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By Arthur L. Murray

"Oil-shale camps are peculiarly favored, in that before they are establishes it can be ascertained with a degree of certainty, that the life of the project is not limited. Unlike camps at metal mines, where the metal content of a given area is frequently an unknown quantity until after years of development, oil-shale camps should, from the outset, be planned and. built as permanent types of camps. Where this procedure is followed camps will be established which better serve the needs of the industry and the cost of their general care and upkeep will be less.Selection of camp or townsite.The site of the camp or town' whether on company property or not, should be selected with care. It should be separate if possible from the location of the plants of the company so as to be free from noise and fumes and so as to provide a change of environment for employees in going from their work to their homes.The principal features governing the site to be selected are as follows:Drainage. The general contour of the surrounding country should be such that drainage is away from the site. The camp or town should, if practical, be situated on higher ground than that in its immediate vicinity.Soil. The nature of the soil on which the camp or town is located may bear a decided relation to health. A porous, well underdrained top soil of at least four feet in depth insures dryness and facilities the placing of foundations and the laying of water mains and sewer pipes. Such a soil also is an advantage in growing trees, shrubs and grass plots, which are a decided adjunct to making the community attractive.Enviroment. The contiguous territory should afford no unwholesome sur¬roundings such as swamps Or accumulations of stagnant water.General Considerations. The water supply to be provided and the method of disposal of wastes influence to a certain extent the location of the camp or town-site. The means of supplying water, whether by gravity or by pupping, and the disposal of sewage, whether by outfall, system, sewage disposal system through septic tanks, broad irrigation or filter beds, or cesspools will govern the location of the site topographically in relation to source of water and point of disposal of sewage.* This article was prepared as part of the paper ""Use and Supply of Water for the Oil-Shale Industry"" by J. J. Jakowsky, to be published by the Department of Metallurgical Research, University of Utah, in cooperation with the United States Bureau of Mines."

Jul 1, 1921

By David A. Orava, Richard C. Swider

"The technical knowledge and practical experience accumulated by industry and others in abating acid mine drainage (AMD) is being proactively applied at every phase of the mine life cycle. This paper traces the mine life cycle from exploration to post closure monitoring and maintenance, and reviews AMD abatement measures that have become an integral component of exploration and mining activities.Attention is increasingly being given to evaluating AMD potential as part of exploration work, and studies related to project feasibility and design. Mining, mineral processing, and waste management options are selected taking into consideration their suitability to inhibit AMD. These inhibition measures are typically committed to in closure plans submit-ted at the permitting stage. Mines are operated and decommissioned, often progressively, as planned and in accordance with environ-mental protection policies."

Jan 1, 1996

By C. I. Godwin

"The relative-value (R-value), discrimination-factor (D-factor), and vector-ratio (V-ratio) method (RDVM) provides a geological knowledge-based statistical and geological-genetic interpretation scheme for geochemical data that enhances discovery in geochemical exploration. The practical advantage of RDVM is that it synthesizes geochemical features geologically related to ore-deposit discovery in three steps: reclassifying element concentrations using log-probability plots into R-values; calculating geologically defined D-factors from R-values; and determining V-ratios. D-factors are the sum of R-values, divided by the number of R-values summed. Based on the analyses selected, D-factors mimic rock or mineral deposit signatures. V-ratios refine interpretations of rock type and vector to orebody locations.RÉSUMÉ La méthode de la valeur relative (valeur R), du facteur de discrimination (facteur D) et du rapport de vecteurs (rapport V) (RDVM), fournit un schéma d’interprétation des données géochimiques basé sur les statistiques et les connaissances géologiques et la génétique géologique; ce schéma contribue aux découvertes en exploration géochimique. L’avantage pratique de la RDVM est qu’elle fait la synthèse des caractéristiques géochimiques reliées géologiquement à des découvertes de gisements de minerais en trois étapes : une reclassification des concentrations des éléments au moyen de courbes de probabilité logarithmique en valeurs R; un calcul des facteurs D définis géologiquement à partir des valeurs R et la détermination des rapports V. Les facteurs D sont la somme des valeurs R divisés par le nombre de valeurs R additionnées. Selon les analyses choisies, les facteurs D imitent les signatures de la roche ou des gisements minéraux. Les rapports V peaufinent les interprétations des types de roches et dirigent vers des emplacements de gisements."

