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By Neil C. Hario

The purpose of this paper is to explore the various designs and design alternates available for large fine crushing plants, and to discuss objectives and criteria upon which these designs are founded. Common practice for size reduction of run-of-mine or run-of-pit ore in preparation for subsequent treatment utilizes a three-stage system. First stage, or primary breaking is generally carried out with jaw or gyratory crushers. The usual output from this stage provides a feed for fine crushing in the size range of 6 to 10 inches. This discussion is limited to the process of fine crushing, and we will further limit it to what is commonly called secondary and tertiary crushing. We define a large crushing plant as one with a minimum capacity of 2,000 tons per hour. Generally, these plants utilize cone type crushers to reduce ore for rod, ball, or pebble mill feed.

Jan 1, 1970

By John Parker

During 1965, a new stoping method was developed at the Bunker Hill Mine at Kellogg, Idaho to enable the profitable mining of a large low-grade zinc orebody. This method, called the Bunker Hill pillar system, incorporates the use of the air-powered Atlas Copco T2GH or CAVO 310 as the prime production component. The method and equipment proved highly successful and was the first step in mechanizing what had been a classic example of a square-set and horizontal cut-and-fill operation. Since that time there has been a realization that the small rubber-tired type of loader could be effectively used to advantage in increasing productivity and decreasing costs in many different stoping and development applications throughout the mine. The net result since 1967 has been that a large and increasing portion of the mine production and an increasing share of the development is being done with small rubber-tired loaders. Presently, ten Atlas Copco T2GH and six CAVO 310 air-operated loaders are in use, having replaced the time-honored slusher which was first introduced into the Bunker Hill Mine in about 1898 in the form of a slip scraper. The recent advent of diesel powered loaders in the one yard size range has in 1970 further accelerated the trend toward rubber-tired mobile equipment at the Bunker Hill Mine. Although The Bunker Hill Company is using small diesel loaders of several different types and manufactures for inclines, declines and level development and will undoubtedly find stoping applications for this equipment, .the bulk of this paper will be confined to the use of the air-operated loader, leaving the diesel equipment to a future presentation. It is sufficient to say that we feel at this time that the Autoloader type air-powered equipment and the small diesel front end-loader

Jan 1, 1970

By Keros Cartwright

Sanitary landfilling has become one of the most widely used methods of disposing of solid refuse. A principal concern of regulatory agencies and the public itself is that landfill operations do not degrade the physical environment, including water resources, and the ground-water reservoir in particular. Ground-water and engineering geology can guide landfill operations into suitable terranes or develop measures to compensate for any natural limitations at a particular site Experience and research in Illinois suggest four activities relating to landfill disposal that warrant attention by geologists and engineers: (1) Regional delineation of favorable and unfavorable hydrogeologic conditions to facilitate planning and preliminary screening of potential landfill sites. (2) Site evaluations, with considerations of geologic materials, topography, water levels, flow systems, and local occurrence and use of water resources. (3) Re- search on aspects of the hydrogeologic environment that control effects of, or are modified by, landfills. (4) Formulation of practices in the siting, construction, and operation of landfills that prevent, mitigate, or isolate deleterious effects. The first two activities are basically in the domain of earth science, requiring the application of fundamental concepts of geology and hydrology and conventional site-exploration methods. The third activity, research, requires contributions from geology as well as other disciplines, including soil physics, sanitary engineering, and chemistry. The fourth calls for policy decisions by regulatory agencies and elected officials, using the contributions of scientists and engineers.

Jan 1, 1970

By P. W. Jeran

The Stereonet Analysis Program (SNAP) is a mathematics tool which, by means of a computer, reproduces mathematically the manual techniques of pre- paring stereograms. This computer program was developed to provide a fast, accurate, and economical means of analyzing fracture orientation data. It is mitten in FORTRAN IV for use on a UNIVAC 1108 operating under an Exec II system, but can be adapted to other systems. SNAP is currently being used to aid in the analysis of cleats and other geologically induced fractures associated with coalbeds that are being mined underground, Methane flows through the coalbed and into these mine workings predominantly through the fracture system. Therefore, knowledge of fracture orientation is an invaluable aid in the development of methane control technology.

