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By Janet A. Johnson, T. B. Borak, K. J. Schiager

INTRODUCTION In the USA regulatory agencies have adopted standards which limit the allowable concentration of ore dust in underground uranium mines. The American Conference of Governmental Industrial Hygienists has recommended a threshold limit value for silica which has been incorporated by reference in federal regulations (30 CFR 57, 1980). The Nuclear Regulatory Commission (NRC) imposes a limit for unprocessed uranium ore dust for reducing the exposure to radioactive materials from inhalation (10 CFR 20, 1980). We have been unable to trace the origin of the NRC standard. Recently the ICRP has published recommendations concerning limits for intakes of radionuclides by workers (ICRP, 1979). We have used the ICRP methodology to compute the dose equivalent commitment to lung and bone from inhalation of insoluble ore dust particles. These values were used to derive air concentrations which would provide an acceptable risk for induction of cancer from occupational exposure. Results indicate that the new ICRP recommendations are more restrictive than the present NRC standard for radioactivity. The maximum allowable dust load in a uranium mine will depend on both the concentration of silica (% Si02) and the amount of radioactivity (% U308). We have combined these standards assuming complete independence of biological hazard to establish boundary conditions for which either silica or radioactivity is the dominating factor. Based on these results we present suggestions for analysis of ore dust to insure compliance with regulatory agencies. SILICA STANDARDS Silicosis, fibrotic lung disease produced by crystalline silica, was one of the earliest forms of occupational disease to be recognized. The pulmonary lesions caused by silica, silicotic nodules, consist of concentrically arranged bundles of collagen fibers. Fusion of these nodules results in progressive massive fibrosis causing alveolar changes which decrease ventillation and blood flow in the lungs. The current Threshold Limit Value (TLV) for mineral dusts is based on the concentration of free silica. The standard is expressed in three forms: (1) Particle count standard: TLV (mppcf) = 300/(% Si02 + 10) (mppcf = million particles per cubic foot) (2) Respirable dust mass standard: TLV (mg/m3 ) = 10/(% respirable Si02 + 2) (3) Total dust standard: TLV (mg/m3 ) = 30/(% Si02 + 3) The most commonly used form is the respirable mass standard. These curent values for silica are based primarily on epidemilogical studies of Vermont granite workers and other occupationally exposed workers. In the Vermont study no cases of silicosis were seen in individuals employed after dust control measures were initiated and whose subsequent exposure averaged less than 5 mppcf. The free silica concentration in the airborne dust to which these workers were exposed averaged 25%. A concentration of 10 mppcf of granite dust is considered equivalent to 0.1 mg/m3 quartz. The current respirable mass standard allows a maximum silica concentration of 0.1 mg/m3. NIOSH (1974) has recommended a reduction in the current TLV for respirable silica to 0.05 mg/m3 Si02. As with radiation standards, the TLV for mineral dusts is an upper limit for time weighted average exposure. It is recommended that dust concentrations be maintained as far below the TLV as current practices permit. RADIATION STANDARDS The present concentration limit for airborne natural uranium in ore dust prior to chemical separation is 75 µg of uranium per m3 of air ( 10 CFR 20, 1980) . This corresponds to 1.85 Bq/m3 (50 pCi/m3 ) of natural uranium, U-238, U-235 and U-234 and is equivalent to 3.7 Bq/m3 (100 pCi/m3 ) of gross alpha activity with radioactive equilibrium between the long-lived alpha progeny through Ra-226. The origin or basis for this standard is not known, but it presumably includes both chemical toxicity and risk from somatic radiation injury. Recently the International Commission on Radiological Protection (ICRP, 1977) has published recommendations concerning the objectives and criteria for limiting radiation exposures. This was followed b y a revision of the limits for intake of radionuclides by workers (ICRP, 1979; ICRP, 1980). The previous compilation of limits for internal emitters was published by ICRP Committee II in 1959 (ICRP, 1959). The latest version includes new methodlogy outlined in ICRP Publication 26 (ICRP, 1977) as well as extensive metabolic information

Jan 1, 1981

By C. C. Graham

In this paper, the problems which occurred on introduction of dense medium cyclone coal washing in Australia are reviewed together with the subsequent measures taken to obtain a satisfactory magnetite. Specification and testing of magnetite for exploration, quality control and in-plant check purposes is discussed. The disposition of Australian magnetite deposits in relation to the main coal producing areas is examined, and comments are made on the economics of mining, milling and beneficiating magnetite for coal preparation uses alone. Future trends in the Australian Coal Industry are predicted, and the need for a planned approach for the future is demons traced.