Jan 1, 2016

By Joshua Hescock, Zach Agioutantis

"The Surface Deformation Prediction System (SDPS) has been developed as an engineering tool for the prediction of subsidence deformation indices through the implementation of an influence function. SDPS provides a reliable and fast method for the prediction of mining-induced displacements, strains, tilt, and so forth at any elevation between the seam and the horizontal or varying surface topography. One of the key aspects in obtaining reliable ground deformation prediction results is the determination of the edge effect offset. The value assigned to the edge effect corresponds to a virtual offsetting of boundary lines delineating the extracted panel to allow for roof cantilevering over the mined out area. The objective of this paper is to describe the methods implemented in updating the edge effect offset code within SDPS. Using known geometric equations, the newly developed code provides a more robust calculation of the offset boundary line of the extracted panel for simplistic, as well as more complex, mining geometries. Assuming that an extracted panel is represented by a closed polyline, the new edge offset algorithm calculates a polyline offset into the extracted panel by the user-defined edge effect offset distance. Surface deformations are then calculated using this adjusted panel geometry. The MATLAB® program was used for development and testing of the new edge effect offset feature. In completing rigorous testing regimes, the new offset features will be integrated into SDPS, further increasing the speed and reliability of the programs resulting in a retrospective increase in capability and flexibility. INTRODUCTION Underground operations have been known to cause mining-induced subsidence inside and outside of the mine permit area (Karmis, Agioutantis, and Andrews, 2008). Additionally, subsidence can impact surface water bodies, such as rivers, streams, lakes, and wetlands (Karmis and Agioutantis, 2015; Newman et al., 2016), as well as infrastructure, such as roads, railroads, pipelines, and buildings. With an increase in regulatory focus on mining-induced impacts to local structures, the calculation of mining-induced subsidence indices has become necessary in determining potential damage and mitigation efforts. The accurate prediction and evaluation of mining-induced ground deformations is required to obtain underground mining permits due to potential impacts to nearby structures, as well as hydrogeological sources. The prediction of ground deformation indices is often a complex task due to the number of input parameters required, such as mining geometries, overburden lithology, surface topography, the rate of mining (Karmis, Agioutantis, and Andrews, 2008)."

Jan 1, 2017

By Jesse Puller, Ken Mills

"This paper describes the Australia, New Zealand Inflatable (ANZI) strain cell, its operation, and recent development for overcoring in exploration boreholes. The ANZI strain cell is an instrument system that uses the overcoring method of stress relief to determine the three-dimensional, in-situ stresses in rock. The instrument has been used successfully for over three decades in numerous underground mining and civil projects, but technical advances over the last decade or so have allowed the system to be deployed in surface exploration boreholes to greater depths than was previously possible. Recent development of a downhole electronic data logger, a wireline-enabled drilling system, and an instrument deployment system has simplified the process of obtaining three-dimensional overcore measurements at depths approaching 1km to a single shift operation.The capability to deploy ANZI strain cells in surface exploration boreholes represents a significant breakthrough for the design of underground mines and underground excavations generally. High-confidence characterisation of the in-situ stresses at the design stage provides the opportunity to design key infrastructure and mining systems to take advantage of the in-situ stress field from the outset before mining begins. Understanding the three-dimensional, in-situ stress field not only provides a measure of the magnitude and direction of loads acting within the rock mass, it also provides insight into the mechanics of all the various processes driving ground deformations, including which geological fault structures are at limiting equilibrium.INTRODUCTIONThe overcoring method of stress relief is one of the most direct methods for determining three-dimensional, in-situ stresses in rock. The Australia, New Zealand Inflatable (ANZI) strain cell combines overcoring with several other techniques to provide determinations of the three-dimensional, in-situ stress field and the properties of the rock and, importantly, provides an indication of how much confidence can be placed in the measurement. This paper describes the advances that have enabled overcoring of the ANZI strain cell in deep surface exploration boreholes and the development of various complementary techniques that build additional confidence in the determination of the in-situ stress."

