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By E. Kendall Cork

The traditional financial objective for a single mine company has been to operate as frugally as possible and to pay out most of the earnings as dividends. If the business is cyclical (as it is for most metals) the dividends might fluctuate quite widely. When the mine is exhausted the company disappears. This is still quite a viable strategy for a single mine company. It is not however a viable strategy for the world as a whole. The mining industry is built by mine development companies who can mobilize the people and capital to bring new mines into production. Their skills must include marketing, engineering, finance and other politics. It is very rare for a property to be brought in without the support of a major company that can provide all these services. The exceptions will usually have some other form of big brother support, for example the U.S. government uranium contracts at guaranteed generous prices. The mine development company will seek as a minimum to perpetuate itself by developing new mines in order to replace those which are running out. The more common and more ambitious objective is to grow -- that is to add to its ore reserves and current production by developing more new mines. The financial objectives for that company are very different. Obviously if all the earnings were paid out in dividends there would be nothing left to work with. The first financial policy then is to spend an appropriate amount on exploration for new properties. The next is to retain enough of the earnings to provide the capital for new projects at least sufficient for the equity. There is no magic formula as to what proportion of earnings should properly be distributed as dividends by a growth-oriented mine development company. As a rough rule of thumb distributing half or more will probably leave too little to work on and 30% or so is probably a good balance. However the circumstances differ widely from company to company. It may be useful to set an objective for the rate of growth of a company's earnings. Some have picked rates such as 15% per annum compounded. Others have set a target in real terms which might appear as 10 or 11% plus inflation. Obviously the arithmetic of compound interest is very attractive; however in practice there is much variation. Indeed current returns from existing operations swing widely with the business cycle and there is no assurance that economic new properties will be found according to someone's arbitrary time schedule. For example, Western Mining Corporation Limited in Australia explored for 30 years with little to show for it, but then found the great Australian nickel deposits and more recently the huge Roxby Downs copper. That long dry spell could not have fitted anyone's arbitrary calendar of growth and yet they would not have found such orebodies without that long period of effort. Should they have abandoned the search? Once a new property has been found or acquired there has to be a threshold rate of return on the new capital to be invested against which to evaluate the property's economics. Conventionally this seems to be 15% after tax, a number common in other heavy industries as well. In some cases it is expressed as a lower number plus allowance for inflation. Discounted cash flow analysis is a very useful tool but it does not make the decision. In the end a "go" decision depends on judgment of many factors some of which are numbers used in the DCF calculation whose credibility must be examined. It is curious how frequently investment proposals come in with the rates of return very close to 15%. The project advocates know that a number much less than 15% will not fly and that a number much more is not necessary. With much higher nominal and real interest rates of recent years, even though before tax, logic suggests that the hurdle rate should also rise. The power of compound interest is so great that 20% is very hard to achieve in any cash flow projection but 18% may be a sensible yard - stick. Once again it is remarkable how many project proposals come in with an 18% return. On the record the mining industry as a whole has not been overly restrictive in choosing its hurdle rates of return. This is shown by the abundance of metals in recent years and the failure of metal prices to keep up with inflation. All of the foregoing is standard text book stuff.

Jan 1, 1985

By Leonard C. Grimshaw

The idea of bonding two dissimilar ferrous metals, and making use of both, is an old one. Tips have been brazed onto tool shanks for many years. The bonding of larger pieces to form whole bars and sheets has also been accomplished, but has received little attention in the technical literature, although a number of patents have been issued covering various methods for its accomplishment. There are three main motives behind the manufacture of composite steels. One is that the physical properties of one steel may supplement those of another; a useful, but at the same time, hard, brittle steel may be backed by a soft ductile one, or a stainless steel may be backed by a steel possessing greater strength. Another motive is direct lowering of cost; an expensive steel may be backed by a less expensive one, bringing down the cost of the piece as a whole. The third motive is an indirect lowering of cost, as when a useful steel is backed by a steel that is easier to machine, so that machining cost on a finished product is lowered considerably. Often more than one of these motives lead to a decision to use a composite steel. Previous Methods There are two methods in use that result in tolerably good bonds between ferrous metals: (1) the casting method, and (2) what we shall call the "heat-pressure" method. This "heat-pressure" method covers processes in which the bond is made between two prepared surfaces by heating them and then applying pressure. Usually sufficient pressure must be used to produce appreciable spread and elongation, or else we arc merely brazing and not truly welding. Casting methods for welding together ferrous metals have been used more than 74 years, and are described in the technical literature as applied