Jan 1, 1982

By D. Collins, J. Winfield, V. Gangrade, B. Slaker, S. Braganza

"Researchers at the National Institute for Occupational Safety and Health (NIOSH) are investigating the unique pillar stability issues associated with room-and-pillar mining in dipping underground stone mines. The objective of this paper is to study the post-blast impact in and around a pillar, using microseismic monitoring. To accomplish this, a microseismic monitoring system has been installed at a dipping underground stone mine in central Pennsylvania. The microseismic system is comprised of 18 uniaxial accelerometers; 12 sensors are installed in a single pillar and 6 sensors are installed in the surrounding area. More than 4,400 microseismic events have been located near the study pillar following the blasts. The number of triggers increased significantly following the blast, and the trigger rate in the first five minutes was 60 triggers per minute and three triggers per minute over the next three hours. The processing of high-quality triggers indicated a large number of low magnitude microseismic events near the blasting face. The event locations were identified more accurately by using a 3D-velocity model, with an average 9 m expected location accuracy for this array calculated using the system data. Seismicity was absent from the core of the pillar, but significant numbers of events were found following cutter roof along a crosscut as it was developed as well as in the location of a rib failure event. Additionally, the events were located in the roof, showing high number of microseismic events within 0–10 m of the roof line compared to 10–30 m above the roof line.INTRODUCTIONGround control stability is essential to any mining operation for ensuring mineworker safety and health and preventing catastrophic failures of underground structures. The National Institute for Occupational Safety and Health (NIOSH) has conducted research in stone pillar design and has established fundamental pillar design guidelines for the underground stone industry, which resulted in the development of the S-Pillar program (Esterhuizen et al., 2011; Esterhuizen and Murphy, 2018). However, the data that makes up the S-Pillar database consists of shallow depth, flat-lying, single-level mining operations. Therefore, to expand this dataset and to develop guidelines for challenging conditions such as dipping and multi-level mines, NIOSH is currently conducting detailed pillar response investigations at mines with these characteristics. The study is being conducted using multiple research approaches, including seismic modeling and tomography, numerical modeling (Sears et al., 2019), stress monitoring, and LiDAR-based laser scanning (Slaker, Murphy, and Winfield, 2019). This paper discusses the findings from the microseismic monitoring system installed at the Pleasant Gap Mine, a steeply dipping underground limestone mine in central Pennsylvania."

Jan 1, 2019

By Jed Greenwood, Lyall Workman, Michael Haggerty, Russell Sheets

Draglines often work from a position on the active highwall or spoil side bench to remove undisturbed waste material and spoil in the previously mined pit. To protect the dragline crew members and the machine, it is necessary that the highwall remain stable while the dragline is present on the bench. In the past several years, we have been involved in determining the causes for highwall failures that included the dragline. While there have been no injuries and limited dragline damage with these incidents, the potential certainly exists for a more serious outcome. In all cases, the operation had completed a geotechnical study to support the ground control plan and pit designs. However, all these incidents included aspects that would not likely have been identified in studies to determine highwall and spoil designs to support ground control procedures. In general, these events included aspects that were localized and would have been difficult to identify in initial slope stability studies either observationally or during the soil testing and modelling efforts. Although the authors do not have quantitative evidence of this, it does seem there has been an increased number of events in recent years. This may be due to loss of institutional knowledge, mining in more challenging areas, or simply an increase in localized variation. This paper will describe some of the issues we have seen and what the causes of failure were. It becomes clear that avoiding similar incidents in the future requires on-going observation and inspection of active highwalls and spoil benches to try and identify local variability and impact on mining. The information can proactively be used to update stability modeling of any concerning issues to determine likelihood of problems and to develop solutions.

