MIXING J. HENRY RUSHTON’ ILLINOIS INSTITUTE OF TECHNOLOGY, CHICAGO, ILL.
Since the yearly review in the January 1953 issue of Industrial and Engineering Chemistry (34) a large number of articles on mixing have appeared in the technlcal literature. There have been a number of general survey articles, but the work of most significance has to do with the application of various principles of fluid mechanics to fluid mixing operations. A correlation of turbulence with mixing is noted in a number of the papers, and it is hoped that more researchers in the field of mixing will follow this trend in applying sound fluid mechanics principles to mixing.
tures and mixing is a very good exposition of what constitutes a mixture and how such mixtures can be obtained. He defines carefully the distinctions between the size and type of sample, “scale of scrutiny,” segregation of parts, and the “goodness of mixing”-which is often referred to by others as degree of homogenization, or as degree of randomness. He also define6 intensity of segregation as a measure of the departure of the composition from the mean value. Following a description of the properties of a mixture, he reviews the fluid mechanics principles of turbulence and the use of similitude in fluid mixing as applied to studies in experimental work and scale-up of mixing data. The article properly emphasizes the fluid mechanistic approach to an understanding of the application of mixing to various chemicals and chemical processes. A mathematical analysis of the randomness of a liquid mixture is developed by Sarolea (39). A review of recent developments in the theory and practice of mixing by Newitt, Shipp, and Black was published by the British Institution of Chemical Engineers (26). The review starts with a definition of mixing and quantitative techniques used to measure mixing. There is a general discussion of the problem together with photographs showing how rotating impellers may be used to bring about mixing in cvlindrical tanks. There is a section designed to explain how a mixing impeller operates with or without baffles to produce eddy currents to bring about various types of mixing. Unfortunately, much of this material is speculative and the reason given for the method by which eddies and turbulence occur is not correct (38). Had the authors carried their photographic evidence farther and discovered the actual flow patterns existing in baffled flow tanks, they would not have arrived a t their theory as to how baffles promote mixing. The remainder of the review deals with the suspension of solid particles, from previously published papers, and gives a good review of the published data on energy requirements t o turn mixing impellers. A review of how propellers, turbines, and baffles are used to bring about mixing is given in a paper by Reavell (50) titled “Practical Aspects of Liquid Mixing and Agitation.” There are no quantitative data regarding performance or power requirements in the paper. Reavell classifies liquid mixing problems in three groups: liquids with or without solids which remain free flowing; liquids with or without solids which are viscous but can still be poured when mixing is complete; and liquids with solids which form stiff pastes when mixing is complete. He discusses types of impellers and types of mixing vessels. Photographs are shown using propellers with and without baffles and should confirm similar information that has long been in our literature. He shows a picture of a cruciform baffle located in the bottom of a cylindrical vessel. This baffle consists of two flat blades on edge put together in the form of a plus sign. Such a baffle is located directly beneath the propeller. The action of this type baffle is very similar to that of the ordinary vertical baffle that he also illustrates. Experience within the past few years has shown that the cruciform baffle has only limited application as compared to the usual vertical type baffles.
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HERE has been a decided increase in research on the effect of mixing in pilot plant operations throughout the chemical field. The Mixing Equipment Co. of Rochester, N. Y., has installed a 70,000-gallon tank for test and research work. It is shown in Figure 1. The tank is 20 feet in diameter and is designed for research work on side-entering propeller type mixers (14, 88).
GENERAL AND REVIEW PAPERS A comprehensive survey entitled “Mixing, Present Theory and Practice,” by Rushton and Oldshue (58) is intended to cover the applications of fluid mechanics to the mixing of liquids, in so far as they have been verified by experimental investigations. Flow patterns of proved shape that appear to be of basic interest are shown and related t o impeller shape, fluid, and tank shape, and arrangement. A discussion is given of the basic ideas of turbulence, its initiation and propagation in a mixing tank, and the quantities of liquid entrained in flowing streams. Data are summarized on quantities of flow from propellers and flat-blade turbines, and on power required to rotate mixing impellers. The relative effect of impeller size operating a t constant energy input on mixing operations is pointed out, and the accompanying flow characteristics are shown. Such information is of considerable use in pilot plant and small scale experimentations, and helps to fix conditions for best scale-up operations. Heat transfer data €or mixing conditions are summarized and placed on a comparable basis. Techniques are given for pilot plant experimentations prior to scale-up. Finally, there is a discussion of the basic mechanical requirements for industrial process mixers. An important article by Boutros ( 2 ) deals with the maintenance of fluid mixers. He discusses the construction of modern equipment used in large scale operations and points out critical problems in installation and maintenance of industrial mixing equipment. The article is well illustrated and points out many of the economic reasons for the mechanical design of rotating impeller mixing equipment. Another summary of present theory on mixing by Rushton, Boutros, and Selheimer (87) also covers the application of machinery to liquids and also to pastes, solids, and other very viscous materials. Suggestions are made particularly for the experimental chemist, to use good mixing techniques that can be translated to larger scale equipment. There is considerable description of the mechanical features of modern mixing equipment, and the reasons for many of the design features. The mixing of liquids in chemical processing is the subject of a review by Rushton (35). It is a survey of applications of mixing equipment to chemical processes. A similar survey by Rushton including material on the mechanical features of mixing equipment was published in the Canadian press (3.4). Another review article by Danckwerts (6)on the theory of mix1
Also, director of researoh, Mixing Equipment C o . , Rochester, N. Y.
