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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 Fred C. Bond

DISCUSSION Milton C. Shaw and Donald R. Walker (Massachusetts Institute of Technology)—For many years the two empirical rules of comminution bearing the names of Rittinger and Kick have been applied to grinding processes to account for the energy required to crush brittle materials. The basis for Rittinger's rule was the thought that the energy to grind a substance went largely into supplying the additional energy associated with the new free surface, while Kick's law was prompted by the concept of dimensional similarity and is a special statement of the concept of constancy of strain energy to cause rupture. According to Rittinger the energy to grind a given volume varies as the change in the square of the mean particle size, v - A (D2), while according to Kick this energy varies

Jan 1, 1953

By Fred C. Bond

DISCUSSION Milton C. Shaw and Donald R. Walker (Massachusetts Institute of Technology)—For many years the two empirical rules of comminution bearing the names of Rittinger and Kick have been applied to grinding processes to account for the energy required to crush brittle materials. The basis for Rittinger's rule was the thought that the energy to grind a substance went largely into supplying the additional energy associated with the new free surface, while Kick's law was prompted by the concept of dimensional similarity and is a special statement of the concept of constancy of strain energy to cause rupture. According to Rittinger the energy to grind a given volume varies as the change in the square of the mean particle size, v - A (D2), while according to Kick this energy varies

Jan 1, 1953

By C. Cánepa

In the treatment of many problems related with the optimization of a given ore dressing process, microscopic studies can provide invaluable assistance. Such studies are generally carried out through mineralogical determinations both qualitatively and quantitatively. Frequently the solution of a specific problem requires the combination of these in adequate proportions. Often the nature? of the problem poses some conditions regarding the way the microscopic determinations are made in order to yield useful information. Most publications applied to mineral beneficiation show results of ore microscopy without mentioning the methodological details involved in the determinative work and therefore it is not possible to judge their reliability and/or their relevance. As methodology must necessarily change from case to case, it is very important for the microscopist to identify first the direct and indirect mineralogical information required to solve the problem. Without such guidelines selection of methods for the qualitative and/or quantitative determinations cannot be made.

Jan 1, 1981

By A. Balint

The Photometric Optical Separation process is introduced and examples of sorting machines are given. Applications of the process are outlined in general terms with reference to specific types of industrial installations. Brief description is given of the capabilities and limitations of available equipment, including cost estimates.

Jan 1, 1967

By R. W. Smith

Living and killed organisms, particularly microorganisms, and extracellular products derived from the organisms are increasingly finding use in minerals engineering. Goals include both enhancement of mineral processing/11.ydrometallurgica,l operations and remediation of mineral industry wastes. Some of the applications, such as biologically assisted leaching of ?sulfide ores and bioxidation of refractory gold ores, are well established commercial ?processes used around the world. Others, such as the use. of organisms for the removal of heavy metal ions from dilute aqueous streams, are nearing commercial application. Many other uses of microorganisms and. their derivatives are potentially possible. These include use of microorganisms in flocculation or flotation of minerals., remediation of organics potentially discharged from mineral engineering operations, degradation of cyanide, the recovery of bitumen from heavy oil reservoirs and tar sands and the solubilisation of lignites and low rank coals. In order to fully exploit these many possible uses of organisms and their derivatives, extensive fundamental .and .applied research work exploring the fundamentals, potential and practicality of the various possible uses of microorganisms in mineral engineering should be vigorously pursued. ?

Jan 1, 1991

By Won C. Park

Experiments showed changes in the mineral content of dolomitic oil shale at temperatures and exposure times which bracket conditions encountered during in situ retorting. Laboratory results correlate with cores from a spent in situ retort at Occidental's Logan Wash test site at Garfield County, Colorado. Dolomite, CaMg(CO3)2, decomposes rapidly to form periclase, MgO, calcite, CaCO3, and CO . Both calcite and periclase are intermediate products that can be stabilized by CO atmosphere at lower temperatures, while steam accelerates the formation 2 of silicates. The decarbonation of calcite appears to involve a direct reaction with both quartz and periclase in forming these silicates. Decarbonation preceeds the formation of akermanite, Ca2 MgSi 207, and diopside, CaMgSi 206, within several hours of heating and is followed by the nucleation of forsterite Mg2SiO4, and monticellite, CaMgSiO4. Under in situ retorting conditions, akermanite and diposide are the major minerals above 800°C. Equilibrium is not attained within 200-300 hours. In situ retorting temperatures above 800°C for extended periods of time should reduce potential ground water leaching by the formation of silicate minerals. These silicates are less soluble than free lime, magnesium or alkali oxides. There is a corresponding decrease in the natural pH of these silicates from approximately 12 down to 7.5 to 9:

Jan 1, 1981

1. Domestic Production and Use: In 1978, 12 companies operated 31 primary aluminum reduction plants, with 3 firms accounting for 65% of production capacity. Washington, Oregon, and Montana accounted for 31% of the total capacity; Gulf Coast States 23%; Northern States 26%; and other Southern States 20%. Based on published producer prices, output of primary metal in 1978 was valued at $5 billion. Aluminum consumption by 25,000 firms was centered in the East Central United States. Of aluminum consuming industries in 1978, building accounted for about 25%; packaging 22%; transportation 23%; electrical 11%; consumer durables 8%; and other uses 11%.

