Mixing

wide variety of unusual impeller designs which are covered in con- siderable detail (4K). Gas-solid contact and heat transfer in typical fluidized rea...
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J. Y. OLDSHUE

Mixina Steady progress is an important aspect of many chemical engineering processes covered in this survey of the 1968 literature

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everal papers added significantly to knowledge of the turbulent velocity fluctuations in mixing vessels (2%-4B). At the other end of the spectrum, viscous mixing can be accomplished by a wide variety of unusual impeller designs which are covered in considerable detail ( 4 K ) . Gas-solid contact and heat transfer in typical fluidized reactors are difficult to control and predict on both small and large scale. There is a growing interest in the use of rotating impellers in these gas-solid fluidized reactors so that reliable and reproducible kinetic data, heat transfer data, and scale-up predictions can be obtained

fluctuating velocity. They found that the root mean square fluctuating velocity was proportional to, among other things, speed and impeller diameter squared. Cooper and Wolf ( 2 B )used a hot wire anemometer probe to measure the velocity from a turbine mixer in air and pitot tubes to measure these velocities in water. Fort and Sedakova ( 3 B ) used a propeller, an axial flow turbine, and a paddle to measure the total circulation in the tank by means of an indicator particle. A simplified mathematical model to establish the rotational velocity profile in a flat-bottom tank was proposed (7B).

(7J,ZJ,5 J ) . Some excellent photographs of gas bubbles around impeller blades appeared (73G). I n biological oxidations which involve solids, liquids, and gases, the role of direct gas-solid mass transfer through a thin liquid film may give an important understanding of the performance of large scale equipment in waste treatment and fermentation processes (76G). An unusually large number of equipment reviews, process reviews, and design methods for liquid-liquid extraction appeared last year. Quantitative data on the mixing of liquids by gas streams compared these results to rotating impeller mixing results (70P,7 3 P ) . The slip velocity between liquids and solids was used to calculate the solid particle Reynolds number in attempting to give a better correlation for liquid-solid mass transfer. I t was concluded, however, that this method did not satisfactorily explain the experimental effects observed (79E). General Mixing

Several reviews treated particular topics and are listed in later sections. The only overall mixing review appeared in IND.END. CHEM.(3A). A very extensive article on various scale-up criteria pointed out that different mixing processes have different applicable scaling rules ( Z A ) . The annual Mass Transfer Review contained references to mixing phenomena ( ? A ) . Impeller Flow and Fluid Dynamics

Schwartzberg and Treybal ( 4 B ) used a streak photography technique to measure fluid velocity and the root mean square of the

Impeller Power Consumption

No articles concerned primarily with power data for conventional impellers appeared during the year. Power data are included in some of the process studies reported in succeeding sections. The use of traditional fluid mechanics equations allows the calculation of power for a smooth rotating disk to be obtained quite accurately (7C). Homogeneous Fluid Mixing with Impellers

A review of impeller flow capacities included data on mixing rates and concentration changes (270). New data on blending processes used radioactive sodium as an indicator ( 7 2 0 ) , neutralization of KOH and HC1 ( Z O ) , and the monitoring of p H of an aqueous acid-base system (740). Hall and Godfrey found that Newtonian fluids mixed faster than non-Newtonian fluids in laboratory sigma-blade mixers (80). Su and Holland presented information on the phenomenon of mixing and on engineering design for nonin non-Newtonian fluids (76D), Newtonian fluids ( 7 7 0 ) . An article by Treiber presented some unique and unusual impeller types for mixing viscous liquids with very clear illustrations of these impellers (790). A review of power consumption and flow patterns was presented by Wohl ( 2 0 0 ) for non-Newtonian fluids. The impulse testing method ( 7 0 0 ) and measurement of average tracer concentration across the actual stream ( 1 5 0 )was used to examine the uniformity in continuous mixing. VOL 61

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T h e use of a model proposing different parameters for a perfect mixing area and a dead zone was studied with particle trajectory, colorimetric, and conductivity methods ( 7 8 0 ) . Cholette et al. ( 4 0 , 7 0 ) developed a critical speed concept and studied the effect of geometry variables on their previously proposed correlation methods. Residence time data for single phase flow of fluids through a multistage agitated column confirmed some proposed mathematical models (730). Two papers discussed chemical reaction in mixing systems ( I D , 71D). The effect of macro-scale mixing on the homogeneous polymerization of styrene in a continuous flow reactor, which was operated with perfect macro-scale mixing, compared paddles and helical spiral impellers ( S D ) . Three unusual processes included the rapid breaking of a barrier between two reactants ( 6 D ) , mixers in metallurgical plants ( 3 0 ) , and water mixing in natural wells and springs (5D).

Solid-Liquid Mixing with Impellers

New experimental data by Nienow ( 7 6 E )show that the impeller speed needed for suspension is a function of impeller off-bottom distance. Another study ( 4 E ) examined the distribution of solid particles in unbaffled tanks. ,4 very extensive review by Buttignol and Gerhart ( 5 E ) summarized the dispersion of pigments in paint processing. T h e use of average velocity gradient to predict the effect of mixing on flocculation systems and water-treating processes referred to typical operations ( 3 E , 8 E ) . The effect of shear rate on carbon black deagglomeration gives quantitative experimental results in a band viscosimeter ( 6 E ) . Mass transfer in a free-fall reactor was compared with a n impeller system (7SE). Both dissolving and crystallizing particles of KzS04were used to examine both aspects of mass transfer (70E). Schwartzberg and Treybal ( 7 9 E ) used slip velocity to calculate the particle Reynolds number and the corresponding mass transfer coefficient. They concluded that this did not explain experimental results satisfactorily. Another paper examined interfacial mass transfer a t the surface of a membrane (77E). Rotating disks are a popular method of examining mass transfer and diffusion (7E, 9E, 72E, 22E). Crystallizers may either have a n impeller in them or use a n external pump. Topics covered included the crystallization of calcium sulfate ( 7 E ) , potassium chromate ( 2 E ) , sodium nitrate (73E), and a variety of inorganic salts (74E). A review of a crystallization symposium summarized several presentations (77E). A unique method of providing continuous countercurrent fluid solids contact, using a n inclined column described previously, was modified by constrictions or weirs (21E). A fluidized bed height can be maintained by using a mechanically driven paddle wheel (20E). In a biological oxidation process, the diffusion of dissolved oxygen into the liquid-solid floc can be one of the rate-controlling steps. An experiment by Mueller et al. (75E)showed the dissolved oxygen concentration a t which the diffusion of oxygen through the Roc matrix controls the oxygen concentration in the floc.

