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d. HENRY RUSHTON ILLlNOiS INSTITUTE Of TECHNOLOGY, CHICAGO, ILL.
SURVEY of developnients in the field of liquid mixing since January 1949 (6) covers a number of publications on a variety of phases of the problom. There are undoubtedly niariy more industrial laborat'ories with pilot plant equipment designed to study the variables of niixing as applied to part,icular processes than a year ago. A41m, an increasing amount of research on mixing is being conducletl in universit,y laborat,ories, and one equipment manufacturer has greatly expanded its fundamental and applied research activities. The most significant developmerits have been some of t,he theoretical approaches to mixing, such as the study of mixing by jet flow ( 1 ) and hitherto unavailable information on niixing accomplished by shaking ( 3 ) .
heretofore been available for evaluating the performance of such equipment. The reported results should be of considerable value in the design of processes requiring t h k type shaking autoclaves and in bench scale and pilot plant operations. The effect of agitation by this means was evaluated by the rate of hydrogenation of nitrobenzene in glacial acetic acid. This same system was used to evaluate agitation in rocking-type autoclaves in, the previous article, hence the present results ca,n be compared directly for the two types of equipment. Before the quantitative hydrogenation experiment's, tl glass cylinder reactor was oscillated in a back-and-forth motion along its horizontal cylindrical axis. As a result of observations in glass it was possible to start, the hydrogenation studies at nearly the optimum conditions of react'or volume, length-diameter rat,io, stroke length, and stroke t,ime. The optimum reaction rate was obtained at' the longest stroke length and at, the lowest number of strokes per minute that were attempted. Under these conditions the rate of hydrogenation was approximately 3.5 times as rapid as the best rate for a rockingtype autoclave.
MIXING W I T H JETS
Theie are a number of induitrial pro( sses utilixirig a jet of liquid to produce turbulence and mixing. t is difficult to analyzr performance of jet misers because the jet streams are usually flowing a t high velocities and it i s difficult to obtain samples for accurate analysis. Jet rniving is usuallv acconiplished in one of two n-ays: a liquid may be sent thi ough a pump and discharged through a small pipe, or holes in n pipe, into a large body of liquid; or the liquid may be sent through a pipe in yhich a selies of orifice plates are used to producc jet &reams. E o doubt all mixing operations invol: ing a rotating impeller are fundamentally dependent on the action of stieams of fluid which behave, a t least in part, like a jet of fluid emerging from a pipe or orifice. An excellent approach to analysis of the problem of mixing due t o a single stream of circular cross section flowing into a large body of fluid has been published by Folsorn and Ferguson (1 ). They start with the postulation of a free jet of fluid issuing from an orifice of finite diameter. Then, assuming that a jet of compressible fluid expands at a uniform rate, they set up a relation to predict the rate of induction of fluid into the turbulent jet from the surrounding quiet fluid. It is then assumed that complete mixing will have occurred for all fluid induced into the jet and that the effective mixing distance of a jet is that distance in which turbulent stability exists. Since the power in a jet of flowing fluid can be computed, i t is possible to calculate the energy required by a jet to induce, and thus mix, a given amount of liquid. They use, as an index of performance, the number of gallons of liquid per minute induced per horsepower supplied. Calculations were made for mixing hydrocarbons such as gasoline in large blending tanks-for example, 100 feet in diameter. Comparisons of performance for mixing were made for a transfer pump of low specific speed to remove and return liquid to n tank, a jet of high velocity liquid, and a propeller mixer. The propeller mixer was found to be almost twice as effective as the high velocity jet or the use of a low specific speed circulating pump. The ideas developed in this paper should be widely applicable as a means of comparison of jet mixing with that accomplished by rotating mixing impellers.
