sutherland Brown, et al., 1971). The quartz monzonite model has also been named the calcalkalic type (CZM Special Volume 15, 1976) and includes mineralized quartz-bearing plutons compositionally ranging from quartz diorite to granite, with the igneous phase closest to ore in time and space commonly being quartz monzonite.

Jan 1, 1978

By George J. Bancroft

It is unnecessary to repeat here the contents of many valuable contributions to this subject which have appeared in the Dansactions and in the publications of the U. S. Geological Survey. As a basis for the further suggestions of this paper, the following are the most important: 1. The investigation of J. R. Don,' showing the gold of certain Australasian veins to have been deposited by ascending solutions, and not by lateral secretion. 2. The theory of Prof. Posepny? distinguishing the vadose from the deep circulation, and ascribing the origin of certain classes of ore-deposits to ascending solutions of the latter class. 3. The theory of Prof. Van Hise,3 as to the underground circulation and the primary enrichment of veins thereby. 4. The paper of Prof. J. F. Kemp,4 showing that ore-deposits are largely the products of " expiring vulcanism." Many. of Prof. Kemp's ideas have been widely adopted by mining men. 5. The theory of secondary enrichment, so lucidly expounded by Mr. S. F. Emmons.V his theory, dealing with the rearrangement of ore-bodies after primary mineralization, has been generally adopted, and seems to me to have been as completely proved as the nature of the case permits. There are two facts which I think should be constantly borne in mind in formulating a theory of the genesis of ore-

Jan 1, 1908

By I. H. Silberberg, R. L. Reed, O. K. Kimbler

interfacial films have frequently been observed at interfaces between certain crude oils and water. Several investigators have postulated that the presence of these films should influence the efficiency of oil recovery in water drive or waterflood operations. They may also influence the stability of emulsions which are sometimes a problem in petroleum production, and may be a factor in the fonation of paraffin deposits in oil well tubing and flow lines. This paper presents a technique with which a modified Langmuir film balance may be used to study the compressibility and collapse pressure of these natural interfacial films. Experimental data are presented for several nude oil-water systems. Data developed are used to infer the phase state of the film as a function of such variables as rate of reduction of interfacial area, ionic composition of the subtrate and pH of the subtrate. A film of known physical characteristics is shown to have a sinnificant effect on oil recovery from an unconsolidated sand pack. Possible applications of these results to petroleum production are discussed. INTRODUCTION The use of water to displace petroleum from reservoir rocks is of major importance both as a primary and a secondary recovery process. As water invades the rock, oil is completely displaced from some pores and left as a discontinuous phase in other pores. The manner in which water moves from pore to pore is strongly influenced by capillary forces. In view of the complexity of reservoir fluid systems, there can be little doubt that complicated interactions take place at both the liquid-solid and oil-water interfaces. One of the more interesting, and least understood, of the phenomena which take place at the oil-water interface is the formation of interfacial films. These films are believed to result from the adsorption of high molecular weight polar molecules at the interface.l.2 Presence of such molecules may cause a striking alteration in interfacial tension. When the oil-water interfacial area of certain crudes is rapidly reduced, a thin region (film) about the interface assumes the appearance of a solid membrane, and striations, wrinkles and gross distortions may occur. If such a film is solid, it should greatly alter the interfacial tension normally assumed to exist between the oil and water phases. If the membrane is continuous, a solid phase would separate the oil and water. Interfacial films between crude oil and water were observed in 1949 by Bartell and Niederhausers who commented upon the apparent rigidity of the films and their possible importance in the petroleum industry. Morrell and Egloff4 had earlier attributed the extreme stability of emulsions of sea water in fuel oil to very stable asphaltic films. Numerous investigators have observed rigid films in the course of crude oil-water interfacial tension determinations by the pendent drop method. Several investigators5,6,2 have separated inter-facially active materials from crudes and attempted to characterize them chemically. Reisberg and Doscher,2 using Ventura crude, showed the interfacial tension against water (as measured by the pendent drop method) to be affected by aging, contraction and expansion of the interface, and the pH of the water. These investigators attributed the adhesion of oil to a water-wetted surface and the distortions of flow paths in glass capillaries to the presence of rigid films. Dodd7 has studied the interfacial viscosity of adsorbed films and found them to be non-Newtonian in behavior. Craighead and Harvey8 reported a series of displacements in tubes packed with 60 mesh glass beads. They interpreted the results as indicating an effect of stearic acid films on waterflood recovery and imply that natural films may produce similar results.

