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By R. E. Collins, Paul B. Crawford

Mathematical equations have been derived to show the effect of the slippage phenomomenon (Klinkenberg effect) on unsteady-state gas flow through porous media. The assumption is made that the slippage may be represented by an equation of the type It is pointed out that most of the existing data on unsteady gas flow may be corrected for slippage by a simple change in definition of the dimen-sionless groups. INTRODUCTION Several solutions to the various problems associated with the unsteady-state flow of gas through porous media have been recently presented in the literature.','" The cited publications have resented solutions for flow under ideal conditjons. The principal assumptions involved include: (a) the density of the gas obeys the perfect gas law; (b) the viscosity of the gas is constant; and (c) the gas permeability is constant. Few, if any, actual gases under reservoir conditions are believed to conform with the above, but the ideal solutions do provide the basis for making improved estimates on the performance of gas reservoirs. The purpose of this paper is to show the performance characteristics when assumption (c) is corrected for the slippage phenomenon or the Klinkenberg effect. This is believed to be a step nearer to reality. MATHEMATICAL DEVELOPMENT Case 1. Gas Flow — Ideal Conditions The equations describing the flow of gas under ideal conditions have been clearly presented in the cited literature; however, for completeness of this work they are repeated here. The basic differential equation describing the flow of gas is Equation (6). It may be derived as follows: The continuity equation, the perfect gas law and Darcy's law are combined to give: Manuscript received in the Petroleum Branch office Aug. 3, 1963 or If — is constant, Equation (5) is rewritten to form the basic Equation (6). or for the linear case A dimensionless equation is obtained by dividing through by (pl)z and making the substitutions shown below: The resulting equation is A similar procedure for the radial case leads to the following equations: where and Equations (11), (12), and (13) are those used by Bruce, et al., and Jenkins and Aronofsky for their computational work.

Jan 1, 1953

By J. V. W. REYNDERS

FIRST of all let me express my affectionate gratitude for the cordiality and good will of your reception. On the part of the men I venture to interpret the character of your greeting, not only as a recognition of the position to which you have been good enough to elect me, but also as an expression of your friendly attitude. However, I cannot pass over the tribute of the ladies so casually: Nor does it seem possible to do justice to my sentiments in addressing them collectively. I would feel more equal to the task if I could have the opportunity to talk to them singly, in doing which I know I may count upon their good sportsmanship not to compare notes. There has been some discussion between Mr. Kelly and myself as to our respective duties on this occasion: The precedents are not clear as to whether the retiring or the incoming president is expected to speak at length. Mr. Kelly's argument was that as the incoming president confines himself to promises for the future his field is a broad one and his opportunities for extending his remarks correspondingly unlimited.

Jan 1, 1925

By ARCHIBALD DOUGLAS

AT various times during the past quarter century proposals have been made that the basic Federal mining law of 1872 be repealed or amended, and that in its place a new and simpler law be enacted to provide for the entry upon, working, and the taking up of claims on the unallotted Federal mining lands in our western states and in Alaska. Serious discussion and study have been given such proposals but little has resulted there from, except perhaps a lively interchange of opinion and the conclusion that though the Apex law of 1872 is in many ways highly unsatisfactory and frequently a fomenter of strife and trouble, it still bids fair to remain with us. Under this act a greater part of the non-ferrous mining industry of the United States has developed. With all its short-comings it is the legal bridge that has carried over the innumerable caravans of adventurers and prospectors who explored our mining frontiers. For without any amendments of substance this act has for fifty-eight years been the guide in the location of our western Federal mineral claims and has stood unchanged during the most important period of our mining history. While Federal and state acts and amendments have been ground out by thousands and tens -of thousands the mining act of 1872, with a :strange tenacity, has remained as constant as the Rock of Gibraltar, and under it states, mining districts, and local customs have developed different codes for its application but its fundamentals have been unaltered. "Use doth breed a habit in a man"; until now the application of the law of 1872 has become a second mining nature.