Feb 1, 2025

By Sean Hunter

Artificial Intelligence has a long history but is currently coming strongly into focus with new advancements. This leads to questions many people are asking: what exactly is AI, how can it be used effectively in mining operations, and what foundation is required to make AI implementations successful? In mining, many AI applications exist, from drill pattern optimization to predictive maintenance. However, many implementations struggle due to data integration challenges. Mining operations generate large amounts of data from many sources, such as fleet management systems, drill sensors, process control systems, and laboratory results. Unfortunately, this data often exists in silos where it’s difficult to get it out, making AI applications unable to leverage it. Worse still, tools that use AI don’t always provide their data back to the system, creating even further data silos. All these problems make it hard to take advantage of the data at the mine, slowing down and reducing the effectiveness of AI. This paper presents a comprehensive approach to organizing mining data using an AI-ready knowledge graph system. We will first explore the evolution of AI in mining, from early expert systems to modern machine learning applications. Then, we will detail how a knowledge graph can integrate business context, operational data, and AI models into a cohesive system that enables more effective AI implementations across mining operations. The proposed method has been developed considering both the unique data challenges faced by the mining industry, while also considering best practices learned from the AI field at large. By following this approach, it’s possible to better utilize existing data, getting higher quality and more complete results faster, and in a way that’s reusable and composable.

Feb 1, 2025

By Robert Klug, Nils Engelke

"In order to extract proportionately small quantities of valuable minerals, mining companies move large amounts of earth. A resulting waste product of this process has traditionally been stored in a semi-liquid phase known as tailings, typically stored in a large pond created by an earthen dam at the low end of a drainage basin. It is generally expected that these dams are stable enough to withstand the pressure of the stored material. Unfortunately, history shows us that this is not always the case. The Baia Mare dam in Romania failed in 2000, causing tragic and prolonged environmental damage to several major European rivers. The Bento Rodrigues dam in Brazil failed on Nov. 5, 2015, and that event resulted in the loss of 16 lives.In hard rock mining, many minerals are imbedded within the ore. As part of the mining process, valuable minerals are extracted from the ore; often, the mineral content is only a fraction of the total ore volume processed. To extract the minerals, the ore is typically crushed and pulverized into very fine particles, then wetted to form slurries. The minerals are extracted from the slurries through a series of flotation and/or sedimentation steps with the aid of water-soluble separation chemicals typically known as reagents. Following the mineral extraction, the resulting residual wetted ore cuttings are labeled as tailings. At the end of the extraction process, the tailings are in a thick semi-fluid sludge state, often with trace elements of the extraction reagents.Historically, these tailings are deposited in giant basins or sludge ponds, where they pose a great threat to the environment while binding large volumes of waste process water.Process water recovery and achievingdry tailingsCurrent generation engineering studies, trials and successful field implementation have shown that an alternate process known as dry stacking is practical. The dry stacking process deposits dewatered tailings into containment areas that are smaller in overall footprint and significantly safer by reducing the transfer of reagents into the tailings storage area. In addition to achieving the dry tailing benefits mentioned, it is possible to recover valuable process water while dewatering the tailings sludge utilizing modern separation technology."

Jan 4, 2018

By Chee Theng

"Mining professionals are a resilient lot. Sure, copper prices are dismal, permitting processes seem interminable and the top mining companies are shedding jobs like a Shetland sheepdog sheds hair. All the more reason to hone technical skills, reconnect with old contacts and get one’s finger on the pulse of the industry.More than 400 did just that in the balmy sunshine and among the saguaro cactus of the Tucson venue of the SME Arizona Conference.Giving the keynote speech was Patrick Merrin, vice president at Hudbay Minerals (see box), while the luncheon speaker was University Distinguished Professor Mary Poulton, director of the Lowell Institute for Mineral Resources at The University of Arizona.“Attendance was great, especially given the copper price,” said Ta Li, vice president of business development at Tetra Tech and 2001 SME President. “The luncheon speaker was one of the better ones in recent years. Her talk contained a lot of fresh ideas, and practical versus theoretical concepts.”Talk about values, not economicsPraise was unanimous for Poulton, who gave a thought-provoking talk on “The New Face of Mining: The Culture Change for Compatible Mining.” Corporate social responsibility has been embraced by the metals mining industry, and it’s being done right, she said. “So why do we have more conflict? Why are there more protests? Why does permitting take longer and longer?” Poulton made a case for an approach based on compatible, rather than sustainable, mining to present a new face of mining that can be compatible with communities, cultures and the environment, and still be profitable. When the mining industry starts to talk about compatibility between what it is doing and what “me,” as the consumer, wants, what “we,” as citizens of a community, want, and what’s good for the “world,” we’re going to see the next culture change happen, she concluded."