Jan 1, 1970

By H. P. Dibbs

An account is given of the application of neutron activation analysis to the rapid, non-destructive determination of copper in minerals, using a 14-MeV neutron source. Elements that interfere in the determination of copper by this method are given, together with the errors in the estimation of copper that result from the presence of varying amounts of these elements. The possible use of a compact "sealed-tube" 14-MeV neutron generator for the field assay of copper in minerals is discussed.

Jan 1, 1970

By Lester J. Crow

This study advances the use of elemental sulfur in structural materials by demonstrating its value in bonding high-strength, well-graded basalt aggregates to form sulfur-basalt concretes. Sulfur is an excellent bonding agent, and the strength of a thermoplastic sulfur-aggregate mixture depends, to a large degree, on the strength and grain-size distribution of the aggregate used. A 3-cubic-foot, electrically powered mixer with heat applied to the barrel was used to mix the sulfur and aggregate. Sulfur content of several mixtures was varied to obtain the best workability with a minimum of sulfur in excess of that necessary to fill the voids. The average grain sizes and grain-size distributions were also varied to determine their effects on strength. Unconfined compression tests of forty-five 6-by l2-inch cylinders yielded average strendths of 3,348 psi to 10,398 psi. The highest strength single cylinder was 10,717 psi. The cylinders were tested from 24 hours to 6 days after pouring; after 24 hours the rise in strength was very slight. From the results obtained it appears that sulfur can be a useful construction material. An evaluation was made of a high-vacuum application for sulfur concrete. Sulfur has a high vapor pressure at elevated temperatures, 50° to 100° C; consequently, significant losses by sublimation can be expected. At lower temperatures the losses are not significant; however, this factor will limit its use at a higher temperature.

Jan 1, 1970

A portable electronic instrument was developed which will measure change of longitudinal wave velocity with change of uniaxial stress in rock columns. The instrument is a solid-state device powered by nickel-cadmium batteries. It uses a probe of two piezo-electric crystals spaced inches apart to send and receive a pulse through a stressed rock. A one-inch cathode ray oscilloscope visually displays the longitudinal wave. A reference chart is used to find the stress. Laboratory results have indicated that the average stress on a sandstone column can be found to within 35 psi. The feasibility of using this instrument to determine stresses in mine pillars is to be studied. The instrument may be used to investigate physical properties of rock.

Jan 1, 1970

By G. W. Diehl, G. A. Griffiths

"Gentlemen, one week ago, I attended the University of Minnesota's Annual Symposium on Mining, in Duluth. A good part of this symposium was dedicated to mill linings of rubber.At this symposium, three mining companies published results from long time full scale tests with rubber linings in mills at four different mines. These were the Republic and Empire Mines of Cleveland Cliffs Iron Company, the Groveland Mine of Hanna Mining Company and the Eagle Mountain Mine of Kaiser Steel Corporation. These papers will be printed in due time and I will not endeavour to relate their full contents, let me only say that in three of the plants, the linings were found to be very economical compared wi.th steel, and that these three are converting over completely to rubber linings, while the fourth, Empire Mine, reported no economical results as far as the shell lining goes, whereas the grates showed promise of becoming economical. The authors of the Cleveland Cliff's paper, however, stated that design improvements in the rubber lining possibly could result in an economical lining also for Empire Mine.That rubber linings in mills, in most cases, show better wear life than steel linings, is known by most of the audience. But, one thing that has not before been disclosed by the endusers is the effect of rubber linings on the grinding economy. All three papers mentioned above reported no change in capacity or grind and two of them reported a decrease in power consumption per ton ground. Hanna Mining reported an average decrease over a three year period for one mill of over 10%. This, of course, puts the economy of a rubber lining in a completely new light. Finally, a point of interest at this meeting was that all three papers emphasized the design aspect, Thus the industry has acknowledged what I believe to be a very important fact - the design of a lining is often more important than the material it is made of."

