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By AIME AIME

LOCAL COMMITTEES. GENERAL RECEPTION COMMITTEE.-Mr. and Mrs. H. S. Chamberlain, Mr. and Mrs. J. T. Lupton, Mr. and Mrs. T. H Lasley, Mr. and Mrs. R. S. Faxon, Mr. and Mrs. H. Clay Evans, Mr. and Mrs. C. E. James, Mr. and Mrs. B. F. Thomas, Air. and Mrs. H. S. Probasco, Mr. and Mrs. W. M. Lasley, Mr. and Mrs. L. W. Llewellyn, Mr. and Airs. T. G. Montague, Mr. and Mrs. E. B. Thomasson, Mr. and Mrs. C. F. Milburn, Mr. and Mrs. C. A. Raht, Mr. and Mrs. C. C. Notting¬ham, Mr. and Airs. Z. C. Patten, Mr. and Mrs. Willard Warner, Mr. and Mrs. S. R. Read, Mr. and Mrs. Carl White, Mr. and Mrs. M. M. Allison, Air. and Mrs. C. E. Buck, Mr. and Airs. H. F. Temple, Air. and Mrs. M. M. Hedges, Mr. and Airs. X. Wheeler, Mr. and Airs. John A. Patten, Air. and Airs. N. T. Montague, Mr. and Mrs. R. H. Williams, Mr. and Mrs. T. R. Preston, Mr. and Airs. Morrow Chamberlain, Mr. and Airs. T. C. Thompson, Mr. and Airs. T. L. Montague, Mr. and Mrs. O. L. Hurlbut, Air. and Mrs. C. A. Lyerly, Mr. and Mrs. Garnett Andrews, Air. and Mrs. M. B. Ochs, Mr. and Airs. Webster James, Mr. and Mrs. D. P. Montague, Mr. and Mrs. Z. C. Patten, Jr., Mr. and Mrs. W. A. Sadd, Mr. and Mrs. J. B. Pound, Air. and Mrs. George D. Lancaster, Air. and Airs. J. F. Johnston, Mr. and Mrs. R. W. Barr, Air. acrd Mrs. W. B. Davis, Mr. and Airs. Douglas Baxter, Air. and Mrs. W. R. Crabtree, Mr. and Mrs. Lewis M. Coleman, Mr. and Mrs. Newell Sanders, Mr. and Mrs. E. Y. Chapin, Mr. and Mrs. W: B. Riddell,. Mr. and Mrs. J. B. Frazier, Mr. and Mrs. John A. Moon, Mr. and Mrs. C. D. Mitchell, Dr. and Airs. J. H. Race, Mr. and Airs. A. W. Chambliss, Mr. and Mrs. J. P. Smartt, Mr. and Mrs. J. F. Tarwater, Mr. and Mrs. L. D. Drewry, Capt. and Mrs. A. B. Putnam, Mrs. Minnie C. Ewing, Mr. G. F. Meehan, Mr. Sam S. Gerstle, Mr. P. A. Brawner, Mr. C. M. Preston, Air. George M. Guild, Mr. L. M. Mansfield, Dr. J. W. Johnson, Dr. J. AI. Hogshead. EXECUTIVE COMMITTEE.-H. S. Chamberlain, Chairman; H. S. Probasco, C. M. Preston, H. Clay Evans, J. T. Lupton, M. B. Ochs, C. C. Nottingham, Al. Al. Alli¬son, R. S. Faxon, C. E. James, C. A. Raht. EXCURSION TO CHICKAMAUGA PARK.-T. C. Thompson, Chairman; B. F. Thomas, G. F. Meehan, Morrow Chamberlain, W. J. Bass, J. K. McGoodwin. EXCURSION TO HALES BAR LOCK AND DAM.-R. H. Williams, Chairman; John A. Patten, Newell Sanders, George M. Guild, Capt. A. B. Putnam. EXCURSION TO ROCK-WOOD.-F. H. Clymer, Chairman; T. L. Brown, T. A. Wright, J. P. Tarwater, T. L. Peterman. INSTITUTE HEADQUARTERS.-The Hotel Patten. THE first session, held Thursday evening, Oct. 1, in the Banquet Hall of the Hotel Patten, was called to order by Capt. H. S. Chamberlain, Chairman of the Local Committee, who, in behalf of the city of Chattanooga, extended a hearty welcome to the members and guests of the Institute.

