R. B. LONG Esso Research and Engineering Co., Linden,
N. J.
M. R. FENSKE Pennsylvania State University, University Park, Pa.
Scale-up of a Novel Mixer-Settler Extractor Reciprocating perforated plates are good mixers for liquid-liquid extraction units. This study of their mixing characteristics gives useful scale-up relationships SuccEssmL SCALE-UP of mixer-settler extractors depends upon understanding the fundamental variables of mixing and settling partially miscible phases and the hydraulics of two-phase liquid flow. The relative importance of these three areas in scale-up depends somewhat on the extractor design being studied. I n some cases, the problems involved are discrete and do not involve serious interactions among these variables. I n those cases, experimental scale-up work can be pitched largely toward the part about which the least is known. T h e other parts can be simply calculated using existing knowledge. Many articles (2-5, 7, 8, 70-72) have been published on the process variables involved in mixersettler units, particularly those pulsing liquids through perforated plates or packing to get their mixing efficiency. However, this article discusses the scale-up of a relatively new ( 7 , 5, 6) type of extraction unit. Since reciprocating perforated plates are relatively new as mixing elements for liquid extractors, it was felt that the weakest link in successful scale-up was lack of knowledge of the characteristics of these mixers. Therefore, an experimental program was undertaken to determine the variables affecting mass transfer produced by perforated plate mixers and to correlate these variables for scale-up purposes. I t now appears that large-scale perforated plate mixers can be designed to handle mass transfer operations in liquid extractors using the principles developed in this small-scale work.
At this temperature the naphtha cut had a viscosity of about 1 centistoke and a density of 0.77 gram per ml. The flow mixing studies were made in a single stage extractor using this same hydrocarbon-water system and using the transfer of pyridine from one phase to the other as a measure of mixing efficiency. The figure (left, below) shows this single-stage extraction apparatus which has a rectangular crosssection and is made of flat steel strip, with the front and back walls of clear plastic to permit visual observation of the degree of mixing and the behavior of the flowing phases. T h e mixing and settling zones are 1-inch high by 1.25 inches wide. The two phases to be mixed are introduced into the mixer stage a t one end just upstream of the mixing zone and flow concurrently through the mixing and settling zones to the phase disengaging tube. This disengaging tube is made of 2-inch i.d. clear plastic pipe with gasketed steel end plates to which are attached the phase exit lines. The light phase flows out of the disengaging tube into a short standpipe from which it overflows through a side arm to a light phase product receiver. This side arm is vented to prevent siphoning in the light phase exit line. T h e heavy phase flows out through the bottom of the disengaging tube and through a suitable metering valve to the heavy phase product receiver. T h e interface level in the disengaging tube and correspondingly at the end of the settling zone is adjusted and maintained a t any position by means of the control valve in the heavy phase exit line. The two
In this extraction unit, the perforated plates themselves are pulsed a n d the liquid phases flow cocurrently through the horizontal mixing zone parallel to the surface of the perforated plates. In this type of unit, the two phases flow cocurrently through the mixing a n d settling zones of each stage a n d countercurrently through the extractor. T h e phases are mixed by horizontal perforated plates located in each mixing zone which a r e moved rapidly u p a n d down to bring about the desired mass transfer without the production of emulsions which will not settle. Both the frequency a n d stroke of the reciprocating mixers are variable.
Apparatus The optimum design of perforated plate was determined by batch experiments in cylindrical glass vessels wherein the horizontal perforated plate was reciprocated vertically by a device capable of varying both frequency and amplitude of vibration. The diameter of the glass vessel was a t least twice that of any plate tested. In this apparatus, the effectiveness of mixing could be observed visually and many valuable measurements were made in this way. T h e system used was water and a narrow boiling cut from a commercial naphtha. Experiments were run at about 75" F.
