A N APPROACH T O CHARACTERIZING
AGITATION B Y DISPERSION PARTICLE SIZE D. M. SULLIVAN’ AND E. E. LINDSEY Department of Chemical Engineering, University of Massachusetts, ,4mherst, Mass.
Geometrically similar, baffled, cylindrical tanks, turbine agitators, and equal energy input per unit mass were employed to disperse two different immiscible liquid systems. Drop-size distribution data obtained b y light-scattering techniques showed that size distributions can be used to measure degree of agitation and that the Sloan light-scattering technique can be used to study size distribution of agitated dispersions having drop diameters of 1 .O to 50 microns.
the term “agitation” encompasses a n and ancient group of physical processes. T h e diversity of these processes arises from the large number of complex factors that play a part in even the simplest application of agitation. I t is not surprising, therefore, that as recently as 1959 it could be said of agitation: “There is no unified mathematical treatment; there is even some question whether it would be worthwhile developing one” (2). I n view of the wicle spectrum of agitation phenomena associated with everything from concrete mixers to electric fans, the advisability of attempting to develop a “unified mathematical treatment’’ may well be questioned. However, within the various groups of agitation processes, sound theoretical analysis is unquestionably essential to the prediction and control of process results. I t is virtually impossible to subject to sound theoretical analysis a phenomenon for which there is no satisfactory quantitative measurement. I n recognition of this, a great deal of work has been directed at the development of techniques for measuring agitation. Significant progress has been made in several areas (6). One important type of agitation is related to the dispersion of immiscible liquids. I n most dispersion work, control of the sizes of the droplets of the dispersed liquid phase is essential for satisfactory results. Since drop size is a function of both the physical chemistry of the liquid phases and the mechanical characteristics of the agitation vessel, measurement of the agitation produced by {.hedispersing vessel is highly desirable. Kolmogoroff advanced a theoretical relationship between drop size and the local rate of energy dissipation per unit mass of agitated dispersions having locally isotropic turbulence (4). Shinnar and Church (>’) compared the theoretical equations of Komogoroff with the experimental data of Rodger, Trice, and Rushton (5) and Vermeulen, Williams, and Langlois (75), and pointed out significant agreement between them. Shinnar and Church concluded that Kolmogoroff’s work provides theoretical justification for the practice of scaling up dispersion N ITS BROADEST SESSE
I extremely large, diverse,
Present address, Research Department, Shawinigan Resins Corp., Springfield, Mass.
equipment on the basis of geometrical similarity and equal energy input per unit mass. Kolmogoroff’s equation assumes local isotropy in the turbulent flow of the system. Under conditions where this assumption is valid, the dispersed phase particle size is a function of only the local rate of energy dissipation. From a practical point of view, the local rate of energy dissipation can be determined only as a n average for the entire agitated mass, obtained by dividing the total rate of energy input to the dispersion by the total mass. Consequently, an agitation system which is characterized by a uniform rate of energy dissipation from point to point throughout its agitated liquid mass could give rise to the most nearly monodisperse dispersion, whose average particle size could be directly calculated from the total rate of energy input. Conversely, a system that does not have a uniform rate of energy dissipation from point to point throughout its agitated mass would give rise to a more polydisperse system. Such a situation would bring about a polydispersity whose range of sizes would be related to the range of differences in the rates of local energy dissipation. Since a stirred baffled tank does not have a perfectly uniform energy dissipation rate throughout its entire agitated mass, it is not likely to produce a nearly monodisperse dispersion. Consequently, such agreement between experimental data and theoretical predictions as that presented by Shinnar and Church might be interpreted as evidence of a correlation between average energy dissipation rates and average drop sizes. For