Jan 1, 1979

The U.S. economy continued to expand during 1986, although at the slowest pace since 1982 when the current business expansion began. Real gross national product (GNP) grew about 2.6%, slightly below 1985 growth but significantly below that of 1984. The continuing expansion was fueled predominantly by rising personal consumption expenditures as well as growing government purchases of goods and services. Fixed investment, although positive, failed to grow at the rate of the overall economy. The trade deficit, which increased more than 30% over the record 1985 level, continued to depress economic growth despite significant declines in the price of petroleum and the value of the dollar. On a more positive note, domestic employment continued to grow--increasing over 2 million from the 1985 level--and inflation and interest rates declined. The unemployment rate dropped slightly to 7.0%. Of direct importance to the minerals-producing industries, expenditures for consumer and producer durables as well as investment in residential construction each grew faster than the overall economy, but investment in nonresidential structures fell more than 10% from the 1985 level. The low level of real capital spending declined about 3% in 1986, following strong gains in 1985 and in 1984. Capital expenditures for new plant and equipment bottomed out in the second quarter and expanded in the third and fourth quarters. The decline in the first half of the year was partially attributed to uncertainty arising from the then-proposed tax bill. Also, there was little impetus for corporations to invest in new capacity since factories were operating at less than 80% of capacity during most of the year, in part because of continued competition from imports.

Jan 1, 1987

1. Domestic Production and Use: In 1977, 12 companies operated 31 primary aluminum reduction plants, with 3 firms accounting for 65% of production capacity. Washington, Oregon, and Montana accounted for 31% of the total capacity; Gulf Coast States 23%, Northern States 26%, and other Southern States 20%. Based on estimated producer prices output of primary metal in 1977 Has valued at $4.6 billion. Aluminum consumption by 25,000 firms was centered 'in the East Central United States. Of aluminum consuming industries in 1977, building accounted for about 25%; packaging 22%; transportation 21%; electrical 11%; consumer durables 9%; and other uses, 12%.

Jan 1, 1978

1. Domestic Production and Use: In 1979, 12 companies operated 32 primary aluminum reduction plants, with 3 firms accounting for 64% of production. Washington, Oregon and Montana accounted for 32% of the total production; Gulf Coast States 20%; other Northern States 32%; and other Southern States 16%. Based on published producer prices output of primary metal in 1979 was valued at over $6 billion. Aluminum consumption by 25,000 firms was centered in the East Central United States. Of aluminum consuming industries in 1979, building accounted for about 24%; packaging 23%; transportation 22%; electrical 11%; consumer durables 8%; and other uses, 12%.

Jan 1, 1980

1. Domestic Production and Use: In 1980, 13 companies operated 33 primary aluminum reduction plants, with 3 firms accounting for 62% of production. Washington, Oregon, and Montana accounted for 30% of the total production; Texas, Louisiana, and Arkansas 19%; Tennessee, Alabama, and North Carolina 15%; other central and eastern States 36%. Based on published producer prices output of primary metal in 1980 was valued at over $7 billion. Aluminum consumption by 25,000 firms was centered in the East Central United States. Packaging accounted for an estimated 26% of domestic consumption in 1980, building 22%, transportation 21%, electrical 12%, consumer durables 7%, and other uses 12%.

Jan 1, 1981

I. Domestic Production and Use: In 1981, 13 companies operated 32 primary aluminum reduction plants, with 3 firms accounting for 58% of production, Washington, Oregon, and Montana accounted for 32% of the total production; Texas, Louisiana, and Arkansas 16%; Tennessee, Alabama, South Carolina, and North Carolina 17%; other central and eastern States 35%. Based on published producer prices output of primary metal in 1981 was valued at over $7.5 billion. Aluminum consumption by 25,300 firms was centered in the East Central United States. Packaging accounted for an estimated 30% of domestic consumption in 1981, building 21%, transportation 18%, electrical la%, consumer durables 8%, and other uses 13%

Jan 1, 1982

1. Domestic Production and Use: In 1982, 13 companies operated 30 primary aluminum reduction plants, with 3 firms accounting for 55% of production. Washington, Oregon, and Montana accounted for 34% of the production; Texas, Louisiana, Missouri, and Arkansas 18%; Tennessee, Alabama, South Carolina, and North Carolina 14%; other central and eastern States 34%. Based on published producer prices, output of primary metal in 1982 was valued at over $5.5 billion. Aluminum consumption by 25,000 firms was centered in the East Central United States. Packaging accounted for an estimated 39% of domestic consumption in 1982, transportation 20%, building 14%, electrical 8%, consumer durables 8%, and other uses 11%.