1/4" HOLES I
SETTLl NG LENGTH
TOP PLAN
WATER
WATER INLET
EXIT
Single-stage extraction apparatus
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1
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END ELEVATION
Detail of mixing element VOL. 53, NO. 10
OCTOBER 1961
791
How the Plates Work In agitating a liquid with an immersed vibrated perforated plate, the liquid flows in apparently continuous streams in opposite directions through each hole in the plate. This can be clearly seen with the plate at the interface between two liquid phases. On the upstroke, the material above the plate jets in part down through the hole and in part out around the periphery of the plate. On the downstroke, part of the material below the plate jets up through the hole and part goes out around the edge of the plate. At vibration frequencies greater than a few hundred cycles per minute, the individual jets cannot be seen and the over-all effect i s that of two continuous streams flowing in opposite directions out of the two sides of the same hole. The lengths of these jet streams are clearly visible. From this mechanism of stirring, any obstructions to flow or burrs on the holes would tend to decrease the flow through the holes and increase the flow around the edges o f the plates. Conversely, any obstruction to flow around the edge of the plate would increase the flow through the holes, Since liquids are essentially incompressible, the solid area of the plate, together with the amplitude of vibration, determines how much liquid i s displaced per stroke. This displacement and the frequency of vibration give the volume displaced per unit time. The hole size and the number
of holes in the plate determine the resistance to flow through the holes and thus fix the relative amounts of the displaced liquid going through the holes and around the periphery of the plate. If the vibrated plate i s placed a t a liquid-liquid interface, each liquid i s driven into the other phase in an apparently continuous stream. By placing the plate about 1 inch from the interface, the phase in which the plate i s vibrating i s pumped through the interface into the second or adjacent phase. For example, if the plate i s in the water phase, the watet i s pumped through the interface into the naphtha phase. However, the material pumped into the water phase i s water plus any stray drops of the naphtha phase which are knocked free b y the agitation of the interface. In this way, it i s possible to stir one phase into the other almost
exclusively except for a small amount of entrainment in the reverse direction. The most violent two-phase mixing occurs when the plate i s at the interface. Obviously, two or more plates can be employed b y placing them on each side of the interface or deep layers of liquid can be mixed b y employing a series of plates positioned close enough together so that each plate can pick up feed from the plate above or below it. The zones between plates will then be mixed thoroughly. From this discussion, small plates give much poorer jets through the perforations than large plates because of the greater tendency for liquid to flow atound the petiphery of the plate. This has been experimentally verified, and means that scale-up based on relatively small equipment i s usually conservative.
phases to be contacted are pumped into the unit through rotameters which serve mainly to indicare constancy- of flow rate. Actual flolv raies are determined by collecting the phases leaving the unit over a measured period of time. A l l floiv rates reported were determined in this way. T h e mixing element (right, page 791) comprised a pair of horizontal parallel perforated steel plates separated vertically by and welded to a cylindrical hub which spaced the perforated plates 0.50-inch apart. The mixer h u b \vas attached to the bottom of a 0.5-inch vertically reciprocating steel shaft by means of a set-screw. T h e reciprocating shaft entered the mixing zone through a closefitting steel tube standpipe above the mixing zone. This standpipe was centered over the mixing zone and served as a mixer shaft bearing as jvell as a means of entering the mixer shaft into the mixing unit without a shaft seal or stuffing box. The top end of the mixer
shaft \vas connected to a variableamplitude cam system by a connecting rod. T h e cam system consisted of a pair of eccentric collars of equal eccentricity, fitted one inside the other. T h e inner collar !vas clamped to a drive shaft, and the outer collar was clamped to the inner one. T h e outer collar could be rotated xvith respect to the inner one and clamped in any position with respect to it. By Trarying the position of the ourer collar xvith respect to the inner one-i.e., by adding or subtracting the eccentricities of the txt'o collars-the amplitude of the reciprocating shaft motion could be varied continuously from zero to 0.5 inch. The drive shaft supporting the eccentric collars was driven by variable speed drive and suitable pulley systems so that any frequency of motion between 30 and 1200 cycles per minute could be obtained. Thus, the mixer drive system allows exceptional variation in the type of reciprocating motion applied to the mixing element. All of the mixers
tested in this unit had the same widthbut could be varied in length, in hole size and spacing. and in the number of plates used in the mixing element.