Jan 1, 2018

By Barry Beith

This report details a study which was designed to assess the effect of retroreflective material on detection and form recognition of workers in the mining environment. Further, the study attempted to determine an optimal configuration of retroreflective material with respect to amount and placement on the body to facilitate detection and form recognition. The study involved a one-fifth scale simulation of the perceptual task found in the underground low seam coal mine. Four different configurations of reflective material were presented in various body positions, common to low coal miners, at three different locations in the visual field, i.e., 10, 25, and 45 degrees from focal line-of-sight. All reflective configurations significantly improve detection and form recognition over configuration (cap only) worn by miners. As the amount of reflective material increased, accuracy also tended to increase. Based on the configurations investigated by this study, the Armband configuration (i.e., refectorized armbands, belt, self-rescuer and battery pack) was determined to be optimum. It is recommended that an actual field evaluation be made using the Armband configuration to establish if simulator results are generalizable to the underground mining environment.

Jan 1, 1980

By Madan M. Singh

This section is unique to the Handbook in that it is the only section that deals with underground excavations for nonmining purposes. The editors were of the opinion that the section should be incorporated because the subject matter covered by the chapters is closely related to mining, and many mining engineers are currently involved in these activities. As we enter the decade of the 1990s activities in this category will increase, enhancing the relevance and utility of the material discussed. As the population increases, especially in metropolitan areas, the necessity to go underground will be greater. At the present time, not only are subsurface shopping malls and pedways connecting buildings becoming commonplace, but structures as diverse as the Civil and Mining Engineering Building on the University of Minnesota campus, a road-and-fleet maintenance facility in Multnomah County, OR, and even an ice cream parlor (Dairy Queen) in northern Wisconsin have been constructed underground. Placing utilities below the surface has numerous advantages and is now customary. Rapid transit and highways through tunnels in urban areas have been the norm for many years, but subterranean stormwater reservoirs, power plants, industrial warehouses, and food storage silos are relatively new innovations. The philosophy of underground defense installations is ancient, but their requirements and designs have trans-formed radically as technology advances. The use of under-ground space for disposition of wastes is modern, since it is recently that environmental concerns and waste disposal costs have assumed increased significance.

Jan 1, 2008

Numerical models play a significant role in the design of safe underground mining excavations and support systems. Advances in the capabilities of numerical modeling software, together with ever increasing computational speeds, have made it possible to investigate the very nature of the large-scale rock mass and its response to mining excavations. The improved understanding of the rock response obtained from modeling enhances our designs, resulting in greater stability and safety of the mining excavations. To help advance the state of the art in this field, the National Institute for Occupational Safety and Health organized the International Workshop on Numerical Modeling for Underground Mine Excavation Design. The workshop was held in Asheville, NC, on June 28, 2009, in association with the 43rd U.S. Rock Mechanics Symposium. The proceedings include 10 papers from leading rock mechanics and numerical modeling experts in the United States, Canada, Australia, and Germany. The papers address a wide range of issues, including various numerical modeling approaches, rock mass modeling, and applications in coal and metal mines.

Jun 1, 2009

By Huw Williams

"Power companies are always looking to increase the carrying capacity of existing transmission lines, and the preferred method is to string heavier capacity conductor lines. However this results in higher wind loading and the potential for towers overturning, if the existing foundations do not have the tensile capacity. On older lines, there is often a lack of information on construction type and dimensions and in practice the as-built foundation can differ considerably from design drawings, due to unforeseen ground conditions along the line route, and no record of the resulting change in design being made.Following successful trials in New Zealand, integrity testing with Frequency Response and impedance profiling techniques is now being used in the region to check concrete foundation properties in-situ and are enabling power companies to get the most out of their assets. INTRODUCTIONIn most regions of the globe, the US included, there is generally a requirement to upgrade transmission line capacities, to cope with increasing power consumption. Problems with under capacity only come to light for the public when blackouts occur, even in developed countries.A large number of transmission line towers are designed with a certain capacity redundancy and will be able to carry greater loads than originally designed for. Power companies are therefore looking for ways to assess their assets and to minimize the costs of upgrade work.Re-assessment of tower foundation capacities using design drawings may not be valid , as constructed foundations may differ considerably from design drawings, to accommodate local difficulties and in some instanced, particularly with earlier lines, there is no information whatsoever. This complicates efforts to determine the capacity of foundations considerably."