Jan 1, 1936

By Leonard C. Grimshaw

The idea of bonding two dissimilar ferrous metals, and making use of both, is an old one. Tips have been brazed onto tool shanks for many years. The bonding of larger pieces to form whole bars and sheets has also been accomplished, but has received little attention in the technical literature, although a number of patents have been issued covering various methods for its accomplishment. There are three main motives behind the manufacture of composite steels. One is that the physical properties of one steel may supplement those of another; a useful, but at the same time, hard, brittle steel may be backed by a soft ductile one, or a stainless steel may be backed by a steel possessing greater strength. Another motive is direct lowering of cost; an expensive steel may be backed by a less expensive one, bringing down the cost of the piece as a whole. The third motive is an indirect lowering of cost, as when a useful steel is backed by a steel that is easier to machine, so that machining cost on a finished product is lowered considerably. Often more than one of these motives lead to a decision to use a composite steel. Previous Methods There are two methods in use that result in tolerably good bonds between ferrous metals: (1) the casting method, and (2) what we shall call the "heat-pressure" method. This "heat-pressure" method covers processes in which the bond is made between two prepared surfaces by heating them and then applying pressure. Usually sufficient pressure must be used to produce appreciable spread and elongation, or else we arc merely brazing and not truly welding. Casting methods for welding together ferrous metals have been used more than 74 years, and are described in the technical literature as applied

Jan 1, 1936

Following closely Marcona Corp.'s announcement of its new Marconaflo process for transporting mineral slurries by ship (see pp. 96-97, Sept. 1969 [ ]), Midland-Ross Corp. (M-R) now heralds its metallized iron pellet process which supplements Oregon Steel Mills1 (Oregon Steel) new Portland, Ore., plant. Harry J. Bolwell, president of M-R describes the company's M-R Pellet as "the most exciting advance in steelmaking in a decade, one which will profoundly affect the industry." In fact, other knowledgeable industry spokesmen believe that with these developments the mini-steel plant era is now here and that this technical development along with the Marconaflo process will revolutionize iron ore shipments and steelmaking. The M-R president predicts that electric furnaces can account for 20% of the annual U.S. steel production by 1975, compared with 14% at the present time because of these developments.

Jan 12, 1969

By James Aston

THREE years ago the writer presented a paper on the trend of development in the wrought iron industry,1 wherein was described a process in the development of which he has been a factor, which at that time had passed through several years of progressive experimental development but which had not then been put upon a commercial scale of operation. The present paper deals with two years of observation and experience in the commercial operation of a plant by the A. A Byers Co. at Warren, Ohio. It will not enter into the controversial field of the relative merit of wrought iron and steel in various classes of service, nor will it elaborate upon the characteristic services or fields of utility to which wrought iron is particularly adapted. It is sufficient to state that the wrought iron industry is upon a substantial basis and that the material finds service in pipe, where its advantages are in superior corrosion, fatigue, welding and threading qualities; in bar iron for staybolts, engine bolts, and rivets, demanding maximum service against corrosion and fatigue; in plates for corrosion service; and in chains, because of welding and shock-resisting characteristics. In short, ability to withstand the stresses of shock and vibration, or the ravages of corrosion, to hold protective coatings, and to give maximum efficiency in welding, are its features of relative superiority. If these features were not well recognized, the wrought iron industry would have shrunk to insignificance in the face of high costs and acknowledged limitations in manufacture. To charge that this industry is built upon a structure of assumption, psychology, and improperly weighed evidence is an impeachment of the integrity or belittling of the powers of observation of users through many centuries of service experiences.