Jan 1, 1970

By J. De Geoffroy, T. K. Wignall

The paper describes a statistical method based on regression and classification analysis which is designed to assist exploration management in the selection of prospecting areas and drilling targets in regional programs. The classification is based on three criteria which are formulated from sets of relevant geological, geophysical and geochemical factors: (a) regression estimates of expected ore values, (b) Bayesian probabilities of success and (c) expected utility payoffs. The advantages of the method are: (a) rational and unbiased ratings for areas or targets in a manner consistent with management's goals; (b) calculation of probabilities of success and confidence intervals for the ratings, and (c) rapid and accurate handling of a large amount of data by computer programs.

Jan 1, 1970

By C. Perez-Rosales

A statistical method for determining simultaneously some of the basic geometrical characteristics of porous media such as porsity, specific surface* mean pore width, mean grain thickness and absolute permeability is presented. The proposed method is characterized by its simplicity and the minimum amount of laboratory equipment that it requires. The experimental procedure used to evaluate the various geometrical characteristics is based 'pan the 'surface analysis Of a a In view of this fact the app1icability Of the method is limited to homogeneous and isotropic materials. INTRODUCTION The behavior of a fluid flowing through a porous medium depends, among other things, upon the internal geometry of the medium; hence the importance of developing efficient methods to determine the geometrical properties of porous materials. This paper describes a statistical method to determine simultaneously some of the basic geometrical properties of porous materials such as porosity, specific surface, mean pore width, mean grain thickness and absolute permeability. The mathematical formulation has been developed that the data required to calculate the various geometrical characteristics of a sample can be easily measured by analyzing a section of the sample with an evenly spaced grid. THEORY A simple way of obtaining information about the internal geometry of a porous material is to throw a point at random over a cross-section of a sample. l-Through this procedure the porosity can be detemined.l,2 By considering that the material is homogeneous and isotropic, and that the point is dropped many times, the porosity 4 is given by where N is the total number of times the point is thrown and n is he number of times the point falls within pore areas. Another simple manner of analyzing the structural characteristics of a porous material is to superimpose an arbitrarily long line on a cross-section so that its length is evenly distributed over the surface area. Through this procedure the porosity can also be determined. If L is the total length of the line, and 1 is the sum of the lengths of the line segments within void spaces, the porosity is given by 4 = —.1.............. (2) The advantage of this type of analysis is that geometrical characteristics other than porosity can be obtained. Thus, if c represents the number of intersections between the line and the perimeter of pores, it can be shown3 that the specific surface, defined as he surface area of pores per unit bulk volume, is given by To give a proper description of the internal geometry of a porous medium, it is necessary to define quantities that characterize the notions of pore size and grain size. Unfortunately, because of the complexity of porous materials, it is difficult to give exact geometrical definitions of what is meant by the ConCePtS of "poresl' and "grains", especially when dealing with consolidated materials. Never theless, one often talks about the "size of pores" and the "size of grains" without defining accurately the terms. A possible solution to this problem follows. Assume that an arbitrarily long line is placed on a section of a sample so that the line is evenly distributed over the surface area (see Fig. 1). 1n a system like this, each line segment within a void space will be, by definition, the pore width in a given location and direction. Consequently, if the

