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By A. N. Roberts, N. W. Stump

New developments in on-stream analysis using immersed radioisotope gages including results from plant installations are described. The control of grinding and flotation using a small digital computer has been complemented by this development. A control scheme for grinding, which is based on maximum throughput at constant product size, and preliminary work in flotation control are also outlined.

Jan 1, 1975

By S. H. Chauvenet

Jan 1, 1882

Jan 1, 1936

By G. Ansel, J. P. Doan

The important literature concerning zirconium in magnesium-base alloys is predominantly contained in patent references. Sauerwald, Eisenreich, and Holubl-4 discovered the profound grain-refining influence of small amounts of zirconium on cast magnesium and the attendant increases in strength and ductility. They extended their work to reveal that limited amounts of certain other elements, including zinc, could be added for further improvement in strength and hardness. British Patent 5111375 relates to the parent discoveries of Sauerwald, Eisenreich, and Holub. All of these references deal primarily with casting characteristics and properties in the cast state. Minor mention is made of desirable tensile strength, ductility, and toughness of wrought Mg-Zr alloys* modified by one or more additional elements. No extensive reference in the literature5. has been found to the particular characteristics of wrought blg-Zn-Zr alloys, with which the present paper is concerned. The work to be discussed represents essentially an extrusion study of the blg-Zn-Zr alloys and indicates that this system is highly interesting in the wrought state both academically and commercially. Accordingly, an important aim of this paper is to describe the hot-workability, tension and compression properties, metallography, and toughness of these alloys. Compositional variations are limited to the ranges 0 to 7 per cent Zn and 0 to I per cent Zr. Experimental Procedure Alloying and Casting Alloying ingredients were cell magnesium, commercial zinc (intermediate grade), and a chloride salt containing approximately 50 per cent ZrCl² and 50 per cent alkali chlorides. This salt is produced by Titanium Alloy Manufacturing Company. Melting, alloying, and pouring procedure essentially followed the crucible process as described by Nelson.6 The magnesium was melted using Dow No. 310 flux, and the temperature raised to 1350° to 1400°F for the alloying operations. After alloying of the zinc, the zirconium containing salt was added in small portions with vigorous stirring. This is an adaptation of the method described in British Patent 533264.7 The alloying efficiency of zirconium was approximately 30 per cent. During the alloying of zirconium, fluorspar was added in amount required as a flux-inspissating agent. Next the melt was refined with Dow No. 310 flux and held quietly for 15 min. Finally billets were cast in a book-type permanent mold

Jan 1, 1947

By E. C. Felton

At the Pennsylvania Steel Works, Steelton, Pa., a series of trials has been made with oil as fuel in steel-heating and open-hearth steel-furnaces with the following results : First Trial.—Hot 14-inch ingots, six to a charge, were heated in two Siemens' heating furnaces in the blooming mill, the oil being put in first in March, 1888. The oil used had been partly refined, so that the paraffine and some of the naphtha were removed. During a run of six weeks the consumption of oil was about 61/2 gallons per ton of blooms, including the oil required to keep the furnace hot over Sunday.

