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By S. C. Langdon, Henry S. Rawdon

The following note describing the behavior of copper under rather unusual conditions is offered for its suggestiveness rather than as a complete study of the question. The examinations described were made because of a request for information concerning the embrittlement of copper when heated in a molten salt bath (sodium chloride) for the purpose of cleaning, as well as softening it. It is well known that metals may be rendered very brittle by electrolytic action in aqueous solutions, in all probability by the action of nascent hydrogen, and it was suspected that perhaps the embrittlement of the copper by means of the molten salt was produced in a somewhat similar manner. It was found that the copper was in contact with iron (or steel) while immersed in the molten salt, through the occasional use of an iron stirring rod, iron forceps for handling the pieces, and an iron pot for containing the fused salt. In the electrochemical potential series iron and copper stand some distance apart, copper being electronegative to the iron. Assuming that the two metals bear 2 similar relation to each other, when immersed in a bath of molten salt, as they do in an aqueous solution, they would be expected to form a galvanic couple, the copper being the cathode. By this means the copper might be embrittled, as often happens in aqueous solutions, by the action of the liberated hydrogen. In this case, however, the embrittlement must be attributed to some other agent than hydrogen. TO demonstrate how copper may be embrittled under these conditions, two small rods, one of copper and the other of mild steel, approximately 3/8 in. (9.5 mm.) in diameter, were immersed in a bath of sodium chloride that had been heated somewhat above its fusion point (melting point of sodium chloride is 801" C.) and an electromotive force of approximately 6 volts from a storage battery was impressed upon the system. The copper was made the cathode and the action was continued for several minutes. When removed from the bath, cooled, and tested for brittleness by bending the specimen back and forth, while clamped firmly at one end in a vise, the copper rod was found to be very brittle, as compared with a rod of the same length of the untreated copper tested

Jan 1, 1921

By Carlos A. Aranda

The Smelting and Refining Department of Cerro de Pasco Corporation is located at La Oroya at an altitude of 3,720 meters (12,205 feet) in the Peruvian Andes. Producing lead, zinc and copper as well as twelve by-product metals and chemicals, the smelter is among the world's most complex. With the intake of high-bismuth ores in 1934, electrolytic lead refining by a modified Betts process was piloted and the plant went into commercial production in 1937 at a nominal capacity of 100 M.T. per day. After expansions in 1950 and 1963, nominal capacity has increased to 250 M.T. per day. Anodes spaced at 10.8 cm centre to centre and starting sheets are both set into the cells by overhead cranes. The asphalt-lined concrete cells are arranged in a Walker side-by-side configuration, and the electrolyte, circulating at 13 l/min./cell, is a solution of locally-produced hydrofluosilicic acid and lead fluosilicate. The corrosion cycle is limited to four days due to high impurity content of the bullion, which has successfully been treated at contents of up to 9% impurities. The cathodes are melted, drossed, and cast into blocks and pigs assaying 99.997 + % lead. The anodes with the blanket of slime adhering, are washed with electrolyte and condensate makeup water to remove the concentrated lead fluosilicate entrapped in the slimes. The slimes are then removed with high-pressure water sprays, centrifuged and sent to another plant for recovery of silver, gold, bismuth, selenium, tellurium, and antimony.

Jan 1, 1970

By G. A. Crowe, W. T. Bishop

WHILE the literature in the United States on general polarographic technique is extensive, very little appears to be directly applicable to the analysis of flotation tailings. For this reason, it seemed worth while to present a few polarographic methods of ore analysis that have been in constant use in the laboratories of the Hercules Experiment Station for the past few years. At the time of our initial investigation of the polarographic method, there was little or no mention of its specific application to flotation tailings. It was therefore necessary for us to establish suitable conditions for the analysis of our flotation tailings and to consider possible interfering constituents. The polarograph, or dropping mercury electrode, method was discovered in 1925 by J. Heyrovsky and M. Shikata,1 of the Charles University, Prague. This method has since received extensive development and the literature contains many articles on the use of the polarograph for the quantitative determination of metals as well as anions, oxygen in solution, and reducible organic compounds. Kolthoff and Lingane,2 by the publication of their book, "Polarography," in 1941 did much to advance the knowledge and use of the polarograph. In chapter 25 of that book, methods for the polarographic analysis of brass, steel and iron products, alloys, and zinc ore are given. Aluminum,3 cadmium,3.4 cobalt,4 copper,3-9 gold,10 iron,3,11 lead, 3,12,13 molybdenum," nickel,4.8,9 tin,15 and zinc3,4,5,7 in ores have been analyzed by the polarograph. However, most of the work on tailing samples has been published in Russian journals and translations are not yet readily available. In this paper we will describe the method that was developed and used in our laboratory for the determination of copper, zinc, and lead in flotation tailings. PRINCIPLE OF THE METHOD The polarograph is an instrument for applying a potential to a mercury pool and a dropping mercury electrode separated by a solution, and for measuring the resultant electrical current. The procedure is essentially a small-scale electrolysis, in which the voltage required to reduce or oxidize the material identifies it qualitatively and the current measures the concentration quantitatively. Different constituents in a sample may often be determined simultaneously provided they reduce at sufficiently different voltages. An example is the determination of copper and zinc in the same solution. The reduction potentials are quite far apart, as shown in Fig. I. The polarographic method is particularly useful in the range of concentration between those normally determined by spectographic and chemical methods. In

Jan 1, 1946

By Edward H. Robie

AT a recent meeting of the AIME Board there was considerable discussion of a suggestion that companies should be more interested in promoting AIME membership among their employes. The advocate of this idea argued that companies benefit greatly if their employes are active AIME members, so even on purely a selfish basis they should use various means to encourage membership. Also he argued that companies in general make no contribution to the support of the AIMS although benefiting from its work, so should not object to making more of a contribution, financial or otherwise, than they do. One Director stated that an investigation had developed the fact that a large majority of members felt it unwise for employers to pay the initiation fees or dues of employes. They felt that AIMS membership should be on a purely personal basis; that the rewards of active membership were sufficient so that it is a good investment for a man in developing his own professional stature, presumably resulting in an increase in salary sooner, or in greater amount, than would otherwise be the case. If an employer paid a member's dues or initiation fee the member would take less interest in the Institute. But this Director felt that an employer should otherwise encourage his employes to join the Institute, attend its meetings, and write papers based on company work for presentation and publication. Another Director reported that his company pays the expenses of AIME members in its employ to meetings; the company also encourages nonmembers to attend AIME meetings but does not pay their expenses unless they present papers of interest to the company. Another Director, representing a supplier, stated that his company's policy was to send some of its staff to all AIME meetings at which papers of interest were to be presented or at which valuable contacts could be made.

