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By Niels Hansen

The substructure formed by drawing at room temperature in aluminum (99.5 and 99.998 pct purity) and in recrystallized aluminum aluminum-oxide products containing from 0.2 to 4.7 wt pct of aluminum -oxide was examined by transmission electron microscopy, and the flow stress of the drawn materials was measured by tensile testing at room temperature. A sub-grain structure was present after a reduction in area by drawing of 10 to 20 pct, and the subgrain size was observed to decrease with increasing deformation. The tensile data show that the increase in flow stress (0.2 pct offset) by drawing from 10 to 95 pct depends on the reduction in area, not on the composition of the materials. Dispersion strengthening and subgrain bowzdary strengtlzening contribute to the flow stress, and these strengthening processes have been found to be linearly additive. The flow stress (0) can be related to the subgrain size &) by the Petclz relation = uo + k . t, where go is dependent on the composition of the products and k is approximately the same far all materials. THE microstructure of dispersion-strengthened aluminum aluminum-oxide products consists of small oxide plates distributed in an aluminum matrix. The matrix structure depends on the manufacturing history, and in hot-worked as well as cold-worked products the matrix is divided by subgrain (or dislocation) boundaries. For hot-extruded products it has been shown1 that dispersion strengthening and subgrain boundary strengthening are linearly additive, and the flow stress (0.2 pct offset.) at room temperature has been related to the subgrain size (ts) by a Petch equation,2,3 s = so + k . ts-1/2, where s0, increases with increasing oxide content. For cold-worked products containing subgrains no systematic work has been reported, and it was the aim of the present study to examine the microstructure and the relationship between the flow stress and the subgrain size for such products. The behavior of' aluminum aluminum-oxide products depends on the purity of the aluminum matrix, and aluminum of the matrix purity (99.5 pct) was included in the investigation. The literature contains few data about the behavior of this impure aluminum, and aluminum of a higher purity (99.998 pct) was therefore also examined. As regards the relationship between the flow stress and the subgrain size in cold-worked dispersion-strengthened products, no systematic work has been reported. For aged cold-worked structures containing fine precipitates (Fe-Mo carbide) a Petch relation has been found,4 and it has been shown that the k value NlELS HANSEN is Head, Metallurgy Department, Danish Atomic Energy Commission, Research Establishment Riso, Denmark. Manuscriot submitted January 9, 1969. IMD is approximately the same as in iron, whereas the s0 value is higher owing to the presence of the precipi-tates. Investigations of metals such as tungsten,' ferrous metals,4,6 and molybdenum7 cold drawn or swaged at room temperature have shown that the flow stress can be related to the subgrain size by a Petch relation when ts is taken as the subgrain size perpendicular to the direction of deformation. For aluminum no work has been reported on the relationship between the flow stress and the subgrain size after deformation at room temperature, whereas for aluminum tensile strained at different temperatures in the range -183" to 375°C a Petch relation has been found by taking ts equal to the subgrain size.' In the present study two aluminum materials (99.998 and 99.5 pct) and three aluminum aluminum-oxide products (containing 0.2, 1.0, and 4.7 wt pct oxide) were drawn at room temperature to reductions in area from about 10 to about 95 pct. The structures were studied by transmission electron microscopy, and the flow stress (0.2 pct offset) was measured at room temperature. EXPERIMENTAL Materials. The materials are given in Table I together with the chemical analysis. The three aluminum aluminum-oxide products were manufactured from aluminum powder that had been compacted and Table I. Chemical Analysis of Materials Al203 Fe SI Material wt pct wt pct wt pct 99.998 pct* - 0.0004 0.0012 Aluminum 99.5 pctt - 0.36 0.16 Aluminum AlMD13† 0.2 0.16 0.12 Aluminum- -Oxide AlMD105† 1.0 0.26 0.18 Products SAPISML960s† 4.7 0.22 0.19 *Other impurities: O.0004 pct max each of Cu and Zn (supplier's analysis). †Other impurities: 0.03 pct max Cu. 0.02 pct max each of Mn, Mg, Zn, Ti. Table 11. Mean Diameter of Aluminum-Oxide Particles in Extruded and in Cold--Drawn Aluminum Aluminum-Oxide Products Mean Diam. of A1203-Plates* Material State A AlMD105 Extruded 540 Cold Drawn 97 pct 510 SAP ISML 960 Extruded 770 Cold Drawn 95 pct 820 *The standard deviation of the mean is approx. 5 ±pct.