Jan 1, 1889

Jan 1, 1946

By J. C. Scully

In June, 1965, Sanderson and scully5 reported at the Conference on Environment Sensitive Mechanical Properties of Materials at the Research Institute for Advanced Studies at Baltimore that thin foils of titanium could be prepared by chemical polishing in a mixture of 44 pct HF and 73 pct HNO3 in the volumetric ratio 2:3. The technique is simpler than that since reported by Rice and Orava. As-received annealed titanium (containing 0.8 pct Fe and 30 ppm H) in the form of sheet 0.05 cm thick is placed in the solution and moved up and down. The reaction is violent but suitable foils are obtained very easily and consistently. A typical micrograph is shown in Fig. 3. The small precipitates were not identified. Yamane and ueda6 observed many spotlike features which they referred to as small dislocation loops. While their spots may be due to the reaction of the warm foil with the air as suggested by Rice and Orava, the precipitates in Fig. 3 are also found when foils of titanium are prepared by electro-polishing at low temperatures and subsequently examined in the electron microscope without any inter- mediate warming. Furthermore, they are not a surface effect. It is necessary to add that alloys of titanium cannot be so easily thinned by the chemical polishing solution described above since it contaminates the a, phase with hydrogen and produces y hydride. These matters are described at length in a paper7 and their relevance to stress corrosion is considered elsewhere.'-* Author's Reply The authors are grateful to Dr. Scully for bringing to our attention his hitherto unpublished technique for thinning unalloyed titanium, and deeply regret the unintended apparent duplication. The chemical thinning solution (7 parts HNO3 and 3 parts HF, by volume) reported by us is the same as that with which, for some period in the past, we had experienced success in the preparation of foils from single and polycrystalline niobium. Its subsequent effective application to titanium was a logical step, which, clearly independently of Scully, was conceived by Mr. Rice, to whom full credit is due. A few comments are warranted concerning some of the details of the preceding Discussion. It is evident to the discerning reader that the two thinning techniques under consideration are chemically almost identical, and in that sense are equally "simple". The chemical aspect is, of course, the one of primary importance in both communications. Thereafter, the relative simplicity is dictated by the mechanics of the actual thinning operation selected by the individual investigator. Our standard dimpling, or dishing, procedure was chosen with a view toward providing, for the electron transparent areas of the sample, the maximum protection from extraneous deformation during handling. That the long, straight dislocations visible in Scully's electron micrograph of a seemingly recovered structure closely resemble handling dislocations would tend to indicate the merit of our adopted technique. Features similar to those which Scully has attributed to precipitates, without any apparent diffraction contrast confirmation, were not observed in any of our clean foils taken from annealed or deformed specimens. This was admittedly somewhat surprising since the 3700 ppm (nominal) Fe in the A-70 commercial-grade titanium examined should have given rise to TiFe precipitates. Presumably these existed but were un-resolvable. Curiously, Scully's "precipitate1' density is fairly high although the iron content quoted was less than one-fourth of that in our material. One is forced to conclude from the evidence that prior thermal and mechanical treatments are responsible for the two different types of structure observed.

Jan 1, 1968

By H. O. Hofman

PAGE I. Introductory,.......... 258 11. Condensed Account of Past and Present Plants,. .. 259 111. The Ores. Table I., Average Analyses,..... IV. Metallurgical Treatment—Roasting OF Ores,... The Allen-O'Hara Furnace,....... The Wethey Furnace,........272 The Pearee Turret-Furnaces,....... 273 The MacDougall Furnace,.......275 Original MacDougall,.......276 Herreshoff,......... Evans-Klepetko,........ General Results (Table II.),.......282 V. Smelting Ores in The Blast-Furnace,...,. Table 111. Examples of Montana Blast-Furnace Smelting,. 284 Table IV. Analyses of Coke and Coke-Ash,. .. . VI. Smelting Ores in the ReveRberatory Matting-Furnace,. 289 Table V. Percentage of Components of Charge,. .. 290 Table VI. Analyses of Flue-Dust and Briquettes,. .. Table VII. Examples of Montana Reverberatory-Smelting,. 292 Table VIII. Analyses of Coals,...... Table IX. Analyses of Producer-Coal and Ash,. .. Details of Practice,........297 VII. Converting Coppr-Matte,....... 302 Table X. Analyses of Materials of Converter-Linings,. . 306 Table XI. Montana Converters,......308 Yield of Metal..........308 VIII. Electrolytic Refining of Copper,..... Refining of Cathodes,........ 313 Table XII. Details of Electrolytic Refineries,. .. . Table XIII. Efficiency of Some Rocky Mountain Coals,. . 316 I. Introductory. In 1901,* this country produced 268,782 long tons of fine copper. Of this total, Montana is credited with 102,621 long tons, or 38.2 per cent.