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A survey of mixer costs has been written up by Lewis ( 2 0 ) and covers cost data for mixers for liquids, solids, semisolids, and miscellaneous. These groups include; for liquids, propellers and turbines; for solids, spiral ribbon blenders and rotary double cone hlenders; for semisolids, double arm sigma mixers, two-roll mills, extruders, and mullei s: misrf~llaneous,planetary mixers
Figure 1. Experimental 70,000-Gallon Installation of Mixing Equipment Co. for Research on Side-Entering Mixers
and colloid mills. The cost charts are useful for orientation] and for most of the heavy-duty mixers the data are very useful, but the data for propeller and turbine type mixers are given without regard to speed and thus may be in error by at least 100%; hence the data given should be used with extreme care (33).
MASS TRANSFER AND TURBULENCE The use of Huid streams to mix liquids makes use of the property
of a stream to induce adjacent liquid, and thus to spread, and also the fact that turbulence within a stream will result in mixing Thus, studies directed toward a better understanding of, and a quantitative appraisal of the behavior of jets or other Huid streams is of particular interest in the broad field of mixing. Studies on the behavior of jets of air expanding freely into air have diiert application to many liquid mixing operations (38). A bulletin by Alexander, Barron, and Comings ( 1 )gives an excellent up-to-dat~summary of the various theories and correlations that have been proposed to evaluate the behavior of expanding jets. They made a study of the theoretical and mathematical techniques to account for the transport of momentum, mass, and heat in turt)ulent jets, and concluded that the method first proposed by Reirhnrdt offers the greatest utility for correlation of measurable quantities in fluid flow and the transport of momentum, mass, and heat within the How. They report a large amount of data in support of the Reichardt hypothesis, which states that the mean product of the instantanee$$axial and radial velocities i R proportional to the change in thc mean of
of fluid within the stream.
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the square of the axial velocity a t distances along a radius. They also show how previously published data on momentum, mass, and heat transfer within a jet can be handled by the same technique, because the turbulent transfer mechanism is common to each. Momentum spreading coefficients for circular cross-section jets are given for axial distances up to 30 diameters and an average value of 0.075 was found to represent all data to within &4%. Experiments were also made to determine the effect of turbulence in the stream a t the discharge of the jet-the turbulence was generated by a wire screen-and concluded that turbulence so induced did not affect the subsequent spread of the jet. The turbulence induced by the screen was approximately 8% of the total turbulence in the fully developed turbulent jet. An article by Fossett titled “The Action of Free Jets in the Mixing of Fluids” (11) is essentially the same paper as published several years earlier by Fossett and Prosser (12). Fossett states that the data in the paper had been published in an earlier work and that his present paper was intended to concentrate on the practical application. The previous paper is more detailed and gives the mathematical background for the theory and results. Furthermore, the discussion following the earlier paper brought out significant features of expanding jets. Thus, to get the complete thoughts developed by Fossett, reference to the earlier paper should be made. The principal information has to do with the blending of petroleum hydrocarbons in large storage and mixing tanks by means of nozzles through which Huid is pumped or recirculated to form an expanding jet. Fossett worked with various size noziles located a t different points and set a t various angles. He gives mixing times for a large number of operations and relates horsepower required to time of mixing for different nozzle arrangements. The data apply to tanks wherein liquid depth is not more than 20 to 25% of the tank diameter, hence care must be exercised in applying the results to deeper liquids. In this paper he makes a very brief reference to the fact that side-entering propeller mixers produce a How of fluid that acts as a jet. He states that frequently such propellers are mounted tangentially and induce rotational swirl of the whole contents of the tank. It is universal practice in the United States to locate side-entering propeller mixers off-center but not tangentially, in such position that swirl is eliminated (38). Fossett stated that by placing two propeller mixers diametrically opposite each other and discharging along the diameter, he could produce How patterns of the same desirable type as with his nozzles. This is certainly correct, but a single side-entering propeller can also be used if properly positioned. Fossett’s data are very useful for cases where one must use a recirculating pump to produce mixing. Attention should be called, however, to a previous publication by Folsum and Ferguson in 1949 (10) which compared the efficiency of mixing by means of a jet produced by a nozzle or pipe using an outside pump, with the mixing produced by a properly positioned side-entering propeller mixer. They showed considerably higher rate of mixing per unit of power input with the propeller than with the simple jet. This is in agreement with current mixing practice in the petroleum field. Unfortunately, Fossett has not made a similar comparison to determine whether or not Fulsom’s conclusions would lead to more economical mixing if propeller mixers were used. The basic reason for Fossett’s original study was 60 find a good way to mix gasolines in very large underground storage tanks used in Great, Britain during the war. His results are excellent and reliable but do not make any comparison with the more economical method using side-entering propellers. The reviewer wishes to make this point clear, so that persons interested in this work will not jump to the conclusion that pure jets are better than jets produced by mixers. The mixing of liquid fuels sprayed into gas streams is the suhject of a paper by Longwell and Weiss (21). They have developed equations, starting from the spread of a jet from a point source, to handle the spread of Huid originating from a finite rir-