Jan 1, 1930

By William J. Priestley

Much time has been devoted, by metallurgists, to the study of steel after solidification and remarkable strides have been made in the heat treatment of steel, but less knowledge is available of the thermophysical activity of the constituents of steel prior to solidification in the mold. It is known that certain elements added to steel produce marked changes in physical properties, also that other elements added to steel produce similar changes, but we have only meager knowledge as 'to. how these elements combine in steel under different conditions of solidification. It is not sufficient to know, from chemical analysis, that a certain element is present in steel. We should know how this element is in combination with the other elements and whether the combination is such as will give the greatest physical properties. Certain elements go into solid solution with the iron, while others segregate to the grain boundaries and combine with the impurities collected there. Until it is known where an alloy produces the most beneficial effect and a means is determined for controlling its physical location by altering solidification conditions, or otherwise, we will not obtain the maximum value from our alloys. When molten steel freezes, it forms a heterogeneous mass of various crystalline constituents; and as the transformation of steel from a liquid state to the solid crystallized state is a critical step, involving as great a transfer of heat as any other operation in the making of finished steel, a variation in the rate of this heat transfer will have much to do with the arrangement of the various constituents in the solid state. The object of this paper is to show some of the effects on steel caused by variations in the rate of cooling in the ingot mold, particularly as to ingotism, segregation, dendrites, and intergranular material.

Jan 1, 1924

By M. G. Benz, J. F. Elliott

The austenite solidus of the iron-carbon system has been determined using a series of diffusion couples, each of which consisted of a specimen of austenite held in contact with a melt saturated with austenite. After the equilibrium distribution of carbon had been established by diffusion at a specified temperature, i.e. the austenite specimen had become austenite of the solidus conzposition, the diffusion couple was cooled, sectioned and anazlyzed for carbon. The solidus was found to be a straight line: A revised iron-carbon temperature-composition diagram is presented, COMPOSITION has a marked effect on the temperature at which austenite begins to melt and the austenite solidus of the iron-carbon system describing this effect has been the subject of many investigations.1-10 The significant results of these investigations are presented in Fig. 1. The experimental methods and purity of the materials used in them are summarized in Table I. In plotting the data in Fig. 1 no attempt has been made to convert these results to the International Temperature Scale of 1948," except for the data of Adcock,5 as this conversion would do little to reduce the uncertainty that exists as to the position and shape of the solidus. A point of major concern in evaluating these data is that the alloys studied, except those used by Adcock, were not binary alloys of iron and carbon, Table I. Also, it would appear that several of the methods did not permit equilibrium to be established through the system being studied. All that can be said for the results of these investigations is that they indicate only approximately the location of the solidus with the uncertainty as to its location at 1 pct C being approximately 100°C. The current investigation was undertaken to provide reliable data by which the austenite solidus could be established. It was hoped that information on the liquidus also could be developed at the same time, but experimental limitations prevented this as austenite segregated from the liquid on cooling. After a careful study of possible experimental methods and extensive laboratory tests, it was decided that the use of a series of austenite-liquid diffusion couples would provide the most reliable results. This paper describes the method and its results and also includes a complete iron-carbon temperature-composition diagram based on what are considered to be the best available data. EXPERTMENTAL METHOD The diffusion couple used for this investigation consisted of a small cylindrical pellet of austenite held in contact, at a specified temperature, with a melt saturated with austenite. The composition of the cylindrical austenite pellet was chosen to be approximately 0.1 wt pct C less than the estimated