Jan 1, 1904

Jan 1, 1905

Future of State and Federal Oil Regulation. BY NORTHCUTT ELY (Trans , vol 118 2400 words) The Interstate Oil Compact, ratified by six states and Congress in 1935, replaced the petroleum code, invalidated with other codes by the Schechter decision This compact endeavors, first, to conserve reservoir energy of oil pools through substantially uniform conservation measures by the states, second, it recognizes the state rather than the Federal Government as possessing the necessary police power for that purpose, third, it establishes an interstate advisory commission, so that orderly production in one state is not penalized by uncontrolled production in another, fourth, Federal interests are recognized in the control of hot oil, regulation of imports and fact-finding forecasts of supply and demand by the Bureau of Mmes It is not as complete an instrument as proposed by the Federal Oil Conservation Board in 1932, but is workable, and will be effective in proportion to the support given it by the industry Three results may follow First, now that fear of Federal control has subsided, the industry may lose interest in the compact and let it fall to pieces, second, if vigorously supported by the industry, the compact can accomplish most of the conservation objectives sought by the Federal control measures now believed unconstitutional, third, if the Compact fails, Federal regulation is almost certain to be revived, and can probably be sustained in connection with neutrality legislation, regulation of interstate pipe lines, and coordination of Federal and state gasoline taxes Nearly every step toward governmental regulation has originated within the industry state proration, the Federal petroleum code, Federal control of imports, Federal control of hot oil are examples The Compact shows a trend toward coordination between the powers of the industry, the state government, and the Federal Government If this arrangement fails through lack of interest by the oil industry, the next step is likely to be absorption by the Federal Government of the other two factors involved in the situation

Jan 1, 1937

[Admissions: H. J. Gruy, Chairman Kenneth W. Robbins W. Frank West Aurel E. Smith R. F. Madera Tom G. Calhoun Kenneth F. Anderson B. M. Goltlieb Advertising: Clark R. Edgecomb, Chairman Bernard F. Klein. Henry N. Lyle R. E. Howard H. M. Krause, Jr. Education: R. L. Whiting, Chairman John M. -Campbell E. T. Guerrero Don D. Little J. C. McCarthy Frank G. Miller Douglas Ragland H. C. Slider R. L. Slobod]

Jan 1, 1961

Jan 1, 1886

By Rossiter W. Raymond

BY the courtesy of Mr. Charles W. Jenks, of Boston, one of the owners of this interesting mine, I am enabled to lay before the Institute a suite of specimens, illustrating its peculiar formation and the paragenesis of mineral species which it presents; and a recent brief visit and rapid reconnoissance of the locality permit me to supplement this exhibition with a general description, based upon personal observation. The mine is situated upon the Culsagee Fork of the Tennessee River, in Macon County, North Carolina, a few miles from Franklin. The most practicable route by which it can at present be visited is by wagon (or preferably on horseback) from Seneca City, S. C., a station on the Charlotte and Atlanta Air Line Railroad. The itinerary is as follows: to Walhalla,* nine miles; Walhalla to Highlands, twenty-nine miles; Highlands to the Culsagee, fourteen miles. By passing the night at or near Highlands, the mine can be reached and examined and the return to Highlands made on the second day; and the round trip, if performed in the saddle, can be completed in three days from Seneca City. It is not easy, with due regard to steed and rider, to do it in less time. The rough and precipitous mountain roads do not permit rapid travel ; and the journey is at best a fatiguing one. But its slight hardships are overpaid by the stimulating effect of the climate and the great beauty of the scenery, both of which are destined to become more widely known than at present, to seekers for health and pleasure. Indeed the town of Highlands, already named, is almost entirely made up of northern immigrants, attracted by these advantages and by the inducement of cheap land for agriculture and stock-raising. The Culsagee or Sugartown fork of the Tennessee traverses the belt of ancient crystalline schists on the west flank of the Blue Ridge. This belt abounds in valuable minerals. Among those of the nonmetallic class may be mentioned graphite, soapstone, serpentine, ashes- * A branch or cross railroad is in operation as far as Walhalla ; but the single daily train runs at an hour not convenient for this expedition ; and Seneca City is probably the best starting-point. At all events, I obtained there an excellent mount for the trip.

Jan 1, 1879

By Frederick Clapp

INTRODUCTION - SCOPE OF DISCUSSION There has hitherto been no systematic effort to make public the available information on petroleum in South America and the object of this paper, therefore, is to broadly discuss the subject as it pertains to South America as a whole, endeavoring to collect in readable form what is known regarding individual fields. This article is not intended to exhaustively discuss individual fields, or to solve the many complicated problems regarding petroleum and natural. gas in the various republics, since those necessitate years of study and work by petroleum geologists, engineers, financiers, and drillers. Neither. can the reader expect absolute accuracy in all statements, since this is impossible at the present time. The writer has, of course, attempted to be correct in all cases, but in a review involving so many countries and extending over so many, phases of the subject, it is to be expected that some errors will have crept in.