Jan 1, 1952

By Butler, P. B.

TRIPOLI is a rather unusual form of silica, which thus far has been found in commercially valuable quantities only in the neighborhood of Seneca, Mo., although there are numerous deposits of somewhat similar materials in several southern states. The latter have not, however, attained any position of real importance, due undoubtedly to definite structural limitations which have rendered them less suitable for the particular uses that have given tripoli its principal outlets. Raymond B. Ladoo, mineral technologist, says': "Since that time (1880-90) the term tripoli has with increasing definiteness been reserved for the Seneca material, and other siliceous materials of similar origin and physical properties."

Jan 1, 1928

By K. G. Davis, P. Fryzuk

VALUES for the equilibrium distribution coefficient, ko, are required for solidification studies. The procedure generally adopted1-3 is to progressively solidify alloy rods over a range of growth rates, under conditions where a high degree of convective mixing is present in the melt. The measured effective distribution coefficients are plotted as a function of growth rate, and the extrapolated value at zero growth rate is taken to be the equilibrium ko. The method is limited by the experimental difficulty in obtaining steady growth rates less than approximately 10-4 cm per sec. Extrapolation from rates greater than this can lead to inaccuracy. In the present investigation, an alternative method for determining ko, previously used by the authors for the Ag-Sn system,' was applied to alloy of thallium in tin. Specimens were grown under conditions where convective mixing was absent, and experimental concentration-distance curves in the region of the initial transient were compared with curves calculated for trial values of ko. The ko which gave the best fit was taken as the correct value. To obtain the calculated curves, a value for the diffusion constant in the liquid near to the melting point was needed. This was determined by the capillary-reservoir method. Diffusion Constants. Details of the experimental procedure used by the authors in the capillary-reservoir technique have been described in previous papers,5'6 the only variation being in the use of Tl204, a ß emitter, as tracer, in contrast to previous work where ? emitters were used. The activity of a ß-emitting sample, as measured in a Geiger counter, is proportional to the surface area. To measure the concentration of thallium along the capillary after diffusion had taken place, the solidified capillary (1 mm diam) was cut into 2.5-mm lengths and each length compressed between parallel steel plates to form a disc approximately 5 mm in diam. The discs were placed in a flat-bottomed dish, covered by a thin lead shield with a central aperture, and counted in a 0 counter with fixed geometry. Each disc was etched lightly in a dilute solution of nitric and hydrochloric acids a short time before counting, to eliminate sur-

Jan 1, 1968

By David J. Dunn

At a time when mill availability is at a premium, production costs are rising, and lead time for mill liner casting is a year or more, mill liner design is an important factor in ore grinding. Testing and selection of the optimum liner profile for a given set of mill operating conditions can improve mill capacity, reduce liner wear rate, and lengthen liner life. The mill liner that grinds best, lasts the longest, and costs the least is a necessity for economic mill operation. After testing four mill liner profiles for 3.96 X 3.65-m (13 x 12-ft) overflow ball mills, Climax Molybdenum Co. found that an improved design increased mill tonnage by 2.72 t/h (3 stph) while reducing finish grind by 1.7% minus 100-mesh, reduced liner wear rate, and almost doubled liner life.

