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By Norman Patton

THE subject assigned is so broad that thorough discussion is well-night impossible within the space allotted, and further, few specific data are available upon which to predicate conclusions concerning the efficiency of present methods of distributing anthracite. This paper treats briefly the various agencies through which both primary and secondary distribution are effected, the methods of transportation and the general interrelation of production, demand, inventories and price. AVENUES OF DISTRIBUTION "Three distinct types of primary distribution are common in the marketing of anthracite. First, though not most important, is the sale by the producer, or operator, direct to the consumer. These sales, other than to employees and the local trade, are generally confined to steam sizes for industrial uses, and are consigned to the sidings or docks of the consumer. Sales of this type often are so closely priced to compete with oil and bituminous that the addition of even a small dealer's margin is sufficient to increase the cost to the point where the business might be lost. Second, the operator sells to a wholesaler or broker for subsequent resale, either to a retail dealer for clearance through his yard or direct to large consumers. Usually this method of distribution is employed by the smaller operators, who do not find it economically feasible to maintain extensive sales organizations. In most instances, the wholesaler retains some 5 per cent for his services, paid, of course, by the producing company whose anthracite he handles. He may, and frequently does, handle the output of several different companies, suited to the varying needs of the

Jan 1, 1935

By P. Chiotti, R. J. Hecht

Vapov pressure data of solid and liquid alloys along with phase diagram data WERE employed in calculating the thermodynamic properties for the Ca-Zn system. The relative excess partial molal free energy for zinc in the liquid alloys was fitted to the relation wnvre i is we tvmpvrutiirc in ucgrees neivtu ana in is the tr~ole fvaction. Relations for the standard free energy of fortnation for the eight cornpounds were developed. ThE phase diagram for the Ca-Zn system as determined by Messing et a1.' is reproduced in Fig. 1. Earlier work on the phase diagram has been summarized by Hansen and Anderko2 and the very limited thermodynamic information for this system has been reviewed by Hultgren et a1.3 The heat of fusion for the compound CaZn2 has recently been determined to be 9260 cal per mole.4 Solubility data for calcium in zinc for the temperature range of 650" to 725°C were fitted by the relation and reported by Johnson and Dilloon5 In the present investigation zinc vapor pressure data were obtained by both the dewpoint and Knudsen methods in order to calculate the thermodynamic properties for liquid and solid alloys. The dewpoint method as employed in this work requires that only one of the components be significantly volatile, in this case zinc, and that the vapor pressure of pure zinc be known. For calculation purposes the vapor pressure data for pure zinc3 were fitted to the relations; for temperatures below 692.7K, the melting point of zinc. The corresponding free-energy relations for vaporization and sublimation of pure zinc are respectively. Some of the calculations also required knowledge of the free energy of fusion of zinc and calcium and the free energy for the 721°K allotropic transformation of calcium. The free energy of fusion of zinc was taken to be the difference between Eqs. [4] and [5], or The free energy of fusion and transition for calcium were based on the enthalpy values of 2040 and 222 cal per g-atom, respectively, as reported by Chiotti et al. 4 and the heat capacity data given by Hultgren et a1.3 and are represented by the relations, In the latter expression the difference in heat capacity between the a and 0 forms of calcium was neglected. MATERIALS AND EXPERIMENTAL PROCEDURES The metals used in preparing the alloys were Bunker Hill slab zinc, 99.99 pct pure, and Ames Laboratory calcium. The average impurities in the calcium in parts per million by weight, ppm, were N-17, H—77, Ba—216, Mg-15, Si—7, C—157, and Fe—9. The zinc was cleaned in dilute nitric acid and the calcium was used as received. The calcium was stored and handled in an argon-filled glove box and when removed from the dry box it was kept in an argon-filled desiccator. Tantalum was found to be a suitable alloy container. The alloy components were contained in a 1-in.-diam cylindri-