Jan 1, 1970

By Clarence Hardy Long

In January of 1969 the United States Department of Health, Education and Welfare, through the National Air Pollution Control Administration, published a series of Air Quality Criteria (4'S) and Control Techniques (6,7) for air pollutants in compliance with the 1967 Clean Air Act which will affect the operation of all fuel burning equipment in the very near future. The design of equipment for the future which will use fossil fuels will also be affected. The purpose of this paper is to discuss some of the modifications which might be anticipated in the future for fuel burning equipment. One class of the several air pollutants looked at first by the USDHEW was the sulfur oxides. Other pollutants, such as nitrogen oxides, will be studied and controls for these will supposedly be written in due time. The obvious use of low-sulfur fuels, coal, oil and natural gas is suggested by the Control Technique(6). Conversion to other sources of power, such as nuclear energy and hydropower, is also suggested. The statement is made that since possible hydroelectric sources are limited and nuclear plants are not yet available on a large scale, the changeover to these sources of power will not be overnight. The bulletin (6) suggests that one possible solution in some areas may be the use of low sulfur coals for short periods of time during periods of severe air pollution. A curve showing the effect of this was given in the 1969 April issue of the Power magazine, where A. E. Boyer and F. B. Kaylor of Stone and Webster also described a computer program called DOSAGE which might be used to check weather, temperature, humidity, wind direction and velocity, and sound an alarm when that 0.1% of the time per season is here that requires the use of low-sulfur fuel. Inversion is eminent! Once this has passed operation on regular fuel may be resumed. This would mean a separate storage

Jan 1, 1970

By David R. Maneval

In 1956 the Legislature of the Commonwealth of Pennsylvania created a "Coal Research Board" in the Department of Mines and Mineral Industries. Over the years through amendments to the original legislation, the scope of authority for research has been expanded from the narrow area of improving and increasing the utilization of coal to covering all aspects of coal technology and any other area of interest which would be of value to the coal industry. In January of 1964, the Board commenced a vigorous program using appropriated funds and funds donated by the coal industry to finance a research program devoted to seeking solutions to the mine drainage problem. A review of published literature on the treatment of mine drainage indicated that much work done up to that point in time concerned only the mechanism of mine drainage formation and theoretical chemistry. Very few applied, developmental, or engineering studies had been devoted to finding practical solutions to the problem of polluted waters being discharged from active or abandoned mines. Projects were therefore undertaken on a wide variety of more utilitarian approaches. This paper will discuss briefly some of the pollution abatement approaches which have been funded by the Coal Research Board of this State, and will describe in some detail a multistage flash evaporator treatment plant now under construction.

Jan 1, 1970

By Henry H. Roos

The productivity of the underground driller has increased 500-600% during the past 20 years. This increase is not due so much to improved percussion drills as it is to improved drill support equipment and modernization of mining methods, Efforts to mechanize drilling in mining operations were made as early as the late 1800's; and, patents on rock drill manipulating machinery date back to 1906. However, the great rush to mechanization began in the 1950's when the development of trackless mining methods gave mining engineers and equipment designers their first opportunity to create improved operating conditions for the equipment and to match the equipment with these conditions. Accordingly, this paper will summarize the developments of the past 20 years and will attempt a forecast of developments that can be expected during the next few years.

Jan 1, 1970

By Donald Carlisle

El presente texto describe las relaciones entre costos, utilidad, cantidades y velocidades de "recuperación" de la mena, así como se consideran las leyes marginales y su velocidad de la recuperación en las minas.

Jan 1, 1970

By John V. Beall

The "free form life," The Wall Street Jourlzal called it. That is what the young people are practicing who have dropped out after successfully completing a college education. The ones described were first-rate students who did not embark on careers but instead selected such nonintellectual jobs as delivering mail, short- order cooking and the like. We couldn't help thinking that it wasn't so long ago, that we had the ideal setup in mining for folks of this persuasion when most college grads were started out as muckers. Actually there isn't much new in this business of doing your own thing. Being a type that takes westerns seriously, we jumped at the chance to catch the rerun of the wide-screen flick "How the West Was Won." There was Jimmie Stewart playing the part of the mountain man, with a canoe full of furs going east down river. Coming west up river, is a settler with his daughters. This mountain man had on his fringed buckskins, his two-year growth of long hair and a tremendous thirst. He had been doing his thing and planned to keep right on doing it. However, one of the pretty settler girls had other ideas. The same fate probably awaits today's individualistic youths.