Nov 1, 1908

By P. van Meurs, C. van der Poel

From observations of the linear displacement of oil by water from a porous medium as visualized in transparent models, new insight into the mechanism of vircous fingering, as occurring in the case of unfavorable oil-water viscosity ratios, has been obtained. A mathematical description of the observed phenomena leads to formulas. expressing both oil production and pressure drop across the formation as a func-tion of cumulative water injection with the oil-water viscosity ratio as a parameter. Theoretical results are compared with those obtained from scaled laboratory experiments in sand-filled rubes in which water was injected at the one end and production was obtained from the other end. In the second part of the paper the same principles are used to calculate a more realistic production scheme in which production of oil and water is obtained from wells regularly distributed over the field. Results show satisfactory agreement with production data of an actual oil field. Application of the theory is extremely simple as only a limited number of readily available parameters have to be known and results are presented in an analytical form. INTRODUCTION When oil is displaced from a porous medium by water having a viscosity lower than the oil. the oil-water interface is essentially unstable and has the tendency to break up into what are called "fingers" or "streamers". This Viscous fingering has been noted before by Engelberts and Klinkenberg' and has recently been demonstrated in transparent models by van Meurs-. It is highly questionable whether it is at all possible to perform relative permeability measurements In the laboratory reproducing the same distribution of water and oil in the cores as Present in practice. Therefore, we based our descriptive theory on an idealized model which was "tailored" to the fingering mechanism as observed in transparent models under scaled conditions. This approach was the more attractive, as a highly simplified model had already yielded an adequate description of the process. Though we are aware our theoretical approach can be extended in several ways, it is given here in its simplest form to explain the fundamental principles and to avoid complicated formulas. SIMPLEST CASE OF A LINEAR DRIVE Observations and Theoretical Model In Fig. 1 a series of photographs shows how water penetrates into a formation saturated with an oil which is considerably more viscous than the water. The technique for obtaining these photographs, using transparent models, has already been described?. The fingers can be clearly observed and are seen to be mainly parallel to the flow direction. Note that the contours of these fingers are not smooth but show protrusions of water enclosing oil pockets.

By John V. Beall

Let's start at the beginning, Mr. Turner. Where and when were you born? In Lansing, Mich., on July 31, 1880. And what was your education? I went to the University of Michigan, where I got an A.B. degree in 1902; then to the Michigan College of Mines at Houghton, graduating from there in 1904 with a B.S. and an E.M. What was your first job in the mining industry, Mr. Turner, and what were you paid? In the summer of 1902, 1 was a field assistant for the U. S. Geological Survey in southwestern Idaho and southeastern Oregon, working under Israel C. Russell, professor of geology at the University of Michigan, who incidentally, had just returned from an expedition to study the effects of the eruption of Mt. Pelee, on Martinique. I was paid $60 a month and found; in addition to doing geologic and hydrographic work, I cooked many of the meals for a party of four, and wrangled four horses. I slept for four months under the stars, without a tent.

Jan 1, 1949

By J. F. Myers

AT the Regional meeting in Columbus, Ohio, in September 1949, the authors presented a progress report of the first year's operation with a Hardinge tricone mill in closed circuit with a Dorr hydroscillator. The present report covers our findings on this grinding circuit to January, 1950. In order to clarify our position, the authors wish to state that no invention or discovery is claimed. The Tennessee grinding circuit is simply an engineered arrangement of known equipment arranged to incorporate all of the recognized efficiency factors of comminution as they are known today. As we concluded our first report, it was not clear how effective the Tennessee mode of operation would be on harder ores. The only information we had at that time was that the Bond grindability test at 48-mesh gave 6.04 g of undersize per revolution. A later test on the same sample at 100-mesh reduced this to 2.04 g, which is definitely in the harder ore class, and which makes the reported 8.80 kw-hr per ton of -200-mesh produced a very creditable figure.

Jan 1, 1950

By AIME AIME

T HE 121st meeting of the Institute held in New York City, February 16 to 19, 1920, was a great success despite vicissitudes of weather of unusual severity. On account of tremendous snowstorms, only two members of the Canadian contingent arrived, and several of our members from the west arrived thirty hours late. Two weeks prior to the meeting, the heaviest snowstorm in 34 years wrecked the surface transportation in New York; and it was only by special dispensation that arrangements were effected, with the New York Street Cleaning Department to clear away 39th street in front of this building so that vehicles could reach the curb. The total registration of members and guests was 1138.