Jan 1, 1967

By A. M. Kivari

OPERATIONS at the cement plant of the Permanente Corporation, in the hills about 45 miles south of San Francisco and 12 miles west of San Jose, are interesting to the members because of the adoption of modern hydrometallurgical methods for handling and beneficiating raw materials. Closed-circuit grinding, classification, hydroseparation, flotation, agitation, and thickening are familiar terms at this cement plant. These methods make it possible to process refractory limestone into suitable materials for the manufacture of modern cements. Construction of the plant, having originally a design capacity of 7000 bbl. of cement per day, was started in June 1939, and the first clinker was ground on the following Christmas Day. At present the capacity is about 12,000 bbl. of finished cement per 24 hr., most of the production being low-heat cement. [t] About 3130 tons of limestone, 620 tons of clay and 100 tons of gypsum are required daily for this output. Occasionally iron oxide is added to the clay to obtain the desired composition. This, together with the gypsum, is purchased from outside sources. Up to the present time, the corporation has produced low-heat, normal, moderate-heat, moderate-sulphate-resisting, high-early-strength, oil-well, modified-oil-well, and plastic cements. Most of the present production is for Shasta Dam, near Redding, Calif., the total demand being 5.800,000 bbl. of cement. Following are some of the cement require¬ments of the Shasta Dam specifications: [PER CEN'I Chemical composition: Loss in ignition2.25 Insoluble residue0.75 S032.25 M905.00 Uncombined lime in clinker (CaO)T.25 Percentage of iron oxide to alumina ratio1.5 Compound composition: Tricalcium silicate (3CaO.Si02)Not more than 35 Dicalcium silicate (2CaO.Si02)Not less than 40 and not more than 6,5 Tricalcium aluminate (3CaO.Al203)Not more than 7 Tetracalcium aluminoferrite (4CaO.A1203.Fe203) Not more than 20 Fineness:] The average specific surface in the bin sampled shall be not less than 1800 sq. cm. per gram and no individual sample less than 1600 sq. centimeters. Compressive strength: The average compressive strength in pounds per square inch of three mortar cubes composed of one part cement and 2.75 parts fine testing sand, by weight, shall be equal to or greater than the following: [ ]

Jan 1, 1941

By O. B. Ellis

Although thousands of tons of stainless steel have been used successfully for many types of equipment, there have been few cases of failures due to the phenomenon described as stress corrosion cracking. During the past seven years only six cases of such failures have been drawn to our attention and investigated in the Research Laboratories with which the author is associated. These failures oc¬curred in two coffee urns, two wool con¬ditioning units, one dyeing machine, and another in a part of a steam-jacketed stock pot. In each case the equipment failed in a comparatively short time after exposure to conditions of high humidity at tempera¬tures in the range of 100 to 200 F. The failures in all cases were characterized by general embrittlement and cracking of the stainless steel, with only slight indications of general corrosion except at the cracks. The first failure of this type was a coffee urn returned for investigation in 1937. The top and bottom sections showed a general corrosive attack and embrittlement and cracking of the stainless steel. The chemical analyses of these sections were as follows:

Jan 1, 1945

[Cyanidation: Fresnillo, Mexico. 112. 734, 739. Abs.. YB84. 34 gold ore: before or after amalgamation. respective merita. 118, 538 high residue avoided by milling in water, 118, 542 Homestake mill, 112,607. 614 impoverishing gold ore before cyanidation justified. 118, 539 Kirkland Lake district, 112, 648, 649. Abs., YB84.32 literature prior to 1932. See Source Book. McIntyre Porcupine mines, 118, 638 mercury as an aid to extraction of gold, 118, 53 8]