Jan 1, 1962

By Michael Tenenbaum

A REVIEW of process metallurgy of iron and steel during 1944 in many ways reflects the political and military developments of the year. Early in 1944 the tremendous wartime emergency expansion program was virtually completed and the industry directed its efforts to maintaining maximum production wherever needed. The vigorous production programs inaugurated to support the Normandy invasions did not persist as Allied armies approached Germany. General public apathy which developed with the prospect of an early ending of the European fighting was reflected in a general relaxation in armament programs. Toward the end of the year, as the prospect of a prolonged war became real, the entire program revived considerably and the need for steel became acute. Between January 1940 and October 1944 more than 12,400,000 tons had been added to the nation's steelmaking capacities, and over 12,700,000 tons added to the blast-furnace facilities. The total cost of this enormous program was more than two billion dollars. By July 1, 1944, total steelmaking capacity had exceeded 94,000,000 tons, with blast-furnace capacity rated at 68,400,000. Annual steel production, which was 88,900,000 tons in 1943, increased slightly during the past year and was estimated at 89,500,000. Production of pig iron also increased somewhat from 61,800,000 tons in 1943 to an estimated output of 62,500,000 in 1944. This review deals with a few of the numerous factors involved in maintaining the wartime iron and steel program at the level necessary to accomplish this enormous output.

Jan 1, 1945

By N. A. Ziegler

THE chief difficulty in determining oxygen in steels is its tendency to form a variety of compounds. Almost every element, found as an ingredient in steels, maybe expected to be present as an oxide. Some of these oxides have widely differing properties, and consequently behave differently when attempts are made to reduce them by the vacuum fusion method. As I pointed out in a paper published in the Transactions of the A.S.S.T., Vol. 20, No. 1, many experimenters are spending considerable time and effort in attempting to deter¬mine the degree of completeness of the above reactions, and hold different opinions on the matter. In studying this subject the following table, taken from Hodgman and Lange's "Handbook of Chemistry and Physics" may be used as a guide.

Jan 1, 1933

By Herman F. Kaiser, Charles S. Barrett, Robert F. Mehl

The copper-silver system presents several points of special interest in the study of segregate structures. The system is simple eutectic, with limited solid solutions terminal with the pure component metals. The extent of solid solubility decreases with decreasing temperature for both the copper-rich and the silver-rich alloys, thus offering a possibility for the formation of Widmanstätten figures and also a possibility for aging after quenching. In contrast to the structures studied previously the structures in this system are unique in their origin, for one terminal solid solution will precipitate the other, and vice versa. In most of the other systems for which crystallographic data on the precipitation (or transformation) process arc available, either intermetallic compounds or intermediate phases partake in the decomposition process; the absence of such phases thus distinguishes this system. The lattice structures of the two solid solutions are identical in type, differing in lattice spacing by approximately 10 per cent; because of this it seems difficult if not impossible to predict on the basis of present theory either the outward form of the precipitate or the lattice orientation relationships between matrix and precipitate. The eutectic temperature in the copper-silver system' is 779" C. At this temperature copper dissolves 4.3 atomic per cent (7.0 weight per cent) of silver in solid solution; this solid solubility decreases to zero at room temperature.² Silver at the eutectic temperature rctains 14.0

Jan 1, 1935

By Charles S. Barrett, Herman F. Kaiser, Robert F. Mehl

The copper-silver system presents several points of special interest in the study of segregate structures. The system is simple eutectic, with limited solid solutions terminal with the pure component metals. The extent of solid solubility decreases with decreasing temperature for both the copper-rich and the silver-rich alloys, thus offering a possibility for the formation of Widmanstätten figures and also a possibility for aging after quenching. In contrast to the structures studied previously the structures in this system are unique in their origin, for one terminal solid solution will precipitate the other, and vice versa. In most of the other systems for which crystallographic data on the precipitation (or transformation) process arc available, either intermetallic compounds or intermediate phases partake in the decomposition process; the absence of such phases thus distinguishes this system. The lattice structures of the two solid solutions are identical in type, differing in lattice spacing by approximately 10 per cent; because of this it seems difficult if not impossible to predict on the basis of present theory either the outward form of the precipitate or the lattice orientation relationships between matrix and precipitate. The eutectic temperature in the copper-silver system' is 779" C. At this temperature copper dissolves 4.3 atomic per cent (7.0 weight per cent) of silver in solid solution; this solid solubility decreases to zero at room temperature.² Silver at the eutectic temperature rctains 14.0

Jan 1, 1935

By D. W. Fuerstenau

On page 1243, column 1, the first line of the author's reply should read "D. W. Fuerstenau (author's reply)---," rather than D. E., as printed. In the sentence immediately preceding the first equation (page 1243, column 2)' the word "none" was omitted. The sentence should read: "However, if enough ore is put into the mill [so] that none of the energy put into the mill is wasted on metal-to-metal impact, then the product should have size modulus determined by the relation: ..."