Liquid-Liquid Mixing with Impellers

An unusually large number of reviews and proposed design methods on extraction column design and performance appeared throughout the world (9F-71F, 73F, 75F, 77F, 79F, 25F, 26F). Consideration of break-up of drops ( 7 6 F ) was accompanied by other experiments on mass transfer rates in liquid-liquid dispersion (20F, Z7F). Measurements of interfacial area are helpfTd to understand the overall extraction process (4F, 5 F ) . Excellent data on continuous phase mass transfer coefficients appear in two articles (74F, 23F). Attempts were made to relate these coefficients to existing correlations for other types of particle systems. Data on mass transfer and chemical reaction using a Sherwood stirred cell (27F) were presented. Experimental studies on actual multistage mixing columns included rare earths (GF), propionic acid-water-toluene (72F), light aromatics (24F), phenol extraction ( 3 F ) ,and ammonia as a solvent (ZF). 122

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Other experiments looked a t axial mixing phenomena in multistage columns (7F, ZZF). Misek ( 7 8 F ) ran experiments to determine whether the feed stream or the solvent stream should be dispersed as a function of the separation coefficients. The use of a pulse extraction technique with a rotary agitator offered considerable promise for efficient operation ( I F ) . il study was made of the dispersion band in a mixer-settler for the waterkerosine system ( 8 F ) . Gas-liquid Mixing with Impellers

Tsao (76G)related the depth of a vortex in a Waldhof fermenter to many variables including Reynolds number and Froude number. Photography was used to study the bubble size and interfacial area in gas-liquid contacting systems (73G). Additional data on the oxidation of sodium sulfite in a mixing tank varied gas rate and impeller speed over wide limits ( 8 G ) . Another study examined the effect of pressure on the liquid phase mass transfer coefficient and found that there was a n effect above several atmospheres of pressure (18G). The important case of drawing down gas from the head space of a closed reactor was studied by Boerma and Lankester ( I G ) . Other studies used a mixing vessel, in addition to other devices, to study the kinetics of oxygen-sodium dithionite (6G) and absorption of isobutylene into sulfuric acid (3G). The possibility of direct contact between gas bubbles and solid particles through thin interfacial films in biological oxidation was studied in detail by Tsao (15G). Little prior data existed on the possibility of this direct absorption mechanism. The design of a pilot plant for continuous fermentation (72G) and the important step in the biological oxidation of the dissolution and dehydration of COZ ( 9 G )were studied with a range of mixing and chemical variables. The description of a new pressurized continuous reactor features a method of preventing countermixing of different phases (IOC). Testing of aerators in large basins in waste-treating facilities needs translation methods from standard conditions to field conditions ( 7 IG). Detdiis of surface aerators in waste-treating facilities include data from 5- to 30-hp and liquid volumes from 30,000 to 325,000 gal (2'2). An example of adjusting experimentally dissolved oxygen concentrations in testing surface aerators gives a method for practical testing (5G). 4 paper by Kumke et al. (7G) discusses the translation from an aeration stabilization plant for waste-treating to a completely mixed activated sludge system. A rotating impeller distillation column (17G) and a rotating porous body for dispersion of droplets into gas streams were described (4C). The optimum size impeller in a flotation cell was studied in a suspension of lead sulfide and silica dioxide (74G). Heat Transfer with Impellers

Son-Newtonian fluids were the subjcct of two reviews (SH, 7ZH). The effect of solids in suspension on heat transfer was treated in detail by Frantisak et al. (5H).Experimental data on heat transfer with very high viscosities in a Z-shaped screw-type agitator ( 6 H ) appeared. A relationship for various modes of heat transfer in stirred vessels was presented (70H). Extensive data on scraped surface exchangers were presented by Bott, Azoory, and Porter ( I H , 2H). Luyben ( 8 H )discussed the effect of mixing on the stability of an autorefrigerated reactor. Analytical solutions for chemical reactions and heat transfer in a multicompartment back-mixed column were presented (723). Direct-contact heat transfer coefficients between immiscible liquid layers with simultaneous boiling and stirring were determined experimentally ( Q H ) . Several papers discussed the design and economics of thin-film evaporators ( 7 7H, 13H, 15H). Two theoretical papers werc the mathematical model of heat transfer in Couette flow between concentric cylinders ( 7 4 H ) and natural convection around a vertical cylinder ( 3 H ) .

mpeller Foam Condensation

The use of a self-priming pump to break foam in a fermentation process on a laboratory scale was developed (41). A discussion of many different methods of froth removal in industrial processes was presented by Cechnicki (11). Papers describing foam fractionation separation contained descriptions of the methods used to break and collapse foam (21, 31). Gas-Solid Mixing with Impellers

Description of power consumption and stirring effects data on the power number and fluidized solids gives information useful for these kinds of apparatus ( 3 J ) . The residence time distribution and other stirring effects were measured for impellers in fluidized solids beds ( 2 J ) . A description of two reactors included one using hydrogenation of C2Ha with a nickel powder ( 4 J )and the hydrogenation of powdered iron in a stirred laboratory unit for gassolid reactions ( 5 J ) . The measurement of catalyst kinetics was described (7J). Paste Mixing with Impellers

Three studies were directed a t rubber mixing processes (2K-4K). The effect of a sequence of adding in mixing components to cement mortar mix was described ( 7 K ) . Solid-Solid Mixing

“How to Buy Mixing and Blending Equipment” (IOL)treated present-day industrial practice. Solids mixing is a key element in achieving low-cost and high-quality production ( I IL). Bourne ( 7 L ) used an example of making specifications on two blending properties to illustrate a new blending calculation method. The balance between mixing and segregation in industrial mixers was discussed by Williams (73L). Other general descriptions of solids blending processes used statistical methods ( 7 4 5 ) and presented a general review (9L). A new model for mechanical agitation for beds of solid particles studied the power requirements as a function of bed geometry and many other properties of the solids and impeller (5L). The use of radioactive isotopes as blending tracers included iron nitrate, 65JgFe(N08)8 ( 4 L ) , 24Na benzoate and 82Br naphthalene (12L),‘33Baand I4C (2L),and 24NaC1 (SL). The mixing of salicylic acid and potato starch was studied in cube- and v-type mixers (715). The use of colored layers of granular materials fixed in paraffin after a certain number of impeller revolutions gives a permanent sample for analysis (6L). Wet and dry silica gels were used as a unique method of studying the effect of diffusivity on mixing (3L). Vibrating, Reciprocating, and Pulsating Mixers

A resonant air-pulsed water column was used on open and packed columns with gas holdup as a criterion ( 2 M ) . Two papers discussed pulsed extraction columns ( IOM, 12M). Axial diffusion from a cylinder with pulsed flow used hydrochloric acid in water as a test system ( 7 M ) . A mixer-settler was operated with vibrating perforated plates and was particularly applicable for small scale processes ( 3 M ) . Electromagnetic mixing is used in alloy melting ( S M ) ,and vibration of iron disks was used for zone melting (1.44). Another study examined the effect of vibrations on mass transfer from a sphere for the system benzoic acid-water ( 4 M ) . The effect of ultrasonic energy on several different processes was described in detail ( 5 M , 6 M , 8 M ) . A turbulent film reactor used a mechanism to actually vibrate the entire reactor. Vibration frequencies varied between 500 and 1500 Hz ( I I M ) .

