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By H. C. Spaulding

The rapid increase, during the last few years, in the number and magnitude of applications of electric power-transmission to commer cial uses in this country, has been due principally to three causes: first, the ability and enterprise of those who have been identified with the progress of electrical industries, since electric illumination became an economic fact instead of a laboratory-experiment: sec ondly, the readiness of the American people to adopt new and ad vanced methods as soon as their superiority has been fairly demon strated; and thirdly, tile economy and flexibility of the apparatus employed, when properly designed and constructed, and installed under suitable conditions. Basing our judgment on the world's advance in scientific devel opments during the past century, we may reasonably conclude that in no other country would the pioneeis of electrical invention, whose names have now become household words, have received the prompt and plentiful financial support which has enabled them to inaugurate undertakings of exceptional magnitude, even in this era of tremendous monetary organizations. And, on the other hand, we have seen, in the numerous financial and engineering failures inseparable from such rapid development, the natural results of a too implicit faith in electrical omnipotence. It is not to be wondered at that conservative engineers have been slow to adopt this new and mighty agent in the solution of exten sive problems, and under circumstances where a single failure means not only a greater or less financial sacrifice, but the loss, in a greater or less degree, of professional reputation. Be mechanical engineer, while recognizing the fact that thousands of horse-power are to-day transmitted by electrical means, from sunning the lathe in a dentist's office to the operation of a fifty-ton travelling crane; from passing a cooling draught of air through a

Jan 1, 1891

By Richard G. Sandberg

Sphalerite concentrates prepared during processing of Missouri lead ores contain small percentages of cobalt and nickel which adversely affect zinc electrolysis. The Bureau of Mines has evaluated solvent extraction and precipitation techniques to remove and recover cobalt and nickel from zinc sulfate solution prior to zinc electrolysis. Prepared zinc sulfate solutions containing about 190 gpl of zinc and 50 ppm of both cobalt and nickel were treated using various combinations of complexing reagents, solvent, pH, concentration, time, and temperature. The following complexing reagents gave the best results: a-nitroso-ß-naphthol, ß-nitroso-a-naphthol, 1,2 cyclohexane dione dioxime (nioxime), di-2-pyridyl ketone oxime, and dimethylglyoxime. These reagents in suitable solvents lowered the cobalt and nickel levels to <0.1 ppm. Stripping the complexed reagents from the solvents was not possible except for nioxime. Direct addition of the appropriate reagent to the prepared zinc sulfate solution resulted in the precipitation of cobalt and nickel. Several possible flowsheets are presented for the removal and recovery of cobalt and nickel. Good zinc deposits were successfully electrowon from zinc sulfate solutions purified by solvent extraction and precipitation.

Jan 1, 1978

By J. L. Bruce, N. B. Braly, F. A. Linforth, Wm. B. Daly, Paul A. Gow, C. L. Berrien, R. H. Sales, P. F. Beaudin, John Gillie, G. W. Roddewig

Butte mining district is situated in Silver Bow County, in the southwestern part of Montana. Butte originated as a placer mining camp, gold having been discovered in 1864, on Silver Bow Creek, near the southerly end of what is now Main Street. The Butte placer gold was heavily alloyed with silver, and only commanded $13 an ounce. Placer mining was vigorously prosecuted along Silver Bow Creek and its tributary gulches for about 5 years, at the end of which time, in 1870, the Butte camp was practically deserted. In the meantime, the quartz veins prominently traceable over the hillsides were located, the first location, July 12, 1864, being made by the Missoula Mining Co. and called the Missoula Lode Claim, and later relocated by G. 0. Humphreys. Reasoning from the presence of the gold placers, free milling gold and silver ores were eagerly looked for by the early prospectors. Claims covering the great Rainbow and other silver lodes were located in the 60&apos;s. The presence of valuable silver ores in these veins caused the staking of many claims, believed to be valuable only for silver, but which later, at depth, proved to be enormous copper producers.