Jan 1, 1961

By Morris J. Elsing

FOR MANY YEARS lead and zinc have had the so-called protection of a tariff and it is the purpose of the following brief discussion to show what' such protection actually accomplishes with a view to forecasting the possible results of the present copper tariff. In analyzing the subject, tabulations of the United States production, consumption, imports and exports, including ore and concentrates and all of the metallic products, of both lead and zinc have been made for each year since 1900. Of these data, the relationship of the imports and exports and the relative foreign and domestic prices are shown in Table 1. The conclusions drawn from these figures are listed below. 1. The United States is an exporter of zinc. 2. The United States is an importer of lead. 3. The average price of zinc at St. Louis for the last 32 years has been no higher than on the London market even though zinc and zinc ore have "enjoyed" a protective (?) tariff of varying amounts per pound for 22 years of this period. 4. The average price of lead on the New York market for 32 years has been 1.2c. per pound higher than on the London market, the tariff varying from 0.75 to 1.5c. per pound of lead in ore, and 1 to 2c. or more on manufactured lead.

Jan 1, 1932

By R. S. Handy

THE properties of the Patiño Mines and Enterprises Consolidated, Inc., a New York corporation, are near Llallagua in the department of Chayanta in the west central part of Bolivia, South America, about 80 miles southeast of Oruro and 250 miles southeast of La Paz, the largest city in Bolivia and its virtual capital. The properties are accessible by railroad from three points on the west coast-from Mollendo, Peru, across Lake Titicaca, from Arica by way of La Paz, and from Antofagasta, Chile. The latter route, although the longest, is recommended by the companies as affording a more gradual introduction to the high altitudes; the mine being 13,000 ft. above sea level. The company operates its own railroad from its properties at Uncia to Machacamarca on the Chile & Bolivia R. R., a distance of 60 miles. This railroad is well equipped and well operated, and its location among the mountains surrounding Uncia represents excellent engineering skill. In fact all of the railroads, although they are of only a meter gage, are remarkable for the excellence of their construction, the arrangement of their dining and sleeping cars and the precision of their operation. There is only one drawback to rail- road and hotel accommodations and that is the absence of heating facilities, which does not seem to affect the natives but keeps a tenderfoot's teeth chattering continually. The company is a consolidation of the Patiño company, owning properties at Uncia, with the Compafiia Estanfera de Llallagua, a' Chilean corporation owning contiguous properties at Llallagua. Before the consolidation these companies were deadly enemies, and there still remain at the surface plant at Uncia the fortifications and underground defences provided during the warfare between the two factions. Also, in the Azul, or "Blue" tunnel at the junction line between the two properties is a strong steel barricade still bearing marks of the bullets fired during the various armed tilts between the workmen of the two companies. The headquarters for the mining operations and the milling plant have been moved since the consolidation from the original location at Uncia to the Llallagua side of the mountain, where the Chilean company's operations were carried on. The historic old town of Uncia, with its massive stone buildings of Spanish design, is a wreck, while the Llallagua side is being rapidly built up with modern structures.