792
INDUSTRIAL AND ENGINEERING CHEMISTRY
Perforation Size Nine 4-inch diameter flat circular plates of 0.062-inch thick steel were perforated Tvith round holes covering a range of hole diameters from 0.125 to 1 inch and with a ratio of hole ared to solid area ranging from 0.016 to 0.36. Each of these plates was vibrated a t an amplitude of about 1 mm. and a fixed frequency of 3600 per minute with the center of the stroke a t the liquid-liquid interface. The results obtained are given in Table I . T h e data are plotted i n Figure 1 as depth of penetration of the water jets into the naphtha phase and show that the 0.25-inch diameter holes are definitely superior to the 0.125- and 0.50-inch holes for any given ratio of hole to solid area. T h e naphtha jets
MIXER-SETTLER EXTRACTOR penetrate the water phase about the same distance as the water jets i n the naphtha phase. This means that for a given required depth of stirring, a plate using 0.25-inch holes could have a larger ratio of hole to solid area than if it had 0.125- or 0.5-inch holes and thus does not need to displace as much liquid per unit time. Another factor of importance is the distance between hole centers. However, since the distance between centers is dependent on the ratio of hole-to-solid area for a given hole diameter, this variable has not been studied separately. A similar series of tests were made with the variable frequency unit a t an amplitude of 5/16 inch. These results are given in Table 11. T h e plates used were 6 inches in diameter and covered a range of hole size from 0.25 to 1 inch. T h e results shown in Figure 2 indicate that for an amplitude of 5/16 inch, the best mixing is obtained with holes from 0.5 to 1 inch in diameter. Holes larger than 1 inch might also give good stirring, but as the diameter increases, the number
Table 1.
of holes per plate to maintain a given open-to-closed area ratio gets quite small so that the mixing is poorly distributed over the surface of the plate. Thus, the optimum ratio of hole diameter to amplitude of vibration is between 3 and 6 for a 1-mm. amplitude and between about 2 and 3 for a 5/16-inch amplitude. Figure 3 shows that the decrease in mixing depth with increasing hole area can be compensated for by operating a t higher mixing frequencies. T h e data shown are for 5/16-inch amplitude. Slots and square holes having the same area per hole as round holes give about the same depth of penetration of the streams as round holes. Thus, there is no major effect of hole shape. T h e data obtained on hole size and hole shape allow several generalizations to be made concerning the effect of varying the ratio of hole-to-solid area. T h e larger this ratio for a given hole size, the better the stirring is distributed over the plate. T h e smaller the ratio, the farther the streams are thrown and the more violent the over-all agitation.