Jan 1, 1920

By Cadwallader Evans

MY endeavor in this paper will be to tell something of the accomplishments and current problems of the anthracite producer and to suggest some of the avenues for technical development that seem to me to be the most necessary and likely to bear fruitful results. The several subjects, that I find of most interest will be taken up individually with brief reference to the future trend. Underground Mining and Loading ?In this field great progress has been made in the last twenty years, beginning with the introduction of the scraper system. The electrical hoists for the operation of scrapers have been improved, and give little trouble, but there is an open field for the improvement of the auxiliary apparatus, particularly in the application of roller-hearing sheaves to the guiding of scraper ropes. Also notable in the last six or seven years is the introduction of shaker chutes, so that far more anthracite is now loaded over them than by scrapers. This trend should continue to be manifest, particularly if those who are looking ahead and who are charged with the development of this specialty continue constantly to study and improve the mechanical design of their shakers.

Jan 1, 1938

By P. P. Gregory

ESTIMATION of re- serves in prorated sand fields has been discussed by S. A. Judson, H. D. Easton, Jr., and W. A. Schaeffer, Jr., in a paper that appears in Vol. 114 (1935), of the A.I.M.E. TRANSACTIONS. The purpose of this present paper is to extend the investigation to prorated flush limestone fields and to outline a method of procedure in determining the amount of oil originally in place and the amount of oil that can be recovered from such fields. Although it is possible to use the decline curves to estimate the amount of recoverable oil in certain limestone fields that are allowed to produce the oil at or near capacity production, such a method cannot be used in fields under severely restricted production rates. The problem is exceedingly complex due to fluctuation in the allowable rates of oil production over a wide range and at frequent intervals, and especially because of the heterogeneous nature of the reservoir itself. A well completed in a large solution cavity, capable of producing great quantities of oil per day, may be offset by a well of very limited capacity. Also, it is di5cult to arrive at an average figure for porosity in a given limestone reservoir due to abrupt variations in the character of limestone, in many instances even between two ad- joining wells. It is a safe statement that uniformity of porosity and permeability in limestone reservoirs .is nonexistent. It is evident, therefore, that the method of estimation of re- serves on the basis of per-acre content can give only approximate results.

Jan 1, 1935

By J. R. Thoenen

IN five years mineral wool has grown to a thirty-million-dollar industry from one whose output was valued, in 1933, at $1,700,000. Ten years ago, in 1928, there were only seven producing companies, with an annual output of but 50,000 tons. By 1936 fifty or more companies were producing half a million tons. The industry is still growing vigorously and will profit from the expected activity in building in 1339, for two-thirds of this material is used for building insulation and to assist in fire-retarding, in both new and old homes. It is as useful in the South, to protect against heat, as in the North, to keep out the cold, if one may speak nontechnically. It is a concomitant of air conditioning, that new addition to the American standard of living that began in theatres, department stores, and railroad dining cars, and is rapidly progressing down to small homes. Here, then, is an industry that is only beginning to have a present, and one with an almost certain important future; one that depends upon mining and the by-products of mining for all of its raw materials; one that every progressive mining man should know something about.