Jan 1, 1936

By J. J. Jakosky

All electrical geophysical methods depend for their operation upon the effects produced by the flow of an electric current. By studying these effects it is possible to predict the general axis of current flow. The greater flow of current is in the path of greatest effective conductivity; and since the effective conductivity of a mineralized zone is different from that of its surrounding envelope (usually much greater), it is possible to locate such a mineralized zone by the distribution of current. Due consideration must be given, of course, to geological structure, to type of mineralization, and to other factors. A number of methods are used to cause this flow of current, and various methods arc available for detecting the presence of such current flow and for studying its effects. In a rather detailed way, this paper will discuss the theoretical and practical phases of the inductive methods of geophysical prospecting. Electromagnetic Generation of an Electeomotive Force The inductive method is so named because the current flowing in the conductor is obtained by electromagnetic induction, instead of by the use of ground electrodes through which a current is passed as in the applied potential systems, or by direct contact with the orebody. An alternating current flowing in a coil will create an electromagnetic field around the coil. This field will have the same frequency as the current and will radiate or travel outward from the coil in closed magnetic or flux circuits. These flux circuits (in air or a homogeneous medium) will be perpendicular to the plane of the coil and will extend or travel outward with uniform velocity in every direction. Maximum feld exists in the plane of the coil. Such a coil used for transmitting or as the "energizer" will exhibit similar figure-eight characteristics to those exhibited by the direction-finding coil which will be described in detail later.

Jan 1, 1929

By Fred C. Bond and

This paper is a continuation of two earlier papers,12 and presents new data on the grindability of various ores and other materials—the results of several years of intermittent research work on the nature of grinding and interpretation of test results. It is divided into five parts: 1. The tabulated results of several hundred grindability tests on a wide variety of ores. 2. A method of correcting screen analyses and calculating from them the surface and other properties. 3. A description of a new method of measuring the "surface energy" of an ore by pendulum impact tests. 4. Test results. 5. A general discussion of the test results and their application to grinding problems. 1. GRindability of Various Ores This part is a continuation of the paper listed as reference No. 1. The method of testing is described in detail in that paper. The sample to be tested is crushed to all through 6 mesh in rolls set at 1/16-in. opening in closed circuit with a screen. Of this sample 700 C.C. is ground dry in a laboratory ball mill under constant conditions of mill speed and ball charge in closed circuit with a screen of the desired size at 250 per cent circulating load. The mill is cylindrical, 12 by 12 in., and rotates at 70 r.p.m. It contains a charge of 285 iron balls weighing 20,125 grams and ranging from 1½ to ¾ in. in diameter. Each test is continued for a sufficient number of periods to establish equilibrium at 250 per cent circulating load, or until the composition of the circulating load is constant for successive periods. Tests are conducted at the mesh size to which the ore is to be ground in practice, and the results are expressed as the net production in grams of screen undersize per revolution of the mill. This is designated as the

Jan 1, 1939

By Fred C. Bond and

This paper is a continuation of two earlier papers,12 and presents new data on the grindability of various ores and other materials—the results of several years of intermittent research work on the nature of grinding and interpretation of test results. It is divided into five parts: 1. The tabulated results of several hundred grindability tests on a wide variety of ores. 2. A method of correcting screen analyses and calculating from them the surface and other properties. 3. A description of a new method of measuring the "surface energy" of an ore by pendulum impact tests. 4. Test results. 5. A general discussion of the test results and their application to grinding problems. 1. GRindability of Various Ores This part is a continuation of the paper listed as reference No. 1. The method of testing is described in detail in that paper. The sample to be tested is crushed to all through 6 mesh in rolls set at 1/16-in. opening in closed circuit with a screen. Of this sample 700 C.C. is ground dry in a laboratory ball mill under constant conditions of mill speed and ball charge in closed circuit with a screen of the desired size at 250 per cent circulating load. The mill is cylindrical, 12 by 12 in., and rotates at 70 r.p.m. It contains a charge of 285 iron balls weighing 20,125 grams and ranging from 1½ to ¾ in. in diameter. Each test is continued for a sufficient number of periods to establish equilibrium at 250 per cent circulating load, or until the composition of the circulating load is constant for successive periods. Tests are conducted at the mesh size to which the ore is to be ground in practice, and the results are expressed as the net production in grams of screen undersize per revolution of the mill. This is designated as the