Jan 1, 1925

Mixed integer programming (MIP) has been used for optimizing production schedules of mines since the 1960s. The major problem in the long-term production scheduling for an entire orebody is that the number of integer variables needed to formulate an MIP model is too large to solve the formulation. This number may reach well over one hundred thousand. To overcome this difficulty, this paper presents two new algorithms to reduce the size of the problem. These algorithms assign an earliest and latest possible start date for each machine placement, eliminating the integer variables that correspond to machine placement before its early start date and after its late start date. A case study based on Kiruna Mine, the second largest underground mine in the world, is summarized in the paper. It shows substantial improvement in the solution time required using the new algorithms. This increased efficiency in the solution time of the MIP model allows it to be applied to Kiruna Mine, with the potential to increase substantially the net present value (NPV) of the project.

Jan 1, 2008

By D. J. Jr. McAdam

RESULTS of investigation of corrosion-fatigue of metals at the U. S. Naval Engineering Experiment Station have been presented by the author in four papers. 1,2,3,4 In those papers references were given to the work of Haigh in 1917.5 The investigation at Annapolis included a variety of ferrous and non-ferrous alloys. The experiments showed that even slight corrosion simultaneous with fatigue may cause failure at stresses far below the ordinary endurance limit. The experiments also showed that, for most metals, severe stressless corrosion prior to fatigue is much less damaging than even slight corrosion simultaneous with fatigue. The term "corrosion-fatigue" was restricted to mean the simultaneous action of corrosion and fatigue. The combined effect of corrosion followed by fatigue was called "prior-corrosion fatigue." A stress-cycle graph representing corrosion-fatigue is a curve approaching a horizontal asymptote, the ordinate of which may be called a "corrosion-fatigue limit." To avoid confusion in later discussion, the term "endurance limit" will be restricted to mean the fatigue limit obtained by tests in air with specimens as free as possible from stress concentration and from corrosion. The endurance limit as thus obtained presumably represents an inherent property of the metal.

Jan 1, 1929

By Stewart WJ

Australia&apos;s first offshsore well was spudded in on 27th December 1964 and resulted in the discovery of the Barracouta gas field. Further exploratory drilling led to the discovery of the Marlin gas field in December 1965, the Kingfish oil field in April 1967 and the Hblibut oil field in June. 1967. In September 1968, a small oil reservoir was found in a sand below the main Barracouta&apos;gas reservoir. The Snapper gas field was discovered in May, 1968 Information on exploration activities associated with the discovery of oil and gas in the Bass Strait area may be found in the paper, "Exploration in the Gippsland, Bass and Otway Basins, Australia" by B. M. Hopkins. _ Development of the commercial fields is being undertaken on an equal participation basis by Hematite Petroleum Pty. Ltd. and Esso Exploration and Production Australia Inc. Esso Standard Oil (Australia) Ltd. is responsible for the design, construction and operation of the production facilities.

Jan 1, 1970

By Sanja Zlatanic, Michael P. Della Posta

New York State’s Metropolitan Transportation Authority (MTA) has undertaken the largest transportation project in New York City. The East Side Access Project (ESA) will introduce MTA’s Long Island Rail Road (LIRR) service to the East Side of Manhattan, to a new terminal located beneath the existing, landmark Grand Central Terminal(GCT). Construction of the Manhattan Segment of the project will affect overlying operating facilities of two other MTA entities, Metro-North Railroad (MNR) and New York City Transit (NYCT) and major Midtown Manhattan buildings. The paper describes the evolution of the GCT concept at Manhattan from a shallow alternative proposed by a Major Investment Study (MIS), that would require extensive underpinning of multi-story buildings and have considerable impact on MNR and NYCT operations, to a deep alternative with lesser risk and potential for disruption.

Jan 1, 2001

By Kuipers A. J

Aberfoyle has been applying computer methods to mine geology in small to medium-sized underground mines since the early 1980&apos;s. Recently, the installation of DATAMINE software at the Hellyer Mine in Tasmania has allowed development of computerised applications which assist both mine geologists and mine planning engineers on a daily basis.Comprehensive data is entered into a database prior to survey coordinating to produce a processed database which can be accessed for construction of a variety of plots. The folded and faulted nature of the orebody contacts at Hellyer has necessitated the use of the structure contour method to provide a complete 3-D spatial interpretation. Computer-generated contact intersection points are hand-contoured before digitising and wireframing as a digital terrain model. This wireframe model can be sectioned in any plane for mine planning.

