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By C. F. Cornell, Henderson, A. F. Dunyon, D. A. Dahlstrom

IN processing magnetic taconites several steps of crushing, grinding, classification, and magnetic separation are required to produce a 60+ pct Fe concentrate. Usually the final concentrate is in a slurry form of 55 to 70 pct solids by weight and is further characterized by a particle size of 60+ pct -325 mesh. In taconite plants already completed or under construction the conventional method used to obtain pellets suitable for blast furnaces is to filter the concentrate slurry, ball the filter cake, and then harden the green pellets in a traveling grate or in a vertical shaft furnace. Large tonnages must be handled in minimum floor space, with reduced maintenance and lowest possible operating cost. Filtration must therefore achieve two objectives: 1) high filtration rate-in terms of pounds of dry solids per hour per square foot of filtration area-at a low filtrate solids concentration, and 2) a filter cake moisture that will always permit efficient balling within the normal fluctuations of plant operating conditions. If moisture contents are too high, balling may be impossible or result in a mushy ball without enough green strength for the firing operation.

Jan 3, 1957

By T. Krauthammer

A combined numerical approach is proposed for the analysis of rock-liner interact ion in tunnels under the effects of severe dynamic loads. The method is based on employing finite element formulations which describe the linear behavior and incorporating it into a finite difference code which can describe the behavior of a jointed rock medium. This method can be applied for the analysis of tunnel systems in rock, and for studying the requirements for adequate support of the tunnel.

Jan 1, 1984

By C. A. Sobotowski, J. Eagan

Computer programs applicable to coal mining have been available for some time, especially in the academic sector. However, the computer has not routinely been applied to actual mining operations. This paper discusses how a computer system was set up as an important tool in mining design and decision making. The project was completed within the allotted timeframe of two months by taking advantage of existing technology. Key points include the selection of programs to meet the specified needs of the project, conversion of the programs to be compatible with a computer of a different manufacture, simplification of the data entry process, development of procedures for using these programs, and an explanation of how the reports generated from the programs were used for mine planning and decision making.

Jan 1, 1983

By A. E. H. Bergmann

INTRODUCTION The Sachtleben Chemie GmbH in Duisburg, a subsidiary of the Metallgesellschaft AG, operates a new sulfuric acid plant that employs fluid bed roasting of pyrite concentrates. The plant produces about 300,000 tons per year of pyrite cinders from the fluid bed roasting unit. The cinder product consists of 58 percent iron and is about 80 percent by weight smaller than 50 microns. This cinder product was found to be a competitive source material for the cement industry as the iron-containing additive. However, the extreme fineness of the cinder and its dusting tendency were undesirable and an agglomerating technique became necessary. In order to keep the price of agglomerated pyrite-cinders at a competitive level, the agglomerating method must be chosen such a way the capital and operating costs are low. Initial experiments were carried out on a laboratory scale to make an appropriate choice of the agglomerating method. Major goals of agglomerating the cinders were to improve the transportation, storage, and proportioning and metering properties. Minimum specifications are put on the size, size distribution and shape of the product. Criterion for handling is that a minimum of minus one mm. fines are produced after several handlings, while for storage, it is also desirable for the agglomerated product to survive several months in open air. Thermal agglomeration processes such as sintering one known to produce excellent products, but are by far too expensive for our application. For the same reason, granulation, balling, and pelletizing tests with addition of organic binding agents, such as tylose, starch, sulfite wash, molasses, etc. were not continued. The costs for the binding agent was considerable, which is probably due to the high pore volume of our cinders (35 %). Furthermore, the pellets or granules

Jan 1, 1977

By G. H. Billings

The following data were collected some years since in the course of a series of experiments with oil as a substitute for coal in puddling, the earlier form of the Archer apparatus being employed. While I am not at liberty to give the name of the works at which the tests were made, I can personally warrant the accuracy of the record, and feel justified, therefore, in making this contribution to a discussion in which all trustworthy figures are likely to be helpful. Oil in Puddling. Starting with everything cold, we used 3518 pounds of oil to get the furnace in condition to charge a heat. After charging, we ran until we took out 13,340 pounds of puddled-blooms, using 8437 pounds, or 1333 gal1ons of oil. At 49 cents per gallon, the cost for oil per gross ton of blooms was $10.91; with coal at $4.871/2, and a consumption of 1.5 tons per ton of blooms (the usual quantity is ton for ton), the cost for coal is $7.31. The quantity of oil consumed in heating the furnace to the proper temperature and to make the bottom, is not included in the oil consumption stated. The quantity used was 3518 pounds of oil. Usually, the furnace need only be lighted, but in this case it had been repaired, and it was necessary to make a new .bottom. This required the quantity of oil necessary to make three heats of blooms, or 2109 pounds. Deducting this from the 3518 pounds leaves 1409 pounds of oil as the quantity consumed every week in lighting up.