Jan 1, 1929

By Thomas T. Read

EVERYONE engaged in the teaching of mining engineering will, I suppose, agree that the most difficult subject to teach is "Mining Methods." One primary difficulty is that the students taking the course have either had no previous experience in mining, or else they have had; either seeming to be somewhat of a drawback. The students who are unfamiliar with mines find it difficult to visualize underground conditions, as described and illustrated with sketches and maps, while those who have had underground experience seem to 'find it difficult to visualize anything much different from that which they have already seen. This reminds one of the remark about the Presbyterian doctrine of predestination, to the effect that "you are damned ,if you do; and damned if you don't."

Jan 1, 1930

By MALCOLM FRASER

I was delighted to be invited to be patron of this Joint Conference, but the challenging task you have set yourselves, and your speakers' depth of expertise, deny anyone, even the patron, the opportunity to be patronizing. Australia's history has been inextricably linked with the fortunes of our great mining industry. That link will remain. Just as the gold rushes of the last century, and the discoveries at Kalgoorlie and Broken Hill changed the lives of generations, so the more recent development activity in iron ore, bauxite, nickel, coal, and uranium are having a significant impact on the lives of Australians today. The minerals industry has contributed to Australia's jobs and prosperity. Mining is not free of problems, but so long as safeguards are strong and appropriate the net benefits the mining industry brings Australia will continue to be enormous. We rely on our mining industry to find, prove, develop and sell our minerals profitably, and my Government is committed to maintaining a healthy mining industry. In the past year there have been positive signs of a resurgence in exploration and development. The North-West Shelf ventures are spending $50 million on a feasibility study to work out the extent of future investment in that project; exploration expenditure for minerals other than petroleum increased by 34 per cent in 1976-77 to $134 million; petroleum exploration increased dramatically last year almost doubling to $94 million-this year it is projected to reach $125 million.

Jan 1, 1978

By Eli T. Conner

WITH Thomas G. Fear, chairman of the Coal Di- vision, presiding, the coal miners opened their program Monday morning with a general session at which three papers were presented. The first, "The Classification of Coal for Stationary Steam Generation," was presented by the author, Thomas W. Harris, Jr. In discussion, H. T. Coates inquired if it would not be possible to pick out a geographical coal section, certain seams or a group of mines, which would rank high in a desired feature or features, perhaps giving different -- - local sections or different mines something to designate a rating ("good," "fair," and "poor"). This might be done relative to anti-clinkering, free-burning, ,anti-slagging, smokelessness, friability and grindability. These might be listed or arranged on a map or diagram so that the prospective customer could find a coal that rated particularly high in desired characteristics. C. A. Reed pointed out, in part, that coal producers and sellers have found a bad but necessarily present condition in the country, especially with the smaller user of coal. This is entirely due to the fact that the employer expects his purchasing representative to be a genius and have expert knowledge of everything he buys, coal included, whereas in the larger plants he has and uses expert knowledge from the active organization when necessary. J. B. Morrow said that size rating was important in classifying coal and he emphasized that it was impossible to come to a definite basis on analysis alone.

Jan 1, 1933

AALL, Christian H.,(M'49), Asst Res Dir Monsanto Chemical Co Anniston, Ala AALSETH, Earl P ,(J,51), Amerada Petr Corp Geological Dept Williston N Dak AAMOT, Olav Crone, (M'29), Met Pacific N W Alloys, Inc , Box 6215, Hillyard P 0 Spokane 14, Wash AARING, Floyd D ,(J'48), Petr Engr P 0 Box 130, Calgary, Alta Canada AARCNSON, Hubert Irving, (S'47), Carnegie Inst of Tech., Pittsburgh, Pa ABADIE, Henry G ,(M'43), Asst to the Sup- of Operations, Long Beach Oil Development Co ,255 So Santa Clara Ave Long Beach, Calif ABBISS, H. J., (A'50), Min. Engr., Buchans Mining Co., Ltd.. Buchans, Newfoundland ABBOTT, Clarence Eugene, (M'04), 901 Insurance Bldg , Raleigh, N C ABBOTT, George, (S'52), Mass Inst of Tech Cambridge, Mass

Jan 1, 1952

By F. R. Milliken

EXPERIMENTS, in what has come to be known as flash roasting began some ten years ago. The principle underlying the operation was not a new one, but the experimental work started at that time was the first that was carried through to a logical conclusion, followed by construction and operation of a pilot plant, and then full-scale production. For a short working definition, flash roasting may he considered the instantaneous and complete oxidation of finely ground sulphide particles, partially suspended in air or gas, the oxidation reaction evolving enough heat to make the reaction self-sustaining, or nearly so.