Jan 1, 1968

It was a pleasure listening to this paper. Gary Works' problems were a lot more extensive than the trunnion bearing problems encountered at the Weirton Steel Division. In our two-vessel shop bearing failures are critical in that with a bearing failure on an operating vessel and the second vessel under rebuild, we are down until the vessel rebuild is completed or the bearing is repaired. The first bearing problem at Weirton occurred after we had been operating three years. The failure occurred during the 8th heat following "bum-in" of the vessel. Immediate steps were taken to change the damaged float bearing without an extensive search for the reason the bearing failed. Once the campaign was run out the bearings were inspected and found to be damaged. Field checks revealed that the bearing pedestals were not properly located and as a result the freedom of the float bearing was restricted. The trunnion pin end to end dimension had decreased due to distortion and deflection in the trunnion ring. These dimensions were within tolerances. The damage to our bearing was similar to that in the exhibits from U.S. Steel-Gary Works. Steps taken to correct what was found in the field checks were as follows: 1. The pedestals were relocated to center the bearings. 2. 4" diameter pins were installed to locate the housing in the pedestals. 3. The bearing pedestals were opened up to allow the bearing housing to move slightly in the pedestal. 4. Lubrication fittings for greasing between the bearing housing and the pedestal were installed.

Jan 1, 1972

By James Douglas

At this last meeting of our Institute for the year 1899, it is appropriate that we should look back at the past. To review the century's progress in the exact sciences and the resulting arts that fall within the scope of our labors is beyond my ability. But I wish to draw your attention to some phases of that progress, almost as important, which lie within the zone of sociology, touching at so many points the domain of applied technology. One of these is suggested by the library of technical literature which this century has produced —not the least important contribution to which is our own Transactions. The nineteenth century has witnessed the beneficial spread of democracy in politics. Under the impulse, to no small degree, of the same spirit, there has grown up a brotherhood of fellow-workers and a sense of fellow-ownership in the secrets of nature. Though the Patent Office has assumed such proportions as to hare become a source of national revenue, and a multitude of inventors, great and small, are seeking through its agency to secure some pecuniary profit from their devices, there is even greater eagerness among both interested and disinterested workers in the field of technology to publish their observations, and even their discoveries, and to give them to the world without remuneration. The motives influencing the great body of writers who, without any pay, use the technical journals and such media of communication as our Transactions, in order to give to the brethren of their craft the results of

Jan 1, 1900

By J. Szekely, R. G. Carr

A method is presented which allows the extension of the Ergun equation for the description of gas flow through packed beds in a nonisothermal regime. The pressure profile in the packed bed is calculated by the establishment of a differential energy balance and the iterative integration of the integral equation thus obtained. The predicted values of the pressure distribution were found to be in excellent agreement with those measured experimentally, under carefully controlled conditions. MANY metallurgical processes are carried out in systems in which a gas stream and particular solids are contacted in a packed bed arrangement under strongly nonisothermal conditions. Ore sintering, the firing of pellets, the operation of regenerators, blast furnace technology may be quoted as examples. Although many aspects of these systems have been extensively studied, an important variable, the pressure distribution and the relationship between pressure head and flow rate, received only little attention to date. The purpose of the paper is to present a brief survey of relevant previous work, followed by a more rigorously formulated model, together with experimental results that afford ready comparison of theoretical prediction with measurement. PREVIOUS WORK A great deal of information is available in the chemical engineering literature on flow phenomena in porous media.' The experimental results pertaining to gas flow were generally interpreted in terms of models based on the analogy with the flow through a pipe of an incompressible, isothermal fluid. Of the numerous, semiempirical correlations that have been proposed to relate pressure drop to the volumetric flow rate, the Ergun equation2 is generally regarded as the most satisfactory: The strong nonisothermality of the metallurgical systems previously mentioned would render the direct applicability of Eq. [I] rather doubtful as both density and viscosity are temperature-dependent. Ergun has used Eq. [I] for estimating the pressure drop in the stack region in the blast furnace by neglecting the viscous term and evaluating the gas density at the integral mean temperature.3 His calculations showed a rather variable agreement with measurements and it was uncertain whether the discrepancy found was attributable to the model or to the inaccuracies often inherent in measurements on an industrial scale. Other work on nonisothermal systems includes studies of the pressure distribution in sinter beds, notably by Voice et a1.4 and Mitchell.5 Mitchell developed a method involving the subdivision of the bed into several zones and assigning average property values (temperature, gas density, and so forth) to each zone. The pressure drop was then calculated for each zone by using an expression analogous to Eq. [I]. This method was an improvement over that described by Voice et al., but even here prediction and measurement differed by as much as 30 pct in certain cases. It would appear that no really satisfactory methods are available for the prediction of pressure drop in packed beds with a strongly nonisothermal regime. The method involving subdivision of the bed into small enough sections, that may be regarded as isothermal, would show promise; however its validity has to be tested by both a rigorous formulation and comparison with experimental data obtained under controlled conditions. In the following a formulation is presented together with experimental data allowing ready practical evaluation of the theory. FORMULATION The mechanical energy balance over an infinitesimal section of a packed bed may be written as follows:

Jan 1, 1969

By P. S. Rudman

Crystal-structure occurrences in binary phase diagrams of fifth- and sixth-period elements, zirconium through palladium and hafniun through platinum, are surveyed with the conclusion that average .group number GN is the dominant correlative. This is interpreted in terms of curves of enthalpy differences between competitiue structures that are continuous func -tions of GN. It is further reasoned that the absolute formation energies may also be continuous functions of GN and if so can be simply obtained from the regatives of the heats of sublimation of the elements. It is shown that from such a heat of formation-GN plot the heats of mixing of alloy systems can be quantitatively predicted. For example, for sixth-period alloys very large exothermic heats of mixing are predicted for systems that span GN = 6 (i.e., Hf-Pt, Ta-Os, ...). Thermodynamic data with which to test these predictions do not appear to be available. If in the latter transition (A subgroup) elements we eliminate from consideration the fourth period where magnetic terms contribute to crystal-structure stability, as shown in Table I, there is a very regular sequence of structures. Using the group number (GN) assignments of Table I, which differ from the usual assignments of 8 to the elements listed as 8 through 10, it is perhaps trivial to say that the phase occurrence is a unique function of GN. However, the interesting aspect of alloys from among these elements is that the alloy structures also appear to correlate with GN. The GN for an alloy is given as GN = SixiGNi, where xi and GNi = atomic fraction and GN of component i, respectively. It is difficult to credit anyone in particular with having discovered this correlation, so many people have implicitly or explicitly employed it in the last 10 years. However, Bloom and Grant' in their correlation of s-phase occurrence with total number of d + s electrons were certainly one of the first to appreciate the correlation and Hume -Rothery2 appears to be responsible for the use of average GN as defined above. Only in the last few years have the phase diagrams of enough alloy systems been determined for this correlation to be surveyed with any degree of completeness. We shall here, in an abbreviated format, summarize the available phase-diagram literature and discuss some consequences of the GN correlation. BINARY DIAGRAM SURVEY In Figs. 1 to 3 the phase occurrences are summarized. In Fig. 4 the occurrence limits for the more common structures are summarized. That the GN of an alloy falls within the occurrence limits of a particular structure is a necessary but not a sufficient condition for the appearance of that structure. The preceding figures certainly illustrate that GN is a dominant correlative for structures of these elements. Many of the diagrams have complications, with ordering and other phase changes occurring in intermediate phases, that cannot be clearly accommodated in such a schematic survey and have hence been left out. Such omissions cannot, however, negate the GN correlations discussed here. Relative atomic size is also an important crystal-structure determinant and since atomic size varies quite regularly with GN for these elements it is possible that the apparent GN correlation is basically a size correlation. In Fig. 5 relative size occurrence limits are given for intermediate phases and extended terminal solutions. The relative volume, ?v/(v) - 2(vA - vB)/(vA + uB), has been taken as the measure