Jan 1, 1990

By T Laurencont, C Unger

The Mount Morgan minesite, located approximately 40 km SW of Rockhampton in Central Queensland, comprises 270 ha of unrehabilitated land which is the currently the major source of acid mine drainage run-off and seepage to the adjacent Dee River. Additionally, the minesite hosts an Open Cut Pit which contains 9000 ML of acidic and metal-rich water. In the absence of active management of water in the pit, there is a 50 per cent probability of an uncontrolled spill occurring in future years. The development of a contingency plan for management of overflow from the pit in the short term, has incorporated findings from numerous studies relevant to the Open Cut Pit including, but not limited to, water balance, contaminant source identification, toxicity testing, water quality profiling and limnological modelling, and estimates of probability of overflow. Extensive stakeholder consultation and peer review were also undertaken during the formulation of the contingency plan. The medium-term goal of lowering the water level in the pit to reduce the current high probability (50 per cent) of uncontrolled overflow to acceptable levels of risk is proposed to be achieved by a campaign of chemical water treatment. The treated water will be discharged to the Dee River, and sludge returned to the pit. The methodologies used for the selection and development of the water treatment process, that is proposed to involve treatment with lime, are described. Water treatment is the short- to medium-term component of a long range rehabilitation plan for achieving a negative pit water balance, and sustainable management of acidic water across the whole site. Achieving this ultimate goal will involve: reducing the inputs of water to the Open Cut Pit such that the annual water balance is zero or net negative, thus removing the need for water treatment in perpetuity; maximising, by surface rehabilitation works, the quality of run-off reporting to the Dee River; and minimising the volume of acidic seepage reporting to the seepage interception system. Possible strategies for achieving this long range goal consistent with overall site rehabilitation objectives are currently being developed and costed.

Jan 1, 2003

By R. E. H. Pomeroy

Early in 1917, it became evident, owing to existing and pending market conditions, that a substitute for crude petroleum must be found for firing the smelter furnaces. After a review of the plants then existing, it was deemed advisable to depart from their practice and to adopt the following described system of distributing pulverized coal to the furnaces. The principal advantages of the proposed system, which influenced this decision, were: (I) Equal safety; no pulverized coal is stored at the furnaces; (2) greater ease of operation, furnace fires being controlled by regulating valves in burner branches, as in gas firing; (3) better organization; all machinery, including pulverized coal feed, is under one roof, and the organization is separate from the furnace department; (4) greater cleanliness; all machinery is under vacuum; (5) greater flexibility of application, the coal and air mixture can be piped where needcd. The design of the plant is the result of the combined efforts of the local engineering staff and of the machinery manufacturers. Many new features were embodied in this design to insure greater safety, cleanliness, and efficiency of handling. After 14 months of continuous operation, the plant has proved entirely satisfactory. The building is of structural steel, covered with corrugated steel, with many windows and is painted light gray inside and out. The building floor is of concrete with ample drains to the sewer, and the building is equipped with fire and service water piping. Fig. 1 shows the east side of the building and the incline conveyor from the raw-coal bins. The plant is operated entirely by electric power. All alternating current is 550 volts, 3-phase, 60 cycles. The pulverized-coal feeding niotors and control mechanism are operated by 220-volt direct current supplied by motor-generator sets in the building. Autamatic push-

Jan 1, 1921

By Holliday R, Floyd JM

A laboratory investigation was carried out to determine the distribution of gold between the products of lead-zinc concentrate smelting in the Imperial Smelting Furnace (ISF). Bullion, speiss and slag from the ISF at Cockle Creek were used as the starting materials to evaluate the effect of gold and copper content of products on the distribution of gold between phases under conditions simulating those in the ISF hearth. The ratio of gold in bullion to gold in speiss has a mean value of approximately 1.6 and is independent of the gold content of the bullion. The distribution coefficient of gold between bullion and speiss is dependent on the copper level in speiss and is lowered by increasing copper content in speiss. The ratio of gold in bullion to gold in slag is in the range 25 to 5700 and dependent on the gold content of the bullion. For low gold concentrations in bullion of the order of 1 g/t and a bullion to slag ratio of 1:3 the gold loss to slag is expected to be approx- imately 23%. In all tests the gold in slag remained low, in the range 0.05 to 0.5 ppm provided metal prills were not suspended in Slag.