Jan 1, 1939

By J. H. Swisher

An experimental study has been made of the possible mechanisms for foam stability in the system CaO-SiO2-Cr2O3, where Cr2O3is the foaming agent. The degree of lowering of surface tension by Cr2O3 was determined at 1600 "C for high -silica melts. Measurements were also made of foam stability under standardized conditions. The results of the two sets of measurements then were correlated by applying the Gibbs and Marangoni theories of film elasticity. It was demonstrated that the Marangoni elasticity effect is probably the largest single contributor to foam stability, although the high uiscosity of' silicate melts makes some contribution in controlling the rate of drainage of liquid from bubble lamellae. ThE tendency of metallurgical slags to foam has frequently been observed during steel-refining operations. In the open-hearth furnace,this tendency is considered undesirable because it slows down the rate of heat transfer from the burners to the molten-metal bath. On the other hand, it is sometimes desirable to have a "foamy" slag in the basic oxygen converter.' A more effective blanket over the steel bath is made by a "foamy" slag, and loss in yield of metal due to splashing is minimized. In addition, a flush slag can be removed more easily in this condition. Since slag-foaming problems in the field have been attacked largely on an empirical basis, it appeared desirable to obtain a better basic understanding of the mechanism of foam stability. The experimental work was directed almost entirely toward the behavior of Cr2O3 as the foaming agent in CaO-SiO,-Cr2O3 melts. In the first stage of the investigation, the degree of lowering of surface tension by Cr2O3 was determined at 1600°C. The second stage consisted of measuring foam stabilities under standardized conditions. The two sets of experimental results then were correlated by applying various theories of foam stability. For convenience in interpreting the surface-tension and foam-stability results reported here, a portion of the CaO-SiO2-Cr2O3 phase diagram2 is reproduced in Fig. 1. EXPERIMENTAL 1) Surface-Tension Measurements. Very little information is available in the literature on the lowering of surface tension of slags by foaming agents. Kozakevitch 3 mentioned that the addition of 1.5 pct Cr2O3 lowered the surface tension of FeO slightly. In another system, some data on the lowering of surface tension of foaming slags by P2O5 were reported by Cooper and Kitchener.4 The technique used for the surface-tension measurements was the maximum bubble-pressure method,' using a single tube immersed to various depths in the melt. This method has been used extensively in high-temperature systems, such as in liquid metals, slags, and glasses.6,7 It has the advantage that the contact angle between the liquid and the tube material need not be known. The equation used for calculating surface-tension values from maximum bubble-pressure measurements is the Schroedinger equatioq5 which can be written as follows:

Jan 1, 1964

By Goerge F. Weaton

Since 1909, when an agreement between Minnesota's Tax Commission and the University of Minnesota's School of Mines was worked out, it has been the annual responsibility of the School to evaluate and classify the iron ore deposits within the State. These unique duties of an academic institution have provided School officials with an excellent view of the past, present and probable future of the mining industry in Minnesota as the average grade of iron ore (excluding taconite) * diminishes while at the same time it competes with beneficiated taconites and foreign high-grade ores for use in America's eastern blast furnaces. SYSTEM OF EVALUATION In the latter part of November of each year, the Mining Division of the Department of Taxation makes a preliminary study of the active mines which the Department wants the School of Mines to review. These are discussed with the engineers of the Ore Estimate Division of the School of Mines and with the mining companies. After these discussions, a list of the mines of each of the major operating companies is submitted to the Ore Estimate Division of the School of Mines with the request that these properties be reviewed by them as of the next assessment date (May 1st). At the same time, a letter is sent to the mining companies requesting that they submit to the Division their own estimates on the selected mines operated by them, together with all computations, drill records, maps and cross-sections. The mining companies are re- quested to send in this information during the first half of the year, and, as far as is possible, they have always complied with this request promptly. Much of this information received by the School of Mines is of a confidential nature and is treated as such.

Jan 1, 1965

By F. A. Forward, A. H. Ross, J. Halpern

Application of the carbonate leaching process to carno-tite ores has often been limited by the difficulty of obtaining simultaneous high recoveries of uranium and vanadium. The chemical aspects of this problem are discussed and the effect of prior roasting procedures on this discovery is described. IN treating carnotite ores by carbonate leaching it is often necessary to subject the ore to a prior roast. Among the advantages that may result from roasting are: 1) improvement in settling and filtering characteristics of the ore; 2) destruction of carbonaceous impurities that would otherwise contaminate the leach solution and consume carbonate reagent; and 3) substantial increase in extraction of vanadium, which is usually low when the un-roasted ore is leached. Recovery of vanadium may be an important factor in processing carnotite ores, and the fact that vanadium is usually recovered in good yield by acid leaching has often been an economic advantage over results obtained with carbonate leaching. It has been found that response of an ore to carbonate leaching, following roasting, depends primarily on its composition and on the conditions of the prior roast treatment, particularly with regard to the roasting temperature, the atmosphere maintained above the charge during roasting and cooling, and the presence of certain reagents. These factors, especially the last, virtually determine the extractions of uranium and vanadium attainable by carbonate leaching, as well as the reagent consumption on leaching, whereas adjustment of the leaching conditions has only a limited influence. These variables were examined systematically to elucidate roasting and carbonate leaching of carnotite ores and to establish a treatment yielding high recoveries of both uranium and vanadium. Tests were conducted on samples of four different Colorado Plateau ores, described in Table I. Roasting Procedure: The roasting tests were conducted in an electrically heated furnace in which the temperature was controlled to ±15°C. The ore (usually a 500-g charge) was ground to —100 mesh, mixed with the desired reagent, and spread in a silica tray to a bed depth of about 1/2 in. During the roast the charge was rabbled at intervals of 15 min. To provide free access of air the furnace was usually ventilated; however, in a few experiments a controlled atmosphere such as carbon dioxide or hydrogen was maintained above the charge. Leaching Procedure: The pulp, generally comprising 500 g of ore and a 2000-cc solution containing 80 g per liter of Na2CO8 and 20 g per liter of NaHCO3, was agitated in an autoclave at 120°C, under 30 psi 02. Samples were withdrawn periodically, and the solution and ore residue were analyzed. Under the conditions employed, maximum attainable extractions were generally achieved in 4