geometrically similar vessels, both Kolmogoroff’s theory and experimental data (15) indicate that the energy input per unit mass of a dispersion provides a means of characterizing the agitation, in the sense that similar results for average drop size can be obtained in such vessels, However, this characterization fails when applied to geometrically dissimilar vessels. Furthermore, it sheds no light on size distributions. I n many instances, the distribution of sizes is as important as the average size. Clearly, a more satisfactory measurement of dispersion agitation is necessary. The size distribution curve of any dispersion should bear a direct relationship to the distribution of energy dissipation rates in the agitated vessel which produced it. I n our work, a n attempt was made to determine whether such relationships VOL. 1
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did exist and, if so, whether they could be used to measure agitation in terms of particle size distributions. For this purpose, a reference immiscible liquid system was agitated a t two different speeds in each of three sizes of geometrically similar tanks. For each condition of agitation, size distribution data were obtained by light-scattering methods. Under similar conditions of agitation in one of the tanks, a second liquid system was studied. On the basis of these results, the performance of the second liquid system in the other tanks was predicted. T h e experimental results were in good agreement with the predictions. Particle Size Measurement Several methods of measuring drop sizes were considered. Photomicrographic methods requiring the preparation of slides would have necessitated the addition of drop-stabilizing agents to the dispersions. Dynamic photomicrographic methods would have posed a serious problem of field depth through windows in the sides or bottom of the tanks. T h e counting of particles of various sizes by making the continuum electroconductive and passing the dispersion through orifices would have necessitated the addition of undesirable conductive materials to the dispersion. Light transmittance methods, while ideal for determinations of average drop surface area, would not have yielded satisfactory size distribution data and would have been largely restricted to dispersions having drop diameters greater than 50 microns (5).
'"
The use of light scattering seemed to be the most advantageous method of measuring average drop sizes and size distributions of unstabilized dispersions having drop sizes of the order of several microns (a range of particular interest in emulsion polymerization). The technique has been fully described by Sloan, Wortz, and Arrington ( 8 ) . Only the points necessary for interpretation of results are discussed here. Light passing through a dispersion is scattered by it. There is a relationship between the intensity of light, Z, scattered a t any angle, 0, from the incident beam and the size of the particle that scatters it. Sloan has defined conditions under which a plot of ZP us. 6 can be used to obtain information about the average particle size and the distribution of particle sizes. The principal conditions are that: There is no angular dependent absorption of the incident light; the transmittance of the incident beam is between 40 and 80% of the incident beam intensity; and the radius of the particle is in the region of 0.1 to 100 microns. Under these conditions, a plot of log IO2 us. e for a monodisperse system has the appearance of curve A in Figure 1. The location of the peak of the curve along the abscissa corresponds to the size of the particles as shown by the radius scale plotted below the abscissa. This scale holds only for spherical particles, the shape assumed throughout this work. Curves B, C, D, and E indicate the progressive change of the lightscattering curves as the dispersion becomes more and more polydisperse. A change in average size would be accompanied
c
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3 4
4
2Z
2 -
4
a
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t 3 n
2
8 -
6 4 -
-
SCATTERING ANGLE e,
20
02
0.5
Figure 1 A. Monodisperse. 68
.
I?
DEGREES
5
10 20 SPHERICAL PARTICLE RADIUS,
2
I
50
100
\ 2 0
MICRONS
Theoretical light-scattering curves B,C,D,E. Polydisperse,
I&EC FUNDAMENTALS
F. Binodal dispersions ( 8 )
Figure 2. C
Agitation tank Condenser
OUT
OUT
1
A
Projected and partially cutaway views of light-scattering cell
Figure 3. A.
Along light beam.
6.
Horizontally across light beam.