Jan 1, 1889

By W. M. Lehrer

RECENT development of high-temperature brazing alloys has required information regarding the eutec-tic temperature and composition of the Pd-rich section of the Pd-B system.. Literature on this subject was found to be scanty with no complete system yet determined. Buddery and welch1 report an inter-metallic compound occurring in the Pd-B system at 6.33 wt pct B (PdsBz). Another source, Sieverts and Bruning,2 indicates that after annealing at 700°C, a 1.6 and a 2.0 wt pct B alloy were two phase whereas a 0.75 pct B alloy was single phase. Recent work3 using a hot-stage microscope has proposed a eutectic temperature of 743OC. This method utilized the observation of the onset of incipient melting at grain boundaries. The eutectic composition, however, was not determined. METHODS AND PR0CEDURES Five alloys were prepared by triple inert arc-melting high-purity palladium (95.98 pct) with additions of 2 to 6 pct purified amorphous boron. The alloys were crushed within a hardened steel mortar with a steel pestle. The 2 pct alloy, however, was too tough to be crushed in the above manner so was crushed by successive reductions through a rolling mill. Approximately 17 to 18 g of the crushed alloy was used in the thermal analysis. The alloys were melted in pure quartz crucibles. The thermocouple protection tubes were also of quartz and fused along the inside wall of crucibles to prevent floating of the thermocouple. This was an expediency as centering of the thermocouple in the melt would have been preferable. Melting was done in a tube furnace with a slow flow of tank helium maintained as a protective atmosphere. Heating and cooling rates were maintained at 3.5OC per min through the critical temperature ranges by means of a synchronous motor hook-up to a furnace controller. All specimens were heated to 100°C over the indicated liquidus on heating prior to reversing to the cooling cycle. Specimens emerged from the furnace with mirrorlike brightness attesting to the protective quality of the helium atmosphere. Thermal arrests were detected by the differential thermocouple technique using chrome l-alumel couples and nickel as the reference specimen. Arrests were recorded on a Leeds-Northrup automatic X-Y recorder. The specimen temperature and temperature difference were read to + 7.5OC and ± 1.5OC, respectively. These readings were well within the sensitivity of the instrument amplifier. Chromel-alumel couples were used in lieu of Pt-Rh as very few arrests were contemplated in excess of 1200" to 1300°C, the approach of instability. No standardization was performed on these thermocouples subsequent to their use. RESULTS The thermal arrest temperatures obtained are plotted in Fig. 1 as a function of wt pct B. The composition function was obtained by chemical analysis of portions of the specimens after the thermal analysis was completed. The 2 to 6 pct nominal alloys were found to have 1.80, 2.35, 3.65, 4.18 and 5.90

Jan 1, 1960

By J. Blodget Britton

During the last three or four years I have had occasion to examine, chemically, various samples of matter commonly called flue-dust or cinder, found deposited in the flues and hot-blast chambers and under the boilers of blast furnaces, and also in the flues and under the boilers of puddling and boiling furnaces. Recently several of these examinations mere made quite in detail, and as the results reveal, I believe, information of no inconsiderable importance, I am induced to communicate them to this Institute. A sample of deposit obtained from the flues of one of the blast furnaces at the works of the Phœix Iron Company, at Phœnixville, Pa., was found to have the composition given in Column I of the following table: I. 11. 111. Composition of Dust from Dust from Dust from Deposits. Blast Furnace. Puddling Furnace. Boiling Furnace. Protoxide of iron,... 1.51 3 08 1.18 Peroxide of iron,... 20.21 33.29 41.00 Alumina,....6.57 12.89 7.54 Lime,.....3.98 .48 .61 Magnesia,.....69 .09 .19 Protoxide of manganese,. . 1.66 .39 .12 Oxide of zinc,....2.84 ........ Oxide of copper,. .. ..06 ........ Silicic acid,....36.00 40.69 38.99 Sulphuric acid,... 7.55 .43 Phosphoric acid,..94 ..94 Arsenious acid,. .. .38 Antimoniousacid,... trace.......... Chlorine,....03 ..03 Cyanogen,.....09 ........ Ammonia,.... trace......... Pottlsh with some sodn,. .. 16.61 ........ Carbonic acid,. .. .. .59 ........ Alkalies, undetermined matter, and loss,.......29 4.49 6.96 100.00 100 00 100.00 Metallic iron,. 16.31 25.70 29.64 Phosphorus,. .. .. .41* 1.55† 1.30†

By K. S. Benson

DEPLETION is a subject of vital importance to the mining industry. Yet, in spite of its importance, its significance is not generally understood. The purpose of this discussion is to clarify the main aspects of the subject from the viewpoint of a metal mine taxpayer.