Jan 1, 1970

[Appalachian Petroleum Section: James M. Kimbrough, chairman; John H. Adair, first vice-chairman; Walter L. Diddle, second vice-chairman; Byron M. Finch, secretary-treasurer. Balcones Section: Robert V. West, chairman; Frank W. Jessen, first vice-chairman; Zane V. Morgan, second vice-chairman; Brantley G. Myers, secretary-treasurer. Meets 4th Wed., Petroleum Club (San Antonio) or Terrace Dining Room (Austin) Billings Petroleum Section: Charles B. Evans, chairman; L. M. Lyon, first vice-chairman; Gordon E. Lansford, second vice-chairman; Fred. A. Haddenhorst, secretary-treasurer. Meets 3rd Tues., Billings Petroleum Club. California Coastal Section: Robert L. Richardson, chairman; David K. Hayward, first vice-chairman; W. Jackson Bransford, secretary; William N. Harwell, treasurer. Meets 3rd Thurs., Pierport Inn, Ventura. Caracas Petroleum Section: Edwin A. Moo re, chairman;. Jose Cirigliano, vice-chairman; Frank B. Davis, secretary; Robert N. Powers, treasurer. Meets 2nd Tues., Caracas Theater Club.]

Jan 1, 1961

By John C. Cosgrove

IT was just five minutes past midnight, on Wednesday, Jan. 5, 1938, that Mrs. Cosgrove and I sailed from New York City. Our trip was to completely circle the globe, to cover over 40,000 miles and stop at thirty ports-from New York to Trinidad, to South America, via South Africa to the Orient, to India, to the Malay States, to Indo-China, the Philippines, Australia, New Zealand, Fiji, and across the Pacific home via Honolulu. It is not my intention to make this a complete, technical study of coal or coal mining in the various countries that .we visited but more to outline the general in- formation that the mining engineer and coal operator would absorb in his travels. Coal is the universal fuel and is in use wherever there is commerce and industry. Even on our ship, which, like practically all ocean liners was an oil-burner, a considerable quantity of coal was used for cooking.

Jan 1, 1939

CONTENTS PAGE SOUTHWARD, GLENN B.-Coal Mining by the V System. Discussed by Glenn B. Southward, Howard N. Eavenson, Edward B. Raiguel, Thomas de Venny, J.. J. Rutledge, Graham Bright 1 ARMS, RAY W.-Dry Cleaning of Coal. Discussed by Ray W. Arms, S. A. Taylor, Howard N. Eavenson, W. R. Crane, F. F. Jorgenson, G. R. Delamater. 6 EAVENSON, HOWARD N.-Data About Labor Employed in Various Bituminous Coal Mines. Discussed by Howard N. Eavenson, George H. Ashley, E. A. Holbrook, S. A. Taylor, R. V. Norris 14 Coal Mining by the V System Discussion of the paper of GLENN B. SOUTHWARD presented at the New York Meeting, February, 1924, and issued as Paper No. 1300-C, with MINING AND METALLURGY, February, 1924. MEMBER.-How do you pay your men for loading? GLENN B. SOUTHWARD.-Everything is on time basis. MEMBER.-How many men do you have loading across one of the diagonal faces? GLENN B. SOUTHWARD.-From four to five, depending on the length of the face. Our loaders are so arranged that each will give about twenty-five tons per loader a day. MEMBER.-How much timber do you use? GLENN B. SOUTHWARD.-A little more than will be used in room-and-pillar work, but not a great deal more. We have not attempted to recover much of our timber. MEMBER.-IS the mine union or non-union? GLENN B. SOUTHWARD.-Non-union. HOWARD N. EAVENSON, Pittsburgh, Pa.-I went .through that mine some weeks ago, and think that the author has been very conservative in his statements about the amount of loadings, etc. EDWARD B. RAIGUEL, Huntington, W. Va. (written discussion).¬Page 7 shows 60 men employed in day and night shifts, inside the mine, producing 750 tons per day. Let us reduce these figures to a man-hour basis, for comparison with Mr. Eavenson's figures on West Virginia mines, as follows:

Jan 6, 1924

By L. R. Weisberg, E. A. Miller

Single-crystalline films of silicon of good quality were vacuum-deposited on sapphire. The improved crystallinity was achieved by the strict exclusion of oxygen from the evaporation system, including the use of a "oxygen-free" silicon source. To minimize possible contamination of the source, the silicon was sublimed from the solid at about 1390° C. using a simple electron bombardment system to heat the silicon. This resulted in deposition rates of about 5 to 7 µ per hr and film thicknesses of 4 to 20 µ. The vacuum during deposition was ordinarily about 5x 10-8 Torr, DESPITE the success achieved in the chemical vapor deposition of silicon on sapphire using Silane,1-4 vacuum deposition has not provided comparable properties. For example, Chu et a1.5 vacuum-deposited silicon on single-crystalline substrates of A12O3, Sic, ThO2, and other compounds, and, although some epi- but the use of ultrahigh vacuum (about 1 to 3 x10-9 Torr) during deposition did not significantly improve the results in the oxygen-free system. The crystalline quality of films deposited on (0001) sapphire was found to be considerably superior to (1102) sapphire surfaces. Using (0001) sapphire, single-crystalline films were deposited at temperatures as low as 780° C and as high as 1075°C, with the best crystalline quality obtained at about 1000°C. At this temperature, hole mobilities over 250 sq cm per v-sec were achieved. taxy was indicated, single-crystalline films were not produced. More recently, Salama, Tucker, and young6 evaporated silicon on single-crystalline sapphire, but only poor crystallinity was observed, and low carrier mobilities were measured. In the present experiments, good-quality single-crystalline films of silicon on sapphire have been achieved by specifically excluding oxygen from the evaporation. This included not only the use of a "clean" vacuum system but, of special importance, the use of an oxygen-free silicon source. This has also been shown to provide a dramatic improvement in silicon homoepi-taxy.7 As a result, silicon-on-sapphire films with hole mobilities over 250 sq cm per v-set were achieved, and single-crystal films were grown as low as 780°C and as

Jan 1, 1969

By AIME AIME

CORROSION of tanks, pipes and other equipment in the oil fields is becoming worse as the production of high- sulfur crudes in the Texas panhandle and west Texas areas increases. It has been estimated that .in certain fields of that State one tank out of every five has to be replaced every year because of the high sulfur content of the crude. One suggested method for combating tank corrosion is the use of .materials which have a high resistance to the corrosive action of hydrogen sulfide and high-sulfur crudes; aluminum is one of these materials. As a result, the United