Jan 10, 1917

By Rollin E. Hook, Attwell M. Adair

The yield and fracture behavior of recrystallized chromiztm have been studied in order to gain an understanding of the recrystallization embrittlement-rheotropic recovery phenomenon. The duc tile-brittle tensile transition temperature of recrystallized chromium was found to vary from 225 ° to -80°C as the ratio of specimen diameter/mean planar grain size decreased. The applicability of this observation to other bcc metals is briefly discussed. Brittle fracture in recrystallized chromium was found to be initiated predominately from intercrystalline rupture nuclei. Single crystals exhibit a high degree of ductility at 23 "C. The experimental data indicate that grain boundaries play a significant part in the yield and fracture behavim. Pres training significantly reduces the transition temperature, and high temperature aging does not result in re-embrittle-ment until complete recovery or re crystallization occurs. SEVERAL theories have been used to explain the recrystallization embrittlement-rheotropic recovery phenomenon in chromium. Wain, Henderson, and ohnstone' propose a Cottrell dislocation locking mechanism due to nitrogen, and Weaver and Gross and weaver 3 propose a strain-induced precipitation mechanism involving a chromium nitride precipitate. The researches of many investigators seem to leave little doubt that brittleness in chromium is promoted by interstitial impurities. Smith and seybolt4 have shown that the ductile-brittle transition temperature is lowered as the interstitial content is reduced. weaver3 provides evidence for a 150°C reduction in the tensile transition temperature as the nitrogen content is reduced from 20 to 5 ppm. Maykuth and affee' have suggested that the amount and orientation of grain boundary impurities may be responsible for the brittle nature of recrystallized chromium. This suggestion was based on their findings that wrought iodide chromium possessing a fiberous grain structure is ductile in tension at room temperature while a recrystallized grain structure is completely brittle. Previous investigations have not studied this phenomenon sufficiently to determine its cause. Perhaps this has been largely due to previous experimental findings that brittle fracture observed in chromium has been almost entirely transgranular.' In addition McNeil and imb,' who investigated coarse-grained as-cast chromium, describe the point of initiation of fracture as cleavage, close to the (100) plane, near or at grain bound-daries, or at included particles or voids. However, Hook, Adair, and ipsitt found that fracture in coarse-grained recrystallized chromium is initiated by intergranular rupture and then propagates nearly entirely by cleavage. This result, together with their finding that room temperature ductility in bending is observed for single crystals and coarse-grained polycrystalline specimens for which the number of grains through the specimen diameter is small, suggests that grain boundaries may play an important role in the brittle behavior of chromium. The recrystallization embrittlement problem can be resolved into two questions. These are, whether the controlling mechanism is predominately one of crack initiation or crack propagation, and whether brittle fracture is initiated predominately by slip or twin induced intergranular rupture or by cleavage. The following research was designed to study the role of grain boundaries on the brittle fracture of chromium in an effort to resolve these questions. EXPERIMENTAL PROCEDURES, RESULTS, AND DISCUSSION General Procedure. All tensile specimens (except 0.04 in. diam wires) were prepared from 1/4 in. diam swaged rod fabricated from one ingot. Details of fabrication are given elewhere. The results of impurity analysis for the swaged rod and for the

