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By J. F. Wilson

Steady-state flow theory, previously applied to displacements with two mobile phases, is extended to cover down-structure flow involving three mobile phases: oil, gas and water. When used with normal reservoir fluid properties, the theory predicts the existence of four distinct flow regimes and the conditions under which each regime exists. The predicted behavior is verified by a parallel-plate model study. INTRODUCTION Special problems exist when a water flood is contemplated in a dipping reservoir having a substantial gas cap. Normally, the gas-cap region is one of very low oil saturation. If oil is moved into the gas cap during the flood, a loss in recovery results. Efficient recovery of the oil underlying the gas is therefore difficult. In two reported field water floods, injection into the gas cap has been used to solve these problems. At the West Norfolk Garr Sand Unit, injection into the upstructure region of the reservoir was made for the stated purpose of filling up the gas cap with water.' The purpose in the Sholem Alechem Fault Block "A" Sims Sand Unit was to form a continuous water barrier between the gas cap and oil band.' A laboratory model study preceded this flood and was described in the same publication. Both of these gas-cap water injections gave satisfactory results, but the published data are insufficient to allow generalizing to other field conditions. The present investigation was also undertaken to obtain results for a specific field problem. However, these results will be shown to be in agreement with an extension of the Dietz3-5 mathematical model to three-phase flowing systems. The agreement between the theory and the model studies indicates that the mathematical model can be used to describe completely the flowing system under some conditions, and to indicate the general type of flow to be expected under all conditions. FLOW THEORY The Dietz equations for two-phase flow are derived "' for the case of constant-velocity linear flow in a homog- eneous porous medium. The transition zone between the fluids is assumed to be of negligible extent so that the displaced and displacing fluids are separated by a sharply defined interface, as illustrated in Fig. 1. The density and mobility of the displacing fluid are constant over the region behind the interface, and the same properties of the displaced fluid are constant over the region ahead of the interface. To extend the Dietz equations to three-phase systems, we postulate the flowing system shown in Fig. 2 and determine the conditions under which it can exist. The

H. 0. HOFMAN, Boston, Mass (written discussion*).-The paper by Mr.. Pyne gives clear evidence of the difficulties the metallurgist is likely to encounter when he tries to recover in the blast furnace the metal from old chromite lining used as a refractory material in the copper reverberatory furnace. It appears that chromite cannot be fluxed at temperatures which usually prevail in copper blast furnaces. This calls to mind the freezing-point curve drawn by M. Simonis1 of mixtures of chromite and kaolinite. The chromite used in the experiments contained 52.9 per cent. Cr203, 22.6 FeO, 4.8 AI203, 9.6 Si02, .10.1-MgO; FIG. 1. the kaolinite was clay from Zettlitz with 98.5 per cent. clay-substance: The accompanying curve shows that the eutectic mixture with 35 per cent. kaolinite and 65 per cent. chromite freezes at Seger cone No. 15 (1435° C.), while kaolinite fuses at cone No. 35 (1770° C.) and chromite at cone No. 42 (2000° C.). The curve indicates that the difficulty in the blast furnace can be overcome by having at the smelting zone a temperature much higher than is usual in copper smelting; a charge composition similar to that prevailing at the Mansfeld copper smeltery -which gives with 23 per cent. coke a, slag of the composition Si02, .49.09; .(FeMg)0, 5.58; (CaMg)0, 16.02; A1203,-16.02-might flux and fuse chromite.

Jan 3, 1918

By R. Gatewood

The solution here offered is at once simple and important in its direct and indirect bearings. According to the principles of surface-tension, which will be found sufficiently enlarged upon for present purposes in Clerk Maxwell's excellent little treatise on The Theory of Heat, a mechanical mixture of liquids will frequently of itself divide into groups, consisting of liquids mixing among themselves but withdrawing from the other liquids. The following simple and familiar illustration will suffice: " If we mix water with alcohol, the liquids diffuse into each other. If we now attempt to mix oil with the alcohol and water, the two liquids separate from each other of themselves, and in the act of separation sufficient force is brought into play to set in motion considerable masses of the fluids." Maxwell goes on to show that this relative energy is one of arrangement, depending on the nature of the fluids and the area of the surface of contact, the act of separation tending to reduce this surface to a minimum consistent with equilibrium; that this surface-tension exists between a solid and touching fluid, either liquid or gaseous, being of one sign or the other, in the case of a liquid, according as it tends to draw itself up into a drop on its surface or to spread and wet the solid. After considering various cases, lie states that which particularly interests us, thus : " When a solid body is in contact with two fluids, then, if the