Jan 1, 1929

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

By G. R. Love, C. C. Koch

The changes in superconducting properties with aging time have been studied ,for the pecipitation reaction in a Tc-30 at. pct V alloy. Superconducting critical temperature, upper critical field, and relative critical current density were determined by ac susceptibility techniques. Aging produces changes in critical temperature of both matrix and precipitate which can be rationalized by compositional effects. maximum flux pinning (critical current density) occurs at a time during aging when subgrain boundaries are completely decorated with precipitates and the subgrain centers remain precipitate -free. The particular effectiveness as barriers to flux motion of planar defects which enclose regions of low deject density is discussed. THE precipitation of a second phase can dramatically modify the superconducting properties of type I1 super-conductors. According to Livingston and Schadler1 one might expect changes in the primary, secondary, and tertiary superconducting properties of the material. Changes in matrix chemistry caused by precipitation can alter the fundamental superconducting parameters; critical temperature, Tc, and thermody-namic critical field, Hc. The concimitant changes in electron mean free path (reflected in normal state resistivity) can affect the critical fields Hc 1, IIc2, Hc3. Finally, the presence of precipitate particles may hinder the motion of flux lines and may considerably improve the current-carrying capacity in high-field superconductors. The influence of precipitation on superconducting properties has been studied in a number of systems.2 Magnetization measurements have been used to study the influence of precipitates on flux pinning in lead-base alloys by Livingston3 and Evetts et al4 In these alloys precipitates induced magnetic hysteresis and flux trapping. The amount of hysteresis increased with the volume fraction of precipitate and decreased with coarsening of the precipitate. Jn an Al-Zn alloy5 and an A1-Ag alloy6 the initial precipitate size was presumably smaller than a coherence length and coarsening increased magnetic hysteresis5 and critical current density.6 The influence of precipitation on superconducting properties has also been studied in several of the commercially interesting Ti-Nb7-10 and zr-Nb11 alloys. The maximum in critical current density for these alloys was confined to a narrow range of either isothermal aging time" or isochronal aging temperature7 during the precipitation reaction. Thus, experimental evidence and theoretical considerations suggest there is an optimum precipitate size, spacing, and density, and a critical composition with respect to the matrix for flux pinning. What these "optimum" values might be and the relative importance of each is still not clear, although a few generalizations can be made. It is generally accepted1' that particle sizes smaller than the coherence length or larger than the inter-flux line spacing are poor pinning centers. In high Hc2 materials, precipitate sizes for maximum values of critical current density lie in the range of 50 to 2000Å,9,7 and there are indications that increasing dissimilarity between precipitate and matrix produces increasing pinning force.13 Because of several interesting features of the aging reaction in a Tc-30 pct V alloy, we have chosen to study the influence of precipitation on the superconducting properties of this alloy. The physical metallurgy14 and a survey of the superconducting properties" of the Tc-V alloy system have been reported. The Tc-V phase diagram is presented in Fig. 1. At 1500°C the Tc-30 pct V alloy is in the single phase 6 field. Samples quenched from the 6-phase field have a CsCl structure X-ray diffraction pattern at room temperature and it has been proposed that the 6 structure is closely related to the bcc lattice.14 When held isothermally below the eutectoid temperature, 115O°C, the 6 phase decomposes into the CsCl and hcp phases.

Jan 1, 1970

By J. Ostachowicz, B. Holynska, M. Lankosz

The paper presents an analyzer and the method for the continuous determination of weight percentage of ore grains with diameter smaller than 75 pm in mineral slurries. The method is based upon the measurement of characteristic x-rays of copper excited by primary radiation of two different energies 16.5 keV and 60 keV from Pu238 and Am241 sources respectively. Additionally the backscattered primary radiation is measured in order to correct the variations of the solids content in the slurry.

Jan 11, 1979

By C. Kremer Bain

DURING the past several years of diamond drilling in Washington County, Mo., the St. Joseph Lead Co. has discovered a concentration of commercial lead-zinc ore at four different points within an area of 36 square miles. The largest and to date the most promising group of these orebodies is located in the Indian Creek area. It was considered to be of sufficient value to warrant development.