EFFECT O F AGITATION ON MASS TRANSFER
Several studies have been reported dealing with transfer of material from one phase to another while mixing impellers are operating. The results are of interest not only because they may be useful directly in engineering and process design, but they are of special interest along theoretical lines. Much of the information about mixing has been empirical and qualitative, and too little attention has been given to a consideration of thc fluid mechanics involved. The review of the two papers which follows, points t o the techniques used for correlations oi mash transfer data with mixing variables and also emphasizes the limits of applicability of data due to the experimental nirthods used. IIixson and Smith ( 2 ) studied the effect of rotating propellers on a, liquid-liquid extraction. An equation mas developed to relate the weight of solute transferred from one liquid t o another immiscible liquid in ternis of an extraction coefficient. It was then demonstrated by experiment that the extraction of iodine from its water solution by carbon tetrachloride followed the equation developed. The equation is a first-order or unimolecular rcaction rate equation. Part of the constant of integration of the equation is called the extraction coefficient. The experimental data substantiate the well-known fact that in a first-order reaction the time required for a given fraction of one substance originallq present to undergo change (in this case to transfer to another phase) is independent of the initial concentration. The novelty of this work was the claim that the extraction coefficient can be used as an index of the rate of extraction because of its ability to describe the performarice of an agitator. However, the experimental work was performed with rotating three-blade marine-type propellers in small, smooth wall glass vessels without the use of baffles. Since very few industrial mixing operations are carried out without the use of baffles, or their equivalent, i t is difficult to apply the results of this work directly t o large scale industrial operations. Hence, the greatest value of the work is to show that the first-order reaction rate equations hold for the extraction of iodine in water by carbon tetrachloride and that the technique of sampling and calculation
SHAKING AUTOCLAVES
Last year an article appeared on agitation with rocking-type autoclaves and was followed recently by an article by the same authors (3) on studies in shaking autoclaves. No data have 74
!anuary 1950
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INDUSTRIAL AND ENGINEERING CHEMISTRY
gives an extraction coefficient which is some function of the amount of agitation. The work was performed in vessels of three sizes (largest, 25-cm. diameter), and in each case the linear dimensions were adjusted to give geometrical similarity. The authors noted that the coefficients could not be correlated adequately by the use of Reynolds number (or relations derived therefrom) and attributed the failure t o the fact that differences in particle size may have nullified geometrical similarity within the body of liquid. I n other words kinematic and dynamic similarity did not exist even though geometric similarity did exist. It has been pointed out by Rushton ( 5 ) that dynamic similarity cannot exist in two different sizes of unbaffled mixing tanks when the same liquid is used in each case. One of the postulates of dynamic similarity is that kinematic similarity must exist together with geometric similarity in order t o achieve dynamic similarity. When mixing impellers rotate in unbaffled tanks a swirl results in all cases (except the critical off-cmtered position) and the Froude criterion of fluid dynamics must be considered. Hence the Froude number must be the same in tanks of two different sizes, and the Reynolds number must be equal in both tan similarity. The Weber num%er describes similarity, and no doubt this parameter extraction of iodine from water by carbon tetrachloride. As it is theoretically impossible to achieve dynamic linear scales when more than two of the dyn a part, it is to be expected that dynamic similarity ca , for the experimental technique used. The above theoretical discussion of fluid mechanics principles, as applied t o the publication just reviewed, is pertinent t o show the limits of applicability of mixing experiments performed in unbaffled tanks, or under other conditions which preclude
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dynamic similarity. To emphasize that smooth wall containers were used in this experimental work is not merely t o note that baffles (or their equivalent) were not used, and therefore the results are of very little industrial interest, but rather t o emphasize that when vortex and swirl exist in a mixing tank, it is not possible t o reproduce dynamic similarity in a different size tank with the same liquid a t the same temperature. Experiments on mixing should be set up with these fluid mechanics requirements in mind so that the results will have the widest application. A study on the rate of solution of solid benzoic acid pellets in sodium hydroxide solution, with agitation by means of flat paddles in baffled tanks, was reported by Mack and Marriner ( 4 ) . From their work the authors propose a correlation of the time required for mass transfer with power number, the Reynolds number, and other pertinent dimensionless ratios. The derived