Jan 1, 1959

By AIME AIME

AN unusually interesting meeting devoted to the discussion of the ways and means of improving coal mining practice, through the larger use of machinery underground, was held in the Auditorium of the Engineering Societies Building on March 11. The meeting was organized by the Materials Handling Division of the A. S. M. E. and held under the auspices of the Metropolitan Section of that Society and the National Coal Association. The New York Section of the A. I. M. E., which had been invited to participate, found itself unable to do so formally because of a conflicting date for its March meeting but informally did its part to aasure the success of the meeting. As a result of the discussion at and preceding the meeting, the National Coal Association, through Walter Barnum, chairman of its research committee, has asked the A. S. M. E. and A. I. M. E. to join the Association in a study of the present problems of the bituminous coal industry. Messrs. Harry L. Gandy, Calvin W. Rice and H. Foster Bain have been selected to act as a committee which shall develop plans for a joint program.

Jan 1, 1926

By A. C. Rubel

WHAT does management expect of W and from an engineer? First and foremost, it expects that he should become, and therefore should fit himself in every way to be, a part of management so that he may assume as much and as many of the responsibilities of management as his ability and the opportunities of the job permit. Let me make clear at the start that the profession of pure, technical engineering offers but limited opportunities at the top levels because of the inherent organization of engineering work. The line of succession to top jobs may be likened to a cone with a broad base and an extremely sharp point. Consider any oil company, large or small, or any operating function of that company, and you will find few top engineering jobs in the organization. This is true by the nature of the work handled. There will be a few district engineers depending on the spread of operations, a chief petroleum and production engineer, perhaps a few research engineers, possibly some technical executive assistants, and that is usually all. The road to these jobs is a long one and the competition is tough. The larger the organization the greater the opportunity, but always the ratio of engineers to top engineering jobs is only a small one.

Jan 1, 1947

By V. E. Christensen

AT most smelting plants, forced draft, induced by high stacks or fans, is used to carry the gases away from the furnaces, roasters, or sintering plants. Gases moving under forced draft carry varying amounts of solids in the form of dust and fume. Where the weight of the solids is material, and the metal content high, it is usually profitable to treat the gases to recover these solids. Baghouses, Cottrell treaters, and settling chambers are the common forms of plants used to recover solids from gases. To check on the efficiency of these plants it is necessary to know the volume of gas leaving the plant and the amount of solids carried by the gas. As the volume of gas is equal to the product of the velocity of that gas and the cross-sectional area of the flue, the determination of the volume includes the measurement of the area of the cross section and the determination of the velocity. The velocity is generally measured by means of the Pitot tube and Ellison differential pressure gage, although low velocities are best determined by means of an anemometer. The dust concentration is determined by passing a measured volume of sample through a filter and weighing the dust caught. From this the dust concentration per unit of volume may be calculated. It is necessary to assume that the gas is homogeneous or that each cubic foot of the gas contains the same weight of dust as every other cubic foot. Having the volume of gas passing through a flue per unit of time, and the dust concentration of the gas per unit of volume, the amount of solids may easily be calculated.

Jan 1, 1935

By Robert M. Weidenhammer

For years before the war, Coal had the reputation of being a sick industry. Currently it is operating at peak production and succeeding pretty well in keeping out of the red. But, says Mr. Weidenhammer, it will have a relapse as soon as the war ends unless (1) working capital can be built up; (2) it gets the support of the people and Congress; and (3) a truly long-range national fuel policy is formulated.