Jan 1, 1885

By P. Ramachandrarao, T. R. Anantharaman

CONSIDERABLE interest has lately been evinced as regards the nature of chill zones in solidified metals and alloys. Biloni and Chalmersl were the first to show through their study of segregation substructures in some nonferrous alloys that the formation of the dendritic region may be preceded by a diffusionless solidification process, viz., predendritic solidification. Subsequently Bower and Flemings2 tried a special solidification technique wherein the liquid was drawn into a narrow copper mold with polished surfaces and concluded that convection might trigger some multiplication mechanism leading to grain refinement. Using uncoated and partially coated surfaces for molds in the Bower-Flemings technique as well as in conventional molds, Biloni and Morando3 have very recently brought out the importance of the rate of heat extraction on the mechanism of solidification. We report here on the surface structures and substructures observed in a Sn-1 wt pct Pb alloy solidified at even higher cooling rates (riz., l05 to l07 ºc per sec) than those employed by earlier workers. The alloy was made by melting tin (99.99+ pct) and lead (99.9+ pct) in a silica tube under vacuum. Small quantities of the homogenized alloy (0.5 to 1.0 g) were then quenched (or splat-cooled) from the melt by the "gun technique" developed by Duwez et al.4 The thickness of the resultant foils varied from specimen to

Jan 1, 1970

By William Klement

KNELLER' has recently reported that extensive metastable solid solutions may be obtained in Cu-Fe alloys by simultaneous vapor deposition. This note reports that solid solutions, apparently single -phase, can be obtained for Cu-Fe alloys containing 0 to 20 and 85 to 100 at. pct Fe by rapid quenching from the melt; the inability to extend the solid solubilities further is related to the liquid miscibility gap, Fig. 1, as for Cu-Co alloys.2'3 Accurate lattice spacings of the copper-rich fcc and iron-rich bcc solid solutions have been obtained. Homogeneous alloys were prepared by casting4'5 and sintering2 from elements of 99.9+ pct purity. The quenching techniques were as before,' except the iron-rich alloys were liberally covered with argon while at elevated temperatures. Flakes about 1 sq mm in area were obtained and investigated with the Debye-Scherrer technique, as previously described.2,4 All X-ray work was done at 25° 2°C using filtered copper and cobalt K radiation. Relative visual intensities of the diffraction lines for the phases in the quenched alloys are shown in Table I. The lattice spacings of the fcc structure for alloys containing up to 80 at. pct Fe are plotted in Fig. 2. The variation of these lattice parameters with composition is in good agreement with the re- of cementite spots usually present (all hkl reflections are allowed) and the ease of confusing them with ferrite or martensite reflections. Copies of the report can be obtained by writing to the Materials Research Department, Rocketdyne. 6633 Canoga Avenue, Canoga Park, Calif., 91304. A copy is also available at the Engineering Societies Library, 2nd floor, 345 East 47th Street, New York, N.Y., 10017. Photocopies, either full-size or microfilm, may be purchased from the Engineering Societies Library. sults6 of Andersen and Kingsbury, Fig. 2, although there is some disagreement in absolute value. This discrepancy may be due to the different temperatures at which the X-ray measurements were carried out and perhaps to the different extrapolation procedures. Also, Andersen and Kingsbury6 state that their lattice spacings were computed relative to the wavelengths given by Siegbahn in 1933; this reference has not been found and it is assumed that the well-known 1931 wavelengths were used, the lattice spacings then being in kx units which are converted into angstroms by the factor 1.00202. There is no support for the contention that solution of iron decreases the lattice parameter of copper, as con-