Jan 7, 1951

By Leo Dana

As a part of an investigation conducted by the Cement Section of the Bureau of Standards, at the plant of the Security Cement & Lime Co., Security, Md., the High-temperature Measurements Section was called upon to measure temperatures in a dry-process, coal-burning kiln. Although the measurements were made only under the conditions existing in one plant, the methods employed and the conclusions drawn apply, in a general way, to those existing in most plants. As far as we have been able to learn, no sufficiently thorough methods of making accurate pyrometric measurements in the sintering zone and in the rear end of rotary cement kilns have been described. It is believed that in this investigation, data were obtained that can serve as a foundation for further study of the problems of pyrometry in cement kilns. IMPORTANCE OF TEMPERATURE MEASUREMENTS IN ROTARY CEMENT KILNS The manufacture of Portland cement is today fairly well standardized. The various steps in the manufacture have been developed to such an extent that the process is almost automatic. In spite of these strides the efficiency of utilization of heat in the kiln is very low and an undue proportion is wasted; for example, about 50 per cent; ordinarily goes up the stack. In order to prevent these losses, not only should means be provided to utilize the waste heat but instruments, such as pyrometers, should be installed to study and control the operation with the view of minimizing the losses. At the same time, such control will produce a more uniform product. The saving in-fuel that may be effected by the proper use of pyrometers would be much more than their cost. Where these pyrometers should be installed and what they can show are very briefly indicated in the following paragraphs and discussed in greater detail later.

Jan 9, 1919

By George Holderer

THE Enos Coal Mining Co. owns an area underlaid by coal, of approximately 5000 acres. This property is situated 9 miles from Oakland City, in the southern part of Indiana. The mine has been in operation 5 years, during which time some 350 acres have been stripped, and stripping is now proceeding at the rate of about 100 acres per year. TOPOGRAPHY These coal lands consist of gently-rolling agricultural fields which in times past were farmed for wheat. There is no timber and but very little brush to contend with. The overburden varies from 10 to 60 ft. in depth. A thin bed of slate overlies the coal, followed by limestone, which varies from 3 to 15 ft.; this, in turn, is followed by sandstone, slate, shale and clay. There is a very wide variation in the thickness of all of these beds. The coal has an average thickness of 5 ft., and is a good grade of high-volatile bituminous. MINING OPERATIONS Briefly, the sequence of operations is: drilling holes with churn drills; blasting with L. 0. X.; stripping overburden to, uncover coal and, finally taking up the coal, which is sent to a tipple for cleaning and sizing. In order to show what is being accomplished by the use of L. 0. X., results will be shown from May to November, 1926, inclusive, and compared to the same period in 1925. No work was done in No. 1 pit during May, 1925, hence all figures are unduly low for this month.

Jan 2, 1927

By G. B. Pryde

IN laying out a new mine, provision should be made for the ultimate recovery of as much coal in any given bed as is consistent with safety and economic mining. Though each mining district, if not each individual mine, has problems that make the adoption of any hard and fast rule impossible, certain basic principles are adapted to practically all conditions. One of the most vital is the provision for barrier pillars of ample dimensions to protect all haulage and permanent airways during the life of the property. Where conditions permit, room or butt entries should be driven on the strike or slightly to the raise and rooms turned at right angles to said entries. The width of rooms and room pillars is governed by conditions prevailing in the mines under consideration. A safe rule is: In advancing, extract not more than 25 to 35 per cent. of the entire seam; in exceptionally thick seams, considerably less than 25 per cent. should be taken. Rooms usually vary in length from 250 to 350 ft. (76 to 106 m.) with a barrier pillar of not less than 80 ft. between the last crosscut in rooms, and entry and room crosscuts should be driven on sights; room crosscuts should be driven at right angles to the direction of the rooms. In mines under excessively heavy cover or where roof conditions are bad, rooms should be driven narrow and a barrier pillar left at every fifth to tenth room. This barrier should be of such dimensions that one or more rooms, with pillars of usual dimensions, may be turned through it when the barrier is no longer required. Two of the advantages of such a barrier are the protection of the panel against peaking of roof load during pillar extraction and the easy closing of the entry in case of fire.