Jan 1, 1943

By Richard W. Smith

Why are we losing our liberties? (1) . . . because our local chambers of commerce come to the National Chamber's annual meeting, vote for a policy on federal economy, and then go to Capitol Hill and ask for a federal project for their area. (2) ... because our mining men ask for a subsidy to mine submarginal deposits that can't be economically mined in a free economy. (3) . . . because 18,000 men and organizations all over the country recently wired or wrote a Congressional committee asking that the Army Engineers be exempt from the President's power to reorganize the Executive Branch of the government under the recommendations of the Hoover Commission.

Jan 1, 1949

Thomas Haight Leggett, London, Eng. (communication to the Secretary): Mr. Hammond has given us a concise yet complete description of the Witwatersrand gold-fields, and the character of the operations which have resulted in their remarkable development.

Jan 1, 1902

By H. J. Gerritsen

From presently available components a portable, rugged, reliable apparatus can be built which will be able to detect methane concentrations of 0.1% and lower in air. Sensitivity and design considerations of the apparatus are given. Ways to build even simpler and cheaper apparatus in the future are indicated. Traditionally the problem of detecting and monitoring the presence of dangerous gases present in small concentrations in air has been a difficult one. Whether canaries,' or sophisticated chemical or thermal conductivity methods are used, they seem to be either slow, cumbersome, or otherwise not completely satis factory. A seemingly natural way of gas detection is to measure the strength of absorption undergone by light of a wavelength that the gas to be detected absorbs. This method has been difficult to apply in view of the low power output over a narrow wavelength range in the infrared from traditional glow bar light sources. Besides, the apparatus to select such a narrow band of wavelengths is quite costly and complex. The use of a laser solves these problems simultaneously. Although a variety of lasers are available to detect a variety of gases (such as carbon monoxide or methane) whose early detection would be desirable, this paper deals exclusively with the use of lasers for methane detection. ABSORPTION SPECTRUM OF METHANE IN AIR The absorption spectrum of pure methane is very well known.2-4 There are four fundamental vibrations, all occurring in the infrared of which only two absorb strongly. They occur at 3.3 µ and 7.7 µ. The absorption spectrum is quite complicated due to the fact that the methane molecule can rotate in a variety of rotational quantum states. These rotational states are furthermore split by anharmonic forces such as the Coriolis force.4 When methane is present in air at atmospheric pressure, much of the very fine structure due to the anharmonic force is washed out since the pressure broadening is of the same magnitude as the splitting due to anharmonicity. For most of the spectrum at 3.3 µ, the rotational lines are typically separated by 0.01µ while the individual linewidth is 0.0001 µ. It is thus very important that the laser emit at a wavelength that coincides with one of these rotational lines. Before elaborating on the point that such a laser exists and how it performs, it is necessary for later discussion to point out that in the

Jan 1, 1967

By Reynold Q. Shotts

Data are presented which show that fractions of varying densities-from the same coals are oxidized at different rates by nitric acid. From oxidation data, the approximate quantity of "bright" and "dull" components may be calculated. Definite relationships between oxidation rate and rank are shown for density fractions from at least two bituminous coals.

Jan 1, 1950

By H. S. Price, J. C. Cavendish, R. S. Varga

A numerical formulation of bigh-order accuracy, based on variational methods, is proposed for the solution of multidimensional diffusion-convection-type equations. Accurate solutions are obtained without the difficulties that standard finite difference approximations present. In addition, tests show that accurate solutions of a one-dimensional problem can be obtained in the neighborhood of a sharp front without the need for a large number of calculations for the entire region of interest. Results using these variational methods are compared with several standard finite difference approximations and with a technique based on the method of characteristics. The variational methods are shown to yield higher accuracies in less computer time. Finally, it is indicated how one can use these attractive features of the variational methods for solving miscible displacement problems in two dimensions. INTRODUCTION The problem of finding suitable numerical approximations for equations describing the transport of heat or mass by diffusion and convection simultaneously has been of interest for some time. Equations of this type, which will be called diffusionconvection equations, arise in describing many diverse physical processes. Of particular interest here is the equation describing the process by which one miscible liquid displaces another liquid in a one-dimensional porous medium. The behavior of such a system is described by the following parabolic partial differential equation:

Jan 1, 1969