Jan 1, 1965

By Charles C. Hawes

DETERMINATION OF SILICA OXIDE iron ores usually are found in intimate association with silica and phosphorus compounds. Their quantitative separation and purification sometimes present difficult problems to the chemist. Silicic acids may represent various degrees of dehydration. They are exeedingly weak, but combine with metallic oxides and form some of the most stable oxides in nature, the silicates. When iron ores are treated with hydrochloric acid, they yield practically all their iron. However, apart from rare exceptions, varying amounts of insoluble residues of silica, alumina, lime, magnesia and compounds of phosphorus, sulphur, titanium, chromium and others will be left. If the oxides of silicon, aluminum and titanium are present in small quantities, the insoluble residue is generally very small, but the presence of these oxides is more usual in larger quantities. Therefore, only a special treatment can break the bond between these elements. Ore Residues Acids remove the soluble constituent of the ore, leaving the insoluble residue, which chemically is rock or gangue and must be treated accordingly. Alkali carbonates are used frequently to break up the residue, but other fluxes have also been recommended, such as a number of lead and boron salts. The introduction 0f these salts, which offers certain advantages, requires, however, their removal before the other constituents can be analyzed, and this elimination is sometimes difficult. Usually in quantitative analysis silicates are dissociated by fusing them in a platinum crucible with sodium carbonate, thereby forming sodium silicate, Na2SiO3, sodium aluminate, Na2Al204, sodium titanate, Na2TiO3, and carbonates of other elements. All the carbonates are soluble in hydrochloric acid, but also some silicic acid is formed that must be rendered insoluble. To this end the solution is evaporated several times, as the first evaporation still leaves as much as 5 per cent of the silica soluble. Even after a number of evaporations, minute quantities of silica may be found with the iron and alumina present. Perchloric Acid as an Agent for Dehydrating Silicic Acid Perchloric acid, HC104, (60 per cent), has been used for years as a solvent, but few chemists have used it to dehydrate silica. It is derived from anhydrous perchloric C1207, which is most unstable and dangerous. Perchloric acid is a strong oxidizing agent, which boils at 203°C. It is more effective in rendering silica insoluble than any other known agent, and most rapid in action. After perchloric acid is added to a mixture containing silicic acid, the resultant solution is

Jan 1, 1945

By Charles C. Hawes

DETERMINATION OF SILICA OXIDE iron ores usually are found in intimate association with silica and phosphorus compounds. Their quantitative separation and purification sometimes present difficult problems to the chemist. Silicic acids may represent various degrees of dehydration. They are exceedingly weak, but combine with metallic acids and form some of the most stable oxides in nature, the silicates. When iron ores are treated with hydrochloric acid, they yield practically all their iron. However, apart from rare exceptions, varying amounts of insoluble residues of silica, alumina, lime, magnesia and compounds of phosphorus, sulphur, titanium, chromium and others will be left. If the oxides of silicon, aluminum and titanium are present in small quantities, the insoluble residue is generally very small, but the presence of these oxides more usual in larger quantities. Therefore, only a special treatment can break the bond between these elements. Ore Residues Acids remove the soluble constituent of the ore, leaving the insoluble residue, which chemically is rock or gangue and must be treated accordingly. Alkali carbonates are used frequently to break up the residue, but other fluxes have also been recommended, such as a number of lead and boron salts. The introduction of these salts, which offers certain advantages, requires, however, their removal before the other constituents can be analyzed, and this elimination is sometimes difficult. Usually in quantitative analysis silicates are dissociated by fusing them in a platinum crucible with sodium carbonate, thereby forming sodium silicate, Na2SiO3, sodium aluminate, Na2A1204, sodium titanate, Na2TiOs, and carbonates of other elements. All the carbonates are soluble in hydrochloric acid, but also some silicic acid is formed that must be rendered insoluble. To this end the solution is evaporated several times, as the first evaporation still leaves as much as 5 per cent of the silica soluble. Even after a number of evaporations, minute quantities of silica may be found with the iron and alumina present. Perchloric Acid as an Agent for Dehydrating Silicic Acid Perchloric acid, HCI04, (60 per cent), has been used for years as a solvent, but few chemists have used it to dehydrate silica. It is derived from anhydrous perchloric C1207, which is most unstable and dangerous. Perchloric acid is a strong oxidizing agent, which boils at 203°C. It is more effective in rendering silica insoluble than any other known agent, and most rapid in action. After perchloric acid is added to a mixture containing silicic acid, the resultant solution is