Jan 1, 1970

By H. Kazemi

An ideal theoretical model of a naturally fractured reservoir with a uniform fracture distribution, motivated by an earlier model by Warren and Root, has been developed. This model consists of a finite circular reservoir with a centrally located well and two distinct porous regions, referred to as matrix and fracture, respectively. The matrix has high storage, but low flow capacity; the fracture has low storage, but high flow capacity. The flow in the entire reservoir is unsteady state. The results of this study are compared with the results of the earlier models, and it has been concluded that major conclusions of Warren and Root are quite substantial. Furthermore, an attempt has been made to study critically other analytical methods reported in the literature. In general, it may be concluded that the analysis of a naturally fractured reservoir from pressure transient data relies considerably on the degree and the type of heterogeneity of the system; the testing procedure and test facilities are sometimes as important. Nevertheless, under favorable conditions, one should be able to calculate in-situ characteristics of the matrix-fracture system, such as pore-volume ratio, over-all capacity of the formation, total storage capacity of the porous matrix, and some measure of matrix permeability. INTRODUCTION The analysis of flow and buildup tests for obtaining in-situ characteristics of oil and gas reservoirs has received considerable attention in the past decade. Most of the available techniques result in reliable conclusions in macroscopically homogeneous reservoirs or in the homogeneous reservoirs with only certain types of induced and/or inherent heterogeneity (such as wellbore damage, etc.). In general, the greater the degree of heterogeneity, the less the reliability of the information deduced from the pressure transient data. A commonly encountered heterogeneous system is a naturally fractured reservoir where two types of distinct porosities occur in the same formation. The region containing finer pores may have high storage and low flow capacities. This is called the matrix. The remaining region may have high flow capacity with low storage. The latter region is generally the set of interconnecting fractures and fissures of the rock, and for this reason it is called the fracture. Ordinarily, we wish to obtain the permeability and porosity of each region and perhaps the frequency of the fracture distribution in a reservoir. Such information is necessary for reservoir engineering. Other information, such as wellbore damage, will be useful in evaluating possible remedial work for such fields. Few authors have suggested theories to aid in calculating the in-situ characteristics of a naturally fractured reservoir similar to what we have described above. Pollardl suggested that a naturally fractured reservoir contained three distinct regions: a damaged or an improved region surrounding the wellbore, and the two remaining regions the same as described earlier. He suggested that the flow was taking place from the tight matrix into the highly conductive fractures, then into the we wllbore region and finally into the well column. He concluded that the average pressure buildup in each of these distinct regions can be expressed approximately in terms of an exponential decay function of time. He also hypothesized that the decay coefficients for each of these functions were significantly different from each other; consequently, each of these functions became dominant in turn, in the process of pressure buildup. Thus, by a proper graphic plot of the logarithm of wellbore pressure differences vs buildup time, each of these functions could be determined (see Fig. 1). Pollard suggested methods of determining the wellbore damage and fracture volume. Later Pirson and Pirson2 extended

Jan 1, 1970

By Ronald D. Hill

The occurrence of acid mine Drainage (AMD) with coal mining has been well documented. (1) Less documentation is available of its association with other types of mining, e.g., copper, gold, zinc, and sulfur. Yet there are many locations in the western states where acid mine drainage is as great a pollution problem as in Appalachia and in some cases, because of the high copper, zinc, and arsenic concentrations, they present an even more difficult problem. Until a few years ago, it was generally believed that the neutralization of acid mine drainage was uneconomical thus, AMD was allowed to discharge freely into our streams. However, the demand for good water finally dictated that the mining industry be included under pollution laws. In 1964 the Commonwealth of Pennsylvania passed a law requiring that all active mine discharges meet a discharge standard of pH 6-9, iron less than 7 mg/1, and the water must have a net alkalinity. Several other states now require active mines to treat AMD. In all but a few cases, lime neutralization, often in conjunction with aeration, has been the treatment method used. The high cost of lime as compared to limestone and the poor quality sludge, (slow settling, large volumes, and low solids content) has stimulated work in the utilization of limestone. This paper reports on the current state-of-the-art of limestone treatment of AMD.