Jan 12, 1976

Abadilla, Quirico A., Geol.. Lago Pet. Corp Box 172 Maracaiho, Venezuela. IIAbbw. Robert Graham. The W. W. Sly Mfg. Co.Train Ave.. Cleveland. Ohio. Abbotf A. N., Mines Supt., Maznpil Copper Co.. Ltd..Conception del Oro, Zac., Mexico. Abbotf Clarence E, Mgr.. Mines & Quarries, Tenn. Coal. Iron & R. R. Co., 1242 Brown Marx Bldg., Birmingham, Ala. Abbott. Louis Benjamin. Chief Engr.. Consolidation Coal Co. ... .Elkhorn Div., Jenkins, Ky. Abeel, George 8.. Jr., Cons. Min. Engr...4612 West 17th St., Los Angeles, Cal. Abel. Albert E.. Asst. to Pres.. Valley Mould & Iron Corp..Hubbard, Ohio. Abel. Raymond L Asst. Prof., Dept. of Pet. Refin.. Univ. of Pittsburgh. .. .Pittsburgh. Pa. Abernathy. George Elmer. Prof. of Geol. & Min.. Kansas State Teachers College. Pittahurg. Kans. Abernethy, D. Carl, Jr. Min. Engr., Hudson Coal Co. .Scranton, Pa. Abw, Hirouhi. Min. & Met. Engr., Min. & Met. Dept., The Higher Technical School, Osaka, Japan. Aborn. Robert H.. Research Assoc.. Mass. Inst. of Tech..Cambridge, Mass. Abouchar. Bylvain Sley. Min. Engr. & Geol., c/o S. H. Sekaly, 13 Rue El Nimr, Cairo, Egypt. tAbozeid. Mahmood. Pet. Min. Engr., Marland Oil Co. of California, Subway Terminal Bldg., Los Angeles, Cal. Abraham. Arthur W.A. pt. 40, Barcelona. Anzoatmui, Venezuela. Abrahams. Alexander I.. Gen'l Mgr., Racon Electrical Co.. ..... .Slough, London, England. tAbrahamuon, C. W., Min. Engr.. The Mond Nickel Co., Ltd.. ..... .Levack. Ont., Canada. Abstein, Henry T.. Engr. & Mgr.. Profile-Tamarack Mines Co.. ...... .Yellow Pine, Idaho. tAcker, E. WC.. Met.. ........ .I28 East Washington Lane. Germantuwn. Philadelphia, Pa. IlAckerman, D. E.. Research Engr.. Research Lab., International Nickel Co., Bayonne, N. J. tAckerman. Ernest R., Pres., Lawrence Portland Cement Co.. . .Plainfield, Union Co., N. J. Adachi. Jinzoo.A..d dress Wanted Adachi, Yuichi, Chief Engr.. Anzan Steel Works, South Manchuria RY. Co., Anzan, South Manchuria. China. (Via Dairen). Adair, Arthur C, Valuation Engr., Internal Revenue. Treasury Dept.. . .Washington, D. C. Adami. Arthur E., Prof. of Min. Engrg., Montana State School of Mines. Butte, Mont. Adami. Charles J.. Min. Engr., Gen'l Mnr., St. Jos~ph Lead Co.. ....... .Bonne Terre, Mo. Adama, C. W., Pres. Adams Pacific Corp .I66 Montgomery St., San Francisco. Cal. Adams. Cuyler .Dee rwood, Minn. Adams, David T, 514 Wrigley Bldg.. Chicago, Ill. ADAMS, FRANK DAWSON, Logan Prof. of Geology and Dean, Faculty of Applied Science. McGiU Univ., Montreal. Que.. Canada. Adams. Gale L, Research Engr.. General Pet. Corp...Los Angeles. Cal. Adams. George I.. Prof. of Geol. & Mineralogy. Univ. of Alabama. .Tuscalmsa, Ala. Adams. H. H.. Cons. Gml..Room 415, W. T. Waggoner Bldg., Fort Worth. Tex. Adams, Henry, Cons. Min. Engr. . 934 Park Ave., Plainfield, N. J. Adame, Henry H. 285 Madison Ave., New York. N. Y. Adams. Henry Farnum. Engr.. Charge Experimental Work, Inspiration Concentrator. Inspiration Cons. Copper Co.. Box 364, Inspiration. Ariz. Adams, Huntington, Min. Engr, 149 Broadway, New York, N. Y. Adams. Leland D, V.P.. Leslie-California Salt Co., 166 Montgomery St.. San Francisco. Cal. Adams. Louie W.. Illinois Steel Co Gary, Ind. Adama, XL L. Min. Engr.. Old Ben Coal Corp., Mine 12.. Christopher. IU. Adams, Robert M. Robert M. Adam Co. .I201 Fidelity Bldg., Duluth, Minn. Adams. Sidney F.. Geol., Empire Zinc Co .Gilman, Colo. tAdams, Waldo Peck..P ittsfield, Pike Co.. Ill. Addams. Charles 1. Min. Engr.. Bo x 663. Phoenix, Ariz. Addicka, Lawrence. Cons. Enar..... .61 Maiden Lane. New York. N. Y. Addison, Herbert, V.P.. Big Horn Collieries Co ,412 Colorado Bldg., Denver, Colo. Adkemn. J. Carson. Min. Engr.. HY Grade Manganese Co., Inc..Woodstock, Va. Ady. Joseph Wesley. Jr.. Min. Enar., 314 Mining Exchange Blda., Colorado Springs, Colo. Affelder. William Lewis. Asst. to Pres., Hillman Coal & Coke Co. & Allied Companies. 2006 First National Bank Bldg.. Pittshurgh, Pa. Ameck, B. F.. Pres.. Universal Portland Cement Co. .. .210 South La Salle St., Chicago. Ill. Agabeg, Edgar C.. Cons. Min. Engr.. ..... .Evelyn Lodae. Asansol, E. I. R. Bengal, India. tAsar. William M.. Aest. Prof. of Geol.. Kirtland Hall, Yale Univ.. ... .New Haven, Conn. Agaeniz. Rodolphe L, Pres.. Calumet & Hecla Consolidated Copper Co. ...... .Boston, Mass. tAgens, William Holmes. District Mgr.. Traylor Engrg. & Mfg. Co., 362 I. W. Hellman Blda.. Los Aneeles. Cal.

Jan 1, 1928

By H. E. Cline, T. H. Alden

A study zvas made of rate-sensitive plastic deformation and superplasticity in alloys of lead and tin. These alloys (lead, PO-19 pct Sn, Sn-38 pct Pb, Sn-2 pct Pb, tin) were extruded, aged at room temperature, or melted and resolidified to produce a variety of ~nicrostrnctures. Flow stress us strain rate data were obtained frorn tension tests for strain rates between 10-6 and 1 min-1. The curve log o .us log £ was S-shaped jor fine-grained materials and approxinzately linear for coarse-grained nzaterials. At constant grain size, the behavior was relatively insensitive to conposition. High rate sensitivity (d log o/d log k) and superplasticity occurred at intermediate strain rates in fine-grained materials and are believed to be associated with a transition with strain rate in the mode of plastic flow. This transition was shifted to higher strain rates with increasing temperataire or decrensing grain size. The high rate rneclzanisrn is presunzed to be slip, while rnetallographic evidence sug-gests that the low rate lnechanism is pain boundary sliding. PEARSON' discovered that extruded eutectic alloys of Pb-Sn and Bi-Sn could be elongated as much as 2000 pct in tension. The ability for stretching decreased with aging time or annealing to increase the grain size. At high strain rates, or if the material was in the cast condition, normal ductility was observed. Following deformation of the extruded Pb-Sn eutectic at low rates, Pearson observed an equiaxed granular structure on an initially flat surface, while rapid straining produced elongated grains. He attributed the large deformation in the extruded alloys to the persistence of extremely small grains to a temperature sufficiently high for inter granular flow. Avery and backofen2 measured the strain rate sensitivity of the flow stress, m = d In old In 6, in the Pb-Sn eutectic and established a correlation between m and the tensile elongation. In the extruded eutectic alloy the strain rate sensitivity was 0.1 to 0.2 at rapid rates and the elongation was small, while at low rates m increased to 0.4 to 0.6 and superplastic elongation was observed. They also noted a grain size effect. In the case of the cast Pb-Sn eutectic the strain rate sensitivity remained at 0.1 over the range of strain rates of their experiment (3 x 10"3 to 2 min-I). These authors suggested that diffusional (Nabarro-Herring) creep was the mechanism by which deformation occurred at low strain rates, while climb-controlled creep occurred at high rates. Two predictions of this model are that, at low strain rates, the strain rate sensitivity approaches 1, i.e., Newtonian viscosity, and that the strain rate at constant stress varies as D/L2, where D is the coefficient of self-diffusion and L the grain size. More recently, a mechanical and microstructural investigation of the dilute superplastic alloy, Sn-5 pct Bi, has been done.3 The results show that the high strain rate sensitivity is associated with a transition with strain rate of the mechanism of plastic flow. At low strain rates, grain boundary sliding and its associated accommodation processes were evident, while at high strain rates quasi-uniform slip was concluded to be the dominant deformation process. The following experiments were performed to extend our knowledge of the phenomena of superplasticity to a larger range of strain rates, compositions, temperatures, and microstructures in the Pb-Sn alloy system. The question of why a cast structure does not exhibit viscous behavior although it appears to have a fine microstructure2 was investigated.