Jan 1, 1968

By T. M. Dr. Drown

(Read at the Philadelphia Meeting, February, 1878.) ZINC is, as is well known, very brittle at a temperature of about 210° C. (410° F.), and may then be readily pulverized in a mortar. By sifting it may be obtained of uniform grain. I have been accustomed to prepare products passing through 40, 60, and 80-mesh sieves, and also by bolting through a fine handkerchief. The principal analytical uses to which I have hitherto applied this material are to the reduction of iron directly from the ore by heating it with the pulverized zinc, and the reduction of ferric to ferrous compounds in solution. In the first case the pulverized ore, 0.5 gram or less, is intimately mixed with about ten times its weight of the pulverized zinc (the finer the zinc the better), in a porcelain crucible, and this mixture is covered with about the same amount of zinc. The crucible is then heated at the top of the flame of a Bunsen burner, at a dull red heat, for about ten minutes. The crucible should not be covered. When cool, the crucible, with its contents, is placed in a flask treated with hot dilute sulphuric acid, and brought quickly to a boil. The zinc and reduced iron are dissolved in a few minutes and the flask is then tightly corked and allowed to cool. When cool, the iron is directly titrated by potassium permanganate.

Jan 1, 1878

In recent years, with the advent of new steelmaking procedures, the emphasis has turned away from conventional teeming and has been directed toward continuous casting. This paper points out the fact that there are still new methods being considered to decrease the problems and costs associated with conventional teeming. Although Inland has had no experience with the repair of mold lugs, we do find some problem with damaged ears associated with mechanically capped steel. When pouring bottle tops, any crane movement or leak from the pouring nozzle may result in steel over the top of the mold which, in turn, may result in the shearing of the mold lugs during stripping. Recent back pouring practices increase the chances of this occurring. At Inland's steelmaking shops, we have tried to combat this problem by various methods such as burning the steel from around the top of the mold at the pouring stand with oxy-gas torches. Last year, No. 4 BOF began a conversion from round to elliptically shaped bottle top caps. This change has greatly reduced the chance of splashing due to crane swing by increasing the dimension in the direction on normal swing. The answer to this particular problem is, however, tighter control of pouring performance. We are presently engaged in a process of re-education of personnel and experimentation with different materials and designs of nozzles, heads, and sleeves to help us achieve our goal.

Jan 1, 1972

By B. Ramaswami

INTERNAL oxidation occurs readily in silver due to the rapid diffusion of oxygen in silver.' It has a marked effect on creep in polycrystalline silver2 and raises the critical resolved shear stress in single crystals of silver.3 However, the effect of oxygen on the work-hardening parameters of silver is not known. It is the aim of this paper to describe the effect of internal oxidation on the work-hardening characteristics of single crystals of silver and an Ag-0.1 at. pct A1 alloy. The materials used were: 99.99 pct Ag from Handy and Harman and 99.993+ pct A1 from Alcoa. Single crystals, 6 mm by 6 mm in cross section of silver and Ag-0.1 at. pct A1 of mo.5 orientation, i.e., the orientation with the Schmidt factor m = 0.5. were grown by the Chalmers technique.4 One set of specimens, referred to herein as oxidized specimens, was annealed at 940°C for 24 hr in a muffle furnace, in air, and furnace-cooled to room temperature. Another set of specimens, referred to as nonoxidized specimens, was annealed in oxygen-free helium at 940°C for 24 hr and furnace-cooled over a period of 7 hr to room temperature. The annealed single crystals were tested at room temperature in a floor-model Instron testing machine. The results are presented in Figs. 1 and 2. A

