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By R. Hogg

The various sub-processes which, together, make up the unit operation of froth flotation all depend on the characteristics of the feed solids, the solution phase, the air bubbles and the mechanical/hydrodynamic action of the machine. Characterization is obviously necessary for evaluation and process control, but the relationships between characteristics and process response are often unclear. A model-based characterization scheme is proposed in which material and system characteristics are evaluated in the context of simplified models for the individual subprocesses. The general basis for such an approach is discussed using the process of particle attachment and the influence of mineral liberation as examples.

Jan 1, 1989

Edward Keller, Baltimore, Md. (communication to the Secretary): When, at the New Pork meeting, February, 1899, Mr. Douglas gave an abstract of his highly interesting paper on the Copper Queen mine, he invited the members of the Institute, in his usual progressive spirit, to make a full scientific investigation of the region of that mine during the prospective excursion to Bisbee, Arizona. I volunteered to examine some of the metallurgical processes and products of the works, and obtained from Mr. Douglas a valuable series of samples. Upon the issue of his paper, however, I found that he had already a considerable volume of analyses of those products, and that little was left for me to do in that respect, except to duplicate his results, the importance of which work would not have been commensurate to the time and labor involved. I selected, therefore, only some points which he had not made entirely clear, or concerning which I was skeptical. The details of most of my work will appear in a future paper. From Mr. Douglas's figures I have calculated the values for the elimination of impurities in the so-called Leghorn converter, introduced by him at the Copper Queen works, and have found them to be as follows: Percentage of Elimination of Impurities in Pour Blows of a Converter. No of ' Selenium Sulph'r Iron. Zinc. I Nickel. Lead. Antimony Arsenic. and Blow- ! Tellurium .. 1.......... 99.4 99.6 88.0 92.6 94.4 81.6 83.8 40.3 2.......... 99.0 99.6 98.1 92.5 96.8 71.9 76.6 38.1 3.......... 98.8 99.5 93.5 91.4 96.3 63.8 80.6 25.3 4.......... 99.8 99.5 95.8 95.8 97.5 65.3 76.9 36.3 Average 99.2 99.6 93.8 93.1 . 96.2 70.6 ! 79.5 35.0

Jan 1, 1900

By Nicholas J. Palethorpe

BACKGROUND Before addressing the above topic in any detail, it is pertinent to provide some background on Australia for those people who have not been there or who have a limited knowledge of our continent. Australia is approximately the size of the continental U.S.A. (excluding Alaska) covering an area of approximately 7 million square kilometres. It has a very dry climate which has led to a concentration of people in major cities scattered around the continents perimeter. Australia's population is currently approximately 15 million. Of the work force of 6.3 million, 72% work in tertiary industries, 20.2% in manufacture, 6.5% in agriculture and 1.3% in mining. Agriculture accounts for 46% of exports, mining for 31% and manufacturing for 23,. Economic activity is based on:- Agriculture This is capital intensive and covers extensive areas and is reliant on low cost farming. A.range of foods and fibres are produced with over 70% of production being exported. Such products are of course subject to the usual vagaries of world market demand and market access, particularly in regard to the operation of trade blocks such as the E.E.C. Mineral Resources A wide range of minerals and an abundance of iron ore, coal, gas and uranium resources provide an increasing volume of exports. However, Autralia's oil resources at present only supply approximately 70% of local requirements. Industry This is diverse and encompasses the processing of agricultural products and mineral ores as well as helping to supply the consumer and capital goods needs of the whole community. However, the small scale of local markets, the geographic isolation of Australia and relatively high wage costs have limited the scale of Australia's industry. Advanced technology has overcome some of these difficulties and high tariff and import quotas protect local producers from the full force of international competition. In 1980/81 Australia's Gross Domestic Product amounted to $130 billion with approximately 24% of this being devoted to investment. In the past decade Australia has experienced inflation rates ranging from 5% to 17% and only modest real growth rates ranging from 0.4% to 5% per annum. We have also experienced, as have many other industrialised nations, continuing wage and price increases. Unemployment presently stands at 6%. MINERAL DEVELOPMENT As the above figures indicate, Australia's continuing prosperity is very dependent on the mineral and agricultrual sectors of our economy. The dependence on these sectors is highlighted by the table below which indicates our position in a global context. [Australian Production of Minerals in a World Context Western World % Total Western World Position Mineral Production 1980 1st Rutile 75 Ilmenite 31 Zircon 70 Bauxite 36 Iron Ore 11 Tungsten 14 2nd Lead (Conc.) 15 3rd Manganese Ore 14 Brown Coal 11 (1979) Zinc (Conc.) 10 4thSilver (Conc.) 10 Nickel 6 5th Tin (Conc.) 5 6th Black Coal 5 Gold 2 Source: Mining Annual Review 1981] The total value of all mineral and fuel exports in 1980/81 is estimated at $5.9 billion. This prominence in the world mineral production has largely been achieved in the last 15 - 20 years. In fact, in the early 1960's, Australia had only 2 major mining export centres, Broken Hill in New South Wales and Mt. Isa in Queensland. This growth is highlighted by the fact that in 1963, for example, we exported only 9 tonnes of iron ore and less than 4 million tonnes of coal. In 1980/81 we exported 75m. tonnes ',of iron ore (valued at $1,117m.) and 47m. tonnes of coal valued at $1,965m.). The growth in our mineral industry has come about because of a number of factors. Abundance of Mineral Resources We are particularly well endowed with mineral resources, as indicated below.