However, when the ratio is zero-Le., there are no holes in the plate-there is only a small amount of agitation around the periphery of the plate. As the ratio approaches infinity, no noticeable agitation is produced. At an amplitude of I-mm. and a frequency of 3600 cycles per minute, the maximum ratio of hole-to-solid area allowable to produce satisfactory mixing is between 0.15 and 0.20. If the amplitude is increased to 5/16 inch, the maximum ratio is increased to 0.7 for a frequency of 1600 cycles per minute as indicated in Figure 3. Friction through Holes
T h e effect of resistance to flow through the holes was determined by increasing the plate thickness from 0.063 to 0.25 inch for a plate having four 0.25-inch diameter square-edged holes. I n this case, the penetration depth was cut approximately in one half a t the 1-mm. amplitude and a frequency of 3600 per minute. This loss i n penetration for thick plates could be recovered by in-
Comparison of Stirring Ability of Different Types of Vibrated Perforated Plates with the System: Branched Decanes-Water Vibration is in a vertical direction. Frequency of vibration = 3600 cycler per minute. Tests made at room temperature. Plate is located at the liquidliquid interface and is a 4-inch diameter d.isk of ‘/le-inch thick steel with the holes punched or milled out Penetration Depth of Ratio of Arnp1itudeb Streams,O Inches, into Number of Hole Size, Hole Open to Upper Lower of Shape Closed Areaa Vibration. Mm. Inch phase Holes phase Remarks 2 0.143 0.9 1.0 Round 0.25 0.25 4 Round 0.75 0.164 0.9 0.25 0.25 Round 8 0.143 0.9 0.25 0.50 0.5-0.75 Round 2 0.032 1.1 1.0 0.50 1.0 Round 68 0.362 0.9 0.25-0.5 0.25 0.25-0.5 Round 0.123 0.9 2.0 0.25 28 1.0 Round 4 0.016 1.3 4.5 0.25 3.5 Round 4 0.016 1.1 4.0 0.25 4.0 4 Round 0.016 1.3 2.25d 0.25 1. 75d 4 Round 4.5d 0.016 2.5 0.25 3.5d 4 Round 0.25 1.1 3* 5 4 6 1. O d ~ e Narrow side of holes up 0.016 Round 0.25 0.016 1.1 4.01 4 Negligible’ Nozzle tips up 4 Round 0.016 1.1 Negligiblef 4 to 5f 0.25 Nozzle tips down 4 Round 0.016 1.1 2.5f 0.25 6.0f Nozzle tips down, 5/8-inch band around periphery of plate on side opposite nozzle tips 4 0.25 Round 0.016 1.1 3.5e 4.OC Narrow side of holes up Round 4 0.25 0.016 1.1 3.56 4.0e Narrow side of holes down Round 0.138 0.9 0.125 1.0 1.0 128 Round 0.020 1.1 20 0.125 2.5-3.0 2.0 8 Square 0.010 1.1 4.0 0.125 3.0 8 0.064 0.9 1.0 0.125 (width) Slots 0.25-0.5 Circular slots in 2 concentric rings Slots 8 0.125 X 1.5 0.136 0.9 0.5 0.5 Straight slots in 2 concentric squares 8 Slots 0.125 X 1.5 0.136 0.9 0.75 0.5 Straight slots on S/r-inch parallels Slots 8 0.125 X 1.5 0.136 0.9 0.25-0.5 0.1 Straight slots on radii 45O apart 4 0.047 X 1.75 Slots 0.027 1.1 1.5-2 .08 4-58 Straight slots, narrow ends down, forming sides of a 2l/~-inchsquare 4 0.047 X 1.75 Slots 0.027 1.1 3.58 1.58 Straight slots, narrow ends up, forming sides of a 21/~-inchsquare 4 0.016 X 1 75 Slots 3.56 0.008 1.1 0.5e Straight slots, narrow ends up, forming sides of a 21/2-inch square 4 0.016 X 1.75 Slots 0.58 0.008 1.1 3.58 Straight slots, narrow ends down, forming sides of a 21/~-inchsquare a Ratio of open to closed area = (total area of holes)/(solid area of plate). Amplitude is the distance between the highest and lowest points of the stroke. By streams is meant the material coming through the holes. Plate is made of steel 0.25-inch thick. e Holes are tapered through from one side. f Holes are punched in the form of nozzles. Note: The stirring distances were measured for holes near the center of the plate. I
Comparison of Stirring Ability of Different Types of Vibrated Perforated Plates with the System: Branched Decanes-Water
Table II.