Jan 1, 2005

By Miroslav Raudensky, Kallol Bera, Jaroslav Horsky, Jee G. Chang, Ampere A. Tseng

"A combined experimental and finite element approach to study the local heat transfer coefficient is presented in this paper. The heat transfer coefficients at different cooling regimes in a roll are quantified by an inverse heat conduction technique; the heat transfer phenomena involved are then discussed. A discussion of the application of the heat transfer information found in the present study for better design of a roll cooling system is also included. Finally, an identification of areas where further work is needed is presented.IntroductionIn metal rolling processes, the roll is used as a tool to deform the workpiece at very high speeds. As shown in Fig. 1, the heat transfer phenomena involved in the process are complicated by the interaction between the roll and the strip, mainly including 1) the heat transferred from the workpiece to rolls in the contact regions, 2) the heat created in the interface due to the deformation of the workpiece and the friction between the workpiece and roll, and 3) the heat removed by watercooling as well as the ambient air. All of these transport phenomena occur at extremely high pressure, high speed, and high heat flux; these make the control of the roll temperatures an extremely challenging problem.In hot rolling, proper cooling of rolls can lead not only to improve the roll shape quality by controlling the thermal crown of the roll, but also to extend the roll life by minimizing the thermally induced stresses [1,2]. Also, knowledge of roll temperatures can contribute to insights about the roll/workpiece interfacellubricant behavior, and lead to the desired surface condition of the workpiece. Therefore, adequate roll cooling or control of roll temperatures is of critical concern to mill designers and process engineers. In order to have proper operation of the process, a good understanding of the influence of cooling practices on the roll is essential [3]."

Jan 1, 1994

By P Thwaites

The mining industry uses many types of mineral and metallurgical plants to produce saleable product from ore mined. Plant design history has left current operations with a mixture of manual operation and various forms of automated process controls. Consequently, we typically see high-variability in the continuous operations together with a shortfall in the attainment of full capacity or higher utilisation of consumables.At a level of best practice, ‘operational performance excellence’ focuses on process control, using automation and control systems to deliver process optimisation. This more sophisticated delivery is a great deal more difficult than the first stage of equipment selection/installation. It includes the appropriate selection of the right instrumentation and control system, key process knowledge, individuals with a solid control engineering background/experience and the essential backing/support of the operations management team together leading to higher-value delivery. Robust solutions can be realised, considerably minimising process variation, thus leading to process optimisation. This approach results in an easier, efficient and safer process while providing considerable returns for the plant owners.How variable are your processes, and do you maintain optimised process performance with dedicated resources, modern instrumentation, ‘best practice’ control systems and performance monitoring tools? In this paper, these questions and their possible answers are discussed.I say we can do much more and be ‘more efficient’ in our efforts to remain competitive. This area remains a major opportunity for improved efficiency, minimising tailings losses and other milling costs.CITATION:Thwaites, P, 2014. Manual control, process automation or operational performance excellence – what is the difference?, in Proceedings 12th AusIMM Mill Operators’ Conference 2014 , pp 13–40 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Sep 1, 2014

By Christiana Mystrioti

Greece is the only EU country with extensive nickel laterite deposits. Since the 1960s, the Greek laterites are treated for ferronickel production via a pyrometallurgical route, which involves pre-reduction of the ore in rotary kilns and reduction smelting in electric arc furnaces. Due to the rising cost of energy and the decreasing grade of mined laterites, the pyrometallurgical treatment is economically marginal. For this reason, alternative treatment processes are currently under investigation. Potential applicability of hydrometallurgical treatment, using either H2SO4 or HCl, under atmospheric pressure conditions, for Ni and Co extraction from two low grade laterite ores, was examined in the present work. The two samples were selected to represent the different mineralogical composition of the saprolitic and limonitic ore deposits of the Greek laterites. The investigated parameters were temperature (65–90 °C), acid concentration (1–4 N) and solid to liquid ratio (10–30% w/v). The results indicated that HCl was more efficient than H2SO4 for the treatment of the saprolitic ore; Ni and Co extractions were very high for both elements, up to 98% and 96% respectively, while H2SO4 could leach efficiently Ni, up to 100%, but extracted only 34% of Co. Hydrochloric acid was also more efficient for the treatment of the limonitic ore, with Ni and Co extractions up to 98.3% and 87.6% respectively. With H2SO4 the maximum extractions were 71.3% for Ni and 52.1% for Co.