Jan 9, 1953

This is a most interesting paper and some data in it are corroborated by work I did at Watertown Arsenal some time ago with iron powder. I would like to ask Dr. Wulff to say just a little more about the compressive and tensile stresses on the surface of compacts. JOHN WULFF (author's reply).-Our work has not yet been completed; although enough data have been obtained with cylindrical compacts of iron to permit some conclusions. Briefly, in a compact 3/4 in. high and 1/2 in. in diameter pressed at 48 tons per sq. in., the residual stresses on the surface measured by X-ray diffraction techniques are as follows: The radial stresses on top center and bottom of compacts are practically zero; the longitudinal residual stresses on the side walls are near the top quarter of the compact about seven tenths that of the yield point of mild steel in tension; at the center surface of the compact they are in compression and in magnitude about 0.3 that of mild steel in tension; near the bottom, they are practically zero. F. V. LENEL.?- I was particularly interested in the work that Messrs. Wulff and Seelig reported on the influence of lubrication on the density of parts. In connection with the work of the American Society for Testing Materials on determining the green density of a compact, we ran into considerable difficulty in getting reproducible results of green density determinations. It was much easier to get a reproducible green density when the lubricant was mixed with the powder than when the lubricant was applied to the die walls; particularly when the die was not perfect-i.e., if it was somewhat rough or out of round. In this case, it was almost impossible to get reproducible green densities when the die walls were lubricated, while it was not too difficult to get reproducible

Jan 1, 1946

By A. H. Rhoades, D. T. King, R. J. Gray

Tests and methods of detecting oxidized coal are studied. Particular emphasis is placed on the microscopically discernible changes that accompany the chemical and physical changes affecting the technological properties of coal during oxidation. Coal samples were used from the low-volatile Pocahontas No. 3 Seam, McDowell County, W.V., and from the high-volatile Cedar Grove Seam, Mingo County, W.V. Tests conducted include: carbonization, free-swelling index, phase inversion, froth flotation, Gieseler plasticity, oxygen by difference and by neutron activation, volatile matter, pH of coal slurries, alkali solubility, and electrostatic charge.

Jan 1, 1977

By B. Silliman

THE remarkable outflow of natural gas recently developed in Western Pennsylvania, and along the valley of the Ohio and its tributaries, has called attention to an important series of patents for improvements in glass-fnrnaces and the manufacture of glass, which the brothers Siemens have made since 1872. The basement-patent of this series, is No. 127,806 of the U. S. Patent office, and is of date June 11th, 1872. This has been followed by eleven other patents (including one re-issue), all for improvements in glass-furnaces, or methods of manufacture, of which the latest is of date July 11th, 1882. Nine of these patents were issued in 1880-82. The following is the list of these patents, in order of dates, viz.: 1872. June 11th. No. 127,806 (U. S. office), Improvement in glass-furnaces; 17 sheets drawings, 5 pages text. This is the basement-patent. 1877. April 17th. No. 139,800. Improvement in the manufacture of glass; 3 sheets drawings, 2 pages text. Boats and floating vessels swimming in the liquid glass of the tank-furnace. Re-issued in 1880. q. v. 1880. April 27th. No. 226,931. Furnace for annealing and tem pering glass. " July 13th. No. 220,846. Glass-melting-furnace. " August 3d. No. 230,668. Glass-melting-furnace; 4 sheets drawings, 2 pages text.

Jan 1, 1885

New York Meets first Wednesday after first Tuesday of each month. J. E. JOHNSON, JR., Chairman EDGAR RICHARD, Vice-Chairman D M LIDDELL Secretary, 7 Wall St.. New York. N. Y. C. A. BORN, Treasurer JOHN V. N. DORR LEWIS W. FRANCIS Boston Meets first Monday of each winter month. R. L. AGASSIZ, Chairman JAMES G. CARLETON. Vice-Chairman E. E. BUGBEE Secretary-Treasurer, Mass. Inst. of Technology, Cambridge, Mass. W. E. C. EUSTIS G. A. PACKARD Columbia Holds four sessions during year. Annual meeting in September or October. W. H. LINNEY, Chairman OSCAR LACHMUND, Vice-Chairman LYNDON K. ARMSTRONG, Secretary-Treasurer, P. O. Drawer 2154, Spokane, Wash. STANLY A. EASTON S. SHEDD