Jan 1, 1945

By E. P. Klier

THE work of Klier and Lyman1 on the bainite reaction has led to the full description of this reaction for medium-carbon low-alloy steels. Certain experimental data reported by Klier and Lyman appear, however, to be improbable of obtaining in very high-carbon steels. The study herein reported consists of an analysis of the transformation characteristics of a 3 per cent chromium, 1 per cent carbon steel by means of X-ray and metallographic methods. From the results obtained it is concluded that the bainite reaction in this steel is more complicated than that reported by Klier and Lyman for the low-carbon low-alloy steels. However, the mechanism of bainite formation in this steel appears to be essentially the same as proposed for the low-carbon low-alloy steels with the modification that the first volumes to transform are carbon-rich rather than carbon-poor. EXPERIMENTAL PROCEDURE The analysis of the steel studied was: Cr, 2.89; C, 1.02; Mn, 0.33; Si, 0.35; S, 0.012; P, 0.020. The stock was received from the Carpenter Steel Co. in rolled bars. Specimen Preparation Specimens were austenitized at 1200°C. (2192°F.) for 25 min. in purified nitrogen. The resultant A.S.T.M. austenite grain size was 0-1. Isothermal transformation was allowed by quenching the specimens into liquid metal baths controlled to ±5°C. at 540°C. (1004°°F.) and above, and to ±2°C. at 490°C. (914°°F.) and below. Following the desired degree of transformation all specimens were water quenched. Metallographic Examination Specimens 1/4 in. round by 1/4 in. were used for metallographic examination. Etchants used were Vilella's reagent (1 gram picric acid, 10 ml. hydrochloric acid to make l00 ml. ethyl alcohol solution) and alkaline sodium picrate (electrolytic). Vilella's reagent was effective in revealing all microconstituents, while the alkaline sodium picrate developed the carbon-rich structures or carbides only. X-ray Examination Two X-ray techniques were used-the Debye-Scherrer method and a back-reflection method. The small specimens necessary for the Debye-Scherrer method were austenitized and then allowed to transform, or were cut from the larger metallographic specimens. The metallographic specimens were used for the back-reflection X-ray analysis. When it was desirable to determine the structure of the carbide present, sliver specimens were electrolytically etched to develop a carbide coating, then were exposed in the cameras. This technique was frequently necessary to allow positive identification of the carbide.

Jan 1, 1945

By H. Conrad, K. Janowski, E. Stofel

In a previous paper,1 the occurrence of (0001) and (0111) twins was reported for compression tests of 60-deg-oriented sapphire rods in the temperature range from 1100° to 1300° C. Subsequent to this initial work, additional tests have been conducted, and twinning has been found to occur at temperatures as high as 1500° C. Also, the temperature and strain-rate conditions for the two types of twins and for slip have been established in more detail. The present note covers this more recent work. The compression-test data are summarized in Table I. The techniques for identifying the twins are optical examination up to X1000 and X-ray analysis.' It is evident that (0711) twins are pre-

Jan 1, 1965

By J. L. Rodda

A large amount of time has been devoted to the microscopical study of the copper-zinc alloys, emphasis naturally being placed upon the commercially important alloys of the system. Suitable methods are available for microscopically recognizing the two phases richest in copper, but none appear to have been developed for the positive identification of the other phases. This is, however, accomplished, for the phases normally encountered, by an electrolytic method described in the following pages. Five phases of the copper-zinc diagram (Fig. I) are considered for the purpose of this paper: the solid solution of zinc in copper, alpha (a); the intermediate phases, beta (ß), gamma (?), and epsilon (e); and the solid solution of copper in zinc, eta (11). Beta prime is not considered a separate