Jan 2, 1921

By E. T. Dumble

(San Francisco Meeting, September, 1915) THE history of the several petroleum deposits of Texas and Mexico, or of the sediments in which they now occur, if the deposits are not indigenous to such sediments, is known in a general way only, but it nevertheless casts strong light on the conditions surrounding them and is of great importance in the search for and exploitation of then. The petroleum deposits of Texas are separable into two main divisions: 1. The deposits of northwestern Texas, which are directly connected with the Oklahoma fields to the north, and have no representatives at all in the Mexican area. 2. The deposits of the coastal area, which extend into Louisiana on the east and connect with those of the Mexican coast to the south. Early in the Pennsylvanian period a series of bituminous shales and limestones were laid crown over a broad area in Texas, Arkansas, and Oklahoma. These are known as the Bend series in Texas, the Caney shales in Oklahoma, and the Fayetteville beds in Arkansas. Following their deposition an uplift occurred, forming the Lampasas geanticlinal, which runs northeastward from the old Paleozoic land area of the Llano region toward Red River. The Bend series is petroliferous in places and has furnished a few producing wells on each side of the Lampasas uplift. This uplift forms the barrier and. dividing line between the two divisions of the Texas petroleum deposits. To the west of it, in waters which were the southern extension of the interior continental seas, in connection with the sediments and coal beds of the Pennsylvanian and Permian, great quantities of petroleum were deposited either as oil or as "potential petroleum." These sediments have been subject to very slight disturbance, and only very gentle folds. are found, with no signs of volcanic action in any part of the area. The conditions, therefore, indicate that the greater part, if not all, of the oil in this area is indigenous to the beds in which it is found.

Jan 8, 1915

By R. S. Shoemaker, F. W. McQuiston

CARLIN GOLD MINING COMPANY 1974 Operating Data to October MINE LOCATION: 40 miles from Elko, Nevada ORE DESCRIPTION: Gold with minor amounts of mercury occurring in siltstone and carboniferous limey shales. TYPE OF MINE: Open pit ORE HAULAGE TO MILL: By trucks up to a distance of 12 mi1es MILLING CAPACITY: 2500 tons per day ORE GRADE: 0.20 oz per ton oxide ore 0.25 oz per ton carbon type ore PRODUCTS: Gold bullion 993 fineness, by product quicksilver RECOVERIES: Oxide ore 887'0 Carbon ore 83% POWER FOR GRINDING: 7 Kwh/T POWER, other than grinding: 14 Kwh/T WATER SUPPLY: Pumped from wells 2- 112 miles through 13,000 ft of 8" buried pipe 6 ft underground. Consumption 0.60 tons of new water per ton of mill feed. TAILINGS: By 10" woodstave pipe a distance of 2500 ft to mine waste filled dam. RUNNING TIME: 10 ft x 10 ft mill on oxide ore, 98% 7 ft x 8 ft mill on carbon ore, 937'0 Principal causes of lost time, power outages and problems of feeding gaseous chlorine to carbon ore agitators. LABOR, TONSIMAN SHIFT: See detailed data sheet ILL BUILDING DESCRIPTION: Framed structural steel with sandwich type walls of marine plywood, then packaged pre - fabricated insulation and outer sheeting of galvanized corrugated steel.

Jan 1, 1975

By W. N. Best

THIS paper is not intended as a scientific discussion of the combustion of oil but is written from, the standpoint of an operator who has the experience and qualifications necessary to guide others in producing the most economic results in the use of liquid fuels. Oil, in this paper, usually, means petroleum or its products but incidental reference is made to other liquid and gaseous fuels, so that the term may be considered, as referring to all liquid and gaseous hydrocarbons in comparison with solid fuels, as coal and. wood. However, only a few of the principal factors in the use of oil as a fuel can be given. The present, and prospective, high price of coal is causing users of fuel to renew inquiry as to the merits of other forms of fuel for industrial purposes. Crude oil (petroleum) is proving to be one of the world's most valuable mineral resources. The recent discovery that oil underlies a considerable area of the United States, Mexico, and other parts of the world to a greater extent than was formerly believed and the large production of some of the wells in these areas shows the probable quantity of fuel oil that may now be available. Through the energy of Lord Cowdrey, who was one of the pioneers of the oil industry in Mexico, oil has been discovered in England; some prominent geologists believe that it may be found yet, in quantity, in Great Britain. For years, oil has been known to be of great value in the manufacture of metals. It has proved incomparable in forge shops, steel foundries, heat-treating furnace s, and wherever accuracy of temperatures is essential, or where a maximum output is desired as well as quality of metal. In some types of equipment, the output produced with oil as fuel is double that obtained with coal and, at a reduction of 50 per cent, in the cost of the fuel. For example, in drop-forging plants, the metal is always waiting for the man when oil is used as fuel, whereas with coal, the man must wait for the metal to become sufficiently heated.