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cular area, and also from a ring source. Plots of functions foi such use are given. Experimental data confirm the distributions predictable from the equations, and account can be made for wall effrcts. No doubt such a technique for predicting the spread of injection streams of fuel oils into air streams can also be applied to the injection and expansion of jets of one miscible fluid into another, although the authors do not refer to the measured data alI eady in the literature for this phenomenon. Schlinger and Sage studied mass transfer in turbulent gas streams (41). They were able to correlate the mixing of a jet of gas with a surrounding stream in a closed circular pipe, with the turbulence as indicated by the eddy viscosity. Schlinger, HSU, Cavers, and Sage (40)report work on the temperature distribution nssociated with turbulent flow. They report data on nonisothcrmal flow of air between parallel plates. I n the Russian literature an article by Kishinevsky (18) develops a theory and mathematical correlation of absorption operations during intensive mixing. He has tried to relate the kinetics of absorption in a first-order reaction to turbulence as existing in a mixing vessel. The degree of turbulence is proposed as being invci scly proportional to the time required for renewing :t reaction intc.1 face layer. KOexperimental data are given. h paper by Garner and Skelland (13) has to do with liquidliquid mixing as affected by the internal circulation of droplets. Exti action operations arc often carried out between two immiscible liquids by means of a mixer or some type of continuous t o w r operation. This article is concerned with the mixing within :I drop of liquid and the relation between the turbulence outside the drop and the mixing within the drop. The experimental work was performed by allowing masses of drops to fall through a column of immiscible liquid. The Reynolds number was used as an indev of turbulence in the continuouq phase. Studies were made with drops of different size and mass and a mechanism of diffusion and circulation within the drops was postulated to explain the experimental data. They conclude that circulation and mixing inside droplets take place readily only when a solute is present and onlv when the drag (or Reynolds number) is above Rome critical value. The transitional Reynolds number is dependent for a givcn drop size on the viscosity of the continuous phase, the viscosity of the dispersed phase, and the interfacial tension or othcr characteristic of the interface. continuous countercurrent extractor has been described and performance data given by Reman (51). The extractor consists ot a vertical tube containing horizontal plates with center holes and a central shaft holding flat circular disks placed between the horizontal plates. The disks are rotated and when two liquids arc allowed to flow countercurrently, a dispersion of one phase in the othcr is made. The unit is somewhat similar to the one described hy Rushton and Oldshue (38) and works on the same general principle. Reman states that the apparatus is very flexible in operation and has many applications. He gives performance data on throughput capacity and compartment efficiency for the system methyl isobutyl ketone, acetic acid, and water. The column described is 64 mm. in diameter and the rotor disks are 30 mm. in diameter and have been operated a t speeds of 500 to 2000 r.p.m. Stage efficiencies up to 40y0are reported. Xramers, Baars, and Knoll (19) have written an excellent paper describing the rate of mixing of an electrolyte in water by three different impeller types-a propeller, a flabblade turbine, and an angled flat-blade turbine-with and without baffles. The time required to bring about mixing was measured by a conductivity cell technique. For the system used, the time required for mixing was a straight-line function of impeller speed; hence the authors reported their data as the number of revolutions required to produce the desired mix. Power data are given for some of th? situations used; for these cases it is clear that mixing time is inversely proportional to power input. The comparisons tabulated for the mixing due to the different combinations of impellers and A\
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baffles :ire useful, and when compared on it basis of equal power input, show the difference between the variables tested. A bulletin has been published by Wingard, Vinyard, and Craine (47') describing experiments designed to measure the mixing efficiencies of several types of mixing impellers. Five t j pes of impellers were used to mix oil and water.. Samples of the emulsions formed n'eie settled and the volume of each phase was compared with the original volumes used in the tank. From such data the pei cent mixed was calculated, and these values were used for mixing efficiency. The impellers were a two-blade flat paddle, a f our-blade flat paddle, a two-blade 45' paddle, a two-blade propeller, and a Hoesch-blower type impeller. They were used with and without baffles, and power consumption was measured. The (lata are sound but the conclusions of the authors are not based on R comparison at constant power input; hence they are misleading and are in error. Their data, however, are susceptible to proper comparison, and when this is done, the results are contrary to the conclusions of the pap". I t is unfortunate that studiea such as this are not evaluated properly, because it has been repeatedly pointed out in the literature on mixing that comparison of mixers must be made on equal poaer input basis; otherwise there is no way to determine how best to utilize the energy input to the impellcrs. Mixing of liquid sticams passing through beds of solid spheies \vas studied by Wicke and Trawinski (46). Hydrochloric arid was traced by conductivity measurements, and hot kvater by therrnorouple measurements. ltcsults are expressed as mising coefficients Petroleum hydrocarbons are transported over long distances in pipelines, and two liquids can be pumped as slugs-one behind the other-for long distances. However, there is some small