Vibration is in a verticol direction. Amplitude from highest to lowest points of stroke = "16 inch. Tests made at room temperature. 1/16-inch thick sheet steel with the perforations punched or milled out Plate Diameter, Inches
Ratio of Open to Closed Area"
Number Hole Size, Inch
of
Hole Shape
Holes
Plates are disks of
Frequency of Vibration (Cycles/l\Iin.) Necessary to Stir Upper Phase into Lower Phase to a Depth ____of Barely stirs 1 Inch 3 Inches 4 Inches 2 Inches
Vibrated plate is at interface in middle of its stroke 6 Round 0.175 0.25 86 0.081 44 Round 0.25 6 Round 6 0 093 12 0.5 0.093 Round 12 0.5 6b 0.166 Round 6 20 0.5 0.342 6 Round 36 0.5 0.70 58 6 Round 0.5 0.125 6 4 Round 1.0 0.109 4 24 Round 0.25 0.364 4 Round 0.25 65 0.151 4 0.5 8 Round 0.068 4 8 SlOtSC 0.125 (width) 0.127 4 8 Slotsd 0.125 X 1.5
180 100 80 80 85 68 94 93
420 270 250 194 286 340 574 304 326 500 314 360 356
600 460 350 280 418 630 980 404 800 970 420 478 526
780 666 435 404 516 775 1420 476 1360 1366 540 670 844
96 200 300 480 174
880 776 380 320 454 680 1240 408
920 940 490 408 550 845 1600 524
1030 1010 524 500 670 972
1 Inch
1.5 Inches
2 Inches
2.5 Inches
610 740
885 1055
1084 1470
1334
I
... ...
138
118
...
900
750 510 484 564 960 3.5 inches at 1600/min. 538 3.5 inches at 1600/min. 1620 800 980 1154
Vibrated plate 1 inch above interface a t bottom of stroke
6 6 6 6b 6 6 6 6
0.25 0.25 0.5 0.5 0.5 0.5 0.5 1.0
Round Round Round Round Round Round Round Round
86 44 12 12 20 36 55 4
...
0.175 0.081 0.093 0.093 0.166 0.342 0.70 0.125
...
...
1-ibrated plate is a t interface in middle of its stroke
26 2b
0.094 X 0.79 0.25
Slotsd Round
4 6
0.116 0.116
... ...
...
.. ., .,
...
...
...
612
...
Stirring Depth a t 1600 Cycles/i\lin.
2.75 inches 2.25 inches
,4 1-inch wide steel band has been fastened t o the periphery of a Ratio of open to closed area = (total area of holes)/(solid area of plate). Straight slots arranged Slots are circular and arranged in two concentric rings. the plate SO that it extends l/Z-inch on each side of the plate. in the form of one or more squares concentric with the center of the plate. S o t e : The stirring distances were measured for holes near the center of the plate.
creasing the amplitude to 2.5 nim., or by putting knife edges on the holes in the middle of the plate by milling in equal taper from both sides of the plate. However, \vhen using relatively thin plates, it is not necessary to sharpen the edges of the holes through the plate in this way. The direction of mixing can also be made strongly preferential either in the u p or down direction by proper design of
the plate. For example, with 0.25-inch thick plates, the holes can be tapered from one side only to form a knife edge orifice on one side of the plate. I n this case. the plate will pump prefrrentially in the direction of the taper. This applies to either slots or round holes. The same effect can be obtained in thin plates by punching the hole out in the form of a nozzle. I n this case, the nozzle tends to give more unidirectional mixing
H O L E SIZE, SYMBOL A
I
INCH I /a
I
RATIO OF H O L E AREA TO S O L I D AREA
I -1
1 05
Figure 1. A single plot describes design factors for a perforated plate operated at 1-mm. stroke and 3600 cycles per minute
794
INDUSTRIAL AND ENGINEERING CHEMISTRY
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in thc direction in which the nozzle is pointed. Furthermore, the nozzle in a thin plate does a better unidirectional mixing job than the tapered hole through a thick plate. These directional pumping schemes can be used effectively when two plates are attached to a single shaft and positioned so that the interface is between the two plates. I n this case, the strongest jets of fluid impinge on the interface and create extreme turbulence.