Jan 1, 1963

Z. W. Bartlett, J. C. Carrington, H. C. Petersen and K. T. Price were elected vice-presidents of the Freeport Sulphur Co. Blandford C. Burgess was transferred on January 1 to the new Defense Materials Procurement Agency as strategic materials specialist. In May the Region III headquarters of this organization was moved to London. L. C. Campbell was elected president of National Coal Assn. Mr. Campbell, who has been a member of the National's Board of Directors and Executive Committee for many years, is vice-president of the Coal Div. of the Eastern Gas & Fuel Associates and in charge of their extensive mining operations in West Virginia, Pennsylvania and Kentucky. Vern H. Christoph has been transferred to Panama Canal Co., Marine Bureau, Navigation Division, Port Captains Office, as an admeasurer at Cristobal, Canal Zone. Eugene Cline, recently graduated from the University of Kentucky, has been employed by Pond Creek Pocahontas Coal Co., at Evanston, Ky. Sanford S. Cole, assistant manager of research at the Titanium div. of National Lead Co., received the Alumni Citation from his alma mater, Alfred University, Alfred, N. Y. This was in recognition of outstanding achievements and services in the field of ceramics which have brought honor to the institution. U. K. Custred, recently graduated from University of Kentucky, and may be reached now at Box 87, Monterey, Tenn. Robert E. Dwyer, executive vice-president of Anaconda since 1940, was recently elected president of this company and its subsidiaries, Chile Copper Co., Chile Exploration Co., and Andes Copper Mining Co. As president, Mr. Dwyer succeeds the late William H. Hoover who died in Butte, Mont.

Jan 1, 1952

By R. L. Skaggs, D. T. Peterson

The effect of carbon in solid solution on the plastic behavior of thorium was studied by measuring the flow stress of Th-C alloys from 4.2" to 573°K and at several strain rates. Carbon was found to strengthen thorium primarily by increasing the thermally activated component of the flow stress. The strengthening due to carbon was directly proportional to the carbon content and decreased rapidly with increasing temperature up to 423" K. The flow stress also increased with increasing strain rate. The strengthening appears to be due to a strong short-range interaction between carbon atoms and dislocations. A yield point was observed in the Th-C alloys which increased with increasing carbon content. JTREVIOUS study of the mechanical properties of thorium has been confined largely to the measurement of the engineering properties. Work prior to 1956 has been summarized by Milko et al.1 who reported that additions of carbon to thorium sharply increased the room-temperature strength. In addition, the yield strength was observed to decrease rapidly over the temperature range from 25" to 500°C. In 1960, Klieven-eit2 measured the flow stress of thorium containing 400 ppm C. He found that over the temperature range from 78" to 470°K the flow stress was strongly dependent on temperature and rate of deformation. A drop in the load-elongation curve, or a yield point, was observed over most of the above temperature range. Above 470°K, the flow stress was nearly independent of temperature and strain rate. This strong temperature and strain rate dependence of flow stress is not generally observed in fcc metals. It is, in fact, more typical of the behavior reported for bcc metals. Bechtold,3 Wessel,4 and conrad5 have pointed out the striking difference between the commonly studied bcc metals and fcc metals in regard to the effect of temperature and strain rate on the flow stress. Zerwekh and scott6 studied the plastic deformation of thorium reported to contain 12 ppm C. They found that this material did not obey the Cottrell-Stokes law as expected for fcc metals. In addition, they found values of the activation volume smaller by an order of magnitude than expected for an fcc metal. They concluded that thorium was strengthened by a randomly dispersed solute. Thorium differs from many other fcc metals that have been studied extensively in that it shows a relatively high carbon solubility at room temperature. Mickleson and peterson7 report the solubility limit at room temperature to be 3500 ppm C. The lowest value reported is that of Smith and Honeycombe8 who report the limit to be 2000 ppm C at 350°C. The pres- ent investigation was a systematic study of the flow stress and yield point phenomenon of thorium over a broad range of carbon content, temperature, and strain rate. EXPERIMENTAL PROCEDURE The thorium used in this investigation was produced by the reduction of thorium tetrachloride with magnesium as described by Peterson et a1.' Chemical analysis of the original ingot after arc melting and electron beam melting is shown in Table I. Alloys were prepared by arc melting this thorium with high-purity spectrographic graphite. Threaded specimens with a gage length 0.252 in. diam by 1.6 in. long were used for the constant stress or creep measurements. These specimens were machined from rod which had been cold-rolled and swaged to % in. diam. Tensile specimens were prepared by swaging annealed 3/8 -in.-diam rod to 0.102 *0.001 in. The as-swaged wire was cut to lengths of 2 in., annealed, and the center 1-in. gage length elec-tropolished to 0.100 ±0.001 in. The specimens were gripped for a length of 3 in. at each end by a serrated four-jaw collet which was tightened by a tapered compression nut. No slipping occurred in the grips and negligible deformation was observed outside the 1-in. gage length. Both the creep and tensile specimens were annealed at 730°C under a vacuum of 1 x X Torr. The resulting structures consisted of equiaxed recrystallized grains with a grain size of 3200 grains per sq mm for the tensile specimens and 2200 grains per sq mm for the creep specimens. After the specimens were prepared, samples were analyzed for nitrogen, oxygen, and hydrogen. The results of these analyses are given in Table 11.