Jan 1, 1968

By D. L. Albright, R. W. Kraft

High-purity materials have been used in producing as-cast, controlled, colony, and degenerate solidification structures in the Fe-FeS eutectic. Experiments disclosed that this eutectic can be classified as normal and has a natural morphology composed of rodlike iron particles dispersed in a matrix of iron sulfide. The metallography of the various structures was studied, and a preferred crystallography was revealed in the controlled specimens produced by unidirectional solidification. The orientation effects found in these latter specimens are an [001] fiber texture in the -mowth direction of the bcc iron bhase and a texture corresponding to bicrystalline behavior in the hexagonal iron sulfide, with the growth direction near to (2111) poles. The observed texture of the iron phase is considered as indirect evidence that the alloy un-dercooled by at least 75°C before solidification. The unidirectional solidification of binary eutectic alloys has produced materials which exhibit a structure and properties markedly dependent upon the solidification process. In many cases a controlled microstructure with pronounced metallographic and crystallographic anisotropy can be experimentally achieved by proper regulation and balance of the growth rate of the alloy, the chemical purity of the starting materials, and the thermal gradient in the liquid at the liquid-solid interface. The purposes of this investigation were to produce various micro-structures in the Fe-FeS eutectic for subsequent study of their magnetic properties and to correlate the different structures with the solidification conditions in order to obtain a better understanding of the structure of eutectics. The Fe-S equilibrium diagram exhibits a eutectic composed of nearly pure iron and stoichiometric iron sulfide (FeS1.00), with the eutectic reaction occurring at 988°C and 31.0 wt pct S.1 Calculations indicate that this eutectic should solidify with about 9.5 vol pct Fe and 90.5 vol pct FeS, which in turn suggests2 that the micros tructure will consist of a rodlike iron constituent dispersed in a matrix of FeS. This characteristic has in fact been revealed some years ago.3 Thus, controlled solidification of this alloy might yield a material whose micromorphology would consist of very small ferromagnetic iron particles, rod-like in shape and aligned parallel to one another, supported in a matrix of antiferromagnetic FeS. Such specimens, because of the magnetic characteristics of the two phases, would be interesting subjects of study as magnetic materials. Hence the magnetic properties were considered in detail and are reported elsewhere.4 EXPERIMENTAL PROCEDURE The specimens of Fe-FeS eutectic were prepared from ultrapure iron (99.99+ pct) and high-purity sulfur (99.999+ pct). The iron was estimated to contain 60 ppm impurities (99.994 pct Fe) after zone purification.5 The ingots of iron were cut into chips, and the lumps of sulfur were ground into powder. In order to redice any nometallic impurities which might have accumulated during handling, the iron chips were annealed for 5 hr at 750° ± 10°C in a dry hydrogen atmosphere. Immediately after this treatment the chips were blended with the sulfur powder in eutectic proportions; the mixture was tamped into transparent fused quartz tubing and then vacuum-encapsulated under a pressure of 40 to 60µ of Hg. Because FeS expands upon solidification it was necessary to re-encapsulate the initial capsules so that oxidation reactions would be avoided when the inner tube cracked during solidification. For purposes of homogenizing the blended mixtures before solidification, the double capsules were heated to 750° ± 20°C and held for 20 hr; after this treatment the reacted product was weakly agglomerated. Each sample was then loaded into an apparatus for very rapid melting and freezing; this was accomplished by passing a molten zone through the specimen, using induction heating and a traverse mechanism. The resulting specimens solidified in the shape of the quartz tubing. Two sizes of specimens were used in this work, 18 mm diam by 100 mm long and 5 mm diam by 30 mm long. Metallographic examination of several ingots of both sizes after the above consolidation indicated no lack of compositional homogeneity and a random "as-cast" structure, because the travel rate was so rapid that unidirectional solidification was not achieved. Unidirectionally solidified specimens were resolidified in the apparatus shown schematically in Fig. 1, This equipment consisted of a kanthal resistance furnace mounted on the carriage of a zone-melting unit so that the heating element could traverse the length of the sample at a selected rate of speed. Large specimens were solidified with the mechanism tilted at ap-

Jan 1, 1967

By H. E. Nold

THE raw materials of the ceramic industry are mostly clays. This raw material is ground, water is added and the mixture pugged into a moist, plastic, rather stiff mass. From this mass the desired units of manufacture are made (bricks, hollow building tile, sewer .pipe, etc.). These units are dried; then placed in kilns and heated until the desired degree of vitrification is obtained.1 For firing ceramic ware, two distinct types of kilns are used; namely, periodic and continuous tunnel. PERIODIC KILNS Periodic kilns are those ordinarily seen in a brick plant. They are either round or rectangular. The raw, dried, formed ware is piled or set in the kilns to depths frequently exceeding 10 ft. The kiln is heated until the ware is matured, then gradually cooled sufficiently to allow men to remove the ware; then the cycle is repeated. The time duration of the cycle may be more than two weeks.