Jan 1, 1929

By James E. McNulty

Coal reserve estimates are prepared using a simple equation: the product of area, bed thickness, density and recovery factors. Each of these elements involves a degree of risk based on certain assumptions. Reserve area, thickness and density rely on certain physical data whose accuracy, reliability and sufficiency may be problematical. Estimates of recovery factors for mining and coal preparation are often subjective. Most reserve estimates assume, sometimes incorrectly, that the subject reserves will be completely extracted. The principle that certain coal resources are reserves, if they can be considered economically recoverable at the time of determination, needs to be reexamined in the light of recent market cycles. Reserve estimating requires the exercise of judgments, the validity of which reflect the qualifications, experience and objectivity of the estimator.

Jan 1, 1985

By J. Marshall Rounsevell

It is probably not too far from the truth to say that the sulfur content of the steel bath at the first turndown of the basic oxygen furnace is influenced by every factor which varies in the operation of a BOF shop. However, the determination from normal shop operating data of the effect of a given factor on turndown sulfur content requires a means for collecting a large quantity of such data and a significant variation of the factor in question in that data. In this paper, operating data from 4000 heats collected on the computer at Inland's No. 4 BOF Shop is utilized to analyze the effect of four operating parameters -- hot metal sulfur content, hot metal manganese content, percent burnt dolomitic lime (dolomite) in the flux charge, and the presence or absence of transfer ladle slag skimming -- on first turndown sulfur content.

Jan 1, 1972

By Sherwin F. Kelly

THE principal interest in the meeting sings arranged by the Geophysical Committee this year centered around the many papers dealing with the practical applications of geophysical methods to solving geological problems in many other parts of the world. The program Wednesday morning dealt with work in South Africa, Poland, and South America. Rudolph Krahmann's first paper gave a perspective of the geophysical investigations upon mineral deposits in South Africa. A striking point in his story was the tremendous increase in magnetic work during the last two or three years. This is largely accounted for by the intensive exploration for the extension of the Witwatersrand gold mining area. The author mentioned many surveys in which other methods were used for the search for ores of copper, lead, and zinc, and in the study of water-bearing and oil-bearing structures.

Jan 1, 1935

By AIME AIME

THERE is a constant reiteration in some quarters that technical societies are autocratic and that democracy is utterly lacking and that members would welcome democratic societies in which they had full, control of affairs. While we may not speak for other societies, than our own, in so far as th's Institute is concerned such charges- can only come from people uninformed as to the circumstances. It. is no curtailment of the democratic privileges of the members that a -slate is prepared by the Nominating Committee to be voted on at the annual meeting. The Constitution of the, institute stipulates how the nominating committee shall; be chosen and who shall compose it, which prevents anything like- a- clique controlling- the situation. The Constitution further provides how the nominees shall be distributed geographically and the by-laws specify geographical boundaries: for-these nomination districts. Further more, any man or complete ticket can be placed in nomination by means of a petition signed-by only; twenty-five members,- and three or four times such an independent slate has been so nominated and elected.

Jan 1, 1920

By Jack Parker, Gonzalo Barrientos

The most realistic mine pillar design is based on observations and measurements in situ. Low-cost reliable instrumentation has made this approach possible. At the White Pine mine, with its thousands of pillars of all shapes and sizes under all kinds of loading conditions, practical pillar design criteria have been developed. The pressure arch theory is explained and work in two test panels o f the mine is described. The pressure arch mechanism, which relies on lateral stress for support, can be applied to puzzling roof and pillar conditions in other mines.