Jan 1, 1969

By Walter H. Bucher

This symposium is designed to lay the basis for a general discussion of the place of geophysics in the training of geologists. As there is danger that in the ensuing debate individual interests may be given emphasis out of proportion to their place, we shall do well to view the whole field of geological inquiry in order to see the problem in true perspective. The Nature of Geological Inquiry "Basic" and "Complex" Sciences It is convenient to divide all science into two major divisions, the basic and the complex sciences. The basic sciences separate out from reality such entities as "substances" and "movements," describe their behavior in terms of arbitrary units of measurement and derive from them by progressive abstractions concepts and patterns of behavior that exist between them, so-called general "laws" and "properties" of nature. The complex sciences, on the other hand, deal, with little or no abstraction, with those objects of reality that are accessible to man in the atmosphere, the hydrosphere, the lithosphere and the biosphere. Their work comprises two types of inquiry. One is concerned with abstractions to the extent of dealing with types rather than individuals—that is, with such things as plants, animals, protoplasm; clouds, streams, gla- ciers; volcanoes and mountain ranges. It comprises the search for general properties and patterns of behavior or "laws" that characterize the objects and their reactions to each other. These properties and laws apply always, everywhere. They are independent of the stream of time. We may call the results of this sort of inquiry timeless knowledge. The other type of inquiry is concerned with the objects themselves—that is, with this animal and that plant; this river system and that mountain chain; this glacier and that valley. Like all concrete objects in nature, they are subject to change with the passage of time, especially when it is measured in years, centuries, eons. The characteristics by which we recognize them —indeed, their very existence—are dependent on their position at this point in the stream of time. This we may call time-bound kntowledge. The so-called descriptive sciences are all bound to the past of which the objects of their study are the product and through which alone their present properties call be understood. They are historical sciences. This obvious fact is easily overlooked, which leads to serious misunderstanding, as we shall see later. Dynamic Geology With this broad picture in mind, let us now examine the nature of geological inquiry, defining, for the purposes of this discussion, geology as the science of rocks. Air is not a rock; water is. Meteorology and climatology are, correspondingly, gen-

Jan 1, 1946

By C. Richard Honeycutt, Frederick C. Langenberg, Guenter Pestel

Otto Schaaber (Institut für Harterei-Technik, Bremen-Schönebeck, Germany)— Langenberg, Pestel, and Honeycutt gave an interesting example of the grain refining effect nonstationary magnetic fields may execute on a solidifying metal. Probably some additional comments, based on more than a decade of experience with this method of influencing crystallization, may be useful. They refer to an attempt to explain the mechanism of grain refinement by such fields, and to recent European developments which have not been mentioned in the paper. I. During studies of the temperature distribution in a metal body near the phase boundary solid/liquid, an anomaly was observed under certain special conditions: a) direction of heat transfer as horizontal as possible, b) steady state (equilibrium, i.e,, solidification resp. melting rate exactly zero). In the liquid phase, immediately adjacent to the phase boundary, the temperature was found to be constant over an appreciable distance in spite of a high value of heat transfer (40.000 to 70.000 keal/ m2h).3 Convection, which might explain this phenomenon, could not be observed. Therefore another explanation had to be sought. The assumption that a metallic melt, especially at temperatures near the point of solidification, contains some sort of atomic arrangement with a higher degree of order than the surrounding liquid, now is generally accepted. Considering the differences in energy between such an arrangement and its environs, a transport of heat even in absence of any temperature gradient is conceivable by continued formation and redissolution of regions with a higher degree of order, i.e., with lower energy level.3 At this stage, it was not necessary to postulate any special condition as to the form or size of these regions or the distance between arrangements to be newly formed and those to be redissolved. However, a simple consideration shows that an energy transfer from one region to another will only be possible without loss of energy, if the distance between will be equal to the lattice parameters, and if, secondly, crystallographic axis or planes will be parallel.4 By the way, this assumption might give a reasonable explanation of the well known orientation effect of the heat flow during solidification. Any measures to prevent columnar crystallization should act upon this ordering mechanism: a) the regions with a lower energy (higher order) should not be allowed to arrange themselves parallel to the direction of heat flow, and their growth should be disturbed; b) all conditions leading to an appreciable heat flow of uniform direction should be avoided or removed. Condition a) may be satisfied by a physical force preferably under 90 deg to the main axis of the columnar crystals (i.e., parallel to the solidification front) acting on the ordered regions; condition b) by equalizing any differences in