Jan 1, 1970

By M. B. Kasen

eralized strain equation appear quite different they are really identical. This identity can be shown in a simple mathematical rearrangement. Referring to Eq. [I], the substitution of ln(1 +?E) for ? (where ?E is the engineering strain) yields: a =s8- (s8?so)e?1/?c) ln(1 +s8??E) [4] or s =s8?(s8?so)(l +?E)-1 [5] Replacing (1 + cE) with its equivalent, (l/lo): s=s8?(s8?so)l/€c [6] Adding and subtracting the quantity (s8 - so) yields: s=s8?(s8?so)+ (s8-so) l-(^)l/£c [7] = s0+(s8?so)ri-(^0)1/^l [8] Letting n = 1/?c it follows that: This equation will be seen to be identical to the generalized strain expression in Eq. [3], the coefficients a and b being equal to so and (s8?so)/?c or n(s8?so), respectively. Confirmation of the relationship noted above was provided by fitting experimental stress-strain data5 for 304 stainless steel (total strain from 0.072 to 1.15) at room temperature at a true total strain rate of 4 x 10-3 sec-1 to Eqs. [I] and [3]. In this study nonlinear regression analyses were used to evaluate the equation constants. The results of this evaluation are presented in Table I. When these constants are used in Eqs. [I] and [3] the curves obtained are coincident. It will also be noted that the value of n is equal to YE,, the value of a is equal to so, and the value of b is equal to (s8 - so)/Ec. These equalities are illustrated in Table I where the Voce constants in parentheses were calculated from a, b, and n values. Excellent agreement is seen to exist. It is concluded, therefore, that the Voce equation is, indeed, identical to the linear expression involving generalized strain. In applying the generalized strain concept to stress-strain data, it has been noted3 that data within what was termed the transition region (first few points in the plastic flow region) must be excluded from the analysis in order to obtain the linearity in Eq. [3]. A similar exclusion applies in the use of the Voce equation since an expression which would describe the strain-hardening region would usually be found to be not too effective in the elastic-plastic fillet2 which connects the elastic line to the strain-hardening region. These considerations further substantiate that Eqs. [I] and [3] do indeed describe identical behavior. Note added in proof. Since this manuscript was submitted for publication, correspondence with Professor S. R. Davies, University of Edinburgh, (of Ref. 3) indicated that his associates have also confirmed the identity between the Voce equation and the generalized strain concept. It is sometimes desirable to obtain a small grain size in super-purity metals. Unfortunately, the absence of impurities, the low recrystallization temperatures, and the low activation energies for boundary motion result in rapid growth of relatively few grains when conventional recrystallization practices are used. For example, Arajs et al.1 were unable to obtain a mean grain diameter less than about 0.4 mm in iron containing 38 at. ppm of impurity. The <1 at. ppm purity range in many modern superpurity metals results in yet larger limiting grain sizes. It is the purpose of this communication to describe a technique by which mean grain diameters as small as 30 µ have been produced in aluminum having an impurity content < 0.5 at. ppm. The technique should be applicable to superpurity metals other than aluminum and has potential applications to grain refinement of commercial alloys. The necessary and sufficient requirements for production of a small grain size are as follows: a) a large number of potential nucleating sites must be created randomly within the cold worked material, b) sufficient thermal energy must be provided at a rate that will simultaneously activate a large fraction of the potential nuclei, and c) the grain growth must be stopped shortly after grain impingement.&apos; A high density of potential grain nuclei may be cre-

Jan 1, 1970

By William Wargo

The basic reason for lining underground cavities is to keep the cavity open during its useful life by providing adequately for the support of the surrounding rock and for the necessary degree of water tightness. This covers the entire field of support methods from the simpliest timber support to reinforced concrete in all its variations as applied to tunnels, galleries or shafts. The problem involved in the design of more efficient and economical lining systems for even bigger cavities has been magnified by increased speed of advance made possible by better blasting tecniques, improved tunneling machines and more efficient material handling. Tunnel lining today requires a disproportionate amount of time and money compared to other operations mostly due to the manuel labor involved in its installation. One solution to this problem is the developement of an entirely new concept in tunnel lining designed notoonly to overcome this bottleneck but also to open up the field for further increases in speed of advance. This new lining system acts first as a fast protective armour then becomes the concrete metal form and ends up as reinforcement sheet inside the concrete lining. This system developed and manufactured by Bernold A. G. of Switzerland since October 1968 has been installed in 25 applications in Europe under all ground conditions from stable rock to unconsolidated ground.