Jan 1, 1965

Last October a committee was appointed by The War Service Association of Manufacturers of Solder and Bearing Metals, Inc. to consider the report of the U. S. Bureau of Standards to the Conservation Division of the War Industries Board, a letter of the War Industries Board, and the discussions of this letter as reported at the meetings of association and to summarize the information thus obtained. The report of this committee has just been printed. The committee agrees with the Bureau of Standards that 99 per cent. tin can be used. It also finds that a very small amount of lead might increase the tendency of the bearing to crack and that lead has a hardening effect on babbitts up to a possible limit of 10 per cent. of lead. Still in the so-called genuine babbitts, in the presence of lead a certain proportion of low melting point eutectic is introduced which admits of the bearing being poured into thinner sections and is decidedly advantageous in the die-casting process in producing a much smoother casting. But the committee recommends that the Bureau of Standards thoroughly investigate this point. Lead-base babbitts, to give satisfactory service, must be carefully made of the proper raw materials. The bronze hearing that has been thoroughly tinned and containing the thinnest possible babbitt lining is now becoming recognized as the ideal bearing. The compositions, recommended by the committee are as follows:

Jan 2, 1919

By H. M. Chance

THE present value of most coal properties resides largely in the coal remaining to be mined, which thus constitutes the most important asset. The object of this paper is to discuss methods commonly used in computing the value of mineable coal. To distinguish clearly between such coal values and the values of other property, the several kinds of property values may be divided into classes; this is necessary to avoid unintentional omissions of items of importance. VALUE OF COAL RESERVES Judicial decisions prescribe, and appraisers commonly accept, current sales value as the preferred means for determining the value of transferable property. With few exceptions a property is worth the sum that can be realized from its sale by a willing seller to a willing buyer, a sale in which compulsion urges neither party, and between whom there is no community of interest to fix a value; or it is worth at least as much as a responsible buyer will offer for it. Actual sales of like property or bids from responsible buyers for the property, or for substantially like property, are the best established methods for determining values. Only in the absence of such sales or bids can valuations by other methods be entertained, and only for reasons of weight can sales values be set aside. Sales of coal in the ground, as customarily carried out through lease, under royalty agreements, are therefore the most trustworthy means available for determining the value of coal reserves.

Jan 6, 1926

By R. Hogg, R. Schaller, P. Luckie

OVERVIEW This paper is a review of two fine particle processing unit operations - classification and mixing. It may appear that these two processes have nothing in common. In fact, the simplified symbols used to represent them on flowsheets - a tipped equilateral triangle such that the base lies along the vertical - are totally reversed. For classification, a splitting action, the apex of the tipped triangle is to the left of the vertical base. A horizontal flow arrow indicating input is drawn to the apex while two horizontal flow arrows indicating outputs are drawn from the top and bottom of the vertical base, respectively. On the other hand, for mixing, a blending action, the apex of the tipped triangle is to the right of the vertical base. Two horizontal flow arrows indicating inputs are drawn to the top and bottom of the vertical base, respectively, while a single horizontal flow arrow indicating output is drawn from the apex. Classification is the process whereby a collection of particles is separated into two or more portions differing in some physical or chemical property. Mixing is the process whereby two or more portions of particles differing in some physical or chemical property are combined into a collection of particles. The common bond that links them together in the same review is the fact that they both require dispersion of the particles in order to achieve successfully their individual objectives.