by a shift of the peak (of the curve along the abscissa. T h e occurrence of two peaks in a single curve, as in F, would indicate that the dispersion contained two maxima of rather narrow particle size in iits distribution curve. These light-scattering; curves should not be confused with true size distribution curves. They are useful, however, because they change in a manner similar to distribution curves. T h e location of the peaks yields accurate data on average size. T h e flatness of the curves gives only semiquantitative
Table I. Values of Dimensional Parameters for Each Tank Relative Dimensions (absolute), Symbol Dimensional Parameter to T Inches
AD AE AW BBC BSC BW PA PE PID QLL RA RE RID SD T TA TH BBA
Agitator diameter Agitator elevation from bottom of tank Agitator width Baffle to bottom of tank clearance Baffle to side wall clearance Baffle width Probe to agitator distance Probe elevation (opening) from bottom of tank Probe inside diameter Quiescent liquid level above bottom of tank Return line to agitator distance Return line elevation (opening) from bottom of tank Return line inside diameter Agitator shaft diameter Tank diameter Torque arm length Tank height Baffletobaffleangle
Exaggerated length of wet length path
data on the distributions of sizes, but such information was adequate for this work. Apparatus
T h e experimental apparatus consisted of three integrated systems: a n agitation system (Figure 2 and Table I), a continuous sampling system, and a light-scattering apparatus. Three sizes of geometrically similar agitation vessels were used to observe a small range of scale-up effects. T h e tanks were of the baffled cylindrical type. The agitators were turbines consisting of six vertical, flat, rectangular blades. Conventional design methods were followed in construction and arrangement of the baffles, agitators, etc. ( 7 , 70). The drive mechanism for the agitators was provided with a variable-speed transmission equipped with a torque-measuring device. The basic components were from a standard Chemineer laboratory agitation apparatus, Model ELB 50 (7). The circulation system consisted of a probe, conduits, low shear bellow pumps with a damping chamber, Flowrator, and return tube. T h e light-scattering system consisted of a light-scattering apparatus similar to that described by Stein and Keane ( 9 ) , equipped with a specially constructed light-scattering cell. T h e important feature of the light-scattering apparatus, its optical resolution, was such that the ratio of the unscattered angular light intensity to zero-degree beam intensity ( I ~ S / Z ~ , ~ ) was 1.4 X 1O-lat 0.5' and 2.75 X lO-'at 1.0'.
T/1.0 T/3
7.5 2.5
9.0 3.0
T/3
.
2.5 0,312
3.0 0,375
4.0 0.500
T/12
0,625
0.750
1 .OO
T/72 T/12
0.104 0.625
0.125 0.750
0,167 1 00
T/3.5
2.12
2.57
3.42
T/3.75
2.00 0.187
2.40 0.187
3.20 0.187
T/1.0
7.5
9.0
T/3.5
2.12
2.57
3.42
T/1 . 5
5.00
6.00
8 .OO
Exclusive of the scattering cell, the entire apparatus was one constructed by, and borrowed from, the Monsanto Chemical Co. Details of construction can be obtained from R. J. Clark, Research Department, Plastics Division, Monsanto Chemical Co., Springfield, Mass. Figure 3 shows the details of construction of the scattering cell. The light path through the cell was adjustable.
...
0.187 0.5
0.187 0.5
0.187 0.5
Materials
.
,
, , ,
... T/0.8
..,
9.4 120'
11.2 120'
12.0 4.0
d.
12.0
15.0 120'
Two different immiscible liquid systems were selected for investigation. T h e first, or reference system (IB/W), consisted of 2-butanol-saturated water as the continuous phase V O L . 1 NO. 2 M A Y
1962
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11
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SCATTERING ANGLE 0
50
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SCATTER N G ANGLE 8
I IO'
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02
10
20
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1
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1
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5 I
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l 20
SP?ERlCAl PART CLE RADIUS
Figure 5.
I
1
I
I I
1
10
DEGREES 2 I
I
1
I
I
50
I
1
1
I
100
200
MICRONS
Light-scattering curves a t low speeds Tank I.D., Inches
A. lB/W B. lB/W
c.
and water-saturated 2-butanol as the discontinuous phase (2.5% of the total dispersion volume). The second system (CH/W) consisted of cyclohexanolsaturated water as the continuous phase and water-saturated cyclohexanol as the discontinuous phase (also 2.570 of the total volume). Partially miscible liquids were selected, in order to minimize interfacial tensions and phase density differences. These conditions were considered helpful in minimizing drop coalescence in the circulation system. Both phases of a system were mixed and simultaneously distilled prior to use. After distillation, the phases were allowed to stratify completely. The appearance of a clean, nonopalescent interface was taken as evidence of sufficient purity for use (14). Charges for the experimental runs were decanted from the stratified phases.