By Larry A. Haas

The U.S. Bureau of Mines, in cooperation with Cleveland-Cliffs, Inc. (Hibbing, MN), investigated ways of enhancing the quality (compressive strength, after-tumble and reducibility) of domestic acid and fluxed magnetite pellets by modifying the oxygen content during the preheat and induration periods of the firing operation . Oxidation of magnetite was best accomplished when sufficient oxygen and time were available before the peak induration temperature was reached. The rate of magnetite oxidation increased directly with the gas oxygen content during the preheat period at 7000 C and above. With 30 pct ( or more) O2 and a preheat rate of 2000 C/min, most of the magnetite was oxidized during the preheat period. With laboratory tube and mini-pot furnace tests, oxygen enrichment during the preheat period improved the pellet properties more in the simulated grate-kiln tests than in the simulated straight-grate tests. The longer induration period with the grate-kiln test resulted in more sintering of the residual magnetite and its reaction with the silicon compounds. When flux was present in the pellets, calcium silicates and calcium and magnesium ferrites were formed. More calcium ferrite was formed when the magnetite was oxidized early and less iron was present in the fayalitic calcium silicate slag.

Jan 1, 1993

By Donald R. Rathburn

Screening during the production of high-grade lump ore for blast furnace burden, particularly from recently developed ore deposits in Australia, South America, and Africa, has resulted in large tonnages of fine iron ore. Certain owners have decided to stockpile these fines until some later date; however, others have either sold these fines "as is" for agglomeration at the steel plant or have established their own pelletizing plants to produce a premium quality agglomerate. Normally these fines consist of the higher oxides of iron and the hydrated oxides. Unfortunately, grinding these types of materials in a wet process produces a slurry that is difficult to filter to obtain the requisite moisture level for the subsequent balling and indurating operations. The purpose of this paper is to review recent developments in fine dry grinding of iron ore and to discuss the various design and operating parameters involved. Although dry grinding of raw feed and clinker has been practiced in the cement industry for many decades, its significant application to the iron ore industry has taken place within the past ten years. Even though the basic concept of dry grinding has been borrowed from the cement industry, the successful application to iron ore grinding has not taken place without some difficulties. Consequently, the application to iron ore has required the solution of several unique design and operating problems.

Jan 1, 1970

The effect of superficial gas rate distribution (Jg profile) on down-the-bank metallurgical response was tested in the rougher-scavenger bank (eight 10-m3 tank cells, 4 roughers and 4 scavengers) at Highland Valley Copper Mine's Cu/Mo separation circuit. Three Jg profiles were tested: (a) as found (i.e., typical practice), (b) increasing decreasing (i.e., increasing from cell 1 to 4 and decreasing from cell 5 to 8), and (c) decreasing-increasing (i.e., decreasing from cell 1 to 4 and increasing from cell 5 to 8). The Jg profile approach proved to be of considerable value. Profile (b) gave the best metallurgical results, i.e., the highest down-the-bank grade/recovery (increase in grade at constant recovery was approx. 3-4% compared to the as found case) and the most efficient Cu/Mo separation (cumulative Cu recovery was reduced by almost half - approx. from 20% to 12%, at 99% Mo recovery). The success of the evaluation prompted the implementation of profile (b). Detailed gas dispersion characterization tests (Jg and Db (bubble size)) showed significant discrepancies between the Jg measured directly (using the McGill University sensor) and the Jg calculated from field instrument readings (volumetric gas flowmeter) and machine dimensions (cell cross-sectional area). Tests were designed to reveal the source of disagreement. It was observed that a significant number of bubbles were not able to float (i.e., they were entrained with the tailings), the evidence appearing to be a significant number of very small bubbles (approx. 200-300 µm) which did not have sufficient buoyancy to rise. Consequently, rather than relying on the field instrument, the evaluation depended on the McGill University Jg sensor, which collects bubbles in a tube near the pulp-froth interface, thus providing significance to the data as the measurements were obtained from bubbles that almost certainly floated.