Jan 12, 1917

By J. D. Hunt, R. J. McDonald

It is proposed that extensive fluid motion occurs between the dendrites of a Partially solid casting and it is suggested the A segregates in steel castings are a direct result of this motion. The fluid flow arises because of density differences between liquid ahead of the dendrites and the interdendritic liquid. Experiments are described on a model system investigating this fluid motion. The importance of interdendritic fluid flow is discussed with reference to longitudinal segregation. SERIOUS macro segregation is often found in large killed steel ingots. Among the most common segregates are those known as A and V, Fig. 1. The A segregates are arranged over the surface of cones, the wide parts being at the base of the ingot. The A segregates are pencil like in shape and extend from the columnar into the equiaxed region. The V segregates are distributed over inverted cones but have a less well defined shape. They occur at the center of the ingot. Because of the commercial importance of macro inhomogenities these segregates have attracted wide-scale attention. The segregates contain alloying elements and impurities which depress the freezing temperature and are thus the last liquid to freeze. A number of explanations have been proposed to explain their presence. It has been suggested1'' that the segregates are the result of the equiaxed zone growing towards the columnar region together with the interaction of convection within the bulk liquid. It has also been proposed that the segregates are the result of nucleation and rapid growth ahead of the dendritic front.3 Neither of these explanations is completely satisfactory because A segregates are pencil shaped and are not found as continuous cones. In this paper an alternative mechanism is proposed, and experiments are described on a model system to determine whether the mechanism occurs in practice. It is thought that A and V segregates are not peculiar to steels but should occur in many other large castings. Fluid motion within the bulk liquid region of a casting has been extensively discussed. Little attention has been paid to fluid motion within the partially solid regions. The work415 that has been done has been mainly concerned with the fluid motion which results from the volume contraction on freezing. The volume contraction is used to explain various types of macro segregation. The present authors suggest that in many cases the fluid flow resulting from volume contraction will be small compared with that due to other causes. When the columnar region is growing, the liquid still remaining between the dendrites has a much lower temperature near the ingot walls than at the dendrite tips. The composition of the liquid in contact with solid will vary with temperature. The density of the liquid will thus vary both because of changes in temperature and composition. The layers of different density liquid will give rise to a slow but steady liquid flow through the interdendritic regions. If there is no density change with composition, the temperature gradient within the dendritic region should give rise to a downward flow between the dendrites, shown schematically in Fig. 2. When the liquid density changes appreciably with alloy concentration this motion could either be en-

Jan 1, 1970

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 W. A. Knoll

THE sinking of a new shaft at the Newport mine, Ironwood, Mich., was started in May 1931 and completed on Aug. 3, 1932. During this period, 2665 ft. of shaft in granite was completed, at, an average advance of 6 ft. per 24 hr. In November of 1930, experimental work was con-ducted oil 65 ft. of shaft through 22 ft. of overburden where ledge was encountered, and this work convinced the operators that all drilling could be clone with vertical holes with the blasting relief to a 4 ½ -in. hole drilled vertically in the center of the cut. The reason for not adopting the conventional V-cut was to get away from damaging the shaft steel. The blasting in a V-cut naturally tends to throw the broken material upward, but with the cut as adopted the relief was in a horizontal direction to a large extent. The scheme of mucking employed made it necessary to keep the steel shaft sets within 511 ft. of the bottom at all times. This could not be clone without serious damage with a V-cut when blasting in granite. The cut as drilled also broke 10.53 ft. per round of drilling, which was considerably more than the experience with a V-cut in the sane material. The extended cut reduced proportionately the delays for charging, blowing smoke and handling drilling equipment in the shaft. Another advantage was the ease in drilling vertical over inclined holes, and the preservation of the proper spacing of the drill holes at the bottom of the cut.