Jan 1, 2015

When Caterpillar announced that it had purchased Bucyrus for $8.8 billion, it was billed as the next great chapter in the history of mining. Surely, when the history books are written, it will be remembered as a deal that changed the face of the mining equipment sector, and it could well be a major milestone in the path toward autonomous mining in the future. In the short term, the deal is a clear indication that the world?s largest equipment maker is bullish on the mining sector. The purchase of Bucyrus allows Caterpillar to expand its mining interest to six product segments (underground, surface extraction, large mining trucks, surface material handling, hauling products and growth markets) with 16 product lines to serve the mining industry. But the commitment doesn?t end there. According to Steve Wunning, president of Caterpillar?s resource industries group, which includes Cat?s global mining division, the commitment to mining goes far beyond the acquisition of Bucyrus.

Jan 1, 2011

By Graham A. Mathieson

The precise definition of an ultimate or economic pit has, over the years, received much attention in the literature on the subject of mine planning. Unfortunately, relatively little has been published in the area of pit sequencing and scheduling--an aspect which is typically of much greater economic significance both during the life of a mining operation, as well as in the evaluation of an exploration project. This paper discusses an overall mine planning methodology with emphasis on the design of an optimal sequence of pit expansions or phases. Although the concepts given are not new, it is hoped that some practical suggestions will be made. The paper will also describe graphical techniques which have been found useful in comparing the merits and impacts of alternate planning strategies and production schedules.

Jan 1, 1982

By K. Kim

A site characterization strategy formulated for the probabilistic design of underground structures is presented, which takes into account the variability of rock properties and the stochastic nature of the rock failure process. It entails determining probability distributions of rock properties by utilizing the theory of extremes and Monte Carlo simulation. Laboratory and field test data are analyzed and presented to illustrate the methodology. The results indicate that the distributive characteristics of rock mass properties can be estimated using empirical relationships currently available. This results of analyses can be incorporated into the design of underground structures, and then, the relative uncertainties of the failure probability of the structures can be assessed.

Jan 1, 1995

By Carl Rampacek

Laboratory and small-scale continuous pilot-plant investigations made at the Tucson Metallurgy Research Laboratory of the Bureau of Mines have demonstrated that the copper segregation process is applicable to the treatment of oxidized and mixed oxide-sulfide copper ores regardless of the gangue constituents. The process comprises heating the ore to a temperature of 750° C. with small quantities- of sodim chloride and coke to produce metallic copper, which then is recovered by flotation. Tests were made on' 23 copper ores of different types containing 0.8 to 5 percent Cu, .The copper recoveries ranged from 73 to 96 percent in concentrates assaying 10 to 62 percent Cu, depending on the grade and type of ore, The direct operating cost for a 1,000-ton-per-day furnace and flotation plant is estimated at about- $3 per ton of ore.

Jan 1, 1960

By Justin R. Patts, Andrew B. Cecala, A. KYLE LOUK, Emily J. Haas

The National Institute for Occupational Safety and Health (NIOSH) and the former U.S. Bureau ofMines (USBM) have given a significant effort over the past four decades in researching and developing engineering controls and interventions to reduce mine workers’ dust exposures during the bagging and palletizing of industrial minerals. Workers performing manual bagging and palletizing of 50- to 100-pound bags typically have some of the highest dust exposures of all workers at mining and mineral processing operations. This paper will provide an overview of available dust control technologies for bagging operations and present the findings of a recent case study that was conducted at four different industrial sand operations to identify the current types of bagging and palletizing technologies being used and to evaluate their effectiveness in reducing workers’ exposures to respirable crystalline silica dust. An evaluation will also be performed to determine if further reductions in respirable dust levels can be achieved by incorporating additional modifications or improvements into the existing technology.