Jan 1, 1982

By OÆShea P. J, Dickson T. W

In April 1994 the Victorian Premier announced new State initiatives, collectively termed the Victorian Initiative for Minerals and Petroleum (VIMP), for exploration totalling $16.5 m over three years. The program, initially centred on the northwest of Victoria, the Eastern Highlands and the Otway Basin, is due for completion in June 1997 and has been designed to attract explorers to highly prospective but currently under-explored parts of the State. Major components of the program include acquisition of geophysical data (including airborne magnetics and radiometrics, gravity and seismic data), stratigraphic drilling, geological mapping and mineral resource data compilation. At the completion of the current program, 70 per cent of the State will have been covered by airborne magnetic and radiometric coverage at 400 m line spacing or better (Figure I) while 20 per cent of the State will have been covered by new geological mapping. The completion of database compilations for geochemistry, mine data and exploration licence summaries during the VIMP program is shown in Figure 2. The new airborne geophysical surveys have been flown partly under the VIMP program and partly by AGSO under the National Geoscience Mapping Accord (NGMA). Data from these surveys have been interpreted and incorporated into the geological mapping in order to enhance the quality of map products, especially in areas of Cainozoic cover. The first series 1:250 000 scale geological map coverage of Victoria was completed by the Geological Survey of Victoria (GSV) in 1977, and was based on compilation of historical geological mapping with minor field checking in most cases. The first metric 1:50 000 scale geology maps were also commenced in the 1970s, but were discontinued in the 1980s in favour of 1:100 000 scale map production. Driven by customer survey findings and with the benefit of detailed airborne geophysical data in the 1990s, the GSV reverted to 1:50 000 scale map production in 1995, with 1:10 000 scale maps made in areas of significant gold production. Geological reports still cover standard 1:100 000 scale map areas, but are now accompanied by four 1:50 000 scale maps. These new series 1:50 000 scale geological maps have been supported by comprehensive mine data and exploration licence summary databases in addition to the new geophysics, and benefit from the advances made in structural geological interpretation over the last decade. The new phase of geological mapping in Victoria, commenced under the NGMA in 1990 and accelerated under VIMP in 1994, has been focused in the central Victorian goldfields and eastern Highlands areas of the State (Figure 1). Results to-date have led to a number of major advances in the understanding of the eeoloeical evolution of Victoria.

Jan 1, 1997

By Don Thompson

It isn?t a lie if you don?t tell the whole truth The pictures National Geographic didn?t print Other photos National Geographic didn?t print?

May 1, 2009

By K. H. Singh

The addition of new data and corrections can be made under the control of a simple editing session. All programs for this system are written in FORTRAN and executabe "MACROS".. After the addition of new data, the whole file Is reinitialized to update the binary file and cross-reference tables. Updating the binary file involves rerunning the initializing program. The creation of graphic plots like cross sections and plan views is menu-driven from a terminal and very user-friendly. Small files containing not more than 10,000 entries (survey and assay points) are suitable for this setup, particularly for computers with less than 2 Megabytes of real and virtual memory. The largest file processed contained 35,000 lines of survey and assay information and required 4 megabytes of virtual memory. Working with this size file slows down the time for the creation of plots and cross sections. Another independent system is more akin to a financial type of data base. It was installed in one Anaconda mine as part of the operation's inventory, warehouse, day-pay payroll, and purchasing data bases. It is a highly hardware-dependent system, in particular, IBM's CICS/VS (Customer Information Control System/Virtual Storage). This is a true relational data base that optimizes storage requirements, supports online inquiry, update, data entry, and data security. While this system has been tested and proven in accounting applications, it requires programming expertice in PL/I and other CICS utility programs. It is well suited for huge data bases (like the 35,000 lines of data), but cumbersome for small engineering files.