Jan 1, 1980

By Eugene H. Cowles

Now that a determined public effort is being made on this side of the Atlantic to create a steel ship-building industry, the materials that are demanded for this purpose assume a new interest to the American metallurgist. In the past, the uses of metals in this country have been almost exclusively connected with the land, while in England their application to marine purposes has been equal in importance to that on shore. In the future the same should be the case here. This is the reason for bringing a somewhat nautical or rather naval topic before a body the chief interests of which are supposed to lie in the mines and mountains of the interior of the country. A modern war-ship or " ocean-grayhound" (like the City of Paris) is an epitome of philosophy and human skill. In her graceful lines we have, as Ruskin might quaintly say, a " builded geometry ;" while in her wonderful machinery for motion, offensive and defensive, we have the summation of the ideas of a host of students who have, at one time or another, during the course of a hundred years of her evolution, contributed their intellectual mites to render her a thing of beauty and of power. Notwithstanding her present perfection, the modern ship contains room for further improvement. One of the most important things about her is the propeller. This active member is of more impor-

Jan 1, 1890

By L. R. Jackson

It is convenient to have a consistent system of notation that will allow the representation of the entire range of complex stresses from hydrostatic compression to hydrostatic tension on plastic flow in a single diagram. Such a system is provided by making use of the fact that any complex stress system can be resolved into a hydrostatic tension or compression and a pure shear. Consider a stress system having the principal stresses This system can be resolved into a new system consisting of the three components and three pure shears. If Sm is positive, the net stress effect is hydrostatic tension; if it is negative, the effect is hydrostatic compression. In order to produce a systematic notation, a quantity that will be referred to as the "triaxial ratio" will be defined by the equation _ Sm Tr = Sm - Sm is given by Eq. I and Sl is the absolute magnitude of the largest principal stress without regard to sign. Table I lists the triaxial ratios for various common systems. Table i.—Triaxid Ratios for Various CommonSyslems Triaxial Ratio Stress System Tr Hydrostatic compression — SI - —St - -S³............................... -1 Torsion or shear -SI - S². S² = O..... O Simple tension SI. SI = SI = 0......... +0.33 Biaxial tension SI = S² S³ - 0......... +0.66 Hydrostatic tension +SI - +S³ = +S³. +1.00 Representation of Strains Strains will be plotted as "true" strains according to the system proposed by Ludwik.1

Jan 1, 1945

By W. R. Ingalls

IN THE years immediately preceding 1914, the American people earned an aggregate income of 33 to 34 billion dollars, of which they saved about five billion, the annual saving being expressed mainly in the form of houses and railway extensions; to a less extent in public utilities, public improvements, factories and mines; and to a very small extent in foreign investments. It appeared needful that we should save and invest annually in these ways about 15 per cent. of our aggregate income in order to keep the development of our plant, so to speak, ahead of our steadily growing needs. The common knowledge that at present our housing and railway facilities are inadequate suggests immedi-ately that we have been running behind the pre-war ratio of reinvestment. Since 1919, we have not had any carefully prepared, authoritative estimates of the national annual income. However, with some experience in this subject, I have ventured to make rough estimates, which rest on solid foundations, although some rather empirical develop-ments are involved. Such estimates would be consid-ered good work in this field if they fell within limits of 10 per cent., plus or minus. Even so, these data are more useful when quickly available than more accurate data that are belated; for recognizing that there is a margin of error we can at least get a reasonable and approximate idea of how things are going.

Jan 2, 1923

By Edward A. Vitunac

The emerging importance of pneumatic conveying systems for bulk materials is largely due to the economic advantages such systems frequently exhibit when compared to alternate methods. Included in these advantages are relative simplicity, ease of installation, flexibility, ease of maintenance, cleanliness, safety and ease of automation to the degree desired. In general, installed costs favor a pneumatic system when compared to competing mechanical systems if the transporting distances are long or to and from many points. In addition, supplemental use such as cooling, heating, or drying may supply the incremental value required to justify its selection.1 The main disadvantages of a pneumatic system are the greater horsepower required per unit weight of material conveyed, material limits in abrasiveness, and density. In addition, material breakage tends to increase at changes of direction and at any obstruction such as that caused by the imperfect butting of two pipe sections in the conveying line. Classification of the material at the discharge may also cause problems in dusting and segregation. Materials weighing less than 4 lb per cu ft tend to cause feeding and collecting problems although they can be conveyed easily. Material between 4 lb and 20 lb per cu ft can be handled with fewer problems, but flow rate is hard to predict. The 20-60 lb per cu ft range offers best results, whereas materials of over 60 Ib per cu ft tend to drop out of the air stream and settle in the pipeline unless careful pro- visions are made to prevent this.2