Jan 1, 1933

By Ravindra M. Nadkarni, Milton E. Wadsworth

The kinetics of cetnentation of copper with iron were observed to follow first-order kinetics and increase with speed of agitation to a limiting value. Maximum rates agree closely with theoretical values based upon a model of aqueous solution diffusion through a litniting boundary film. Back reaction kinetics are shown both theoretically and experimentally to be independent of ferrous iron concentration in solution. The inlportance of attnospheres of air, oxygen, nitrogen, and hydrogen was studied and the results have been correlated with several impovtant oxidation processes involving metallic iron and copper. The kinetics of the reaction of ferric ion with metallic iron were found to be slow in the absence of metallic copper and essentially proportional to the surface area of metallic copper present in the system. THE precipitation of copper on iron is classic as an example of a relatively ancient art applied successfully for centuries with little fundamental understanding of the important parameters involved. There is some indication that the process has been a commercial means to produce copper since the sixteenth century.' The amount of fundamental work on the cementation of copper with iron is not great. Wartman and Roberson2 carried out a series of detailed copper cementation experiments using natural and synthetic mine water. The following were presented as the three principal reactions: Reaction [I] is the desired cementation reaction and accordingly 0.88 lb of iron would produce 1 lb of copper. In actual practice iron consumption would more normally fall in the range of 1.5 to 2.5 lb per lb of copper. Wartman and Roberson attributed the excess consumption of iron to Reactions [2] and [3]. They found that Reactions [I] and [2] proceeded at approximately the same velocity while Reaction [3] was much slower and would be diminished by controlling the contact time. It was also pointed out that increased agitation is beneficial in removing hydrogen bubbles and barren layers of solution at the iron surface as well as removing contaminants resulting from the hydrolysis of iron. Episkoposyan3 and Episkoposyan and Kakovskii4 studied copper and silver cementation on rotating iron disks in chloride solutions. The kinetics based upon a diffusion model were first order and varied linearly with surface area and with angular velocity raised to the one-half power according to the Levich equation. The experimental activation energy for both copper and silver was approximately 3 kcal per per mole. Excess iron consumption was found to increase with temperature. The rate of cementation first increased with increasing acidity and then diminished at high acid concentrations. sutolov5 has presented an excellent review of the Leach-Precipitation-Flotation (LPF) process including a discussion of copper cementation from an electrochemical point of view although few experimental results were presented. From voltage considerations he predicted that cementation should not be influenced by the concentration of ferrous iron in solution. He considered several secondary reactions including Reactions [2] and [3] and pointed out the importance of oxidation of ferrous iron to ferric with oxygen. In addition it was suggested that Reaction [2] was enhanced by the dissolution of metallic copper by ferric iron which in turn consumed excess iron by the cementation reaction, Eq.[1]. Cementation of copper on metals other than iron has been studied by several investigators but, as in the case of iron, the amount of fundamental work is not extensive. Bashkova and kovalenko6 and Bashkova7 studied the cementation of copper on indium from copper and indium sulfate solutions. The rate was found to be first order and to increase with acidity. This was associated with a decrease in potential (EIn — ECu) and the simultaneous reduction of hydrogen ions at low pH. The rate of cementation also decreased with increasing indium concentrations which was postulated to be due to the decrease in the rate of diffusion of the ions in solution. Below 97°C the experimental activation energy was found to have the unusually low value of 2 kcal per mole and was attributed to diffusional control. Above 97°C the rate increased suddenly and was explained as a change in the rate-controlling step to a chemical reaction. In Part I of this study Nadkarni et a1 .1 have reported on preliminary results obtained in a laboratory study of the kinetics of the cementation process. The rate was found to be first order, proportional to the surface area of the iron, and to increase with speed of stirring until a maximum rate was observed. At low stirring speeds the deposit was spongy and adherent. At medium speeds the copper peeled off in bright strips and at high speeds finely divided copper was produced and continually removed from the surface. The amount of excess iron consumed increased with speed of stirring and with temperature. The average experimental activation energy combining results from several types of iron was 5.8 + 1.6 kcal per mole suggesting diffusional control through a limiting boundary film. Traditionally copper cementation has been carried out over the centuries in gravity-fed launders of various design containing scrap iron. More recently rotating drum precipitators and activated launders8'10 have been used. In the latter, copper-bearing solutions are

Jan 1, 1968

By J. E. Sherborne, P. H. Jones, E. C. Babson

A study of the Chapman zone in the Richfield field, Orange County, California, indicates that the quantity of oil recovered by present methods will be only a small portion of the oil originally in place. Since the volume of residual oil is believed to be of large magnitude, an experimental water-flooding operation has been initiated in order to determine whether water-flooding offers promise as an economical method of recovering some of this residual oil. A single injection well was drilled between old producing wells, and a water-treating plant using alum flocculation and chlorination was designed and built. Water has been injected into the input well for six months at rates in excess of 100 bbl. per day. Production from one of the neighboring wells has increased materially, the oil production having risen from 7 to 30 bbl. and the water From I to 40 bbl. per day. While definite conclusions regarding the economic success of water-flooding in the Chapman zone are not justified at this time, it has been demonstrated that water can be injected into the zone on a sustained basis and that this water will displace appreciable quantities of oil from the sand. Introduction As a result of an investigation of subsurface conditions in the Chapman zone of the Richfield field, it was concluded that ultimate oil recovery from this zone would probably be low and that natural water encroachment was so localized as to be of little importance from a recovery stand- point. Furthermore, it was found that in many portions of the zone the wells were approaching an unprofitable level of production. When these data were presented to the management of the Union Oil Co.; their reaction was that an attempt should be made to develop methods of recovering at least a portion of the large quantity of oil remaining in this zone. After some investigation, it was decided that wafer-flooding offered the most likely means of accomplishing this end, but reservoir conditions in the Chapman zone differ so widely from those encountered in any of the flooding projects described in the literature that it was difficult to evaluate the probability of success. Despite encouraging results from laboratory tests, it was not even certain that water would displace an appreciable volume of oil from the Chapman sand under reservoir conditions. Therefore, it was decided to initiate a small-scale project, for two purposes: first, to determine whether water would displace oil from the Chapmall sand and, second, to obtain information and experience for future operations if water-flooding appeared to be a promising method of secondary recovery. Reservoir Data The Chapman zone is the upper of the two producing zones in the Richfield field, being found at depths from 3000 to 3700 fi.. The productive portion of the zolle consists of a large irregularly shaped sand body, which is more than 400 ft. thick at the top of the structure. As the margin of the field is approached, the sand is replaced