Apr 3, 2020

By J. Noll, D. Yantek, B. Kendall, J. A. Organiscak

"A self-tramming remotely controlled mobile Dry Scrubber (DS) was developed by J. H. Fletcher and Co. under a contract with the National Institute for Occupational Safety and Health’s Office of Mine Safety and Health Research (NIOSH OMSHR) to reduce exposure of miners to airborne dust. NIOSH OMSHR laboratory testing showed that the DS averaged greater than 95% dust removal efficiency with the disposable filters and averaged 88% and 90%, respectively, for the optional washable filters in their pre-washed and post-washed test conditions. Although the washable filters could be reused, washing them generated personal and downstream respirable dust concentrations of 1.2 and 8.3 mg/m3, respectively, for a 10-minute washing period. The DS’s velocity pressure regulated variable frequency drive (VFD) fan maintained a relatively consistent airflow near the targeted 1.43 and 4.25 m3/s (3000 and 9000 ft3/min) airflow rates during most of the laboratory dust testing until reaching its maximum 60 Hz fan motor frequency or horsepower rating at 2610 Pa (10.5 in. w.g.) of filter differential pressure and 3.97 m3/s (8420 ft3/min) of scrubber airflow quantity. Laboratory sound level measurements of the DS also showed that the outlet side of the scrubber was noisier and the loaded filters increased sound levels as compared to clean filters at the same airflow quantities. With loaded filters the scrubber reached a 90 dB(A) sound level at 2.83 m3/s (6000 ft3/min) of scrubber airflow, indicating that miners should not be overexposed in relation to MSHA’s permissible exposure level (PEL) of 90 dB(A) at or below this airflow quantity (1). The DS’s washable filters were not used during field testing because of their lower respirable dust removal efficiency and the airborne dust generated from filter washing. Field testing the DS with the disposable filters at two underground coal mine sections showed that it can clean a portion of the section return air and provide about a 50% dust reduction at the face area downstream of the continuous miner (CM) operation. INTRODUCTION Coal mine worker overexposure to coal and quartz dust continues to be a problem at underground coal mining operations in the U.S. The U.S. Mine Safety and Health Administration (MSHA) recently changed the standard for coal mine worker respirable dust exposure from 2.0 mg/m3 average during an eight-hour shift to 1.5 mg/m3 average over the actual working shift, effective as of August 1, 2016 (1). If more than 0.1 mg/m3 quartz mass is found in the coal mine worker dust sample, the applicable respirable dust standard is further reduced to the quotient of 10 divided by the percentage of the quartz in the sample (1). Over 90% of the mechanized mining units operating in U.S. underground coal mines are continuous mining machines (2). MSHA inspector dust samples from 2009 to 2012 showed that 3.7% of continuous miner operators exceeded the 2.0 mg/m3 dust standard, while 8.8% of these dust samples exceeded the new 1.5 mg/m3 dust standard and 9.7% of these samples exceeded the reduced quartz standard (3). Additionally, roof bolter dust samples at these mechanized mining units during this same period have exceeded the 2.0 mg/m3, 1.5 mg/m3, and reduced quartz levels at 1.1%, 3.7%, and 10.6%, respectively (3)."

Jan 1, 2016

By B. A. Wills

With the increasing need to mine lower grade ores, high energy-related costs in comminution are of major concern. Very fine grinding is needed to liberate the very fine mineral particles in these ores. Not only is this expensive but it leads to greater losses in 'slimes'. In the early 1970's, 50% of the tin mined in Bolivia, 30% of the phosphate mined in Florida and 20% of the world's tungsten were lost in this way (Somasundaran, 1979). Gravity concentration techniques become unacceptably inefficient for particle treatment below 25-50µm, and even flotation fails in the ultra-fine range. Two approaches can be adopted to try to overcome this problem. The first involves increasing the efficiency of existing equipment or developing new slimes treatment processes. Gravity devices such as the Bartles-Mozley concentrator have been developed for this purpose and good recovery has been reported from 100µm down to 5µm. Such machines, however, have relatively low throughputs, so that large areas of plant space are generally required. Flotation is rapidly growing in importance for the treatment of ultra-fine minerals traditionally treated by gravity concentration.

Jan 1, 1986

By Dirk van Zvl

The design of cover systems for reclamation schemes in tailings requires estimation or determination of tailings materials properties such as compressibility, shear strength and consolidation characteristics. It is very difficult and expensive to obtain truly undisturbed tailings samples for laboratory testing. In situ testing methods have been developed for economically obtaining large amounts of information. Two of these methods are described, the piezocone and the flat plate dilatometer. Both of these methods provide a rapid means of detailed material identification in a nearly continuous fashion for the entire depth investigated. The equipment is described and typical data from a uranium tailings impoundment is presented. The results are compared and the advantages and disadvantages of these methods are discussed.