Jan 1, 1975

By Fred W. Gordon

The North Chicago Rolling-Mill Co., of Chicago, have four furnaces at South Chicago, built during 1881. Each furnace is 20 feet diameter of bosh, and 75 feet total height, the hearth being 11 feet diameter, and the top 15 feet 4 inches. They are blown through seven 7-inch tuyeres placed 5 feet 6 inches above the hearth level. Cubical contents, 15,000 cubic feet. Each furnace is supplied with 2 blowing engines, 84-inch blowing cylinder, and 36-inch steam cylinder, and 54-inch stroke. These two have one jet-condenser worked by an auxiliary pump. The blast for each furnace is heated by the aid of three Whitwell fire-brick stoves, each 21 feet diameter and 60 feet high. In the batteries of boilers furnishing steam for four furnaces there are 36 double-length boilers, 76 feet long, 48 inches diameter and 16,000 square feet heating-surface. The plant was designed to produce 3600 tons per week, or 900 tons for each furnace, and was fitted as above with such engines, boilers, and hot-blast stoves as were thought requisite for that production ; hence, calculated from the present make—not the least remarkable feature is the economy of construction—there are less engines, less boilers, and less hot-blast power for the iron made than at ally plant within my knowledge, or it could to-day be duplicated for less money per ton of iron made per week than could any plant now in existence, whether using fire-brick or cast-iron stoves for heating the blast. This is a practical demonstration of my assertion in a paper on fire-brick stoves, read before the Institute," that the application of fire-brick stoves in construction really lessens the first cost. In view of the statements just made, I must be most emphatic in assuring the members that nothing is strained or overburdened.

Jan 1, 1886

By Ednlund D. North

Discussion of the paper of Edmund D. North, presented at the Spokane meeting, September, 1909, and published in Bulletin No. 37, January, 1910, pp. 21 to 25. A. SCOTT REID, London, Eng. (communication to the Secretary*) :-As a constructor of several glass mine-models, I have read with much interest the description of the model of the Montana-Tonopah mine-workings by Edmund D. North. As an interchange of ideas and experience is always an advantage, and in view of the fact that such models are coming more and more into vogue, perhaps the following remarks on this subject may prove of interest to mining engineers generally and to Mr. North particularly. In the model of the Waihi gold-mine, New Zealand, which I constructed, a dust-proof case is used. The top, bottom, front, and two ends are of glass; the back only is of wood, painted a dull white, against which the mine-workings show very distinctly. Each mine-level is represented by a horizontal sheet of glass, supported on metal runners fixed to the uprights at each end of the case, in a manner similar to that described by Mr. North. The corner uprights are strengthened by having a metal band screwed to the inside face of each, to which the metal runners or supports for the sheets of glass are screwed in turn. The reason for having this additional strength is that as the mine is developed in depth, and fresh levels are opened, the increasing weight of the glass sheets, added to the model, caused the unsupported wooden uprights to bend slightly, so that the glass sheets-did not fit in with the desired nicety, and co-ordination was, to a considerable extent, lost. Strengthening the uprights in this manner is not important in models of mines in which only a few levels have been opened, or when the sheets of glass are small, but in the Waihi model there are 15 sheets of glass to be supported, and more to be added as development proceeds, and the weight is considerable.