Jan 1, 2007

By Teresa M. Bodas Freitas, Arianna Lupattelli, Peter J. Bourne-Webb, Diana Salciarini, Martina Zito, Donatella Sterpi

The thermomechanical response of thermally-activated (TA) piles under monotonic thermal loads is quite well understood and the remaining uncertainties relate to the effect of long-term, cyclic loading of individual TA piles and pile groups. Recent studies undertaken by the authors have provided insights into the behaviour of TA pile foundations undergoing cyclic thermal loading. Despite their simplicity, the analyses show that key aspects of the observed response of piles in sand, under cyclic thermal loading can be reproduced, providing confidence in the outcomes of the analyses. The studies examined isolated piles and pile groups, and concluded that irrecoverable thermally-induced settlement may be mitigated through the choice of an appropriate margin of safety on the pile shaft resistance under service mechanical load conditions, and the maximum thermal stress can also be readily estimated. This paper consolidates these works and provides guidance regarding the safe geotechnical and structural design of the piles, then looks towards the remaining issues around the safe provision of thermally-activated pile foundations.

May 1, 2022

By T. Murt, C. Oñate

In recent years, environmental considerations have played a prominent role in underground construction projects. The management and disposal of the muck produced by an EPB TBM is an important aspect of this topic. Soil conditioners with higher biodegradability and lower eco-toxicity have been specifically developed to comply with strict regulations in several countries around the world, with the goal of reducing the environmental impact of tunneling on soil, water, and living organisms. This paper highlights innovative sustainable soil conditioners and how they differ from traditional products. Additionally, environmental considerations for TBM projects around the world and in North America will be examined.

Dec 1, 2022

By Rongjie Kong, Shiwei Wang, Guomin Wei

Owing to the selective oxidation and uneven combustion that occur on the surface of carbon anode, some carbon particles detach and form carbon residue, which is defined as spent anode slag (SAS). The highly graphitized and toxic impurities such as fluorite ( CaF2), corundum (α-Al2O3), and cryolite ( NaAl11O17) are crucial components of SAS resource but are difficult to separate from graphite. This study developed a method of using water-soluble (emulsified) kerosene to separate the carbon particles from the toxic impurities in the SAS resource. The flotation purification approach of utilizing conventional kerosene was experimentally investigated and compared with that of using water-soluble kerosene. The results showed that with the use of emulsified kerosene, the maximum combustible matter recovery of the carbon particles was 89.86% while that of using traditional kerosene was 80.30%. The emulsified kerosene was comprehensively examined by various instruments to clarify its adsorption mechanism on the carbon particle surfaces. Because of the superior dispersibility of emulsified kerosene, it effectively envelops carbon particles with a smooth surface, oxygen-containing functional groups, and hydrophilic C–F bonds, thereby increasing the surface hydrophobicity and flotation responses of targeted carbon particles.

Feb 6, 2024

By Guy Reed, Russell Frith

In situ or pre-mining horizontal stresses are arguably the least well understood of the principal inputs into underground coal mining geotechnical engineering design, whether analytical, empirical, or numerical. This is a direct result of both the cost and difficulty of obtaining meaningful stress measurements, the various limitations of the measurement method in terms of sourcing strata types that approximate the assumed conditions of the post-measurement mathematics to convert measured strains into stresses, and a common practice by some geotechnical professionals to preferentially utilise generic values rather than interrogate the available measurement data for cause and effect relationships between horizontal stress magnitudes, directions and a range of associated controls. That numerical modelling simulations attempt to mimic reality but often rely on simplified generic horizontal stress input assumptions is a particular cause for further consideratio The paper attempts to further explore the nature of in situ horizontal stresses using a range of stress measurement results from the Australian coal sector supplemented by several international studies addressing the same basic issue, the result being a number of credible and highly relevant “cause and effect" inter-relationships between the three principal in situ stresses in addition to the influence of rock properties (e. Young's Modulus and Poisson's Ratio), cover depth and the larger-scale structural geological environment. In particular, the paper demonstrates that despite being commonly overlooked as a primary rock/coal material property, Poisson's Ratio and the associated K Effect are intrinsic to understanding 3D in situ stress measurement results and therefore, predicting in situ stress magni- tudes more generally for geotechnical analyses purposes. As a fundamental question, the paper addresses whether it is necessary and of engineering value to characterise in situ horizontal stresses: according to distinct "domains," in the same way that more easily identifiable geotechnical properties such as rock mass ratings, coal seam thickness, ply splits, and cover depth are often treated.