AUTHOR J . Y . Oldshue is Technical Director of the Mixing Equipment Co., Inc., Rochester, N . Y .

Fluid Jets for Mixing

A problem of mixing in long small-diameter tanks by recirculation was presented by Harrell and Perona ( 6 N ) . Mixing characteristics around jets were measured experimentally (ZN, 7 IN, 72N). Reactions in a continuous-flow mixer looked a t the macroscopical mixing and yield of first- and pseudo-first-order reactions (3N-5N). The use of impulse concentration response allowed the performance of a jet mixer to be calculated (7ON). The optimal distance of a nozzle from the mixing chamber in a jet apparatus was calculated theoretically and experimentally (9N). Light-study methods were used to study mixing in a jet apparatus

(7N). Reaction rates under Harris conditions were measured by a combination of on-stream sampling and chromatographic method ( 8 N ) . The mixing of large gas streams in a full-scale mixing chamber for a cold-shot reactor was studied a t atmospheric pressure using air flow as a tracer ( I N ) . Two-Phase Spargerr

Several papers describe the mixing of fluids by means of gas streams. One paper showed that the mechanism was similar to natural convection (73P). Another study compared air mixing with mixing impellers (IOP). Agitation of tall vessels and a useful nomograph are included in the paper by Zlokarnik on the same general topic (20P). Measurements of gas holdup (15P)and mass transfer (74P), were quite extensive. A special type of injector with a ring-shape cross-section nozzle was presented (72P). Several other experiments looked at thermal and mass dispersion A review discussed a variety of in bubble columns (7P,2). bubble column designs ( S P ) . Langemann and Taubert (9P) examined both axial and radial mixing in a bubble reactor. Studies of the ejection of gas and liquid interaction on a vertical wall used the desorption of COZfrom water by air to study the phenomenon involved (7P). The use of air for agitated liquid-liquid contactors was described (6P, 77P). Gas jets and gas bubblers were compared for mixing effectiveness (4P). COZand HZabsorption into a water jet (5P) was studied in an experimental program. Venturi scrubbers are still of interest in many operations ( 3 P , 77P, 78P,79P). An injector jet column was used for the extraction of aromatic hydrocarbons (16P). Flow Distributors

Screen-packed reactors were used for increasing interfacial area for gas-liquid contacting (16Q). The role of packing in the mixing characteristics of a column was covered by Shuki et al. (734). A variety of effects in packed columns was covered (2Q, 44, 6Q, SQ,

70~). A number of investigators looked at mass transfer and mixing effects on perforated plate Pquipment (7Q, 5Q, 7 4 , 9Q, 7 l Q , 144). Methods of scale-up treated the principle of modeling the effect of transverse nonuniformity to make full-scale performance more nearly simulate laboratory performance ( l2Q). The turbulent contactor uses a turbulently agitated packing. I t was studied on SO2 recovery (75Q), and limiting holdup and minimum fluid velocities were obtained (34). Fluidized Beds

Reviews and general discussions on fluidized-bed reactors suggested several design procedures (2R, 6R, 8R, 7 iR). Experimental study of air fluidized beds of cracking catalysts studied back-mixing of gases (IOR). Longitudinal mixing of liquids flowing through fluidized beds presented a generalized correlation (5R). A large number of papers treated the mixing of the solid phase in gas-solid fluidized equipment ( I R , 3R, 4R, 7R, 9R, 72R, 13R, 75R). Astudy of the hydrodynamic properties of a three-phase fluidized bed containing solids, liquid, and gases included a n experimental study of longitudinal mixing in the system (74R). VOL. 6 1

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Flow in Conduits

One study covered the axial dispersion of fluids in a pipeline when they go through elbows and bends (2s). Jepson et al. studied the use of transfer lines as gas-solids reactors (6s). The properties of cocurrent flow of water, air, and quartz particles used a water-soluble tracer gas for experimental studies (IS). Foam formation during the movement of chemical froth in hose and steel pipelines was studied (35’). Several studies on combustion processes including hydrazine hydrogen and oxygen (5.9, and a and nitrogen tetroxide (45’), magnetic roller as a gas mixer (75’)appeared. Mafhernatical Studies of Single-Stage Mixing

A model in which there is mass transfer between the dead space and an active volume in the reactor was derived ( 7 T ) . Krambeck et al. ( 6 T )presented a n engineering model for turbulent mixing systems that allows calculation of both average behavior and fluctuation behavior as well. Four papers treated general types of reaction problems from a mathematical standpoint ( 5 T , Q T ,72T, 74T). T h e problem of scale-up was treated by means of a detailed mathematical model (42”)using kinetic constants in the derivation. Three papers covered the interaction of dispersed droplets ( 2 T , 77T, 73T). Other papers covered gas-liquid reactions ( 3 T ) ,twophase reactions ( 8 T , I O T ) , and countercurrent reactors (773. Mathernotical Studies of Multistage Mixing

A generalization of the tanks-in-series mixing model will be helpful in analyzing multistage processes (3U). A computer model is set up to simulate the effect of mixing in a tubular reactor fed by two segregated miscible streams (5U). Several papers treated the various aspects of back-mixing or residence-time distribution (2U, 4U, 6U, SU-lSU, 2OU-22U). Horn and May discussed the effect of mixing on periodic countercurrent processes (7U). The conversion of two immiscible fluids reacting by second order reaction while in countercurret flow through a series of back-mix reactors showed that equal stage volume is always optimum ( I U ) . Theoretical treatment of heat and mass transfer particle systems shows the possibility of obtaining transfer reversal (79U).