Jan 1, 1937

By R. J. Charles

SEARCH for a consistent theory to explain the relationship between energy input and size reduction in a comminution process has accumulated, over the years, an enormous amount of plant and laboratory data. Although some correlation of these data has been possible for purposes of engineering design and for the advancement of research in fracture, there is still great need of a means of predicting behaviour of a solid when it is reduced in size by mechanical forces. The best known hypotheses proposed to describe the energy-size reduction relationships in crushing and grinding stem from a common origin. The present article analyzes problems of comminution in the light of the precepts of this origin. Its object is to reconcile points of difference between these well known hypotheses and to present relationships more widely applicable to comminution studies. Theoretical Considerations: Most existing relationships between energy and size reduction of a brittle solid stem from a single, simple, empirical proposition.&apos; Although this proposition can be demonstrated by observation and experiment, no theoretical derivation is yet possible. Mathematically, the proposition may be stated as follows: dE = -Cdx/xn [1] where dE = infinitesimal energy change, C = a constant, dx = infinitesimal size change, x = object size, and n = a constant. Eq. 1 states that the energy required to make a small change in the size of an object is proportional to the size change and inversely proportional to the object size to some power n. No stipulations are placed on the exponent n in either magnitude or sign. In 1867 Rittinger2 postulated that the energy required for size reduction of a solid would be proportional to the new surface area created during the size reduction. As far as can be determined there is as yet no physical basis for Rittinger&apos;s hypothesis. Rittinger&apos;s hypothesis can be stated mathematically as follows: E, = K(oa-a-0 . [2] Er = energy input per unit volume, K = a constant, <ti = initial specific surface, and o2 = final specific surface. In the size reduction of particles of size x, to particles of another smaller size, x2, Eq. 2 becomes the well known relation: ET = K&apos; {l/x2-l/xx) [3] where K&apos; is a constant. Eq. 3 may be arrived at from the proposition given in Eq. 1 by integrating and by assigning a value of 2 to the exponent n. J dE = J - C dx/x2 E = Kt (1x - 1x) where K&apos; = C. In 1885 Kick3 proposed the theory that equivalent amounts of energy should result in equivalent geometrical changes in the sizes of the pieces of a solid. For example, if one unit of energy reduced a number of equal-sized particles to particles of one half the size, then the same amount of energy applied to the particles resulting from the first test should result again in a size reduction of one half or a final size one quarter the original size. The Kick concept may be expressed as follows: Ek = K" log x1/x2 [41 K" = a constant and E, = energy per unit volume. The expression for Kick&apos;s law may be arrived at by again integrating Eq. 1 and in this case assigning a value of 1 to the exponent n. dE= J - C dx/x Eh = - C In {x/x2) = K" log (x,/x,) where K" = 2.3 C. Application of Kick&apos;s and Rittinger&apos;s laws to comminution has met with varied success. Gross and Zimmerley4 and Piret5 have shown that Rittinger&apos;s equation applies under certain conditions of experimentation. Walker and Shaw6 express the belief that in metal turning and shaping and in grinding of both metals and minerals the production of very fine particles (less than lP) follows Kick&apos;s hypothesis, whereas Rittinger&apos;s concept is valid for the size reduction of coarse particles. For the practical case of crushing and grinding, however, neither of the above hypotheses has received general acceptance. Bond&apos; has lately proposed that since neither Kick&apos;s nor Rittinger&apos;s hypotheses seem correct for plant design work, an energy-size reduction relationship somewhere between the two would be more applicable. The fundamental statement of Bond&apos;s work