equation was evaluated for one type impellerthe flat paddle-various amounts of baffling, a wide range of speed and power input, three different pellet sizes, two tank sizes, and several liquid depths. Blade size was varied for the two-blade paddle turbines. Also a four- and a six-blade paddie were used. Data correlated well for results in the various size operations, and as baffles were used the results are applicable to scale-up operations. The solubility, or mass transfer, was measured by the time taken to neutralize a dilute caustic solution. The authors assumed a first-order reaction rate and evaluated the constant of integration. However they used time as the measure of the effect of agitation rather than the constant of integration. In the Hixeon and Smith article (2), the constant of integration (from the same basic equation but a different constant due t o the
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VoL 42, No. 1
Illustrati~nsof a variety of applications of agitators to commercial gas absorption processes are given, but i t is pointed out that it is often essential to make pilot plant runs before large scale equipment is designed. It would be helpful to the process engineer operating pilot plant equipment to know what data axe needed on the pilot plant scale to establish proper design for Jarge scale equipment, but such information is apparently not available for the type equipment described in the article. EQUiPMENT FOR MIXING
OOURTESY MIXINO EQUIPMENT COMPANY
M i x i n g with an Off-Centered Propeller
!use of volume ratio necessary in the case of the two-liquid system) was proposed as the measure of agitation. The data of Mack and Marriner can be treated like that of Hixson and Smith, and the constant (or material transfer coefficient) will correlate with the Reynolds number just as time can be so used. Such treatment of the data would probably be of more significance and of wider use than by correlating with time. The data of Hixson and Smith, however, do not lead t o the correlation found by Mack and Marriner because, in the former case, dynamic similarity could not exist when size was varied. The data of Mack and Marriner were taken under bafued conditions where the Froude criterion is uot applicable and, therefore, dyiitirnically similar conditions oan be reproduced fnr.the same fluid system vith various linear icale dimensions, G A S ABSORPTION
.1 discussion of the use of mechacical agitators to produce gas dispersion is given in an article by Valentine (8). We pxrtially describes an agitator especially designed for gas absorption, but details as to construction are omitted. For a gas absorption the factors influencing the selection of equipment are: the relative volume of gas and liquid; the amount of solids present; reactions where the resistance t o absorption is primarily due to the liquid film. It is stated that packed, or other, towers are best suited wheri gas quantitie.; are very large hut that mechanical agitators are often preferable vhen solids are present and when it is necessary to have a large amount of turhulence in the liquid
LIQUIDS
A survey of the products of many mixing cquipment manufacturers and particular purposes for which their mixers art’ designed is given in an article by Smith (7). The survey is the most comprehensive one available; it takes into account virtually all conditions in which mixers are used and indicates manw facturers’ claims as t o advantages and special applications. There are maqy statements, which are dificult to justify, regarding the applicability of equipment. This is no doubt due to the claims of equipment manufacturers and to the very broad scope of the survey. It was pointed out in the article that mixer technology is gradually being put on a more rational design basis, and that many published articles contain a number of contradictory statements. It is unfortunate that, in this survey, trade names, in some cases, are referred to in broad terms to classify impeller type, and clear-cut distinctions are not made between the several basic types of impellers @ridfluid r6gimes produced. Confusion will continue on many points of mixer performance until limits of performance of mixing equipment can be based on quantitative measurements. There are at present in the literature basic data on power characteristics of mixing impellets; these should be kept in m i d and used to modify some of the rather inclusive and general statements made in t h e article. Descriptions o? various mixers are good and the reader will obtain a clear impression of the conqtruction and intended action of the various mixing devices. LITERATURE CITED
Folsoni, R. G., and Ferguson, C. K., T T U ~ LAm. S . Soc. M e c h . Engrs., 71, 73 (1949). Hixson, A. IT., and Smith, M. I.,INU.ENG.CHEM.,41,973 (1949) Hoffman, A. N., Montgomer), J. B., and Moore, J. K., Ibid., 41, 1683 (1949).
Mark, E. bl., arid hfariiner, R . E., Clwm Eny. P m g r m s , 45, 545 (1949).
Rushton, J. II.,Fifth N a t l . Conf. Zrd. Hydraulics, Illinois Inbt Technology, Chicago, Ill. (Oct. 27, 1949). Rushton, J. I$., TND. Eivi;. CHEM.,41, 61 (1949). Smith, J. C., Chem.Znds.,64,399 (1949). Valentine, K S., Chem. Eng., 55, No. 12, 117 (1948) RECEIYED October 2 5 , 1949.
F FIFTH ANNUAL UNIT OPERATIO (Reprints of this and earlier Unit Operations reviews may b e purchased for 50 cents each from the Reprint Department, American Chemical Society, I1 55 Sixteenth St., N.W., Washington 6, D. C.)