REFERENCES GENERAL MIXING (1A) Gomezplata, A , , and Regan, T. M., “Mass transfer,” IND.‘ENG.CHEM.,60 (12), 53 (1968). (2A) Nagata, S., and Yamamoto, K. “Criteria for the scaling up ofmixing vessels ” Memoirs of the Faculty of Eng.,’ Kyoto L‘niv. XXIX, Pt. I (January 196:) Japan. (3A) Oldshue, J. Y., “Mixing,” INn. END.CHEH.,60 (111, 24 (1968). PATENTS (4A) Konecny, V., et al., “Laboratory equipment for chemical reactions under reflux and stirring,” Czech. Patent 127,324 (May 15, 1968); C A , 70, 489523’ (1969). (5A) Schwartz, E., and Csiszar, A . “Device for stirring with adjustable position,” Romanian Patent 48,896 (Xov. Z?, 1967); C A , 69, 37449d (1968). IMPELLER FLOW AND FLUID DYNAMICS (1B) Baraf, L. “Model of the hydrodynamics of stirring,” Rev. Chim. (Bucharest), 19 (E), 468 (1968); C A , 70, 30431d (1969). (2B) Cooper, R . G. and Wolf D., “Velocity profiles and pumping capacities for turbine type impeflers,” Can. 2. Chem. En!., 46, 94-100 (April 1968). (3B) Fort, I., and Sedakova V. “Mixing. XX. Pumping effect of high-speed rotary mixers,” Collect. Czeci. Cdem. Cornmun., 33 (3), 836 (1968); CA, 68, 1 0 6 3 8 1 ~ (1968). (4B) Schwartzberg, H . G., and Treyhal, R. E. “Fluid and particle motion in turbulent stirred tanks. Fluid motion,” IND.EN&.CHEH.FUNDAM., 7 ( l ) ,1 (1968). IMPELLER POWER CONSUMPTION (IC) Ulbrecht, J., and Wichterle, K., “High speed agitators in laminar flow. Simulation of mechanical agitation by rotating disks,” Chem.-Zng.- Tech., 39 ( l l ) , 656 (1967); CA, 69, 1 0 7 9 7 1 ~(1968). HOMOGENEOUS FLUID MIXING WITH IMPELLERS (1D) Bakos M . “Development of chemical reactor engineering,” Magy. Kcm. Lapla, 23’(5), 270 (1968); CA, 69, 20649w (1968). (2D) Begachev, V. I. et al. “Intensity and effectiveness of agitation of mobile media,” Tr. Lening:ad. .k’~uch.-Zssled.Konstr. Znst. Khim. Mashinostr., 1967 (2), 66; C A , 69, 108136n (1968). (3D) Bornatskii, I. E., et 01. “Operations of mixers in metallurgical plants,” Stal’, 28 ( Z ) , 122 (1968); CA, 69, 4454y (1968). (4D) Cloutier, L., and Cholette, A,, “Effect of various parameters on the level o mixing in continuous flow systems,” Can. J . Chem. Eng., 46 (4), 82 (1 968).

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(5D) Davis, G. H. et al., “Annual variation of the tritium content of ground waters of the Vienna Basin,” Verh. Geo!. Bundesabst., 1967 (1-2), 212; CA, 69, 4 5 9 0 4 ~ (1968). (6D) Farber E. A. and San Martin R. L., “Studies and analyses of the mixing phenomenh of liiuid propellants ieading to a yield-time function relation,” Ann. A’. Y . h a d . Sci., 152 (l), 666 (1968): CA, 70, 69721y (1969). (7D) Garceau, J., Cloutier, L., and Cholette, .4., “Effet du diamktre de l’agitateur et de la largeur des chicanes sur le niveau d’agitation en rCgime continu et sur la puissance dissipet,” Can. J. Chem. Eng., 46 (Z), 88 (1968). (ED) Hall K. R. and Godfrev J. C. “Mixing rates of highly viscous Newtonian and noA-Xewtbnian fluids ’(n a laboratory sigma-blade mixer,” Trans. Inst. Chem. Eng., 46 (7), T205-T212 (1968); CA, 69,108029e (1968). (9D)Harada, M . , et al., “Eflect of micro-mixing on the homogeneous polymerization of styrene in a continuous flow reactor,” J. Chem. Eng. (Japan), 1 (2), 148 (1968); CA, 70, 29398s (1969). (10D) Inoue I and Satoh K. “Mixing characteristics in a continuous stirred vessel. AiaiGsis of impulsk teiting method,” Kagaku Kogaku, 29 (7), 518 (1965); CA, 69, 60315r (1968). (11D) Mutzcnberg A. B. and Giger A “Chemical reactions in thin-film equipment,” Trans. Init. Che;. Eng., 4 6 (7),’+187-T189 (1968). (12D) Pippel, W., et nl., “Mixing rocesses investi ated by radioactive sodium-24,” Isotopenpraxis,4 (9), 363 (1968); 7 0 , 7 9 5 0 6 ~8969). (13D) Rehakova, M., and Novosad, Z “Multistage column reactors. IV. Residence-time distribution for one- hase’kow in a mechanically agitated system,” Collect. Czech. Chem. Commun., 33 80),3097 (1968); CA, 69,979958 (1968). (14D) Ruban, E. A., and Kafarov, V. V “Determination of the mixing time in a stirred apparatus,” Zh. Prikl. Khim., 41 ?2), 301 (1968); CA, 69, 20700j (1968). (15D) Snider, D., and Corrigan, T. E., “Measurement of thoroughness of mixing,” A.I.Ch.E. J.,14 (5), 313 (1968). (16D) Su, Y. S., and Holland, F. A. “Agitation and mixing of non-Newtonian fluids. I. Critical study of pbeno&na,” Chem. Proc. Eng., 49 (a), 77 (1968); C A , 69, 7 8 7 4 9 ~(1968). (17D) Su, Y. S., and Holland, F. .4., ibid., Part I1 “Agitation and mixing of nonNewtonian fluids, 11. Engineering design,” 49 (6) 110; CA, 69, 98005~(1968). (18D) Takamatsu T. and Sawada, T. “Mixing efficiency of a mixer,” Kagaku Kogaku, 32 (11),’1115 (1968); CA, 70, 3b432e (1969). (19D) Treiber, H., ‘‘Mixing viscous liquids,” Technik, 9, 442 (1968); Brit. Chem. Eng. Suppi. (Nov. 19681, p 67. @OD) Wobl, M. H., “Mixing of non-Newtonian fluids,” Chem. Eng., 75 (le), 113 (1968). (21D) Yamamoto, I. “Flow in equi ment 111. Mixing bath,” Kagaku Kogaku, 32 (51, 423 (1968):’CA, 70, 5454,f $969):