Jan 1, 1938

By F. J. Fayers, R. L. Perrine

For many years the problem of increasing ultimate recovery of oil from a reservoir has been a subject of interest to the oil industry. At present, a standard secondary recovery technique is to flood the reservoir with water once natural forces of the system are depleted. The permeability characteristics of the rock, together with interfacial forces which exist between the two fluids and the porous material. allow only part of the oil in the rock formation to be recovered by the water-flooding process. Laboratory experiments have shown that when detergents are added to the flooding water, the flow properties of oil in a porous rock arc improved. This improvement results in greater oil recovery. Even though higher recoveries are obtained using detergents, the extra cost associated with the method may make it economically unsatisfactory. To establish economic feasibility requires experimental laboratory measurement of fluid and rock properties together with a calculational procedure to predict field results. Pilot tests in the field may also be required. This paper presents a mathematical procedure for predicting detergent flood behavior. A number of reasonable simplifying assumptions are made to obtain a tractable system of equations. The resulting method may be regarded as a generalization of Buckley-Lev-crett' theory to solve simultaneously for water saturation and detergent concentration profiles. Consequently this type of calculation can be used in much the same manner as Buckley-Leverett theory is used to evaluate a water flood. The mathematical method employed is the so-called method of characteristics for solving hyperbolic partial differential equations. This application of the method is instructive because several other problems in reservoir analysis may be analyzed in a similar manner. FLUID FLOW EQUATIONS The flow behavior of oil and water without detergent through porous reservoir rock is usually expressed by Darcy's law and a continuity equation for each phase. If gravitational forces are neglected, vrg = kr (s)µr v p rg.........(1) vrg = kr (s)µr v p rg.........(1) ? pa va = F ?/?t (sd) where v is the volumetric flux, k represents permeability, S is saturation, and P the pressure. Fluid viscosity is denoted by 11, p is the density, 4 is porosity, and I the time. The subscripts w and o refer to water and oil. The capillary forces in the system lead to a difference in pressure between phases. This may be expressed by the relation: Pm -P0 =Pc(S).........(5) The capillary pressure? P,, is determined experimentally as a function of saturation. DETERGENT BALANCE EQUATION Addition of detergent to the water phase affects the flow properties of the system. Capillary pressure and relative permeability become functions of detergent concentration, c, as well as fluid saturation. That is: P--P (S,c) and k,,,.- - -- k,,,. At low oil saturation values, the presence of detergent reduces capillary pressure and reduces the relative permeability ratio. Detergents are surface-active and adsorb on rock surfaces. The quantity adsorbed, a, will depend on the concentration c of detergent solution and may also depend on the saturation; thus, a = a(S,c). In this analysis we have assumed that the detergents used are water soluble but not oil soluble, and their movement is therefore restricted to the water phase. The dispersion of detergent in water is neglected by comparison with transfer by flow within the system. Detergent movement is determined by the water flux and adsorption: ? cv m = -F ?/?t (cs + a) We will assume that the quantity of detergent in solution is too small to significantly change water density or viscosity. When the permeability and capillary pres-

By William B Price, Ralph W. Bailey

Arsenic, antimony and phosphorus are now used in the brass industry as standard inhibitors in preventing dezincification in condenser tubes. This subject has been thoroughly covered by Barry,l who de- scribed the testing procedure by total immersion of suitable specimens in a I per cent cupric chloride solution at definite temperatures. Effects of dezincification were then determined by loss in tensile strength and elongation of the test specimens after definite periods of immersion. In the crystallography of the chemical elements as tabulated by William Hume-Rothery,2 phosphorus (metallic), arsenic, antimony and bismuth are placed in group V-B and the type of crystal lattice for arsenic, antimony and bismuth is given as rhombohedral. The Metals Handbook3 lists them as 'rhobomhedral hexagonal," with the additional notation that for arsenic this is the ordinary form at 20°C.; other modifications known or probable at other temperatures. In view of these statements and of the fact that phosphorus, arsenic and antimony are effective in increasing the resistance to dezincification, it was natural to assume that bismuth would act in the same manner. A series of tests was therefore carried out employing the methods described by Barry. Much to our surprise, bismuth did not inhibit dezincification, but rather seemed to accelerate it. Tensile-test speci-

Jan 1, 1942