Procedure T h e first step in the experimental work was the determination of the ability of the light-scattering apparatus to respond to variations of the speed of the agitator in a dispersion. For this purpose the IB/W system was introduced into the smallest of the three tanks. The agitator was run a t a low speed and the dispersion was continuously circulated through the light cell. The intensity of the zero-degree light beam through the cell approached a constant value at a decreasing rate throughout approximately one hour. When this intensity attained a 90
I&EC FUNDAMENTALS
D. E.
lB/W CH/W
cn/w
F. CH/W
7.5 9.0 12.0 7.5 9.0 12.0
constant value, it was assumed that dynamic equilibrium had been achieved. (This same indication of equilibration was used throughout all subsequent experiments.) At that point several variations of agitator speed were made, and it was observed that the zero-degree intensity followed these changes. Several changes in the position and attitude of the sampling probe were made without producing measurable effects in the intensity of the scattered light a t several angles of observation. Consequently, the probe was fixed at a geometrically convenient position. Variations in the circulation rate demonstrated that the intensity of the light responded rapidly to this variable as well as to the agitator velocity. At high circulation rates, the effect of agitator speed variations became obscured, while at low circulation rates, the effect of agitator speed was readily observable. Consequently, a constant low circulation rate was selected and used throughout all subsequent experiments. For this constant circulation rate, it was assumed that light intensity response to the effects of varying agitator speeds would yield reliable information about drop size variations. The second step in the experimental work was an attempt to investigate the applicability of Sloan's theory to the results
Shinnar (7) showed that Vermeulen's data for dilute dispersions (75) were in agreement with Kolmogoroff's concepts of equal energy input per unit mass of dispersion (4). Vermeulen's data agree with the equation
...-
2
c
2 3
4 5Z
where p = density N = agitator speed D = agitator diameter u = interfacial tension d = particle diameter I n the experiments with the CH/W system, the same speeds of agitators were used in each tank as in the corresponding tank with the IB/W system. These experiments were otherwise identical to those with the IB/W system. For clarity, only results attained with both liquid systems at a single energy dissipation rate per unit mass are compared in Figures 5 and 6. Similar results were obtained at the higher rates. A typical difference between high and low energy dissipation rates per unit mass is illustrated in Figure 6. A theoretical curve (C) for a monodisperse system of similar average particle size is also shown. I n Table 11, the conditions of agitation and the average particle size results are tabulated.
c > L1
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z c
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il
! 02
SCATFERING ANGLE H
05
13
20
SPHERICAL PARTICLE RADIdS
Figure 6.
Discussion of Results
DEGREES
50
IC0
200
'J CRONS
Light-scattering curves for lB/W system
Tank 7.5-inch I.D. A. Theoretical monodisperse system with same average size as B B . Low agitator speed C. High agitator speed
obtainable on this light-scattering apparatus. For this purpose, two particle size standards were obtained: a polystyrene latex having an average particle diameter of 1.171 microns and a standard deviation of 0.0133 and a mulberry pollen having an average diamaeter of 12 to 13 microns and a somewhat broader distribution. These materials were diluted to conform to Sloan's transmission requirements and separately circulated through, and scanned by, the light-scattering apparatus, after which a mixture of the two standards was similarly treated. T h e lightscattering data obtained are presented graphically in Figure 4. T h e agreement with Sloan's theoretical curves (shown in Figure 1) for monodisperse, polydisperse, and mixed dispersions is evident. I n the next series of experiments, with the IB/W system in the smallest tank, a low speed of agitation was selected which was slightly above the minimum necessary to maintain dispersion. When the dispersion had equilibrated at this speed, light-scattering data were obtained. The agitator speed was then doubled and, after re-equilibration, a new light-scattering curve was obtained. For the other two tanks, the high and low agitator speeds were selected by the use of Vermeulen's equation to produce the average particle sizes obtained with the corresponding speeds in the smallest tank.