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PATENTS (22D) Akaboshi, M., et ai. (to Kurashiki Rayon Go., Ltd.) “Mixing a relativelv viscous liquid [poly(vinyl acetate) I with a relatively no;-viscous liquid (aq&ous sodium hydroxide),” U.S. Patent 3,386,981 (June 4, 1968). (23D) Bugoiu: D., (to Romania,, Ministry 0: Petroleum) “Apparatus for synchronizing the mixing of two solutions and slide valve for taking an average sample,” Romanian Patent 47,938, (Nov. 15, 1967); CA, 69, 11694e (1968). (24D) Roth, W. (to Gcwerkschaft Keramchemie) “Mixing of materials,” German Patent1,277,732 (Sept. 12, 1968); C A , 70, 1 0 8 1 4 9 ~(1969’). (25D) Yamashita, H., et al., “Mixer reactor,” British Patent 1,103,031 (Feb. 14, 1968); CA, 68, 884740 (1968). SOLID-LIQUID MIXING WITH IMPELLERS (1E) Amin, A. B., and Larson, M. A., “Crystallization of calcium sulfate from phosphoric acid,” IND.ENG.CHEM.PROCESS DES. DBVFLOP., 7 (I), 133 (1968). (22) Baranov, G. P., et a!. “Continuous vacuum crystallizers with pro eller pump circulation,” Khim. A‘e,ft.’Mmhinostr.1968 (61, 8 ; CA, 69, 5 3 1 0 8 ~(19687. (3E) Benze, F. “Coagulation and floc stability in shear flow,” Chem.-lng.-Tech., 39 (19), 1116’(1967);CA, 6 8 , 1 4 4 7 3 ~(1968). (4E) Braginskii, L. M., “Axial distribution of solid particles in an apparatus without baffles,” Teor. Om. Khim. Tekhnol., 2 (11, 146 (1968); CA, 68, 88523k (1968). (5E) Buttignol, V., and Gerhart, H. L., “Polymer coatings. Pigment dispersion,” IND.E N G &EliI., . 60 (a), 68 (1968). (6E) Cozzens, S. L., et al., “Carbon black deagglomeration during laminar shear,” J . Paint Tech., 40 (518), 99 (Mar. 1968). (7E) Daguenet, M . , “Mass transfer in solution studies by using rotating ring-disk electrodes,” I n t . J . Heat .hriass Trans., 11 (111, 1581 (1968); C A , 70, 304188 (1969). (8E) Gates, C. D., and McDermott, R . F.: “Characterization and conditioning of water treatment plant sludge,” J . Amer. Water Works Assoc., 60 (3), 331 (1968). (9E) Hansford, G. S . , and Litt, M., “Mass transport from a rotating disk into power-law liquids,” Chem. Eng. Sci., 23 (81, 849 (1968): CA, 69, 8 8 3 1 9 ~(1968). (10E) Ishii, T., and Fujita, S., “Dissolution rate and growth rate of crystal particlesin stirred tanks,” Kagaku Kogaku, 29 (51, 316 (1968); CA, 69, 44865q (1968). (11E) Kaufmann, T. G., and Leonard E. F. “Mechanism of interfacial mass transfer in membrane transport,” A.Z.Ck.E. J.,’14 (3), 421 (1 968). (12E) Kishinevskii, M . Kh., et a!., “Mass transfer from rotating and stationary disks to turbulent liquid flow,” Teor. O m . Khim. Tekhnol., 2 ( 2 ) , 1 9 9 (1968); C A 68, 10637% (1968). (13Ef M,:tusevich, L. N., and Baranov, G. P., “Vacuum crystallizer with a propeller pump, Chem. Prum., 18 (6),301 (1968);CA, 69,53109~(1968). (14E) Mitsuda H et al. “Experimental study of the formation of secd crystals,” Kagaku Kogaku, 26 (11),’1086 (1967):Znt. Chem. Eng., 8 (4), 733 (1968). (15E) Mueller, J. A., B,oyle, W . C., and Lightfoot, E. Y “Oxygen diffusion through zooloeal flocs, Biotech. Bioeng., X (31, 331 (1968).’ ” (16E) Nienow, A. W., “Suspension of solid particles in turbine-agitated baffled vessels,” Chem. Eng. Sci.,23 (12), 1453 (1968); C A , 70, 392420 (1969). (17E) Nyvlt, J., and Dvorak, V., “Industrial crystallisation,” Brit. Chem. Eng., 13 (51, 691 (1768). (18E) Schiemann G . et al. “Heterogeneous reactions in a free-fall reactor,” Chem.-lng.-Tech.: 40 [21-22)’, 1050 (1968); CA, 70, 30362g (1969). (19E) Schwartzherg, H. G., and Treybal, R. E., “Fluid and particle motion in 7 (l), turbulent stirred tanks. Particle motion,” IND. ENG. CHEM.FUNDAM., 6 (1968). (20E) Shasherin R . V. and Verteshev, M . S “Overflow device (paddle-wheel t pe) in a m;ltistage’counrercurrent appariius with a KU-2 cation exchange Juidized bed,” Khim. Prom., 44 (6), 471 (1968). (21E) Shulman, H. L., et ai., “Development of a continuous Countercurrent fluid solkds contactor. Improvement of contacting efficiency,” I N D . END. CHEM. PROCESS DES.DEVELOP., 7 (41, 493 (1968). (22E) Zeh, D . W., and Gill, W . N., “Convective diflusion in rotating disk systems with an imperfect semipermeable interface,” A.I.Ch.E. J., 14 (5), 714 (1968).

PATENTS (23E) “Multistage crystallization apparatus,” British Patent 1,128,718 (Oct. 2, 1968); CA, 70, 1 2 9 0 1 ~(1969). (24E) Moells, H. H., et al. “High-speed sand grinder,” German Patent 1,230,657 (Dec. 15, 1967); CA, 70,’5409u (1969). (25E) Stamicarbon N V “Continuous centrifugal mixing of solids,” Netherlands Application 6,61k,200 ( i p r i l 9, 1968); CA, 69, 2 8 8 2 5 ~(1968). LIQUID-LIQUID MIXING W I T H IMPELLERS (lF),Angelino, H., et al., “Efficiency of a ulsed extraction column with rotary agitators,” Brrt. Chem. Eng., 12 (12), 1893 6967); CA, 68, 41577r (1968). (2F) Barton, P., McCormick, R. H., and Fenske, M . R “Ammonia the versatile liquid extraction solvent,” IND.END. CHEM.Pnooesb DES. DEVELOP.,7 (3), 766 . .. (1968). (3F) Boyadzhiev, L., and Angelino, H . “Removal of phenol from waters with the aid of a rotary-disk pulsed extractor,:’ Z h . Prikl. Khim. (Leningrad)., 41 (lo), 2251 (1968); CA, 70, 31511s (1969). (4F) Fernandes, J. B., and Sharma, M. M “Effective interfacial area in agitated liquid-liquid contactors,” Chem. Eng. Scr.:)22 (lo), 1267 (1967). (5F) Gel’perin, N. I., et al., “Interfacial surface in box-ty e extractors,” Zh. Vses. Khzm. Obshchest., 13 (3), 350 (1968); CA, 69, 60320p (19687. (6F) Gel’perin N. I., Pehalk, V. L., and Shashkova M . N., “Mass transfer and longitudinal kixing in a horizontal tubular multisebtion extractor,’’ Khim. Prom. (Moscow), 44 (ll),858 (1968); C A , 70,304062 (1969). (7F) Goncharenko, G . K., and Gotlinska a A P radial axial resi; british ‘Chem. dence time distribution,” Zhur. Prikl. K i n k . , ‘40 ‘(3;:%?8967) Eng., 12 (12) (1967). (8F) Gondo S . et a[. “Height of the dispersion hand in a settler for the waterkerosine s$ste&” Kdgaku Kogaku, 32 (9), 923 (1968); CA, 70,21236s (1969). (9F) Hanson C. “Liquid-liquid extraction methods and equipment,” Brit. Chem. Eng. hquijment Suppl. (Nov. 19681, p 49, (10F) Hanson C ibid. “Recent research in solvent extraction,” Chem. Eng. ( N . Y . ) ,75 (is),i’35 (1668). (1 1F) Hanson, C., ibid. “Solvent extraction. Theory, equipment and commercial operations,” 75 (lk), 76. (12F) Jacqmain D . et ai., “Countercurrent li uid-liquid extraction column,” Rev. Ferment. 2nd. Aiiment., 23 ( l ) , 7 ( 2 ) ; (Z), 45 8 9 6 8 ) ; CA, 70, 30340y (1969). (13F) Jeffreys G. V “Extraction column design,” Chem. Process Eng., 49 ( l l ) , 111-15,122 11968);”CA, 70, 3037% (1969). (14F) Kagan, S . Z., et al., “Continuous phase mass transfer coefficients for liquid-liquid s stems in a flow-type mixer,” Zhur. Prikl. Khimii, 40 ( l l ) , 2478 (1967); Brit. Zhem. Eng., 13 (5), 708 (1968). (15F) Zbid. “Li uid-Extraction,” Teor. Om. Khim. Tekhnol., 2 (l), 21 (1968); CA, 68,?99002 (1 968). (16F) Karam, H. J., and Bellinger, J. C “Deformation and breaku of liquid droplets in a simple shear field,” IND.”ENCI. CHEM. FUNDAM. 7 &), 576-81 ~