Jan 5, 1968

By A. L. Jr. Pozzi, A. O. Garder, D. W. Peaceman

A new numerical method is proposed for the solution of multidimensional miscible displacement problems. Besides the usual stationary grid associated with numerical procedures, the method uses moving points for which positions and concentrations are computed each time step. Based on the method of characteristics for treating combined transport and dispersion, the method applies equally well to any number of dimensions and, in contrast with other numerical procedures, properly takes into account the physical dispersion, no matter how small. Extensive tests show that accurate solutions of one-dimensional problems can be obtained over a wide range of values of the dispersion coefficient, including zero. They also show that the moving points do not need to be uniformly spaced, and that increasing the number of moving points beyond 2/grid interval does not significantly improve the accuracy of the solution. Two-dimmsional calculations using the new method were carried out to simulate laboratory model displacements in which gravity caused overriding of solvent. Good agreement between observed and computed profiles and measured and computed concentrations of produced fluid was obtained for a viscosity ratio of 1.89; at higher viscosity ratios, fair agreement was obtained Computed results were found to be significantly affected by vertical dispersion, and negligibly affected by dispersion in the direction of flow, in agreement with conclusions based on experimental observations. INTRODUCTION Although miscible displacement processes are potentially of great economic significance, limited progress has been made in developing mathematical methods for predicting the outcome of a solvent flood. Because of the complexity of the partial differential equations which describe multidimensional miscible displacement, numerical methods are a natural approach to their solution. The task of finding suitable numerical approximations to one of the partial differential equations, which involves both dispersion and convective transport, has been particularly difficult. Dispersion in the absence of transport is described by the heat flow equation, a second-order equation of parabolic type. This equation has been very successfully treated by numerical methods. Transport in the absence of dispersion is described by a first-order equation of hyperbolic type. This equation has been treated numerically with some success in one dimension, both by Lagrangian and Eulerian techniques, 1.2 but extension to two or more dimensions has not been satisfactorily accomplished. Usually one of two things happens: either the numerical solution develops oscillations or it becomes smeared by artificial dispersion resulting from the numerical process. When transport and dispersion are considered simultaneously, this numerical dispersion may dominate the low physical dispersivicy that generally characterizes miscible displacement. Stone and Brian2 have developed a new difference equation for treating combined transport and dispersion in one dimension. By suitable choice of certain parameters, they succeeded in markedly reducing both oscillation and numerical dispersion. However, a satisfactory extension to higher dimensions has not yet been found. Peaceman and Rachford3 presented a centered-in-time and centered-in-distance difference equation combined with a 1,transfer of overshoot" procedure which was demonstrated to work well in one dimension. The technique was applied to the two-dimensional miscible displacement problem, but subsequent calculations with zero dispersivity showed little change in results compared with the calculations they presented. This indicates that their method involved a numerical dispersion of the same order as the physical dispersion. The present paper describes an alternate method for solving the combined transport-dispersion