H O L E SIZE, SYMBOL
INCH I /4
I/ 2 I
W
a C
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011 012 oi3 014 015 Oi6 RATIO OF H O L E AREA TO S O L I D A R E A
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Figure 2. Jet penetration can be predicted from plate lay-out for a perforated plate operated at 5/le-inch stroke and 450 cycles per minute
MIXER-SETTLER E X T R A C T O R Plate Size Any two plates having the same size holes and the same spacing of holes, and thus the same ratio of hole-to-solid area, displace the same volume of liquid per hole when vibrated a t the same frequency and amplitude. However, since only part of the displaced liquid goes through the holes and the rest flows around the periphery of the plate, it is apparent that as the plate gets larger, the penetration of one phase into the other increasesthus indicating that a greater percentage of the displaced liquid is going through the holes. With a very large plate, the amount of the material flowing around the periphery of the plate would be negligible, and the characteristics of the mixing could be predicted from the design of the plate and the frequency and amplitude of vibration. For plates 6 inches in diameter and smaller, the holes near the center of the plate produce stronger streams than the holes near the edge. The penetration of one phase into the other for the center holes is about 30% greater than that for the holes near the edge of the plate. I n an attempt to improve the mixing of a 6-inch diameter plate having 12 holes of 0.5-inch diameter, a metal band was attached to the periphery of the plate extending about 0.5 inch on each side of the plate. The addition of the band showed little improvement in phase penetration for the center holes. However. all of the holes in the plate now produced streams as strong as the center hoIes-thus showing considerable over-all improvement due to the addition of the band. It is believed that this band retards the flow of the liquids around the periphery of the plate and thus forces more of it through the holes. The band probably is of less value for larger diameter plates or if flow is confined by a small annulus between the plate and the containing vessel. O n a theoretical basis, it can be assumed for a large perforated plate that 51
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Figure 4. The volumetric efficiency of a perforated plate for pumping liquid through the holes can b e obiained by comparing actual and theoretical jet velocities
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FREQUENCY X STROKE ,FTISEC. VELOCir(sRPTIOOF HOLE TO SOLID AREA W T I O OF PLATE DIAMETER, HOLE SIZE, HOLE AREATO INCHES INCHES CLOSED AREA 6 1/2 0.09 4 112 0.15 STROKE =5/16-INCH
SYMBOL -
v 0
all the liquid displaced by the solid area of the plate must flow through the holes in the plate. Thus, if the frequency and amplitude of the reciprocating motion and the ratio of hole-to-solid areas of the plate are specified, the average velocity, u, of the liquid flowing through the holes can be calculated from this equation:
The volume displacement, V , of the perforated plate per unit time is: V
=
2fLA,
(2)
The factor 2 appears in the volume displacement equation because there are two complete mixing strokes per cycle, each pumping liquid in the opposite direction from the other. Knowing both the velocity and the volume of liquid flowing through the holes, the power received by the liquid from the reciprocating plate can be calculated from the relationship : Energy
=
1/2 mu2
where m is the mass of fluid flowing I
I
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through the holes per unit time. However, the actual power input to the reciprocating plate will be a function of how much energy disappears as friction and as entrance and exit losses as the liquid flows through the holes in the plate in addition to the velocity head imparted to the liquid. Pitot tube readings were taken a t the center of a hole in several different sized plates as the frequency of reciprocation was varied and were used to check the validity of the above theory for actual perforated plates. For these experiments the plate was operated in a single water phase with the pitot tube tip at the mid-point of the stroke of the reciprocating plates. Logarithmic plots of velocity head readings against the theoretical average velocity over a wide range of frequencies gave a series of straight lines with slopes of almost exactly two in all cases. This indicates that the velocity through the holes is a linear function of the frequency as predicted by the theory. The theoretical pitot tube readings were also calculated by converting the theoretical velocities calculated by Equation l to fluid head. The experimental I
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SYMBOL
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p MIXER FREQUENCY, CYCLEWMIN.