Jan 1, 1962

By R. D. Vaughn

The analysis of laminar flow of power-law non-Newtonian fluids in narrow, eccentric annuli is employed in this paper to discuss the problems of lubricant flow in journa! bearings and of errors introduced by eccentricity in experimental studies with concentric annuli on extruders and wellbore annuli. The velocity profile and pressure loss-flow rate equations are developed for the laminar flow region. In addition, the expected error in flow rate and pressure-loss measurements for concentric annuli as a result of eccentricity is determined. For example, a 10 per cent displacement of the core of an almost concentric annul us would cause a 1.8 per cent decrease in the observed pressure loss for a fluid with a power-law exponent n of 0.25. The corresponding increase in the observed volumetric flow rate would be 7. 5 per cent. INTRODUCTION Non-Newtonianism and eccentricity occur simultaneously in two engineering problems: (1) flow of lubricants in journal-bearings and pressure-reducing bushings, and (2) flow of non-Newtonian fluids in plastic extruders and wellbore annuli. The lubricants used for moving parts are often non-Newtonian in character — often they are plastic in behavior. A solution to the problem of flow of non-Newtonian fluids in narrow eccentric annuli is particularly pertinent to this problem. In all experimental studies of laminar flow of fluids in concentric annuli, such as in extruders and well casings, the error due to eccentricity must be estimated or studied. A number of publicationsl-4,6,7 have dealt with this problem for Newtonian fluids; however, I am not aware of work for non-Newtonian fluids. This work is directed to the non-Newtonian problem. Before the solution to the problem is given, the pertinent conclusions from the work on Newtonian fluids will be reviewed. Heyda 1 and Redberger and Charles 2 have published general solutions to the problem of the laminar flow of Newtonian fluids in eccentric annuli, apparently without knowing of the earlier work of Ca ld well 3 and Bairstow and Berry,4 which is reported by Dryden, et al. 5 Although several mathematical routes are encompassed by the work of these authors, the results appear to be equivalent. Redberger and Charles2 show that the error caused by eccentricity in concentric annuli is negligible for small diameter ratios (k < 0.5); however, for large diameter ratios (k + l), the error in the predicted flow rate can be as great as 100 per cent or more. Partial solutions to the problem are available from the work of Dryden,5 Tao and Donovan6 and Piercy, et a1.7 Tao and Donovan examined the case of flow in narrow, eccentric annuli (k + 1) with and without rotation of the annular core. These authors also reviewed previous work on this subject and verified their approach with experimental data. Dryden gives the solution for the limiting case of complete eccentricity or tangency. Piercy, et a l. published an early solution to the problem of narrow eccentric annular flow. The conclusions of Redberger and Charles2 and the experimental proof of Tao and Donovan6 both suggest that the region of large diameter ratios (k + 1) is of main interest and that the parallel planes approximation to the solution in this region is satisfactory. This method will now be extended to the laminar flow of non-Newtonian fluids in narrow eccentric annuli. THEORETICAL SOLUTION The geometrical aspects of the problem are illustrated in Fig. 1. To represent the non-Newtonian fluid the power-law model was selected. This model has many disadvantages which have been pointed out; nevertheless, its simplicity, its frequent and wide applicability justify its use in this work. Fredrickson and Bird8 and Savins9 have used it as a basis for a theoretical study of laminar flow of non-Newtonian fluids in concentric annuli.

Jan 1, 1966