Jan 8, 1920

By W. A. Eardley

FIFTEEN years ago the world's deepest oil well penetrated the earth about 7300 ft. That depth has now been more than doubled. Why has such deep drilling become necessary and how has it become possible? Three factors have had an important bearing: (1) Depletion of shallow zones, making it necessary to search for deeper producing measures. (2) The perfection of prospecting methods, which have been success- fully used to locate favorable buried structures, many at great depth. (3) Improvement in the quality of steels used for drilling.

Jan 1, 1940

By James Munroe

APPALLING as has been the loss of life in the last 51 months, there is one slight compensation : no longer will there be in the world a cripple, in the old meaning of the term. Men handicapped by wounds or disease, there will be, unfortunately, and in numbers beyond what the world has known since the wars of Napoleon; but neither they nor the industries from which they were called off to war will be "crippled" in the sense in which both would have been had mankind not learned the lesson of conservation and come to understand that the most important field for such conservation is not in the forests and' the mines but among men and women. From the beginning of the Great War, France, Great Britain, Belgium, and most of the other Allies have studied the problem of restoring the soldiers and sailors injured through war to physical and economic efficiency; and from their experiences, especially from that of Canada, the United States has learned much. Consequently, our task of preparing for the return of our disabled men has been easier and, in some ways, more comprehensive than theirs. Complex as are the details of the machinery which the United States has set in motion to take care of the men injured by wounds or disease, the plan itself is simple. Taught by European experience, the Surgeon-General of the Army and the Bureau of Medicine and Surgery of the Navy have provided, on both sides of the Atlantic, every known surgical and medical facility for restoring the injured or diseased man to a physical condition as nearly normal as possible. While in the hospital in France or England, on the transport coming to America, and in the hospital here, the disabled man is incited in every way to believe in his future efficiency, to want to be a normal worker, to desire to retake his place in that society of workers from which he went, temporarily, to do the greater work of preserving civilization. Furthermore, since purposeful occupation is now regarded as an essential form of, treatment with most men in the hospital, especially in the convalescing stage, many of these men will have been actually started on the road to earning before they are discharged from the army surgeon's care.

Jan 1, 1919

By Lucien Eaton

THE accuracy with which detachable bits can be sharpened and gauged by grinding has made possible refinements in design that cannot be attained by forging. This applies particularly to gauging, where accuracy is of the greatest importance. Gauge changes of 1/32 in., and even 1/64 in., are now feasible, whereas 1/16 -in. changes are about the limit in accuracy for forged bits. These small changes in gauge are feasible, however, only with certain fundamental principles of design. Within reasonable limits the depth to which a hole can be drilled is dependent primarily upon the loss in gauge, or diameter, of the bit. In drilling there is always a certain amount of "overdrilling"-the bouncing of the bit in the hole and its rotation wear away the walls-so that the actual diameter of the hole is greater than the diameter of the bit. The amount of this overdrilling depends upon the kind of rock being drilled, and is sometimes sufficient to permit the use of the same diameter of bit for the full depth of the hole. If, for instance, a 1 3/4-in. diameter bit overdrills 1/32 in. in diameter, and loses 1/64 in. in gauge in drilling 2 ft. of hole, the bottom of the hole is still 1/64 in, larger than the original diameter of the bit, and a new 1 ¾ -in. bit can be used to drill the next 2 ft. If, however, the overdrill is less than the loss in gauge, the next bit must be of smaller diameter. The first requisite in reducing loss of gauge in drilling is to have the points and corners of the wings of the bit cut circles of the same diameter, thus producing a reaming surface with continuous bearing on the wall of the hole. The greater the reaming surface, the less the gauge loss that is to be expected. If the reaming surface, however, is too large, it may impede the rotation of the bit through excessive friction. This principle was probably first recognized in the design of the Carr bit (Fig. 1), a bit with a single cutting edge of wide angle, a definite reaming edge, and a large center hole. The same idea was followed in designing the double-taper cross bits, which are now standard almost everywhere.

Jan 1, 1939

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 A. Sauveur

In an important paper on The Critical Ranges of Pure Iron presented at May, 1913, meeting of the Iron and Steel Institute…

Jan 1, 1915