Jan 1, 1965

By W. A. Tiller, W. C. Johnston

The solute distribution ahead of an advancing solid-liquid interface is controlled by varying the momentum boundary layer thickness in the liquid adjacent to the interface. Single pass zone-melting experiments on Pb-Sn alloys are described in which the liquid is caused to rotate in the plane of the solid-liquid interface due to the influence of a magnetic .field rotating in this plane. The variation of the diffusion boundary layer thickness with field strength is determined. DURING the freezing of an alloy a partitioning of solute occurs at the solid-liquid interface, the magnitude depending upon the difference in the solid and liquid solubilities at the interface temperature. Because the diffusion coefficient is so small in the liquid relative to normal freezing rates, either a pileup or a depletion of solute occurs at the interface when the partition coefficient, kO, is either less than or greater than unity, respectively. This solute distribution is completely characterized by i) the solute concentration in the liquid far from the interface, C) the ratio of freezing velocityf, to diffusion coefficient, D, iii) the partition coefficient, ko, and iv) the thickness of the diffusion boundary layer, 6,, at the interface (this assumes that an electric field is not applied across the interface). For a particular system, C ko and D are fixed so that the character of the solute distribution can be changed only by a variation of either f or 6c. As is well known, the freezing velocity can be changed by varying the thermal environment of the alloy. Whereas, the thickness of the solute rich layer can be changed by varying the fluid flow conditions in the liquid. It is the purpose of this paper to describe a technique for controlling the fluid flow conditions in the liquid. During most solidification experiments the driving force for fluid flow arises from either mechanical mixing, thermal convection or electromagnetic mixing. The momentum boundary layer thickness, 6m at the solid-liquid interface, within which negligible movement of the liquid occurs, has been calculated for the special case of mechanical mixing where crystals are solidified by the Czochralski technique.l,2 The calculation of 6m for the case of thermal convection has also been made.3 In some calculations it has been assumed that the momentum boundary layer thickness, 6,, may be equated to the thickness of the diffusion boundary layer 6c, at the interface. However, as may be seen from Appendix I this is only true in very special cases and in general where a is a constant of magnitude determined by the particular liquid alloy. Neither calculations nor experimental data exist for the dependence of upon electromagnetic mixing. In this paper experiments are described in which the liquid is caused to rotate in the plane of the interface due to the torque developed on it by a magnetic field, H, rotating in this plane. The variation of is controlled by the variation of H. A magnetic field rotating in a plane perpendicular to the interface has been used for the purification of aluminum. Experimentally, we determined the variation of 5C with H by using the zone-melting technique of pfann5and a theoretical relationship of Burton et a1.2 pfann5 has shown that, after the passage of one molten zone through a long cylindrical charge of uniform concentration, CO, the solute distribution, C,, in the solid is as shown in Fig. 1. The equation describing this distribution is

Jan 1, 1962

By Edward V. D’Invilliers

In connection with some recent professional work in the coalfields of Western Pennsylvania, with special reference to results of coking operations, I was asked to compile a statement giving the estimated cost of mining coal and manufacturing coke at two hypothetical plants of 500 ovens each, giving the relative yield of coal in coke at each plant; and, upon the average number of working days in each of the past five years, from 1899 to 1903, together with average selling price of coke at the ovens, to prepare an estimate of the relative commercial returns in each district. What seemed at first sight to be a comparatively simple proposition, involving only the ordinary elements of mining and coking costs, became complicated by the lack of standard published records of mining costs and sales, which would be applicable to the subject at issue. Upon searching through the usual channels of Government publicatious and the files of our technical societies and mining periodicals, I was surprised to note the absence of fundamental factors that would approximately meet the case in point. The very elaborate and interesting statistics annually published by the National Government' do not supply the required data for the following reasons:—1. Being reported by arbitrary districts, the average values are too general to be applied to special fields. 2. The value of coal charged to the ovens is apparently based upon the regional average value of the coal if sold in the market, and not upon the cost of production. 3. Some plants only use the slack (a by-

Jan 1, 1905

By R. L. Fleischer, R. S. Davis

BICRYSTAL specimens grown from the melt have been used extensively for investigations of the influence of grain boundaries on plastic deformation. The bicrystals are usually of predetermined orientation prepared by seeded growth from the melt in milled graphite boats. This technique has been described in detail by Chalmers.' Since the direction that the grain boundary follows during growth is affected by both thermal conditions and crystallography, a difficulty arises in maintaining the grain boundary position constant along the length of the specimen. This problem is particularly

Jan 1, 1960