Jan 1, 1985

By W. H. McDonald, D. D. Carr

The use of stone in building construction predates written history. From the time that stone was first used, builders have constructed stone buildings predominately from local or regional materials. However, since World War II, the stone business has become increasingly global. For example, French limestone is now sold to builders in the United States, and American granite is shipped to Japan. The internationalization of architectural and construction firms has encouraged this trend. Differences among nations in trade practices, environmental demands and the level of knowledge of dimension-stone characteristics make international trading in stone a risky and potentially disastrous business for unwary participants.

Jan 1, 1997

By M. C. Udy, P. C. Rosenthal

THE use of minute boron additions to steel has been given considerable attention in recent years. Comparisons made between boron-free and boron-containing heats of otherwise identical analysis have indicated, beyond a doubt, the potent effect of boron for increasing hardenability. The actual hardenability increase has been expressed as a multiplying factor, or in terms of the percentage of other alloying elements boron might replace, The present study presents the results of a systematic survey of. the use of boron as an addition to two types of alloyed steels and as a replacement for various percentages of molybdenum in these steels, Both cast and wrought steels of the two basic compositions were prepared. Molybdenum, because of its scarcity at the time the investigation was started, was selected as the element to be replaced by boron. Attention was also given to the effects of boron on other properties of the steels, particularly their notched-bar toughness, to investigate other advantages or limitations of this element as an alloy addition. EXPERIMENTAL WORK Steels Investigated The two basic compositions used in this survey of boron as a replacement for molybdenum are given in Table I. The cast steels were higher than the wrought steels in silicon content to improve the casting quality. [ ] Each of these base steels, both cast and wrought, was made with molybdenum contents of o, 0.10, 0.20, 0.30, or 0.40 per cent, the total comprising 20 steels. In addition, each of these 20 compositions . was prepared with boron additions in amounts of 0.0015, 0.003, and o,006 per cent as ferroboron; and in amounts of 0.002 and 0.005 per cent as two com¬mercial intensifier alloys, designated alloys A and B. The boron-treated steels totaled 100, and the entire series 120, Test Procedure Each steel was melted as an individual heat in a 50-lb., magnesia-lined induction furnace. Ingot iron scrap or mixtures of ingot iron and steel scrap were used for melting stock. Deoxidation was carried out in the furnace with o.10 per cent aluminum. The aluminum addition was

Jan 1, 1946

By C. W. Vierrether

Mineralogical analysis contributes directly to the selection of applicable beneficiation techniques for a given site. Tentative remediation methods for use on the Sharon Steel tailings in Midvale, Salt lake County, UT, were determined in part by mineralogical characterization. A systematic characterization scheme was employed to identify mineral species, mineral associations, and grain size. This paper presents the mineral content and distribution data collected for site characterization. This data was used to determine areas that were representative of the total tailings at the Sharon Steel site. Although this was the main focus of characterization, other useful information was obtained. The approximate location of "old jig tails" was identified and insight on possible arsenic, mobility through the pile was also obtained from the mineralogical study.

Jan 1, 1991

Meeting of Jan. 23, 1914.-The President reported the appointment of Arthur S. Dwight and E. Gybbon Spilsbury as tellers to canvass the votes for the Annual Election of Directors. The President reported the appointment of the Committee on Precious and Base Metals, reorganized in accordance with the list on page xlvi. . The Treasurer was authorized to invest the sum of approximately $1,000, accruing from the sale of Life Memberships during the past year, by the purchase of one gold bond of the Interborough Rapid Transit Co., due 1966, at 5 per cent. The By-Laws of the San Francisco Local Section were approved. The recommendation of the Lord Kelvin Memorial Fund Committee that the balance of the fund unexpended be applied to the establishment of a Kelvin Gold Medal was approved. Forty-two members who had paid up all arrears of clues were reinstated. The sum of $100 was appropriated to the Columbia Local Section. The price of each of the three Volumes of Transactions of the year 1913 was established as $5 in paper and $6 in half-morocco. Forty-three Members, One Associate and four Junior Members were elected to membership in their respective classes.