May 1, 1910

By K. P. Fournier

This report describes work on the problem of predicting oil recovery from a reservoir into which water is injected at a temperature higher than the reservoir temperature, taking into account effects of vis cosity-ratio reduction, heat loss and thermal expansion. It includes the derivation of the equations involved, the finite difference equations used to solve the partial differential equation which models the system, and the results obtained using the IBM 1620 and 7090-1401 computers. Figures and tables show present results of this study of recovery as a function of reservoir thickness and injection rate. For a possible reservoir hot water flood in which 1,000 BWPD at 250F are injected, an additional 5 per cent recovery of oil in place in a swept 1,000-ft-radius reservoir is predicted after injection of one pore volume of water. INTRODUCTION The problem of predicting oil recovery from the injection of hot water has been discussed by several researchers. l-6,19 In no case has the problem of predicting heat losses been rigorously incorporated into the recovery and displacement calculation problem. Willman et al. describe an approximate method of such treatment. 1 The calculation of heat losses in a reservoir and the corresponding temperature distribution while injecting a hot fluid has been attempted by several authors.7'8 In this report a method is presented to numerically predict the oil displacement by hot water in a radial system, taking into account the heat losses to adjacent strata, changes in viscosity ratio with temperature and the thermal-expansion effect for both oil and water. DERIVATION OF BASIC EQUATIONS We start with the familiar Buckley-Leverettg equation for a radial system:* This is sometimes referred to as the Lagrangian form of the displacement equation. If the injection water is at some temperature Ti which is above reservoir temperature TR, then lw, the flowing fraction which is water, is a function of both water saturation and fluid temperature at any given time and position in the reservoir. The temperature dependence of lw results from the temperature dependence of the viscosity ratio µo/µm of which lw is a function. Thus:

Jan 1, 1966

By K. B. Nowels

DATA pertaining to pipe line flow for both oil and gas in horizontal or nearly horizontal pipe lines are both extensive and accurate. However, the pipe formulas used to determine pressure drop for flowing fluids (liquids and gases) under conditions of horizontal flow are not generally applicable to flowing oil and/or gas wells. Except for some data developed in small laboratory set-ups, little or no information was available concerning flow of oil and gas mixtures in vertical pipes, when, in 1928, the writer began the development of a method for computing pressure drops in the pipes of flowing oil wells, as outlined in this paper. In 1929, Uren1 presented some findings based on laboratory experi-ments in which vertical flow of an extremely heavy crude oil was induced, by means of air through a 2-in. pipe, 41 ft. long. The friction factors derived from the experiment, as well as values for pressure drop per 100 ft., are not believed satisfactory in their application to flow problems in the field. Versluys,2 also in 1929, presented a mathematical development of the theory of flowing oil wells, and in 1930, gave a companion paper3 setting forth some principles governing the choice of length and diameter of tubing in oil wells. Since the termination of the study presented in this paper, another. valuable contribution pertaining to the problem, of vertical flow was made by Moore and Wilde.4 Although there were writings dealing with the principles of the gas-lift, a search of the available literature indicated that specific information on vertical flow was lacking with the exception of the writings of Uren, Versluys, and Moore and Wilde, to which reference .has been made.

Jan 1, 1932

By C. M. Nickerson

The possibility of deeper production in the Buena Vista Hills was first considered in 1933. At that time, however, the heavy state curtailment program served to deter any operator from drilling test wells, which, if successful, might upset the proration schedules. Because most of the acreage was held by several major operators and the remainder by substantial independents, the adoption of a plan of cooperative development was considered desirable. Such a plan was formulated for the development of any deeper oil and gas horizons that may be found to exist. This plan, which was signed by the Secretaries of the Navy and of the Interior on behalf of the United States on July 9,1936, is now effective for the development of lands within the area shown on Fig. 1. Unlike most unit plans, the present cooperative development plan permits each operator to drill and produce his own wells. For the purpose of this plan the Buena Vista Hills field is divided into two pools. The present production is classed as the " old pool,"' while any future production below a certain marker which roughly coincides with the bottom of the Santa Margarita formation is included in the "pool" to which the provisions particularly apply. Naval Petroleum Reserve No. 2 lies within the area and constitutes the major portion of the Federal leases subject to the plan. There are 39,040 acres and 27 operators within the area. Twenty-six operators controlling 99.5 per cent of the acreage have signed the agreement. Geology oF the Buena Vista Hills The Buena Vista Hills consist of a low range in the southern portion of the San Joaquin Valley, and are roughly parallel to the adjacent Temblor range to the south. The Elk Hills oil field parallels the Buena Vista Hills a few miles to the north. The subsurface structure is a re-entrant anticline upon the major Midway-Sunset monocline. This anticline is divided into two minor