Jan 1, 1945

By G. C. Wallick, W. R. Foster, J. G. Savins

A comprehensive review of the salient features of the differentiation method of rheological analysis in Poiseuille flow from its inception circa 1928 is presented. Here no initial assumptions regarding the nature of the function relating rheological parameters to observed kinematical and dynamical parameters are required in the data-analysis process. In contrast, the integration method involves interpreting flow properties in terms of a particular ideal model. It is shown that, although both methods represent modes of solution of the same integral equation, being relatively bias-free, the differentiation method offers a more discriminating procedure for rheological analysis. The application to problems involving plane Poiseuille flow is also described. INTRODUCTION In most instances, the approach to the problem of interpreting the rheological properties of various compositions as they are affected by changes in chemical or physical environment, assaying the characteristics of a particular constituent of a suspension, analyzing flow behavior in terms of interactions between components in a system, to cite but a few examples, has been in terms of what Hersey1 terms the integration method. Briefly, it consists of interpreting flow properties in terms of a particular ideal model. The usual practice of the integration method is to choose a model with a minimum number of parameters because, other things being equal, it is desirable to use the simplest model which will describe the behavior of a real material and yet be mathematically tractable for the requirements of data analysis. This expression is then substituted into an equation which relates observed kinematical and dynamical quantities, such as volume flux Q and pressure gradient ], and angular velocity and torque T, in a capillary and concentric cylinder apparatus, respectively. The rheological parameters appear on integrating, in an expression relating the pairs of observable quantities such as those just given. In many instances a particular model provides a good representation of rheological behavior over a reasonable range of compositional and environmental changes. Just as often, however, it is obvious that the interpretation of rheological changes by the integration method is not providing realistic information about changes in flow behavior. A more general method of interpreting rheological data for a given material is to make no initial assumptions regarding the nature of the function relating rheological parameters to observed kinematical and dynamical quantities, e.g., flow rate and pressure drop in capillary flow or angular velocity and torque in a rotational viscometer. This general method Hersey1 terms the differentia-ation method. Instead of integrating, one differentiates the integral equation with respect to one of the limits, i.e., one of the boundary conditions; the resulting expression contains the same observable quantities just given, their derivatives, and the rheological function evaluated at that boundary. By obtaining these derivatives from experimental data, graphically or by a computer routine, they can be substituted into the differential equation and a graphical form of the function derived. THEORY OF THE DIFFERENTIATION METHOD FOR POISEUILLE-TYPE FLOWS In this introductory paper, two flow cases which are important in viscometry are considered (one for the first time) from the differentiation method of analysis, flow in a cylindrical tube and flow between fixed parallel surfaces of infinite extent, the basic integral equations being formulated in a manner analogous to the way they originally appeared in the literature. In addition, the following ideal conditions will be assumed: (1) an absence of anomalous wall effects, (2) isotropic behavior everywhere, and (3) steady laminar flow conditions. Before proceeding it would seem appropriate to preface the analysis of these flow geometries with the comment that the basic philosophy of the differentiation method could be said to stem directly from the efforts of Herzog and weissenberg2 to indicate systematically the various ways of using

By R. S. Wagner, H. Brown

Criteria for nucleation with the aid of twin planes during crystal growth from the melt are discussed. It is shown experimentally that bismuth crystals can grow from a subercooled melt in a twinned bismdtic form. A mechanism of growth based on the presence of at least me twin plane is proposed. It is well known that faceted growth can be observed in crystals grown from the vapor phase, dilute solutions, or from the melt. Faceted growth, in which the crystal is bounded by its slowest growing faces, will occur if the growth rate is strongly orientation dependent. The addition of atom layers on a facet plane can only occur by two-dimensional surface nucleation or with the aid of an imperfection. Nucleation with the aid of dislocations was proposed by rank' and observed to be of particular importance in crystal growth from the vapor phase. Nucleation with the aid of two-dimensional imperfections, notably twin planes, was suggested by stranski2,3 and Frank.4 A twin plane, terminating at the growth interface, can form a reentrant step at which nucleation can occur at a much smaller super-saturation (or supercooling) than required for two-dimensional surface nucleation. Nucleation by a twin plane usually results in a fast growth rate along a crystallographic direction parallel to the twin plane. Such a nucleation mechanism, based on the presence of a twin plane, has been used by Dawson5 to explain the growth and morphology of sheet-like crystals of paraffin n-hectane. In recent years more evidence was found that nucleation by twin planes occurs frequently in crystal growth from the vapor phase and from dilute solutions, for example, in cadmium,' barium titanate,7 silver,8 silicon9 and gallium arsenide.10 In crystal growth from a supercooled melt, however, nucleation by twin planes has so far only been observed in materials with the diamond or zinc blende structure. Bennett and Longini11 were the first to recognize the important role a single twin plane plays in the growth of germanium dendrites. Subsequently, it was found that a prerequisite for continued propagation of germanium dendrites is the presence of two parallel twin planes which form a self-perpetuating system of nucleation sites.12 Sili- con and some III-V compounds such as InSb also grow dendritically by twin plane nucleation. It appears that the following criteria must be satisfied in order that nucleation with the aid of twin planes can occur: A) The growth form of the material must be faceted." B) The formation of twin boundaries, by a fault in layer sequence during growth, by plastic deformation, or by an accidental meeting of properly oriented crystals, must be possible. C) Twinning must form a reentrant step where the twin boundary terminates at the faceted growth interface. D) These three conditions are necessary, but in certain cases not sufficient for continued crystal growth with the aid of a twin plane. Depending on interface morphology, a combination of more twin planes is sometimes required to form a self-perpetuating system of nucleation sites. This investigation was carried out with the idea in mind that nucleation with the aid of twin planes is a more general phenomenon and should occur in those materials, grown from a supercooled melt, which satisfy the criteria outlined above. It has been found that crystals of high-purity bismuth grown from a supercooled melt can grow by the aid of a twin plane. In the first two sections the faceted growth form and the twinning elements of bismuth are discussed. In the last section prismatic crystals of bismuth, which appear to grow with the aid of a deformation twin are discussed.