Jan 1, 1937

By E. J. Efsic, C. M. Wayman

The fcc to bcc y to a transformation in an Fe-24.5 at. pct Pt alloy was studied and found to be martensitic. Large martensite plates are formed in this alloy which are ideal for crystallographic studies; the Ms temperature is about -5°C. Ordering of the parent phase prior to transformation to martensite causes a pronounced lowering of the Ms temperature. For the first time in the case of alloys of iron, measurements of the habit plune, orientation relationship, and magnitude and direction of the shape stvain have been obtained on preselected martensite plates. It is shown that by measuring the initial and displaced (as a result of the shape strain) positions of three or more non-parallel fiducial scratches on one reference surfice the maguitude and direction of the shape strain and the state of distovtion at the parent-mavtensite interface can be determined with a reasonable degree of accuvacy. The agreement between the phenomenolog-cal crystallographic theory of martensitic transformations and the experimental results habit plune, orientation relationship, and nlagnitude and direction of the shape strain) is essentially perfect, and is thought to be the best reported to date for iron alloys. THE comparatively few investigations on binary Fe-Pt alloys have been concerned with magnetic properties, ordered phases, and the equilibrium diagram itself. Various investigations have shown that the equilibrium diagram is of the open y field type; in addition there is a peritectic transformation, a minimum melting point, and three ordered phases: Fe3Pt, FePt, and FePt3. The results of a number of investigators1-6 have shown that the temperature dependence of the y to a (and reverse) transformation in iron-rich alloys is reasonably well-established. The Fe3Pt phase was first noted by Kussman and Rittberg,7 and its existence was later confirmed by Franklin et al,8 Steijn and Donahoe,9 and Berkowitz et al.10 The FePt phase was reported by Isaac and amman' and later confirmed by a host of others.3,6,7,12,13 Kussman and Rittberg7 noted the existence of the superlattice FePt3. Prior to 1956, the 1 to a transformation in iron-rich Fe-Pt alloys was termed "irreversible". In 1957 Klokholm and Donahoe" termed this transformation martensitic, presumably because of its occurrence at temperatures well below those where diffusion normally takes place. This observation served as a point of departure for the present investigation, and in the very early stages of the work to be discussed it was readily verified that the y to a transformation in iron-rich Fe-Pt alloys is indeed martensitic. Quite large martensite plates exhibiting the well-known surface tilt were observed. These plates are ideal in the sense that the boundaries between the parent and product phases were usually very straight. It thus appeared that Fe-Pt martensites would be ideal for crystallographic studies, and this was the purpose of the present investigation. Details of the crystallography of martensitic transformations (particularly for iron alloys) and the phe-nomenological crystallographic theories15-l7 have been discussed many times and thus will require very little elaboration here. The end result of these theories, given in matrix form, is

Jan 1, 1968

By Leonard B. Lipson

Boyer, Morgan and Muskat,' with improvements by Morgan, McDowell, and Doty,l and Laird and Putnam,' have described a scheme for the determination of fluid saturatic in porous media by measuring the x-ray linear absorbing power of particular fluids in the media. This method is one of several which depend on the linear absorbing power of the fluids in the porous medium. Other examples of linear absorption methods involve measurement of dielectric constant, gamma ray absorption, and ultrasonic attenuation. It is the purpose of this note to demonstrate by theortical considerations that the absorption versus saturation curve for a linear absorption method is not necessarily a single valued function of the saturation. Such non-unique behavior must be considered and evaluated before suitable saturation determinations can be made by a linear absorption method. To illustrate the discussion, examples will be given only for the simplest cases of combinations of two different dielectrics. The dielectric constant method was chosen for illustration because it was thought to demonstrate most graphically the point in question. According to Argue and Maass,4 the resultant dielectric constant of a combination of two different dielectrics depends on the orientation of the dielectrics in the electric field of the test condenser used to measure the dielectric constant. One ease involves alternate slabs of dielectrics E1 and E2 perpendicular to the electric field of the test condenser, as shown in Fig. 1A. For this case: l/'E, = A/E, + B/E,.......(1) where E,,, is the dielectric constant of the combination, A is the ratio of the path length through dielectric E, to the distance between the plates of the condenser (assuming the dielectrics have the same cross sectional area as the condenser), and B is the ratio of the path length through dielectric E2 to the distance between the plates of the condenser. It will be noted that the constants A and B are numerically equal to the fractional "saturation" of the region between the test plates of the condenser by the two dielectrics E1 and E2, respectively. Another case involves alternate columns of the two dielectrics parallel to the electric field and forming a continuous path between the condenser plates, as shown in Fig. 1B. For this case: E., = AE1 + BE2.........(2) where E., is the dielectric constant of the combination, A is the ratio of the cross sectional area of dielectric E, to the cross sectional area of the condenser plates (assuming the lengths of the dielectrics equal the distance between the condenser plates) and B is the ratio of the cross sectional area of dielectric E2 to the cross sectional area of the condenser plates. As before the constants A and B are the effective "saturation" of the condenser by the two dielectrics. Still another case is described by Lichtenecker5 where dielectric E2 is shown in the form of small particles distributed at random in dielectric E1. This is shown in Fig. 1C. For this case: log Em = A log E1 + B log E2.....(3) where Em is the dielectric constant of the combination. A is the ratio of the volume of dielectric E1 to the volume of the condenser, i.e., the effective "saturation" of the condenser by dielectric E,. B is the ratio of the volume of dielectric E2 to the volume of the condenser, i.e., "saturation" of dielectric El. Equations (l), (2) and (3) are plotted in Fig. 2 for E1 = 2.5 (oil) and E2 = 80 (water). Equations (1) and (2) may he thought of as representing the limiting cases of the configuration of two fluids which might be expected to exist in a porous medium. Equation (3),