The similarity of results obtained for the IB/W system in all three tank sizes provided a basis of predicting that the results obtained in all three tanks with the CHjW system would also be similar to each other. The dissimilarity between the results obtained with the IB/W and the CH/W systems in any single tank provided a basis of predicting that the same dissimilarities would result in the other tanks. These results were taken as evidence that the performance of the agitation systems had been measured by the size distribution curves of the IB/FV system, in the sense that the performance of two of the tanks with the CH/W system could be predicted. I t seems possible to characterize a series of agitation vessels by the size distribution curves of a reference dispersion, and then, by comparing these curves with that of a different dispersion from any one of the same series of tanks, to predict the performance of the other tanks on the new dispersion. Most of the liquid dispersion curves indicate either a distinct secondary maximum or an upturn toward a secondary maximum a t lower angles-Le., larger particle size. Such secondary maxima may be attributable either to shear effects in the circulation system or to variations in the energy dissipation rates within a given tank. The principal maxima of these curves show a slight but consistant decrease in average particle size with increasing agitator speed. The direction of this shift is in agreement with Vermeulen's equation for dilute dispersions ( 75), but the magnitude is not. Thus, for a single dispersion in a single tank, one obtains from Vermeulen's Equation 1 : hT2D413d513
k
(2)
By solving for the particle diameter, d (3)
the fraction
{ z5 1, now a constant, is obtained.
I n the case where the agitator speed, N , was doubled, by letting d = the particle diameter associated with the high VOL. 1 NO. 2 M A Y 1 9 6 2
91
Table II. Agitation Conditions and Data Av. Particle Diameter, Experiment Figure Microns Polystyrene latex 1.176 3, A Mulberry pollen 15.4 3, B
Polystyrene latex mixed with mulberry pollen LiquidLiquid System IB/W
Tank Diameter, Inches 7.5
IB/W
9.0
IB/W
12.0
CH/W
7.5
CH/W
9.0
CH/W
12.0
3,
c
Agitator Speed Low
High Low High Low High Low High Low High Low High
1.29 16.0
3.45 3.12 3.51 2.86 3.64 2.86 1.60 1.50 1.60 1.54 1.56 1.43
p2y2D413d5/3 = U
speed and d’ = that associated with the low speed of agitator, one gets d = d ’ ( l / 2 ) 6 / 5= 0.435 d‘
(4)
Figure 6 shows the largest decrease in average particle diameter accompanying a twofold increase in agitator speed for the 2-butanol-water system. Here, d‘ = 3.45 microns and d = 3.12 microns. Equation 4 predicts that: d = 0.435 (3.95) = 1.50 microns
which is considerably lower than the experimental value for d. The explanation for this nonagreement apparently does not lie in a failure to meet Kolmogoroff’s criteria of isotropic turbulence in these experiments. Where secondary maxima were clearly evident, they shifted from about 33 to about 1 5 microns, with a twofold increase in 33 microns in Equaagitator speed (Table 11). Letting d’ tion 4 : d
=
0.435 (33) = 14.3 microns
which is in good agreement with the experimental value of 15 microns.
Table 111.
Tabulated Values of Re, e, q , and Drop Size for Various Conditions of Operation RevoluAv. Droj lions Diameter, Microns Liquid per 7, Principal Secondary e, Sq. System Second Re Ft./Sec.3 Microns peak peak B/W 5.73 20:050 0.71 6.10 3.45 32 11.46 40,100 6.73 3.48 3.12 14.3 5.07 25,000 0.63 6.27 3.51 33 10.14 50,000 6.13 3.56 2.86 14.8 4.18 37,150 0.70 6.12 3.64 33 8.36 69,800 6.27 3.54 2.86 16.6 CH/W 5 . 7 3 17,900 0.70 6.33 1.60 , , . 11.46 35,800 7.01 3.56 1.50 .,. 5.07 22,600 0.63 6.46 1.60 ... 10.14 45,200 6.30 3.63 1.54 , , . 4.18 33,000 0.72 6.27 1.56 , , . ‘ 8.36 66,000 6.25 3.66 1.43 , ..