Jan 1, 1958

By R. W. Heckel, H. W. Paxton

The growth of grain boundary films and Widmanstiitten plates of proeutectoid cementite in hypereutectoid steels ulas considered quantitatively in three plain carbon steels and one "pure" iron-carbon alloy. Growth was found to take place at a slower rate than would be predicted on the basis of a model invoking rate control by long range diffusion of carbon. The films in the pure alloy grew faster than those in the plain carbon steels. A possible explanation is suggested. In 1904, Nernsst&apos; and Brunner2 postulated that ionic crystals growing in supersaturated aqueous solutions grew at rates determined by diffusion through the solution to the growing crystal interface. The gradient down which the diffusion took place was assumed to be fixed by the supersaturated bulk solution concentration, the concentration dt the crystal surface and some arbitrary distance. The flux of material to the crystal was described as Flux where D is the diffusion coefficient, A the crystal surface area, Ci the bulk solution concentration, Co the saturated solution concentration, and 6 the thickness of the diffusion zone. It is obvious that the expression is an adaptation of F+ick&apos;s3 first law of diffusion (steady state). This was the initial formulation of what will be defined here as "diffusion controlled growth," i.e., growth limited by the long range diffusion of a component either to or from the advancing interface assuming both phases at the interface to be in equilibrium. This idea of equilibrium interface concentration implies an infinite reaction rate at the interface. Volmer, Zener,&apos; and 11schner6 have derived expressions for the diffusion controlled growth of spherical precipitates in metallic systems. These analyses agree that the growth in a given direction should be parabolic with time. Brown and Hawkes7 observed that graphite, formed both from the decomposition of cementite and from the decomposition of eutectoid austenite in cast irons, grew according to a parabolic relationship and, therefore, concluded that the laws of diffusion controlled growth, as defined above, were obeyed. They, among others, failed to consider, however, that parabolic growth is a necessary, but not sufficient, condition for diffusion controlled growth. Mehl and Dube"&apos; have pointed out that equilibrium may not be realized because the concentration at the interface cannot change instantaneously from that of the bulk to the saturation value. Furthermore, they propose that an equilibrium solute concentration in the parent phase adjacent to the precipitate would remove the thermodynamic activity gradient across the interface and, thus, stop the growth process. Frisch" has also emphasized the importance of interface concentrations that vary throughout the growth of a new phase. The variation in activity across an interface, as discussed by Onol&apos; and Cahn and Hilliard,12 is of fundamental importance to this question. Ham13 considered the data of Turnbull14 on the growth of barium sulfate in aqueous solutions. He concluded that the data could be analyzed in terms of a radiation-type boundary condition. Flux across interface = K (c, - C,) [21 where C, is the concentration in the solution at the interface, Co the saturated solution concentration, and K the proportionality constant. The edgewise growth of Widmanstlitten plates, frequently referred to as the rate of lengthening, was first considered by Zener.&apos;&apos; Basing a mathematical analysis on steady-state (constant velocity) growth he concluded that where G is the growth rate, D the solute diffusivity, Ci the concentration in the bulk, Co the equilibrium interface concentration, C, the concentration in the precipitate, a a constant, Y the radius of curvature of the edge of the plate, and rC the critical radius, i.e., the radius which would increase the activity of solute at the interface at equilibrium under the influence of capillarity to that of the bulk. Zener1&apos;

Jan 1, 1961

By Oliver Bowles

EACH year the broad diversified field of industrial minerals offers a panorama of new and interesting developments that not only concern the welfare of the industries themselves but have a more or less direct influence on the lives of citizens at large. Thus, the home life of multirudes may be affected by new building units that transmit light through walls instead of windows, by illuminated processed marble lighting fixtures and decorations, by the vast impetus given to thermal insulation Ly .mineral wool, expanded vermiculite, and related products, and, more remotely, by fireproof rugs and drap-

Jan 1, 1937