Jan 2, 1914

By William W. Edgerton

The California Department of Transportation (Caltrans), the Contra Costa Transportation Authority (CCTA), and the Alameda County Congestion Management Agency (Alameda CMA) are involved in a unique partnership on the planning and design of the fourth bore of the Caldecott Tunnel, located on State Route 24 in Alameda and Contra Costa counties. The project will add a two-lane bore north of the existing three bores. The project will alleviate traffic congestion in the non-peak direction. This paper provides background on the existing facility, summarizes the need for the new fourth bore, describes the proposed improvements, sets forth the approach for project delivery, and lists some of the challenges that are expected during construction.

Jan 1, 2008

By Mark S. Sanders

Six underground coal mine shuttle cars (three high seam and three low seam) were used to assess visibility using the concept of visual attention locations (VALs) and an improved human eye reference measurement instrument (HERMI Mark II). Each machine was assessed in the inby and outby direction of travel with no canopy and with the canopy in its highest, and lowest position. In addition, the illumination level at each VAL was determined. Results showed that the most important variable determining visibility was operator eye position. When this variable is controlled, the addition of a canopy has no effect on visibility. Further, with eye position controlled, there is no difference in visibility between high and low seam machines. The visibility and illumination assessments found blind spots in the operator's field of view located on the opposite side of the car from the operator and ahead of the machine. Suggestions for reducing the blind spots were made. The report also included a procedure manual for using HERMI and the system of VALs to assess visibility from underground shuttle cars, continuous miners, and scoops.

Jan 1, 1983

By A. Gakwaya, P. Vachon-Joannette, P. Gagnon, J. Lévesque

"Predictive numerical methods are essential tools for reduced development cost and improved high performance designs of modern aircrafts. Their use leads to savings in terms of design cycle time and experimental trials. Composite materials subjected to impact loadings demonstrate various damage modes such as matrix cracking, fiber breakage, delamination and, ultimately, fabric fracture. Composite laminates are extensively used in the aerospace industry, and their damage modeling is complex due to their inhomogeneity and anisotropic behavior. Damage evolution affects both in-service properties and performance of these composites. In this work, the drop-weight impact test has been simulated. Using a material model that accounts for both delamination and intralaminar damage, laminates response is analysed using numerical simulations based on 3-D finite-element models of the commercial code Abaqus/Explicit. Experimental and simulation results are compared, in terms of energy absorption and contact force. The obtained numerical results show good agreement with experimental data.INTRODUCTIONAs primary aircraft structures are increasingly being made from advanced fiber-reinforced polymer matrix composites and are in general exposed to a variety of impact scenarios (bird, hail, debris etc.), an understanding of the impact event and the performance of composite materials during impact is important in the development of new structures. This work is focussed on low velocity impacts that typically occur when foreign objects hit the aircraft during maintenance or other on-the-ground operations. These impacts can cause non visible damage that affect the structural integrity of the composite components. While for metallic structures, damaging impact events typically leave noticeable dents due to plastic deformation, in contrast, for high strength carbon fiber reinforced composites, they can deform elastically to strain levels exceeding 1% and the internal damage can often occur without the formation of a visible dent. The identification and effect of impact damage on the performance of the structure is thus of great concern to the aircraft industry as the durability and damage tolerance of these composite structures are strongly influenced by the size of detectable internal damage."

Jan 1, 2016

By Sri C. Sawmliana, P. Pall Roy

Damage to underground roof and pillars in blasting gallery (BG) panels has been an increasingly important area of study in recent years due to the invention of new explosives and cord systems which has led to the modification and alteration of the design aspects developed by Charbonnage de France (CdF). According to extensive mine experiments conducted by Indian and foreign experts, it has been established that the induced peak particle velocity (PPV) is predominantly related to the emanated seismic energy of a source and the distance from the source. With that concept in mind, nearly 160 experimental blasts were carried out in four BG panels in India under varying geomining conditions. Based on the results obtained thus far, the authors have established predictor equations correlating explosive energy (in Joules) and distance from the shot to that of induced peak particle velocity received at the sensor point. Good correlation was obtained between the actual and the predicted values. It is realized that this equation may be used as an efficient tool to determine the size limit of blasts in BG panels so that the induced particle velocity does not create damage in underground workings as per the established Blast Damage Index (BDI) and other available safety norms.