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(17F) Mecklenbur h J. C and Hartland S. “Two-phase countercurrent extraction with kiLh backkxing,” Chem. E&. 5k., 23 (12), 1421 (1968); CA, 70, 392521 (1969). (18F) Misek, T. “Operating conditions in mechanical liquid extractors,” Chem. Prmysl. ( Z ) , 70 i1968); Int’lChem. Eng.,8 (3), 439 (1968). (1 9F). Mumford, C. J. “Advances in equipment for liquid-liquid extraction,” Brit. Chem. Eng., 19 981 (1968); CA, 69, 602125 (1968). (20F) Oshima, E., and Miyauchi T “Reaction technology. Reaction technology of li uid systems. Dispersion bf h x t u r e s and reaction rate,” Kagaku Kogaku, 30 ( 3 , 4 9 0 (1966); CA, 69,3975s (1968). (21F) Otake T. and Komasawa, I., “Heterogeneous liquid-liquid reactions. Segregatioh of’a dis ersed phase in a continuous stirred tank reactor,” Kagaku Kogoku, 32 ( S ) , 475 (f968); C A , 70, 39258k (1969). (22F) Ro$ V “Longitudinal mixing in the dis ersed phase in rotating disk extractor Cdect. Czech. Chem. Commun., 33 (9x 2855 (1968); CA, 69, 883301 (1968): (23F) Schindler, H. D., and Treybal R . E., “Continuous- hase mass transfer coefficientsfor liquid extraction in igitated vessels,” A.I.Cx.E. J., 14 ( 5 ) , 790 (1968). (24F) Simon F. and Mozes, Gy., “Chemical engineering investigation of the extraction ‘of light aromatic hydrocarbons in a mechanical assembly,” Conf. Chem. Chem. Process. Petrol. Natur. Gas, Plenary Lect., Budapest, 1965 (Pub. 1968), 231-40; CA, 69, 78758%(1968). (25F) Strobe1 W. “Extraction apparatus,” Chem. Tech., 12, 720 (1967); Brit. Chem. Eng.,’13 (7G?II. ( h f o s c o u ) , 44 (IT), 842 (1968); CA, 70, 30446n 69697. (POP) Zlokarnik, M. “Homogenizing liquids with ascending gas bubbles,” Chem.Ing.-Tech., 40 (15),’765 (1968); C A , 69, 8 8 3 9 2 ~(1968).

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PATENTS (21P) Boiko, I. D. (to All Union Scientific Res. Inst. of the Biosynthesis of Protein Substanccs) “Saturating liquids with oxygen,” French Patent 1,493,910 (Sept. 1, 1967); ’CA, 69, 206836 (1968).

FLOW DISTRIBUTORS (1Q) Angelo, J. B., and Lightfoot, E. N., “Mass transfer across mobile interfaces,” A.Z.Ch.E. J., 14 (4), 531 (1968). (ZQ) Baird, M . H. I., et al. “Solvent extraction in an air-pulsed packed column,” Can. J . Chem. Eng., 46 (8),’249 (1968). ( 3 4 ) Chen, B. H., and Douglas, W. J. M., “Li uid hold-up and minimum fluidization velocity in a turbulent contactor,” ibid. 245 (1968). (4 ) Dil’man V. V et a/. “Longitudinal mixing of a liquid in packed scrubbers,” P&. Khim. (&ingrh), 41 ( l l ) , 2488 (1968); CA, 70, 592669 (1969). (5 ) Eduljee H E “Pressure dro and li uid mixing on sieve plates,” Chem. Age %ndia), 17 (8),645)(1966); CA, 6 6 10802?b (1968). ( 6 4 ) Kafarov V. V. et al. “Agitation in the solid phase of a packed extraction column,” T;. Mork.’Khim.:Tekhnol. Znst., 1967 (56), 27; CA, 70, 5495u (1969). ( 7 4 ) Krishnamurthy, R., and Rao, C. V., “Effect of number of holes on masstransfer rates in perforated- late, liquid-li uid, extraction towers: Pegasolbutyric acid-water system,” Chcm. j g e (India), 19 ?2), 106 (1968); CA, 68,88538~(1968). (8Q) Mellish, W. G “A plicability of dispersion results to packed columns,” A.I.Ch.E. J., 14 (4),”668 8968). (9Q) Ot?ke, T., and Komasawa, I., “Longitudinal dispersion,;haracteristics of liquid in perforated-plate columns with countercurrent flow, Kagaku Kogaku, 32 ) . 583 CA. - -( 6~ - , 11968): , - ~ ,, ~ , 69., 60310k 11968). . . (lOQ), Ot,ake, T., et al., “Longitudinal dispersion of fluid through countercurrent liquid-liquid packed bed,” ibid., 29 ( 5 ) , 322 (1965); CA, 69, 107988~(1968). ( l l Q ) ,Piterskikh, D. G. “Mixing of liquids on sieve plates,” Zh. Prikl. Khim. (Lenmgrad),41 (5), 103i (1968); CA, 69, 374949 (1968). (l2Q) Rosen, A. M., 81 al., “Some modellin problems in the development of mass transfer equi ment,” Teor. Osn. Khim. Tefhnol., 1967 (4), 446; Znt’l Chem. Eng., 8 ( Z ) , 243 ( 1 f 6 8 ) . (13Q) Shuki, A.,.:, et nl., “Chemical reactors. Influence of packing on effective reactor volume, INn. ENC.CHEM.PROCESS DES.DEVELOP., 7 (3), 433 (1968). 2 . “Liquid dispersion coefficients on perforated plates with (144) Sterbac::, downcomers TraAs. Znst. Chem. Eng., 46 (5), T167-171 (1968); Pub. Chem. Eng. (London) 219: (1968); CA, 69, 53181r (1968). (l5Q) Tsugawa, H., and Senkai, Y., “Experiment with T.C.A. (turbulent contact absorber),” Ishikawujirna-Harima Giho, 8 (40), 197 (1968); CA, 69, 37413n (1968). (164) Voyer, R. D . and Miller A. I “ I m roved gas li uid contacting in cocurrent flow At.’Energy ca;. Ltd:: Chafk River 1 9 6 z AECL-2765, 29 pp. (Avail. CAN); CA, 69, 98006d (1968).