Jan 1, 1939

By E. J. Duggan

THE mine and mill of the Climax Molybdenum Co. are at Climax, Colorado. Climax is on Fremont pass directly on the Continental Divide, at an elevation of 11,400 feet. DESCRIPTION OF ORE The Climax ore-bearing rock is essentially an altered and highly silicified granite, fully half of the gangue being quartz. Molybdenite is the only mineral of economic consequence and most of it is intimately associated with quartz in the form of fine veinlets and stringers. Other minerals are molybdite, pyrite, and chalcopyrite. While the molybdite may be readily extracted by hydrometallurgical methods, its content is too low to make such operations profitable. The pyrite content ranges from 2 to 5 per cent and that of the chalcopyrite from 0.03 to 0.05 per cent. There is not enough copper to make its recovery attractive and one of the metallurgical problems is the elimination of it and the pyrite from the product. On account of the close association of the molybdenite with the quartz and the necessity of eliminating the pyrite and chalcopyrite from the final product, fine grinding followed by flotation is the only feasible method of concentration. HISTORY Construction of the first milling unit was started in 1017 and it was operated during parts of 1918 and 1910. In the postwar years, there was almost no demand for the product and production was at a standstill until 1024. The Company's research campaign to develop the use of the metal began to show results in that year. From 1926 to 1932 production ranged from 500 to 1200 tons per day. In 1931 an additional mill section was built and production was gradually increased until in 1934 and 1935 about 3000 to 4000 tons was milled per day. This tonnage overtaxed the milling facilities, and as the demand for molybdenum was growing constantly, additional milling equipment was needed. In 1936 and 1937 another crushing plant, six additional mill sections and the necessary auxiliary plants were constructed and brought into operation. This plant was designed to mill I0,000 tons per day, but it was not long before 12,500 tons was being treated during periods of peak demands. During the summer of 1941, to meet defense needs, the mill has been required to treat 15,500 tons per day. This has been accomplished with little plant expansion and at no loss in recovery, as will be described later. To increase capacity still further, one more primary section is now being built. This will bring capacity to 18,000 tons per day, which can be stretched to 20,000 tons at a small sacrifice in recovery. CRUSHING There are two crushing plants: No. I, of 5000 tons capacity (flowsheet in Fig. I) and No. 2, of 15,000 tons capacity (Fig. 2).

Jan 1, 1942

By T. D. Yensen

I. INTRODUCTION IT is safe to say that of all the different materials that go to make up electrical machinery, iron is the most important. Upon its -magnetic and electrical quality depends not only the efficiency of the machine but, to a very large extent, the cost. Aside from the mechanical strength, there are three characteristics of iron that are of importance in this connection, viz., magnetic hysteresis, electrical resistance, and magnetic permeability. In the homopolar machine, where the magnetic flux is unidirectional, permeability is the only important factor, but in all other machines the flux is reversed in one or more parts and causes losses due to hysteresis and eddy currents. The eddy-current loss depends largely upon the electrical resistance of the iron; the higher the resistance the lower the loss, under otherwise identical conditions. These hysteresis and eddy-current losses cause heating of the machine, and as they depend upon the magnetic density in the iron, this density must be regulated so that the heating shall not be excessive. If the hysteresis and eddy-current Josses and the permeability of the magnetic circuit will permit an increase in the magnetic density, or, in other words, a decrease in the amount of iron, this in turn will mean a decrease in the amount of copper needed, with a consequent decrease in the copper loss. It is thus seen that; indirectly as well as directly, the above characteristics have an important bearing on both the efficiency and the cost of electrical machinery. In general, it may be said that iron for electrical machinery should have the following characteristics: (1) low hysteresis loss, (2) high electrical resistance, and (3) high permeability. These are the characteristics that investigators have been striving to attain since electrical machinery first came into use.