Jan 1, 1951

By Leonard B. Lipson

Boyer, Morgan and Muskat,' with improvements by Morgan, McDowell, and Doty,l and Laird and Putnam,' have described a scheme for the determination of fluid saturatic in porous media by measuring the x-ray linear absorbing power of particular fluids in the media. This method is one of several which depend on the linear absorbing power of the fluids in the porous medium. Other examples of linear absorption methods involve measurement of dielectric constant, gamma ray absorption, and ultrasonic attenuation. It is the purpose of this note to demonstrate by theortical considerations that the absorption versus saturation curve for a linear absorption method is not necessarily a single valued function of the saturation. Such non-unique behavior must be considered and evaluated before suitable saturation determinations can be made by a linear absorption method. To illustrate the discussion, examples will be given only for the simplest cases of combinations of two different dielectrics. The dielectric constant method was chosen for illustration because it was thought to demonstrate most graphically the point in question. According to Argue and Maass,4 the resultant dielectric constant of a combination of two different dielectrics depends on the orientation of the dielectrics in the electric field of the test condenser used to measure the dielectric constant. One ease involves alternate slabs of dielectrics E1 and E2 perpendicular to the electric field of the test condenser, as shown in Fig. 1A. For this case: l/'E, = A/E, + B/E,.......(1) where E,,, is the dielectric constant of the combination, A is the ratio of the path length through dielectric E, to the distance between the plates of the condenser (assuming the dielectrics have the same cross sectional area as the condenser), and B is the ratio of the path length through dielectric E2 to the distance between the plates of the condenser. It will be noted that the constants A and B are numerically equal to the fractional "saturation" of the region between the test plates of the condenser by the two dielectrics E1 and E2, respectively. Another case involves alternate columns of the two dielectrics parallel to the electric field and forming a continuous path between the condenser plates, as shown in Fig. 1B. For this case: E., = AE1 + BE2.........(2) where E., is the dielectric constant of the combination, A is the ratio of the cross sectional area of dielectric E, to the cross sectional area of the condenser plates (assuming the lengths of the dielectrics equal the distance between the condenser plates) and B is the ratio of the cross sectional area of dielectric E2 to the cross sectional area of the condenser plates. As before the constants A and B are the effective "saturation" of the condenser by the two dielectrics. Still another case is described by Lichtenecker5 where dielectric E2 is shown in the form of small particles distributed at random in dielectric E1. This is shown in Fig. 1C. For this case: log Em = A log E1 + B log E2.....(3) where Em is the dielectric constant of the combination. A is the ratio of the volume of dielectric E1 to the volume of the condenser, i.e., the effective "saturation" of the condenser by dielectric E,. B is the ratio of the volume of dielectric E2 to the volume of the condenser, i.e., "saturation" of dielectric El. Equations (l), (2) and (3) are plotted in Fig. 2 for E1 = 2.5 (oil) and E2 = 80 (water). Equations (1) and (2) may he thought of as representing the limiting cases of the configuration of two fluids which might be expected to exist in a porous medium. Equation (3),

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 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