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PATENTS (17Q) Kielback, A. W. (Aluminum Laboratories, Ltd.) “Process and a p aratus for mass transfer between a liquid and a gas,” German) Patent 1,274,075 h u g . 1, 1968); CA,69,88254u (1969). (18Q) Lerner B J “Gas-li uid contacting apparatus,” British Patent 1,097,473 (Jan. 3,1968);’ C i , 69, 44882s (1968). (19 ) Schnell H. “Improved mass transfer between gas and li uid in acked c%mns,” GkrmAn Patent 1,268,593 (May 22,1968); CA, 69,28839~(1968. (20Q) Whiton L. C and Petersen A. A “Packing for countercurrent liquid-gas contacting s;stem,’;’U.S. Patent 3,’364,6$6 (Jan. 23, 1968). FLUIDIZED BEDS (1R) Aoki, R., and Yamazaki, R . “Particle mixing in a packed fluidized bed,” Funsai, 1968 (131, 3; CA, 70, 548ip (1969). (2R) Baerns M “Technological properties of fluidized layers of powdered solids,” Chbm.-Zng.-’Tecx., 40 (15), 737 (1968); CA, 69, 97946y (1968). (3R),Baskakov, A. P., and Gimpel’man, E. Ya., “Mixing of the solid particles in adjacent fluidized beds as studied by an unsteady-state method,” Khim. Prom., 44 ( G ) , 412 (1968); CA, 69,448589 (1968). (4R) Carlos C. R. and Richardson, J. F., “Solids movement in liquid fluidized beds. 11.’ Meadrements of axial mixing coefficients,” Chem. Eng. Sci., 23 (8), 824 (1968); CA, 69,883159 (1968). (5R) Chung, S. F. and Wen C-Y “Lon itudinal dispersion of liquid flowing through fixed andfluidized bkds,” >.Z.Ch.g J., 14 (6), 857 (1968). (GR) Gunn, D . J., “Mixing in acked and fluidized beds,” Chem. Eng. (London), 1968 (219), CE 153-CE-172; 69,53142d (1968). (7R) Ivanets, V. N., et al., “Methods for determining the intensity of the linear mixin of loose materials in flow t pe apparatus,” Khim. Tekhnol. TopI. Masel, 13 (lopi, 41 (1968); CA,70,12953w 6969). (8R) Latham, R., et a[., “Back-mixing and chemical reaction in fluidized beds,” Brit.Chem. Eng., 1 3 (5), 666 (1968); CA,69,28856g (1968). (9R) Milosavljevic, J., and Jovanovic, D “Application of the tracer techni ue in the investigation of solid phase mixing ‘in a tapered-bed column,” Nukl. &erg., 4 (3), 6 (1967); CA, 69, 40181 (1968). (10R) Miyauchi T.,et a[., “Fluid and particle dispersion in fluid-bed reactors. Experimental investigations by steady heat-transfer and steady backmixing of adsorptive gases,” J. Chem. Eng. Jap., 1 (1),72 (1968); CA, 70,304171 (1969). (11R) Naik S . C. “Performance of fluidized-bed reactors,” Chem. Age (India), 19 (194), $76 (19i8); CA, 6 9 , 2 8 8 2 6 ~(1968). (12R) Oigenblik, A. A et al. “Effect of the gas distributor on solid- hase mixing and on heat transfer a fluidized bed,” Khim. Prom., 44 ( 8 ) , 615 (1&8); CA, 69, 787351 (1968). (13R) Pippel W., et al., “Mixing of solid in gas solid fluidized beds,” Chem. Tech. (Berlin), 20’(12), 750 (1968); CA, 70, 7 9 5 0 5 ~(1969). (14R) Vail, Yu. K., et al “Turbulent agitation in a three-phase fluidized bed,” Khim.i. Tekhnol. Tapliu. t”Masei, 12,4 (1967); Znt’lChem. Eng., 8 @), 293 (1968). (15R) Woolard, I. N., and Potter, 0. E., “Solids mixing in fluidized beds,” A.Z. Ch.E. J., 14 (3), 288 (1968).

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FLOW IN CONDUITS (1s) Afschar, A. S., and Shugerl, K., “Eigenschafter von Dreiphasen-Fliessbetten mit Gleichstrom von Wasser und Luft,” Chem. Eng. Sci., 23 (3), 267 (1968). (2s) Aunicky, Z. “The longitudinal mixing of liquids in bends,” Can. J . Chem. Eng., 46 ( Z ) , 27’(1968). (3s) Bogdanovich, F. A. “Foam formation during movement of chemical froth in hose lines and steel pipklines,” Izu. Vyssh. Ucheb. Zaued., Energ., 10 (4), 88 (1967); CA, 69, 107965~(1968). (4s) Burrows M. C “Mixing and reaction studies of hydrazine and nitrogen tetroxide b’ using“photographic and spectral techniques,” NASA Tech. Note 1968, NASKTN D-4467, 22 pp (Available CFSTI).

(5s) Jenkins, D. R., et al., “Combtstion of hydrogen and oxy en in a steady-state flow, adiabatic, stirred reactor, Symp. Combust., 1966 (117, 779 (Pub. 1967); CA, 69,108080q (1968). (6s) Jepson, G. et al. “Properties and uses of transfer lines as gas/solids reactors ” Proc. A.Z.Ch.d.-I. d e m . E . Joint Mtg. London, 1965 (3), 41-6; CA, 68, 3151in (1968). (7s) McLaren, K . G., and,Williams, W. T. “Simple, automatic, ma netic-roller. gas-mixing device,” J . Scr. Instrum. [2], 1 (J), 561 (1968); CA, 68, 97%56n (1968),