Jun 25, 2024

By J. D. Verhoeven

In the past 15 years a considerable amount of experimental and theoretical work has been done concerning the onset of convection in liquids as a result of interm1 density gradients. This work, which has been doue in many different fields, is reviewed here and extended slightly to give a rrlore quantitative understanding to the probletrz of conzection in liquid metal dlffusion experinletzts. In liquid metal systems the capillary reservoir technique is currently used, almost exclusively, to measure diffusion coefficients. In this technique it is necessary that the liquid be stagnant in order to avoid mixing by means of convection currents. Convective mixing may result from: 1) convection produced as a result of the initial immersion of the capillary; 2) convection produced in the region of the capillary mouth as the result of the stirring frequency used to avoid solute buildup in the reservoir near the capillary mouth; 3) convection produced during solidification as a result of the volume change; and 4) convection produced as a result of local density differences within the liquid in the capillary. The first three types of convection have been discussed elsewhere1-a and are only mentioned for completeness here. This work is concerned only with the fourth type of convection. Local density differences will arise within the liquid as a result of either a temperature gradient or a concentration gradient. It is usually, but not always, recognized by those employing the capillary reservoir technique that the top of the capillary should be kept slightly hotter than the bottom and that the light element should be made to migrate downward in order to avoid convection. In the past 15 years a considerable amount of work, both theoretical and experimental, has been done in a number of different fields which bear on this problem. This work is reviewed here and extended slightly in an effort to give a more quantitative understanding of the convective motion produced in vertical capillaries by local density differences. The Stokes-Navier equations for an incompressible fluid of constant viscosity in a gravitational field may be written as: %L + (v?)v = - ?£ + Wv - g£ [1] where F is the velocity, t the time, P the pressure, p the density, v the kinematic viscosity, g the gravitational acceleration, and k a unit vector in the vertical direction. A successful diffusion experiment requires the liquid to be motionless, and under this condition Eq. [I] becomes: where a is the thermal expansion coefficient [a =-(l/po)(dp/d)], a' is a solute expansion coefficient [a' = -(l/po)(dp/d)], and the solute is taken as that component which makes a' a positive number. Combining with Eq. [3] the following restriction is obtained: Since there is no fixed relation between VT and VC in a binary diffusion experiment, Eq. [5] shows that the condition of fluid motionlessness requires both the temperature gradient and the concentration gradient to be vertically directed. Given this condition of a density gradient in the vertical direction only, it is obvious that, as this vertical density gradient increases from negative to positive values, the motionless liquid will eventually become unstable and convective movement will begin. The classical treatment of this type of instability problem was given by aleih' in 1916 for the case of a thin fluid film of infinite horizontal extent; and a very comprehensive text has recently been written on the subject by handrasekhar.' It is found that convective motion does not begin until a dimensionless number involving the density gradient exceeds a certain critical value. This dimensionless number is generally referred to as the Rayleigh number, R, and it is equal to the product of the Prandtl and Grashof numbers. For the sake of clarity a distinction will be made between two types of free convection produced by internal density gradients. In the first case a density gradient is present in the vertical direction only, and, since the convection begins only after a critical gradient is attained, this case will be called threshold convection. In the second case a horizontal density gradient is present and in this case a finite convection velocity is produced by a finite density gradient so that it will be termed thresholdless convection. Some experimentalists have performed diffusion experiments using capillaries which were placed in a horizontal or inclined position in order to avoid convection. These positions do put the small capillary dimension in the vertical direction and, consequently, they would be less prone to threshold convection than the vertical position. However, if the diffusion process produced a density variation, as it usually does, it would not be theoretically possible to avoid thresh-

Jan 1, 1969