Jan 1, 1986

By Yuki Tsunazawa, Shuji Owada, Sho Fukui, Chiharu Tokoro

"Since the amount of e-waste has been rapidly increasing all over the world, there is a desire to develop the effective recycling process. E-waste has various kinds of electronic components with valuable and/or hazardous materials. Recycling of them is an important subject from the viewpoint of both the recovery of valuable materials and waste treatment. In common with all mineral processing, the comminution of e-waste is a key process because the liberation states after comminution determine the overall efficiency of metal recovery. Since some of useful critical metals are concentrated in a specific component, a special and selective grinding is expected to be effective. However, the knowledge about the mechanism and the effectiveness of the selective grinding is still limited and unclear.To better comprehend the mechanism, in this study, the investigation of comminution process using the particle-based simulation was conducted. Especially, this study focused on the comminution performance of printed circuit boards (PCBs), which are major components of e-waste. The behavior of PCBs and airflow in a drum typed agitation mill having flexible chains was simulated by the discrete element method (DEM) coupled with computational fluid dynamics (CFD). To model the shape of PCBs, the particle based rigid body model was introduced into the DEM. Since this model could not directly simulate the breakage phenomena, collision energy was calculated to qualitatively evaluate the comminution performance. In addition, the simulation results were compared with the experimental comminution tests using simulant PCBs where some capacitors were solder-mounted. These results indicated that comminution performance was affected by the rotation speed of the agitator. It was also demonstrated that the comminution performance was qualitatively evaluated using the particle-based simulation and this particle-based simulation made it possible to investigate the mechanism of e-waste comminution."

Jan 1, 2016

By Joel H. Watkins

The terms kaolin, china clay, ball clay, and paper clay are more or less loosely and interchangeably applied to a large class of white-burning clays. These clays are made up chiefly of hydrous amorphous (colloidal) aluminum silicates with variable amounts of free silica and other impurities in small quantities. Occasionally also the term kaolinite is wrongly applied to a white-burning clay, for kaolinite is a mineral of definite chemical composition and definite crystalline form which occurs but sparingly in nature. It is not the purpose of this paper, however, to define or classify clays, or to enter into a discussion of the chemistry of clays. It is rather a general description of the occurrence and methods of mining of a kindred group of clays, and a discussion of their future economic aspect. In the Southern Appalachian States, the mining of white-burning clays has in recent years become an important industry. Although these clays are of several distinct types, which occur in as many localities under different geologic conditions, they are for the most part primarily of the same origin. They are essentially the same in elementary constituents, and are largely consumed in the game industrial arts. From the standpoint of a mining engineer, therefore, and for convenience in comparison and correlation, it should be interesting to discuss them under one heading. Kinds of Clay The most important types of clay which are now being actively mined in the Southern Appalachian States and with which this paper is particularly concerned are the North Carolina, Virginia, and Georgia kaolins or china clays (residual); the South Carolina and Georgia kaolins or paper clays (sedimentary); and the Florida and Tennessee plastic kaolins or ball clays (sedimentary). Other varieties which are interesting but which are as yet of little importance are the pocket deposits of white clay in Augusta County, Virginia, the bauxitic kaolins of Tennessee,

Jan 1, 1915

By Hesam Dehghani, Farid Alimohammadnia, Nima Babanouri, Mokhtar Kalhori

In open-pit mining, blasting pattern design is performed to achieve a desired degree of fragmentation for loading, hauling, and crushing operations. Inappropriate fragmentation of rock will result in numerous problems such as incurring extra costs for secondary blasting, production interruption, etc. Wetness of the blast holes is one of the most important factors, which can cause the inappropriate rock fragmentation. Lowering ambient temperature in the vicinity of the explosion, the presence of water in the hole adversely affects the quality of the explosive while dissipating part of the explosion energy, ending up with inappropriate fragmentation problems. In the present research, in order to study blast-induced fragmentation conditions in Baba-Ali Iron Ore Mine, three scenarios were considered: explosion of ammonium nitrate with fuel oil (ANFO) in dry hole, explosion of ANFO in wet hole, and explosion of the emulsion in wet hole. For this purpose LS-DYNA, a numerical simulation code was used. Results of the present research showed that, compared to the explosion of ANFO in wet hole, the explosion of the emulsion produced more uniform distribution of fragment size, while the explosion of ANFO in dry hole resulted in fewer large fragments.