Jan 1, 1962

By B. J. Bayles, J. A. Ford, M. J. Salkind

Unidirecltonally sulidijied AL-A13Ni was found to exliibit excellent microstructural stability to 508°C. Above this temperature the transverse micvostructure coarsened in a manner analogous to "Ostwald Ripening", but the A13Ni whiskers did not spheroidize or foreshorlen. The coarsened whiskers reinforced the matrix as effectirely as the finer whiskevs and no reduction in room-temperature tensile strength mas noled after exposure for 90 hr at 96 pel 0-1 the absollite melling temperature of the eulectic. The slability was auribucted to the presence of low-index (and presurrlably lor-energy) cvystallographic interjaces between phases. The driving force for microstructural coursening was presumed to be the reduction of interfacial energy between the phases. Finer micvoslructures were found to coarsen more rapidly than those which weve imitally coarser. FIBER-reinforced metals have been shown to exhibit good short-time tensile properties at elevated temperatures.1-4 However, many elevated-temperature applications require long-time property retention which dictates the necessity for microstructural stability. Two types of instability are common to fiber composities. The first, chemical instability, is due to chemical reaction between the matrix and the relnforcing phase. Petrasek and weeton5 have shown that chemical reaction between tungsten wire and several copper alloy matrices resulted in degradation of the reinforcing phase and reduction in strength of the composite materials. Kreider and Leverant4 have noted similar behavior for boron-reinforced aluminum above 400°C. The second type of instability arises in systems in which the phases are essentially chemically stable with respect to each other and is characterized by spheroidization and/or agglomeration of the reinforcing phase. parratt6 has reported this type of degradation to occur relatively rapidly at moderate temperatures for nickel and cobalt alloys containing whiskers of silicon nitride, aluminum oxide, and silicon carbide and has identified it as "physicochemical" instability. Although both types of instability are the result of the differences in the chemical potential between the fibrous phase and the matrix, they may be differentiated by the fact that the second type, "physicochemi-call' instability, results in little or no net change in the composition or amount of each phase present. It does, however, result in a morphological change which profoundly affects the strengthening mechanism. Chemical interaction. on the other hand, results in a change in the composition and amount of one or more of the phases present, or the appearance of a new phase. In the latter case, the appearance of the mi-crostructure, that of a fibrous phase aligned in a matrix, may remain essentially unchanged, but the chemical degradation of the fiber results in markedly reduced composite strength. This investigation was initiated in an attempt to evaluate the microstructural and related mechanical property changes of a whisker-reinforced eutectic composite after elevated-temperature exposure. The composite system chosen for this study was the uni-directionally solidified A1-A13Ni eutectic which Lemkey. Hertzberg, and Ford7,8 demonstrated to behave as a whisker-reinforced composite. The microstructure of the unidirectionally solidified material consists of aligned needles of A13Ni in a matrix of aluminum. EXPERIMENTAL PROCEDURE Eutectic ingots having a nominal composition of 6.2 wt pct Ni were produced by melting 99.99+ pct A1 and 99.99 pct Ni in recrystallized alumina crucibles in an argon atmosphere. The analyses of the starting materials are listed in Table I. These master heats were cut up? melted by induction heating, and unidirectionally solidified vertically in 1/2 -in.-ID. 6-in.-long graphite crucibles, in a dynamic argon atmosphere. Therma1 gradients in the liquid were determined by measuring the temperature in the melt as a function of apparatus travel distance, as discussed by Kraft and Albright.9 The rate of solidification was assumed to be equal to the uniform rate at which the crucible assembly was withdrawn from the furnace. Ingots representative of nominal growth rates of 2, 5, and 11 cm per hr were produced and the solidification parameters are summarized in Table 11. Ingots used for met allographic analysis were pre-

Jan 1, 1968

By R. F. Mehl, G. T. Horne

Diffusion coefficients and mobilities were determined as functions of concentration in the a phase of the Cu-Zn system. Use was mode of incremental diffusion couples to determine the Kirkendall effect at various concentrations. Darken's analysis was used to calculate the individual diffusion coefficients and mobilities from these data. The general diffusion coefficient is a single-valued function of the concentration in this system to within the limits of accuracy of the experimental methods used. The form of the various functions (diffusion coefficients and mobilities) of concentration is the same in every case: it is essentially the same as the usual D vs c curve. AS Darken' has pointed out, the knowledge that the movements of different atoms diffusing in the same lattice need not proceed at the same rate is old. Ionic lattices are the classical examples; application of the generalization to lattices with metallic bonding was much more slowly accepted. It remained for Kirkendall'' to show clearly that metallic diffusion need not be symmetrical with respect to both species. Several investigators" have confirmed the initial observation of a "Kirkendall effect:" marker movement accompanying diffusion. They have extended it to other systems and conditions. The theoretical interpretations have been many; ne of the first and simplest of these is that of Darken"' which is essentially mechanism independent. Darken has shown that the Kirkendall experiment permlts a calculation of the individual diffusion coefficients and, coupled with activity data, offers a means of measuring the mobilities of the separateatoms in a binary diffusion process. There is no published information on the effects of concentration and temperature on the individual diffusion coefficients or on the mobility values in binary solid solution; this paper provides such information for zinc and copper in a brass. For purposes of clarity, the overall D value obtained, for example, from the Boltzmann-Matano solution to Fick's law, will be designated as the "general diffusion coefficient;" and the diffusion co- efficients for the separate diffusing species will be designated as the "individual diffusion coefficients." Experimental Procedure The authors have accepted Darken's analysis and have measured mobilities on this basis. The findings of da Silva and Mehl are accepted: that the Matano interface, defined as the origin of coordinates for the Boltzmann-Matano solution to Fick's law, coincides with the original weld interface; that the "shift" of a marker is the distance between the Matano interface and the marker; that the observed porosity is too small sensibly to affect this result; and that the shift is a linear function of the Matano area, the area defined as the absolute magnitude of the area on either side of the Matano interface. Alloys: The a-phase of the Cu-Zn system was chosen for investigation. The measurements were made on incremental couples for two separate reasons: l—it has been questioned whether D, the general diffusion coefficient, is a single-valued function of concentration (a comparison of the D-values for couples with small concentration range, e.g., 10 vs 20 pct Zn, against those from a wide concentration range, e.g., 0 vs 30 pct Zn, will answer that question); and 2—on the Darken analysis, the mobility can be determined only at the concentration at which the marker is observed to lie (this is but one concentration in a single couple) but choosing a series of incremental couples in the range between 0 and 30 pct Zn provides mobility values at several concentrations, thus giving mobility as a function of concentration. Four alloys were chosen; nominally, pure copper, copper with 10 pct Zn, copper with 20 pct Zn, and copper with 30 pct Zn. This allowed six different types of diffusion couples to be prepared, promising mobility determinations at six different concentrations, but having a minimum range of 10 pct Zn. The copper was an especially prepared pure copper supplied through the courtesy of the Ameri-

Jan 1, 1956

By J. T. Norton, A. L. Mowry

S. J. SINDEBAND*—(1) Discussing the properties of the powders used, Mr. Rostoker mentioned a silicon powder as being between 150 and 325 mesh. We always had much difficulty in measuring particle size of silicon powder by screen analysis, because of its tendency to agglomerate. I would be interested in the method used to measure these particle sizes. (2) Mr. Rostoker maintains that the measurement of magnetic properties is more accurate in determining complete homogenization of an alloy, than is the X ray diffraction technique. I wonder whether this is really true. Even when diffusion is complete, magnetic properties will change during continuation of the heat treatment, due to change in density and pore shapes, as has been demonstrated by Mr. Rostoker himself. Which effect is faster, the diffusion of the alloy components or the attainment of final density, will, in my opinion, depend very much on initial material and sintering conditions used. For magnetic applications, of course, the magnetic measurements are most suited for determining the point at which equilibrium conditions are reached. (3) I was glad to see that Mr. Rostoker had used sample sizes which are similar to those I had used previously, and I believe that ring samples of about 2 in. od will become more or less standard samples for the determination of magnetic properties of powder metallurgy products. I should like to ask how the density was changed for the samples on which the effect of porosity was investi- gated, and, further, why the sintering temperature used for this series of experiments was so low. It is somewhat surprising that a 24-hr treatment at 850°C acts so much more to spheroidize the pores than a treatment for 1 hr at 1100°C. But the effect seems to be indisputable. I have made an investigation of the influence of sintering temperature for longer times on the maximum permeabilities of iron powder compacts which was presented at the International Powder Metallurgy Conference in Graz, in 1948, and I hope that these results will be published here within a short time. The results of this investigation are confirmed by Mr. Rostoker's findings that the change of time from 1 to 24 hr changes the permeability behavior considerably in the direction as indicated by Polder and Van Santen for spheroidiza-tion of pores. I do not quite understand Mr. Rostoker's explanation of the influ-