Membership at the end of the year 1951 was 19,711 including 2228 Student Associates. The data in the third column include these Student Associates. 1. This includes all the cash dues income received from new and old members of all grades. 2. All cash initiation fees received. 3. Net income received from advertising in the three journals. The figure was $72,273, for MINING ENGINEERING; $39,844 for the JOURNAL OF METALS; and $31,564 for the JOURNAL OF PETROLEUM TECHNOLOGY. Income in 1950 was $54,572, $30,390, and $18,443 from these sources, respectively. 4. Receipts from individual sales, nonmember subscriptions, and multiple subscriptions of members. 5. Includes Transactions volumes and the Petroleum Statistics volume. 6. Sales of all other printed matter except special volumes sponsored by certain Funds. Includes a considerable sale of preprints and reprints of technical papers. 7. Does not include dividends and interest from certain Funds whose income reverts to those Funds. 8. Miscellaneous income not included in any of the above categories. 9. The total income compares with $493,197 -in 1950, an increase of $29000.

Jan 1, 1952

By H. W. Kropholler, L. A. Cramer, E. T. Woodburn, J. C. A. Greene

A generalized mathematical structure is proposed whereby internal species mass flows within a flotation network are defined uniquely by a matrix of enhancement factors. An element of the enhancement factor matrix is defined as the ratio of the mass flow of that species leaving a given cell in the concentrate to the species mass flow leaving the same cell in the tailings. To predict the enhancement factors, knowledge of flotation kinetics effects is required. Recently experimental data has become available relating to the performance of industrial flotation circuits which indicate that the discrete or discrete-distributed kinetic schemes are capable of reasonably effective simulations. These simulations show the importance of including froth effects. The prediction of performance of networks from small-scale batch tests on flotation streams shows that the model for the froth phase used in the simulations does not scale-up well and that aeration effects are also difficult to predict. The network analysis should be useful in differential flotation of complex ores and it is disappointing-in this context that little information on the kinetics of activation and depression is available.

Jan 1, 1976

By J. J. Snodgrass

Faults, sandstone channels, and abandoned mine workings present severe safety hazards, disrupt mining, and necessitate costly precautions or discontinuance of operations. In addition to fault detection, mining companies have a need to map discontinuities such as seam thinning and previously mined areas in both longwall and room-and-pillar operations. Initial field tests demonstrated successful generation and propagation of higher order guided wave modes. Theoretical studies indicate potential for improved resolution by sensing small details in the coal seam and roof structure. Controlled-waveform source transducers and specialized detectors are particularly useful to preferentially excite and detect the Love (SH) and Rayleigh-type (P-SV) waves, including the higher frequency modes. The distinct observation of reflections using the transducers in the shear wave mode makes feasible the detection of the water-filled voids.

Jan 1, 1986

By C. L. Sollenberger, R. B. Greenwalt

PERHAPS the most widely used dispersants or gangue depressants in nonmetallic flotation are sodium silicates, which vary in silica-to-soda ratio from 1 to 3.75. Typical manufactured silicates in order of decreasing solubility and increasing amounts of silica are Metso, silica-to-soda ratio of 1.00; D, 2.00; RU, 2.40; K, 2.90; N, 3.22; and S-35, 3.75.* References in flotation literature's to the use of sodium silicates are often weak because they fail to mention the type of silicate used. Metso and silicate N have occasionally been mentioned, but when the type of silicate is not mentioned, it is usually assumed to be N, the cheapest of the soluble silicates and the one recommended by sodium silicate manufacturers as a flotation agent.

Jan 6, 1958

By N. A. Gokcen, E. S. Tankins, G. R. Belton

Equilibrium in the reaction H2(g) + O[in liquid iron, cobalt, or nickel] = H2O(g) has been investigated over wide temperature and composition ranges. Oxygen has been found to obey Henry's Law in each of the three metals at 1550°C. The standard free-energy changes for the above reaction are given by: (1550° to 1700°C) ?Foco = -45,360(±290) + 16.16(±0.16)T (1490° to 1700°C) ?Fo Ni = -48,170(±220) + 16.12(±0.12)T (1465° to 1700°C) where the standard state for dissolved oxygen is the I wt pet solution. ThE thermodynamic behavior of dilute solutions of oxygen in molten iron has been the subject of many investigations over the last thirty years,'-'4 the majority of the investigators having utilized the reaction:

Jan 1, 1964