Jan 1, 1937

By G. R. Fritterer

Investigators in the field of temperature measurement have long sought a thermoelectric couple fulfilling the following requirements: 1. It should be useful up to and including high industrial temperatures; i. e., 1000 to 1800 C. 2. Its thermoelectric variation with temperature should be linear and be maintained after heating to high temperatures for long periods of time. 3. It should be reproducible; i. e., different couples of the same elements should have similar calibration curves. 4. Its thermoelectric power should be large so as to allow the industrial use of rugged recording instruments. 5. Chemical reactions with, and physical changes within the elements of the couple should not alter its calibration. No thermocouple proposed to date exhibits simultaneously all of these characteristics, whereas the couple about to be described fulfills all requirements to a satisfactory degree. New Thermoelectric Materials A thorough survey of the literature on thermoelectricity revealed that present-day thermocouples could not meet the specifications mentioned above because their thermoelements are metallic. Metals have a marked tendency to deteriorate chemically and their melting points limit their use to low temperatures. Refractory substances, however, are usually resistant to chemical attack and are quite stable at high temperatures. Hence a survey of refractory substances having thermoelectric possibilities was made. One class of thermocouples considered was that in which carbon and a carbide of some metal or nonmetal were the thermoelements. Previous investigators neglected to study this field but certain recommendations were made by them for the use of couples in which carbon served as one element. These proposals are listed in Table 1. The couples suggested are unsatisfactory because of their low thermoelectric powers, the low melting points of their metallic elements, etc. The

Jan 1, 1933

By J. G. Thompson

Determinations of the hydrogen content of irons and steels invariably are subject to two serious difficulties: (I) the determination of amounts of 0.001 per cent or less of any constituent requires an analytical procedure of unusual precision and accuracy, and (2) the hydrogen content of many samples is dccidedly not stable; i.e., there is no assurance that the content at the time the analysis is made is the same as it was when the sample was taken or at some previous time in the history of the piece. In respect to both the precision and speed of the determination, the vacuum-extraction procedure for the determination of hydrogen possesses advantages over the vacuum-fusion procedure, which has been the recognized standard for the detcrmination of other gaseous elements in sted-— oxygen and nitrogen for example. The basic facts upon which the vacuum-extraction procedure is based—i.e., the evolution of gas from solid steel when it is heated in vacuum, and the fact that the evolved gas is rich in hydrogen—were observed by Graham1 many years ago. Subsequent investigations have shown that hydrogen exists in steel chiefly as interstitial solid solution (i.e., in atomic dispersion) and perhaps to some extent as hydridcs that are unstable and decompose to form atomic hydrogen. In either case practically all of the hydrogen in steel at elevated temperatures exists in the atomic condition and consequently is able to diffuse readily through the metal. In contrast to this, other gaseous elements, such as oxygen and nitrogen, normally are present in steel chiefly in the form of relatively stable compounds such as oxides or silicates and nitrates; i.e., the oxygen and nitrogen atoms are fixed in stable combinations and are not free to migrate. The only oxygen or nitrogen that can diffuse in steel is the small amount in solution (atomically dispersed) and the rate of diffusion of these atoms is much less than that of hydrogen because of their greater atomic volume and lower mobility. Consequently, it is possible to extract most or all of the hydrogen from solid steel in a reasonable time at moderately elevated temperatures, but the procedure is not applicable to the determination of oxygen or nitrogen. It is only within the last decade that these observations have been developed into an analytical procedure for the determination of hydrogen. Apparatus and Procedure The apparatus used at the National Bureau of Standards,6 for the determination of hydrogen by the vacuum-extraction procedure, is shown schematically in Fig. I. The specimen, freshly cleaned and dried,* is suspended on a fine wire within the quartz furnace tube that is connected to the reservoir system and analytical train.

Jan 1, 1945

By A. C. Veatch

Jan 1, 1921

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