Jan 1, 1984

By Joel L. Morrison

The preparation of coal-water slurry fuel (CWSF) has the potential to be a commercially viable technology for the coal industry. The technology base required to prepare stable CWSF using grinding circuits has been developed over the past decade and is now being applied to the preparation of CWSF from wet coal fines which are generated during coal beneficiation. When preparing CWSF, the optimum CWSF formulation must be determined to ensure that the fuel will be stable while having acceptable atomization and combustion properties, and the production run must be monitored closely to ensure that the CWSF quality is maintained. This paper describes the CWSF formulation process, CWSF preparation circuits, and some of typical problems encountered in, and solutions to, the transportation and storage of CWSF.

Jan 1, 1993

By David J. Hatem, K. Bhattarai

The increasing popularity of alternative methods in delivery of underground infrastructure projects has given rise to innovative and collaborative contracting strategies to allocate and manage the unique risks associated with the work. This paper presents approaches and recent examples of how risk has been dealt with using various alternative delivery methods, including Progressive Design Build (PDB) and Construction Manager/General Contractor (CM/GC). Based on the experience gained from these examples, recommendations for an innovative and collaborative risk baselining approach using contingency sharing are presented that should advance the overall goals of equitable risk sharing and compensation.

Jun 13, 2023

By J. R. Nawrot

Reclamation of potentially acid producing coal processing waste requires a 4-foot cover, and/or treatment to allow vegetation establishment. If not planned properly, soil covering alone does not prevent refuse acidification or formation of acid seeps. Adequate neutralization enhancement prior to soil covering can maintain an alkaline environment in the soil refuse interface and prevent acidification. Direct vegetation establishment using only limestone amendment (without soil cover) can successfully reclaim aged and weathered fine (Blurry) and coarse (gob) refuse if adequate neutralization treatment is provided for the oxidized surface zone. Acid seeps, representing an "after-the-fact" verification of an imbalance of acid-base equilibrium may also be corrected using upslope alkaline recharge techniques. Concentrated alkaline recharge pools have been constructed above previously soil covered acid gob at the Peabody Will Scarlet Mine to abate acid seeps. Preliminary monitoring results (1989-1992) from a concentrated alkaline recharge pool demonstration project in the Pit 4 area of the Will Scarlet Mine have documented a 50 to 80 percent reduction in acidity in the principal recharge pool groundwater zone. A 22% reduction in acidity has occurred in the primary seeps located downslope from the alkaline recharge pools. The initial improvements in water quality are seen as a positive indication that groundwater acidity will decrease further and amelioration of the acid seep will continue.

Jan 1, 1993

By James F. Fraser

Construction of a major linear project in any environment is difficult, at best. Construction of a major linear project which includes major subway elements, both cut and cover and tunneling, in the center of an urban environment, approaches the impossible. I believe such a project would be impossible for a private company or a privately owned utility for a variety of reasons. The major two reasons are the funding necessary for such massive projects and the myriad of individual interests associated with private ownership of land. Such projects are possible in the public sector only because the need for the project... as is the case with mass transportation in Atlanta. . .overrides the profit motive. Without the profit motive, private companies, whether utilities or not, are precluded from practical interest in the development of any project. While it is safe to conclude that a profit-oriented business would have no practical interest in developing such massive projects as may include major tunnels, it would be useful, I think, to compare some of the significant differences between private profit-oriented businesses, and an agency, or Authority, such as MARTA, in building a major linear project. SLIDE 1. Comparison of a Private Company and a Public Agency [Item Private Company Public Agency Simplified To make a profit To provide a pre Purpose scribed service]

Jan 1, 1979

By J. Drelich

The flotation limit of fine particles has been re-examined based on the effect of bubble size on contact angle, and a new surface chemistry-limited relationship describing the minimum particle size which can be floated is proposed. In this analysis the critical value of bubble-solid contact radius (re) for which there is no effective attachment between particle and bubble has to be determined. The values of re determined by extrapolation of our experimental data for contact angle versus bubble-solid contact diameter permit the prediction of the flotation limit of methylated quartz particles, with fraction-al coverage of trimethylsilyl groups from 0.07 to 0.51. The limit of fine particle flotation as determined by this theoretical approach agrees well with experimental data reported in the literature.

Jan 1, 1994