MATHEMATICAL STUDIES OF SINGLE-STAGE MIXING (1T) Corrigan, T. E., and Beavers, W. O., “Dead s ace interaction in continuous stirred tank reactors,” Chem. Eng. Sci.,23 (9), 1803 (1968); CA, 69, 1 0 8 0 0 5 ~ (1968). (2T) Gal’Or B and Padmanabhan, L., “Coupled energy and multicomponent mass tranher ‘in dispersions and sus ensions with residence time and size distributions,” A.Z.Ch.E. J., 1 4 (5), 709 $968). (3T) Hashimoto, K et a[. “Effects of mass transfer on the selectivit of the gasliquid reactions,” C h d . Eng. Jupnn 1 (21, 132 (1968); CA, 70, 3 9 2 % ~(1969). (4T) Kafarov V., et a/.$ “Problems of scaling-up batch reactors,” Teor. Osn. Khim. Tekhnbl., 2 (3), 331 (1968); CA, 69, 44880r (1968). (5T) Kilkson, H. “Generalization of various polycondensation problems: T h e concept ofslow h u x , ” IND.ENC.CHEM.FUNDAM., 7 (3), 354 (1968). (6T) Krambeck F. J. et a[. “Stochastic models mixing for chemical reactors,” IND.ENG.C H ~ M F u. ~ & M . , ’ ~(Z), 276 (1968). (7T) Langemann, H., “Axial diffusion and mixing in steady-state, two-phase, countercurrent reactors,” Chem.-Ztg., Chem. A@., 92 ( l l ) , 391 (1968); CA, 69, 44851g (1968). (8T) Ma Yi H and Evans L. B “Transient diffusion from a well-stirred reservoir to k body’bf arbitrary Ahape,;’ A.Z.Ch.E. J., 14 (6), 956 (1968). (9T) Menkes, J., and Tchen, C. M., “Spectrum of turbulence and concentration fluctuations with chemical mixing and reactions,” U.S. Clearinghouse Fed. Sci. Tech. Inform. AD 1968 AD-670737 28 pp. Avail. CFSTI. From U S . Gout. Res. Deuelop. Rip., 68 (16)), 151 (1968): (10T) Schaftlein, R. W., and Russell, T. W. F., “Two-phase reactor design. Tank-typereactors,” IND.ENG.CHEM.,60 (5), 1 2 (1968). (11T) Steidl, H., “Mixing. X X I . T h e distribution function of the characteristic size of drops dispersed in a turbulent medium,” Collect. Czech. Chem. Commun., 33 (7), 2191 (1968); CA, 69,44859r (1968). (12T) Takamatsu T et a[. “The effect of fluid mixing on the maximum yield and the optimum ter)np&aturd profile in a tubular reactor (I-autocatal tic reaction),” Mem.Fac. Eng. Kyoto Uniu., 29 (3), 225 (1967); CA, 69, 1079539 (1J68). (13T) Valentas, K . J., and Amundson, N. R., “Influence of droplet size-age distribution on rate processes in dispersed-phase systems,’’ INn. ENC.CHEM.FUNDAM., 8 (I), 66 (1968). (14T) Vol’ter, B. V., et a/., “Fluctuating rocesses in open chemical systems with complete mixing,” Kolebatel‘n e Protsessy Iiol. Khim. Sist., Tr. Vses. Simp.Pushchinoon-Oka, USSR,1966,207 (Pu8.1967); CA, 69, 98030g (1968).

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MATHEMATICAL STUDIES OF MULTISTAGE MIXING (1 U), Ah!uwalia, M . S., and Levenspiel, O., “Reaction between two immiscible fluids in countercurrent flow in a series of stirred tanks: design equations and optimum operations,” Can. J . Chem. Eng., 46 (6), 443 (1968); CA, 70, 39226y (1969). (2U) f33hoff, K. B., “Accuracy of the axial dispersion model for chemical reactors, A.Z.Ch.E. J., 14 (51, 820 (1968). (3U) Buffham B. A and Gibilaro L G. “A generalization of the tanks in-series mixing moddl,” A.’i.Ch.E. J., 14 (5), 805 (1968). (4U) Corrigan, T E. and Dean M. J “Estimating reactor backmixing effects,” Hydrocarbon Proc&, 47 (7), 149 t1968):’ (5U) Harris, I. J., and Srivastava, R. D., “The simulation of single- hase tubular reactors with incomplete reactant mixing,” Can. J . Chem. Eng., 46 66 (1968). (6U) Hartland S and Mecklenburgh J C “Concept of back-mixing,” Chem. Eng. Sci., 23 (Z), lb6’\1968); CA, 69, 338&, l’b68. (7U) Horn,,? J M . and May R. A. “Effect of mixing on eriodic countercurrent . CHEM.~ R O C E ; S DES.DEVELOP.,7 (3f: 349 (1968). processes, ~ N A EAo. (8U) Hussain S Z. and Kamath N. R “Design of a cascade of semi-continuous reactors,” &it.’Chk Eng., 19 (7j, 987 (i968). (9U) Kastanek, F., and Novosad, Z., “Multistage column reactors. VI. General model of liquid residence-time distribution in a column with plates,” CoNec. Czech. Chem. Commun., 33 (12), 3946 (1968); CA, 70, 39159d (1969). (1OU) Klinkenberg, A,, “Moments of residence-time distributions for cascades of stirred vessels with backmixing,” Chem. Eng. Sci., 23 (Z), 175 (1968); CA, 69, 44856n (1968). , , (11U) Levine, R., “A new design approach for backmixed reactors. I,” Chem. Eng. ( N Y ) , 75 (14), 62 (1968). (12U) Levine, R., ibid., Part I1 (161, 145. (13U) Levine, R., ibid., Part I11 (171, 167. (14U), Mecklenbur h, J C., and Hartland, S., “Design of reactors with backmixing-I,” Chem.%ng.ki., 23 (l),57 (1968). (15U) Mecklenburgh, J. C., and Hartland, S . , ibid., Part 11, “Approximate methods.” D 67. (16U) Meck!enbur&h, J. C. and Hartland, S ibid., Part 11, “Numerical difference between differential and stagewise models,“ p 81. (17U). Mimashi, S . , et a[., “Multiplicity of steady-state solutions for backflow mixin models. Analysis of a continuously agitated reactor,” Kagaku Kogaku, 31 (125.1225 (1968): . ,, . . CA., 69., 1 1 6 7 3 ~(1968). . . (18U) Oigenbljk, A. A., et al., “Effect of sectionalizing continuous reactors in the case of multistage consecutive reactions,” Teor. Osn. Khim. Tekhnol., 2 (3), 425 (1968); CA, 69,28892r (1968). (19U) Padmanabhan, L., and Gal’Or, B., “Analysis of the effect of particle size and residence time distributions on heat or mass transfer with linear source in particulate systems,” Chem. Eng. Sci.,23 (6), 631 (1968). (2OU) Petho A “Determination of the residence time distribution in continuousflowsystem)s,”’khem. Ens. Sci., 23 (7), 807 (1968); CA, 69,88303j (1968). (21U) Prenosil, J., and Novosad, Z., “Multistage column reactors. 11. Methods of determining the backmixin coefficient from residence-time distributions,” Collec. Czech. Chem. Commun.,39 72.1, 376 (1968); CA, 68, 70615g (1968). (22U) Rehakova M and Novosad 2. “Residence-time distribution and fractional conversion for mhtistage reactbr &th backmixing between real stages,” Chem. Eng. Sci.,23 (2), 139 (1968); CA, 69,44854k (1968).

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