Jan 1, 1950

By J. W. Cunningham, W. A. Tiller, D. H. Lane

The effect of ultrasonic vibrations on ingot solidification has been considered both theoretically and experimentally. The theoretical section elucidates the mechanisms by which the ultrasonic vibrations might refine the ingot structure. The experimental section describes a very efficient means of introducing the ultrasonic vibrations to the freezing interface. The application of this technique to the consumable-electrode arc melting process shows that the columnar mode of freezing may be effectively suppressed yielding an ingot structure consisting predominantly of equiaxed grains. The results support the contention that the ultrasonic vibrations increase the nucleation frequency in the layer of liquid adjacent to the freezing interface. CERTAIN structural characteristics of as-cast ingots are undesirable since they create considerable difficulty for subsequent processing and often produce defects in the finished product. These structural defects are illustrated in Fig. 1(a), and are: 1) planes of weakness where columnar grains growing from the different mold faces meet, 2) strength anisotropy due to the preferred orientation of the columnar grains and 3) inhomogeneity due to segregation at dendrite boundaries within the columnar grains and at the columnar grain boundaries. The type of ingot structure that eliminates 1) and 2) and diminishes 3) is the fine-grained equiaxed structure illustrated in Fig. 1(c). Many attempts have been made to produce the desirable ingot structure illustrated in Fig. 1(c) by inoculating, casting with varying superheats, vibrating or stirring, or by irradiation with ultrasonic vibrations. These attempts have met with various degrees of success, the ingots generally having the structure illustrated in Fig. 1(b). All four methods have been the subject of numerous investigations,1"4 the latter producing the most erratic behavior and inconsistent success. The method of ultrasonic irradiation during ingot solidification has shown considerable promise on small-scale ingots (diam 2 in.) but has not yet been successfully adapted to large-scale operation. The present paper considers the application of ultrasonic radiation to ingot solidification both theoretically and experimentally. The purpose of the paper is to elucidate the mechanism by which ultrasonic energy refines the ingot structure and to describe a method for producing the desirable ingot structure in both laboratory scale experiments and in ingots of commercial size. THEORY Conventional Casting—Before discussing the possible effects of ultrasonic radiation upon ingot structure let us first briefly review the reasons for the breakdown of columnar crystallization to equiaxed crystallization during ingot solidification. The following is a slightly oversimplified description. In the conventional method of casting, the alloy having a certain degree of superheat, T, is poured to fill a cold mold which is at room temperature, Tc,. Due to conduction of heat through the mold wall the outer rim of liquid metal cools rapidly to the liquidus temperature and begins to supercool. At some degree of supercooling, nuclei of solid form at random in this supercooled layer at the mold surface. The grains in this chill layer begin to grow inwards producing a solute build-up, thus lowering the freezing temperature at the interface as illustrated in Fig. 2. As growth proceeds, the temperature gradient in the solid conducts away not only the latent heat of fusion evolved during growth but it also conducts away some of the superheat of the melt so that the temperature

Jan 1, 1961

By W. B. Gogarty

With flow of non-Newtonian fluids in porous media, effective viscosities are needed for use in the Darcy equation. These viscosities depend on the rock parameters and flowing conditions. In this investigation, rheological and flow results were correlated to develop an expression for calculating effective viscosities. Surfactant-stabilized dispersions of water in hydrocarbon were used with consolidated sandstone cores of different permeabilities. The average shear rate in a core was related to the permeability and porosity of the core and the frontal velocity through the core. By using the correlation obtained for determining effective viscosity, experimental and theoretical values were compared for each fluid system by determining average and maximum errors. For the fluid system showing the largest average error, the correlation fit 38 experimental points with an average and maximum percentage error of 4.3 and 14.8, respectively. For the fluid system showing the least error, average and maximum percentage errors of 1.8 and 4.3, respectively, were calculated using 29 experimental points. INTRODUCTION Use of non-Newtonian fluids in the petroleum industry is not new. Fluids of this type have been used for many years as fracturing agents and drilling muds. Recently, attention has focused on the use of high molecular weight polymer solutions for secondary recovery. Results have been reported on studies relating to the flow behavior of polymer solutions in porous media.1-4 Each study gives the viscosity in the Darcy equation as a function of the rheological properties of the fluid, the characteristics of the porous medium and the pressure gradient. The functional forms of the reported expressions differ somewhat in each study. The first three studies used unconsolidated porous media while the fourth used a single consolidated core. Because of the limited information available on the flow of non-Newtonian fluids in porous media, further investigation was undertaken in this area. We selected non-Newtonian fluids that did not contain high molecular weight polymers in order to minimize core plugging. The over-all objective was to gain a better understanding of the flow behavior of non-Newtonian fluids in consolidated porous media. Specifically, our goal was to determine the relationship between the average shear rate in a core and the frontal velocity. Because of this goal, it was necessary to determine the effect of permeability on the shear rate-frontal velocity relationship. We wanted to replace the viscosity in the Darcy equation with an expression relating to the average shear rate in the core and the rheological properties of the non-Newtonian fluid. THEORY For a time-independent, non-Newtonian fluid, the apparent viscosity is a function of the shear rate. This relationship is given by µ = F(v')...........(1) With Eq. 1, a single value of shear rate determines the apparent viscosity at that shear rate. With flow in porous media, a spectrum of shear rates occurs at any average throughput. An average shear rate v' can be used to represent the spectrum of shear rates that exists within the core. By using v' and the rheological data given by Eq. 1, an effective viscosity is determined for the flowing fluid. If v' is the correct average, µe becomes the appropriate viscosity for use in the Darcy equation. Under these conditions, flow rate-pressure drop relationships can be determined for non-Newtonian fluids. HOW the correct average shear rate might be related to the frontal velocity through the core and the characteristics of the porous media will now be considered. Later, the experimental data are presented that indicate the validity of these