Figure 3. The compensating effects of mixer frequency and hole area in plate on jet penetration are shown for S/16-inchmixer stroke
0.2
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IO0 200 300 400 MIXER FREQUENCY X MIXER STROKE, IN./MIN
Figure 5. A single curve correlates stage efficiency for a variety of combinations of mixer frequency and mixer stroke VOL. 53, NO. 10
OCTOBER 1961
795
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Figure 6. Stage efficiency correlation in terms of cocurrent transfer units gives straight line log-log plots
velocity heads shown in Figure 4 Ivere, in all cases, below the theoretical values, indicating that higher frequencies are required to produce a given hole velocity than the theory indicates. This higher frequency is needed to offset fluid leakage or slippage around the edges of the plate and is equivalent to greater volumetric displacement per unit time. From these principles and experimental data, it was found that about 6@Yoof the displaced liquid flowed through the holes for a 4-inch diameter plate, and about 80% flowed through the holes for a 6-inch diameter plate. T h e percentages remain constant regardless of the frequency of reciprocating motion. O n the basis of this discussion, the average velocity of the liquid jets can be estimated for an actual perforated plate from u =
K(JL)
(3)
where K is a function of plate size and design. Likewise, the volume of liquid pumped or displaced by the plate per unit time is given by
v = IC'(,%)
(4)
where K' is also a function of plate design and size. Efficiency S:udies
T h e efficiency runs were all made using cocurrent flow of water and a narrow cut from commercial naphtha in the onestage flow apparatus. T h e water-tonaphtha volume ratio was kept constant at 1.0 and the interface was maintained as close 'to the middle of the stage as possible. T h e efficiency was followed by the transfer of pyridine from one phase to the other. I n each run, one of the phases contained essentially no pyridine in the feed while the other contained about 5% pyridine. The feed phase containing the pyridine was varied but this had no effect on the stage efficiencies obtained. I n each run, the product
1
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FEED RATE SYMBOL GAL PER MlN
e 0 V
fa
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.
MIXER LENGTH
IF!CHES
0 4 0 2
8 4
04 0 6
4 4 18
60 0
1
/ J.L,
Figure 7. Scale-up correlation relates transfer units per second to mixing intensity in terms o f product of mix frequency and stroke
concentrations were allowed to reach the steady state before sampling and the efficiency was then determined from the equilibrium distribution of pyridine between the two phases. Pyridine analyses were made by the Schultze method (9). T h e efficiency can be evaluated either as the number of theoretical stages dvailable in one actual stage, or in terms of the number of cocurrent transfer units equivalent to the actual stage (73). I n Figure 5 the efficiency in terms of theoretical stages is plotted against the product of mixer frequency and mixer stroke for a variety of different amplitudes. T h e detailed data are given in Table 111. T h e mixer element (right, page 791) n a s used in these experiments at a flow rate of 0.2 gallon per minute of each phase Figure 5 shows that this mixer has a characteristic efficiency curve Lvhich is essentially independent of the amplitude of the mixing even though a fourfold variation in amplitude was used to obtain the data. Figure 5 also shows that there is very little to be gained by mixing the phases beyond the point where about 957, stage efficiency is achieved. More intense mixing does not improve the stage efficiency appreciably and causes the production of large amounts of fine droplets which are difficult to settle. This demonstrates the desirability of building flow mixing units with variable speed mechanical agitators so that mixing conditions can be adjusted to the requirements of the system to be mixed-thus maintaining optimum conditions regardless of flow rates or physical properties of the phases. Several short tests were also made to find the effect on mixing efficiency of interfacial tension, phase viscosity. flow rates, and impeller length. Phase viscosity and interfacial tension showed only slight effects. However, flow rate and mixer length proved to be very important effects and could be correlated.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1
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20 40 60 100 200 400 MIXER FREQUENCY X MIXER STROKE, I N / M I N
FEED RATE MIXER LENGTH L I N E SYMBOL GAL. PER MIN. INCHES
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