Jan 1, 2004

By William J. Campbell

The Federal Bureau of Mines provided five test materials--amosite, short-and long-fiber chrysotile, crocidolite, and nonfibrous tremolite--to the National Institute of Environmental Health Sciences (NIEHS) for studies on the biological effects of orally ingested asbestos-related materials. An inter-agency agreement between the Bureau and NIEHS made possible this program to characterize these test materials. The Bureau in turn received support through contracts with the Ontario Research Foundation for the milling of amosite and crocidolite, and with the University of Maryland for microscopic measurements. The five test materials, which were supplied in quantities of 960 to 1,200 pounds each, were characterized by chemical-instrumental analysis for elemental composition, surface area, density, X-ray diffraction, infrared spectroscopy, thermogravimetric analysis, mineralogy, and particle size analyses. Particle size distributions were emphasized because of the current theories relating adverse biological effects to length-width characteristics of durable elongated particles.

Jan 1, 1980

By J. Jara

Oxygen, ozone and air were evaluated in the oxidation of ferrous iron in the presence of hydrochloric acid ranging from 0.1 to 4 M HC1. Stoichiometric coefficients were determined through mass balances of gases and ferrous titration. The molar ratio ferrous to ozone increases from two at 0.1 M HC1 concentration to six at 4 M HC1. For oxygen the same ratio is constant and equal to 2 and it is in agreement with other works. The stoichiometric coefficient of hydrogen ion was not defined due to the effect of hydrolysis of ferrous and in particular ferric ion on measuring acid concentration by titration with sodium hydroxide. Agitation, gas flow and pressure contribute in the utilization of gas. A technique to compare the gas efficiency at several conditions is discussed and it is based on the relationship between oxygen and ferric during time. There is a strong compromise between gas efficiency and ferrous conversion. Oxygen efficiency decreased with time due to ferrous depletion. The gas efficiency ranged from 3 % (low level of agitation) producing 25 g Fe(III)/h to 12 % at 1000 rpm with 60 g Fe(III)/h converted. At 405 kPa absolute the oxygen efficiency was in the range of 80 % producing 300 g Fe(III)/h. The replacement of chlorine with oxygen to enrich molybdenite concentrates by reducing copper to less than 0.2 % was evaluated. Oxygen can be employed in batch or continuous operation and it can treat molybdenite concentrates with high variation of copper content. The dissolution rate is mainly controlled by oxygen addition in which utilization of oxygen plays an important role. Improvement on safety and environmental conditions is feasible by using oxygen instead of chlorine gas. The economics indicate good opportunities to implement oxygen without significant modifications to the actual circuit and enough benefit when oxygen is well used.

Jan 1, 2007

By Herbert Hoover

THERE is one problem of the new administration that has received the attention and thought of the organized engineers of America for many years past. This is the problem of the reorganization of the Federal Government. The, inadequacy, the wastefulness, and the inefficiency of our federal organization was evident, enough under pre-war conditions. These inadequacies, these inefficiencies, these wastes were exhibited to the country during the war at the cost of millions. Congress has placed the problem in the hands of a very able Congressional Joint Committee, but if this Joint Committee succeeds in securing the imminently necessary results it will only be by full insistent support to it by public opinion. Many attempts have been made at reorganization before but all, of them have gone to the same crematory-the interminable differences in opinion among the executive and legislative officials over details.

Jan 1, 1921

By Wen Xuan

Concentrados ?midos de minério de ferro podem se congelar durante o inverno e ficarem presos nos vagões de transporte, dificultando o descarregamento e a operação. Este problema vem sendo observado nas minas de Kryvyi Rih, Ucrânia e Mont-Wright, Canadá, onde o minério de ferro possui respectivamente 10,5% e 3,5% de umidade e, durante os invernos rigorosos, as temperaturas podem chegar a valores abaixo de -20°C. Nestes locais, uma grande quantidade de energia e tempo tem sido gasta para aquecer e descongelar os vagões. Este artigo mostra que polímeros superabsorventes, como o poliacrilato de sódio, podem evitar o congelamento e facilitar as operações de descarregamento e manuseio, além de possuír fácil aplicação, sendo eficientes quando aplicados apenas no fundo dos vagões, sem a necessidade de se misturar o polímero com o concentrado de minério de ferro.

Aug 17, 2017

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