92
I&EC FUNDAMENTALS
Two criteria of locally isotiopic turbulence are that the Reynolds No. of the main flow be very large (Re + a) and that the width of the agitatci blade be much larger than the micro scale of turbulence (TV >> 7 ) . In Table 111, in which are tabulated various parameters, it is seen that all Reynolds S o . were greater than 17,000 and that the largest value of 7 was less than 7 microns. Since the smallest agitator width used was 0.312 inch-Le., 7930 microns -it is apparent that isotropic turbulence prevailed throughout all runs. Since the shift of the principal peaks with increased agitator speed did not follow Vermeulen’s Equation 1, but that of the secondary peaks did, a criterion of the validity of the equation within isotropic turbulence must be invoked. Shinnar (7) notes that: 0.016
is applicable only when d > q. I t is evident from Table I11 that this condition has not been met by the particles associated with the principal peaks of the light-scattering curves. That the particles associated with the secondary peaks seem to follow Vermeulen’s equation may be attributable to the fact that for them the condition d > 7 was met. Although equations which are purported to hold in the region where d < q have been published (72, 75). the method of handling cases where d !2 q has not been fully developed. Unfortunately, this is the case for the particles whose sizes are associated with the principal light-scattering peaks in this work. One final comment on the occurrence of more than one node in the scattering curves is in order. Vermeulen’s equation was used as the basis of scaling up the sizes of the tanks. Using the speeds indicated by this equation, good agreement was obtained between the entire light-scattering curves of all three tanks in both the IB/W and the CH/W systems. O n the other hand, the equation did not predict the proper shift in principal peak position for changes in agitator speeds in any single tank. The conclusion is that Vermeulen’s equation is valid for size scale-up, even though the criterion d > 7 is not met, but for velocity changes it is valid only for d > 7 . The latter effect was noted by Vermeulen.
Conclusion In this exploratory work, a number of assumptions and arbitrary decisions were made. These gave rise to questions about the importance of the contributions of the circulation system; the distortion of the droplets in the illuminated volume of the light-scattering cell ; the extrapolation of the results obtainable in workable ranges of agitator speeds, concentration, etc., into the ranges inaccessible to the light-scattering techniques; and many others. Nonetheless, the results definitely indicate that size distribution curves do reflect variations in agitation parameters and that they hold some promise as useful tools in the investigation and control of dispersion particle size, As much as 60 minutes may be required to attain steady state in a system of this kind. One final comment will be made on the effect of drop phase viscosity, Rodger, Trice, and Rushton ( 5 ) showed that in contrast to data published elsewhere (3, 77, 73) the effect of increasing drop phase viscosity for constant continuum viscosity was a decrease in drop size. Since the CH/W continuous phase viscosity was about thc same as that of the IB/W system, and the CH/W drop phase viscosity was nearly ten times that of the IB/W system, the results of this work were in agreement with those of Rodger et al.
Acknowledgment
literature Cited
T h e authors are indebted to R. S. Stein and R. J. Clark for suggesting and assisting in the light-scattering work; to the Research Council, University of Massachusetts, for funds which made it possible to employ a valuable assistant, Eugene Daniels, in obtaining the data; to the Shawinigan Resins Corp. for a n academic leave during which most of this work was done; and to the Monsanto Chemical Co. for loan of the lightscattering apparatus. Finally, valuable advice was obtained from C . E. Carver, F. €3.Norris, and D. C. Chappelear.
(1) Bates, R. L., “Fluid .4gitation Handbook,” p. 14, Chemineer, Inc., Dayton, Ohio, 1956. (2) Chem. Eng. News 37,70 (Oct. 26, 1959). (3) Clav. P. H.. Proc. Roy. Acad. Sci. Amsterdam 43. 852, 979 (1940). (4) Ko