Jan 2, 1916

By E. L. Dougherty, J. W. Sheldon

A numerical method for computing the dynamical behavior of fluid- fluid interfaces is described. Results of studies made to assess the accuracy and economy of the method on a computer are reported. It is concluded that it is practical to obtain digital computer solutions for fluid- fluid interface problems with two space dimensions. PROBLEM DEFINITION We consider two-dimensional flow in a rectangle as shown in Fig. 1, where a fluid-fluid interface divides the rectangle into two regions. The pressure is specified along the lower boundary (the injection boundary) and upper boundary (the withdrawal boundary). There is to be no flow of fluid across the side boundaries, which are walls of symmetry for the flow, and px = 0 along these boundaries. The fluids are incompressible, the absolute permeability and porosity is constant, and each fluid has its own constant mobility. Thus, the pressure satisfies Laplace's equation in each region. Across the interface, pressure is continuous and the normal component of fluid flux is 1. These conditions are shown in Fig. 1. The velocity of a point on the interface in the direction of the normal from Fluid 1 into Fluid 2 is U,/ Q, where Un is the normal component of volumetric flux at the point on the interface, i.e., For brevity, we call the problem defined above "Problem A". Problem A is a simple example of a dynamical fluid-fluid interface problem. However, the same numerical methods which we use to solve Problem A can be extended to the solution of a large number of fluid-fluid interface problems which are mathematical models for various oil recovery processes,l hence our interest in Problem A. We define the interface by prescribing the x, y coordinates of a finite set of points. These points are called "interface mesh points" and are illustrated by triangles or asterisks in the figures. Fig. 2 is a procedural (flow) chart displaying the main steps in the solution. We comment briefly on some of these steps in this section and then give further details in subsequent sections. For mobility ratio greater than one it is well known that Problem A is unstable.*2 Small amplitude,

Jan 1, 1965

By K. M. Rolls, R. M. Rose, H. B. Shukovsky

Studies of the phase structure, critical current density, and resistive critical magnetic field of a 45 pct Nb-55 pct Zr superconducting alloy after final-size heat treatments are reported in this paper. A combination of optical metallography, X-ray diffraction, and electrical-resistivity measurements were used to determine the phase structure. Superconductivity measurements, made with heat-treated wires, are correlated with microstructure. Although no quantitative relationship between microstructure and critical current density is found, it is shown that SINCE Kunzler1 as well as Berlincourt, Hake, and Leslie2 first described the high-field, high-current-density superconductivity of Nb-Zr alloys, it has be- the critical current density is highest when the microstructure is finely divided by fibering, coring, precipitation, or fine-scale phase dispersions. The resistive critical field is very sensitive to the compositions of the phases present. Since the alloy investigated here is near the maximum resistive critical field for the Nb-Zr system, any phase decomposition results in a lower H,. Elimination of the effects of cold work lowers H, also. A possible interpretation of the latter in terms of internal surface superconductivity is suggested. come apparent that the resistive critical field and the current-carrying capacity of such alloys are, in large measure, dependent on composition and processing. The resistive critical magnetic field (Hr) for low current densities has been found to increase progressively with zirconium content until a flat maximum is reached between 50 and 65 pet Zr.3 For any single composition, a characteristic maximum value of H, is attained by heavily cold-drawn wire.4 critical current density (J,) depends not only upon cold work but also, apparently, upon microstructure. Heat treatments of cold-worked wires generally

Jan 1, 1965