By P. A. Roberts

A modified in situ leaching method for extracting gold from oxidized gold ores using a non cyanide lixiviant is proposed. A non cyanide lixiviant is suggested because of the obvious concerns posed by injecting cyanide bearing solutions into the subsurface. Oxidized gold ores are the initial focus because earlier research on the use of sodium thiosulphate as a lixiviant under anaerobic conditions indicated that the presence of pyrite led to rapid thiosulphate breakdown. A reconnaissance research programme, involving ore characterization and hydrometallurgical testwork on samples from four Australian ore deposits and preliminary reactive transport modelling studies was carried out. This work showed that lixiviant-oxidant combinations of sodium thiosulphate and ferric EDTA, and iodide and iodine are both capable of extracting high percentages of accessible gold from the selected samples under anaerobic conditions. The ore characterization and reactive transport studies, suggested that both physical and chemical methods of permeability enhancement may be required to lift bulk permeability and the availability of gold for dissolution to sufficiently high levels to obtain adequate gold recoveries. Physical permeability enhancement could be achieved by blasting and/or hydraulic fracturing of the ore. Assuming that such methods prove to be both necessary and economically viable, the mining method would no longer be regarded as simple in situ leaching. Therefore, the term ?in place leaching? has been adopted for the proposed gold extraction system

Jan 1, 2009

By W. M. Weigel

SALT production in Louisiana and Texas at the present time is entirely from salt domes of the interior and coastal groups. Before and during the Civil War salt was recovered from numerous salines and salt springs by evaporation in open &apos;kettles. The location of these in nearly every instance was near what is now known to be a salt dome, and the source of the salt in the salines and spring waters was that in the salt core. The tops of many of the shallower domes have been subjected to erosion1. The discovery that the salt occurred as large masses of rock salt in the form of domes was made in May, 1802, at Avery Island, La., by John Marsh Avery, grandson of the original owner, John C. Marsh, who built the old salt works in 18122. The first shaft for mining was sunk on the Avery dome in 1867 by Chouteau and Price. It was 90 ft. deep, about 58 ft. being in solid salt. It was abandoned in 1870. There are three general groups or fields of salt domes; interior Louisiana in northern Louisiana, interior Texas in northeastern Texas, and the coastal domes nearer the Gulf Coast and extending from the Mississippi River to the Rio Grande. This last group contains by far the greatest number of domes. As many of the coastal domes especially are prolific producers of petroleum and a few of sulfur, their geology has been intensively studied and fully covered in the literature. The depth to the top of the salt varies from near the surface, where shallow ground waters have dissolved the salt to just below recent deposits, to several thousand feet, where the depth has been estimated only by geophysical methods. The diameter of the salt core varies from less than ½ mile to over 2 miles. Only domes where the salt is compara-tively near the surface have been developed for commercial salt. Three deeper domes, which will be described later, have recently been developed or are in process of development, as a source of brine for chemical use.

Jan 1, 1935

By L. N. Brown

The use of sheet and strip metal has increascd rapidly during the last few years and manufacturers have been called upon for an ever-increasing tonnage, better drawing quality, and better surface. The automobile industry is probably the most insistent in striving for a better product and a desire to reduce costs. Confronted by these demands, the mills have directed their efforts toward the delivery of material. Their personnel has been occupied largely with the problems incident to production, as any increase forced the use of new sources of raw material with their problems. These problems, combined with those met in the daily routine, have demanded immediate attention, with the result that the standardizing of heat treatments, quality, or temper, etc., have been neglected. Considerable work in standardizing has been done by many companies, but no acceptable method has been developed. The following method, therefore, is given with the hope that some method that can be accepted by the manufacturers and users may be developed. The problem of selecting a material with such properties that the losses in processing are a minimum is interesting and difficult. A description of the properties required is likewise difficult, largely because of loose terms. Another handicap is the number of methods of testing which have not been standardized and concerning which little information is available. In the selection of drawing or forming stock, it is advisable to eliminate as many variables as possible; consequently the method of testing the material is of the utmost importance. The method should be rapid and comparatively easy of application, as it is more important that a large percentage of the stock be tested with reasonable accuracy than that