Jan 1, 1970

By J. Szekely, G. P. Martins

A formulation is given for describing the rate of expansion of spherical bubbles rising in liquids the freeboard of which is evacuated. The computer solution of the resultant differential equations has shown that, for low freeboard pressures (less than about 5 mm Hg), on approaching the free surface the bubbles expand much less rapidly than predictable from equilibrium considerations. In other words, in this region the pressure inside the bubbles will be significantly larger than the static pressure in the liquid corresponding to the position of the bubble. These theoretical predictions were confirmed by experimental work, using two-dimensional air bubbles rising in mercury. The important consequence of these findings is that the expansion of gas bubbles in vacuum degassing operations will be a great deal less than expected from hydrostatic considerations. This would lead to a significant reduction in the available interfacial area and may explain the apparent poor efficiency of many vacuum degassing units. VACUUM degassing as a treatment for liquid steel has gained widespread popularity in recent years; the number of known installations exceeds several hundred at the present time.&apos; Although much information is available on both the thermodynamics of the system and the overall performance of various industrial units, much less is known about the fundamental aspects of the process kinetics.2-4 The basic physical situation common to virtually all vacuum degassing operations is the interaction between gas bubbles (swarms of bubbles) and the surrounding molten metal, held in a container, the freeborad of which is at a low absolute pressure. Once formed (or introduced from an external source) the bubbles will ascend, due to the buoyancy forces, and, during this ascent, a significant increase in their volume will occur. This progressive increase in the bubble volume is due to two factors: a) the continuous reduction in the static pressure acting on the bubble during its rise; and b) mass transfer into the bubble from the surrounding molten steel. In a recent paper Richardson and Bradshaw developed equations5 for describing mass transfer into gas bubbles from molten metals at reduced pressures. However, in deriving these expressions it was assumed that the pressure inside the bubble was identical to the static pressure in the adjacent liquid. In other words, the volume of the bubble was considered to be in equilibrium with the pressure of the fluid adjacent to it. This assumption, thus their analysis presented, was thought to be reasonably accurate for most of the bubble&apos;s ascent; however, it was unlikely to be valid in the immediate vicinity of the free surface, held at a low pressure. It was pointed out in the discussion6 that the region close to the surface may be of considerable importance as both the driving force and the interfacial area available for mass transfer are at their highest value here. The &apos; &apos;anomalous" behavior of gas bubbles when approaching a free surface at low pressures was recently confirmed in a preliminary investigation by Szekely and Martins. ?1 Here high-speed motion photography was used to study air bubbles rising in a column of n-tetradecane with a freeboard pressure of 0.1 mm Hg. It was found that significant distortion of the bubbles occurred on approaching the free surface; furthermore, the expansion observed was much less than what one could expect from hydrostatic considerations, i.e., factor a previously discussed. It follows from the foregoing that a detailed study of these phenomena would be justified both from fundamental considerations and because of their potential relevance to technology. The purpose of the paper is to present a more realistic formulation for the expansion of a gas bubble approaching a low-pressure region, together with a comparison of the theoretical prediction with experimental measurement. An inert bubble will be considered in the first instance; it is thought that the understanding of the fluid mechanics is an essential first step toward the realistic formulation of the mass transfer process. This latter problem will be the subject of a subsequent publication. FORMULATION The Physical Model. Consider a spherical bubble, of initial radius Ro, rising in a fluid, having a density pL. Initially let the bubble be at a distance H from the free surface, and at a pressure Pgo, as illustrated in Fig. 1. Pgo, the initial pressure in the bubble, is given by the following equation: pgo = Po = Ptp +pLgH [ la] where Po is the pressure in the liquid corresponding to the initial position of the bubble and Ptp is the pressure at the free surface. The fluid pressure at

Jan 1, 1970