Jan 1, 1983

1. Domestic Production and Use: In 1983, 12 companies operated 27 primary aluminum reduction plants, with 4 firms accounting for 65% of production. Washington, Oregon, and Montana accounted for 35% of the production; Indiana, Kentucky, Maryland, New York, Ohio, and West Virginia 35%; Tennessee, Alabama, South Carolina, and North Carolina 14%; other central States 16%. Based on published producer prices, output of primary metal in 1983 was valued at over $5.7 billion. Aluminum consumption by 25,000 firms was centered in the East Central United States. Packaging accounted for an estimated 37% of domestic consumption in 1983, transportation 19%, building 17%, electrical 9%, consumer durables 8%, and other uses 10%.

Jan 1, 1984

1. Domestic Production and Use: In 1984, 12 companies operated 27 primary aluminum reduction plants, with 3 firms accounting for 57% of production. Washington, Oregon, and Montana accounted for 35% of the production; Indiana, Kentucky, Missouri, and Tennessee 25%; Alabama, Arkansas, Texas, South Carolina, and North Carolina 20%; other States 20%. Based on published producer prices, output of primary metal in 1984 was valued at $7.2 billion. Aluminum consumption by 25,000 firms was centered in the east-central United States. Packaging accounted for an estimated 35% of domestic consumption in 1984, transportation, 20%; building, 18%; electrical, 9%; consumer durables, 8%; and other uses, 10%.

Jan 1, 1985

The value of domestic raw nonfuel mineral output in 1985 was estimated at $23.7 billion, 2% above the 1984 value of $23.1 billion. This crude mineral output was the basis for approximately $244 billion worth of processed materials of mineral origin. [ ] A U.S. company permanently closed its alumina plant in St. Croix, U.S. Virgin Islands, reducing domestic alumina capacity by 10%. Another U.S. company sold its 26% interest in an alumina plant in Jamaica to its two U.S. partners. On completion of the purchase agreement, the two remaining partners promptly closed the plant for an indefinite period, citing a world oversupply of alumina and unacceptably low prices.

Jan 1, 1986

Real economic growth for 1988 may fall short of the 3.3% projected by the Department of Commerce in August 1988 because the summer drought and intense heat in many areas curtailed output more severely than expected. The economy grew at an average annual rate of 3.0% for the first three quarters of the year, slowing in the second and third quarters. Export growth, which occurred even as the dollar edged up compared with other industrial country currencies, was an important factor in the expansion. Notable gains were posted in sales of machinery, computers, aircraft, chemicals, and telecommunications equipment. Imports increased, but not as much as exports, and the U.S. trade position was still much improved from that of 1987. Personal consumption expenditures grew slightly faster than the economy as a whole. Purchases of consumer durables showed notable strength in the first half of 1988, but slowed down in the third quarter. Despite the moderate rise in interest rates, business spending for new plant and equipment also rose and contributed to 1988 gross national product (GNP) growth. Both new business investment and export demand spurred orders for U.S.-made machine tools. Orders for machine tools for the first 8 months of 1988 were almost triple those in the corresponding period in 1987.

Jan 1, 1989

U.S. demand for building and construction materials, such as construction aggregate, gypsum, and cement, remained strong in 1989. Cement imports declined slightly, representing about 17% of apparent consumption compared with 19% in 1988. Mexico, supplying 29% of the total, was the primary source of imports, followed by Canada with 21 %, Japan with 14%, and Spain and Greece with 10% each. Mexico was also the target of an antidumping petition, filed by producers in Arizona, Florida, New Mexico, and Texas, alleging that Mexican cement was being sold in these areas at less than fair value. This was the second petition filed against Mexico in the last 3 years. The International Trade Commission made a preliminary determination that the cement industry in these regions was materially injured by Mexican imports. U.S. demand improved for construction aggregate for the fourth consecutive year and was at a near-record level. The U.S. gypsum industry performed well, even though new housing starts decreased for the third consecutive year. Increased U.S. exports of gypsum wallboard and strength in the remodeling markets offset the impact of declining housing starts.

Jan 1, 1990

The value of processed materials of mineral origin was estimated to have exceeded $310 billion in 1990. U.S. raw nonfuel minerals mine production in 1990 was estimated at $33 billion, a 3.1 % increase over that of 1989. The value of minerals production increased in all but 3 of the last 30 years. The metals component of production value has fluctuated much more than the industrial minerals component. This reflects the greater volatility of metal prices. In 1990, total employment in metal mining continued the increase that began in 1987. This growth was partially offset by a slight decline in employment in industrial mineral mining, resulting in an overall in-crease of 1.1 % to 179,100 in 1990. Continuing high (by historical standards) metal prices led to expansions at some mines, as well as opening or reopening of additional mines, resulting in increased employment.

Jan 1, 1991