Jan 1, 1923

By J. J. Rutledge

On Sept. 4, 1914, Mine No. 1 of the Union Coal Co., Adamson, Oklahoma, suddenly caved, entombing thirteen miners whose bodies were never recovered. The seam of coal mined, the Lower Hartshorne, averaged 5 ft. in thickness and dipped at an angle varying from 22" to 30n. The strata overlying the coal seam were sandstones and shales. The mine was worked by the pillar-and-room method, the rooms being driven directly up the dip of the seam. All coal was blasted off the solid. Rooms were turned on short centers and room pillars were thin and irregular, as shown in Fig. 1. Fig. 2 is a cross-section of the form; showing the mine workings. Some cracks had been observed on the surface, it is said, at least a month before the squeeze occurred, but the collapse of the mine workings came very suddenly. As is usual when squeezes occur on such steep dips and the pillars fail, the crush progressed rapidly down the dip until it reached solid coal; there was a line of break, or draw, over in the solid coal. Several well-defined cracks appeared on the surface, after the mine had squeezed, but there was no appreciable subsidence of the surface, the weight seemed to be thrown entirely to the dip. About one year after the squeeze, and after the workings of the adjoining mine, NO. 4, had been retimbered and made safe, the writer inspected the tenth north (right) entry, or lift, off of No. 4 slope, which was below and fairly near the lowest caved portion of mine No. 1. The roof shale was composed of thin layers, which had been bent in somewhat the same manner as the leaves of a book having flexible covers are bent when the book is folded or rolled up in the hands. Though the mine workings are immediately beneath the streets and buildings of the mining town of Adamson, business was not disturbed by the squeeze, so far as any subsidence of the surface was concerned. No surface monuments were available and no elevations were taken, but the mine workings had been accurately surveyed and traversed, and the streets of the town overlying the mine workings had been carefully platted on the mine map, so that it was possible to locate accurately the cracks on the surface.

Jan 1, 1923

By R. F. Mehl, B. Lustman

The formation of intermediate phase layers in cementation processes has been subjected to extensive qualitative investigation though to relatively little quantitative study; this work has recently been fully summarized by F. N. Rhines.&apos; It is necessary here only to cnumerate the general conclusions drawn concerning the kinetic laws governing the growth of intermediate layers and to state what is known concerning the structural changes accompanying the generation of phase layers. I. When the intermediate phase is protective in type—i.e., when its density is less than that of the base metal, so that a continuous coating is formed and maintained—the isothermal growth of the phase follows a simple parabolic equation: X2 = kt [i] where X is the thickness of the alloy layer, k thc reaction rate constant, and t the time. The applicability of this equation to diffusion processes is tested by plotting the square of the thickness versus time, or by plotting the thickness versus the square root of time; the resultant achievement of a straight line in such a plot has been considered sufficient proof of the validity of this equation. Exceptions have been found where liquid phases are involved in the reaction, where the diffusion layer is cracked,2 and where thin semimetallic oxide and sulphide coatings are formed on metals.$ In the first two cases the thickness increases linearly with time, and in the latter it is a logarithmic function of time. 2. The rate of thickening varics with temperature according to the Arrhenius equation: k = Ae-Q/RT [2] where k is the parabolic rate constant of Eq. I, or some other rate-descriptive function, A is the action constant, e the base of natural logarithms, Q the heat of activation, R the gas constant, and T absolute temperature. This equation has been found to be generally valid except when transformations occur during reaction in either the base metal or in the reaction layer; in such instances Eq. 2 is still applicable with different values for the constants A and Q above and below the transformation temperature. 3. Ali phases that are stable at the temperature at which diffusion occurs will appear in the interdiffusion of two components. In some cases certain of the phases may be too thin to be observed and identified easily. Nonequilibrium phases have never been noted in thick reaction layers; i.e., layers of a thickness that may be discerned microscopically. The relative thickness of each phase in a diffusion layer is proportional to the concentration gradient and to the rate of diffusion in that phase.4 The reaction layers tend to have a

Jan 1, 1942

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&apos; 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&apos;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.&apos; However, the vibrations of isolated bubbles, as distinct from foams, have not been investigated previously. The following equation, presented elsewhere,&apos; 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&apos;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