I n d . E n g . Chem. Res. 1990, 29, 676-682
676
An Experimental Investigation into the Complete Suspension of Floating Solids in an Agitated Tank Ronald W. Thring*vt and Michael F. Edwards Schools o f Chemical Engineering, University of Bradford, Bradford, West Yorkshire BD7 IDP, United Kingdom
Experimental work is reported on the drawdown of floating solids by agitation inside a tank. The effects of baffle configuration, type of impeller, solids concentration, and impeller clearance from the tank bottom, on the minimum drawdown speed and associated power input, are discussed. The baffle configuration did not significantly influence the minimum drawdown speed but strongly determined the power required. T h e power number increased with the number of baffles in any configuration. T h e drawdown speed was highly dependent on the type of impeller: highest and lowest values were recorded for the propeller and paddle, respectively. Solids concentration and impeller clearance from the tank bottom had a small effect on the minimum drawdown speed. However, the latter strongly affected the associated power input. Two preferred stirrer/baffle arrangements determined were (1) one baffle (three-bladed propeller) and (2) four baffles (six-bladed turbine) a t an impeller clearance of two-thirds of the liquid depth from the tank base. In several chemical processing operations, mechanical agitators are used to suspend solids in liquids to enhance solid-liquid mixing for catalytic and mass-transfer purposes. Suspension of solids heavier than the liquid medium has received extensive attention, and several correlations for calculating the required speed of agitation for complete suspension have been developed and published (Aeschbach and Bourne, 1972; Baldi et al., 1978; Musil and Vlk, 1978; Narayanan et al., 1969; Nienow, 1969; Rieger and Ditl, 1982; Schwartzberg and Treybal, 1968; Weisman and Efferding, 1960; Zwietering, 1958). Comprehensive book reviews on bi- and triphase contacting in stirred vessels have been published recently (Harnby et al., 1985; Mann, 1983; Ulbrecht and Patterson, 1985). However, only a few studies have been reported on the suspension or drawdown of floating solids in liquids by agitation (Hemrajani et al., 1988; Edwards and Ellis, 1984; Ellis et al., 1986; Joosten et al., 1977). The suspension of floating solids is of particular interest in the fields of fermentation, minerals processing, sewage treatment, and polymerization reactions. In such industries, a number of operations such as mixing, aerating, and chemical reaction(s) are carried out. In designing equipment for such processes, it is necessary to satisfy all the requirements, such as the degree of mixing, the reaction rate, and an acceptable power input. Often, not all these operations are compatible, and some degree of optimization is necessary. This paper describes experimental work carried out to study the effects of solids concentration, type of impeller, clearance of impeller from the tank bottom, and baffle configuration on the minimum speed and power input required to draw down floating solids in a liquid by agitation.
General Considerations 1. Variables Affecting Suspension of Solids. In the design of any effective mixer for suspending a slurry, the impeller speed and construction and the vessel geometry are important features. The uniformity of solids suspension depends on the properties of the solid-liquid system considered, such as particle size, shape, and density; solids
* Author to whom correspondence should be addressed.
Present address: Department of Chemical Engineering, University of Sherbrooke, Sherbrooke, Quebec, Canada J1K 2R1. OSSS-5S85/90/2629-0676$02.50/0
concentration; and density and viscosity of the liquid phase. 2. Impellers. Selection of suitable devices is a function of vessel shape and the physical operation to be performed. Impellers for the suspension fall into two basic categories depending on the method by which they generate motion in the mass. The first and simplest is represented by the several types of paddles, such as the single- or multiple-straight-blade designs. These provide mass motion by physically pushing the material in its path and entraining the adjacent mass in a generally rotary motion. Little or no velocity head is imparted to the fluid. The second, more commonly employed, types include propellers and cone and disk turbines. Each of these develops a velocity head, causing the fluid mass to be discharged at a velocity greater than the surrounding mass. The impelled fluid, plus entrained adjacent material, flows in a definite pattern throughout the vessel and returns to the “eye” of the impeller. 3. Circulation Patterns. For the purpose of suspension of solids, circulation within a tank is one of two kinds: (a) “downwardly and upwardly directed, which physically draws down or lifts up the dispersed phase; (b) “universally directed”, which distributes the solids into the fluid. The propeller generates the axial-type flow pattern. Depending on the direction of the rotation, the flow pattern may consist of upflow along the tank axis and return flow downward along the walls, or the reverse. The turbine in the position directly above the vessel base provides the maximum stream velocity at the vessel location where maximum lifting velocity is required. The discharge is radial, sweeping the vessel bottom and making only one directional change at the vessel wall to flow vertically. In the raised position, it produces a figure-eight pattern. It depends on the upper recycle stream to draw down the slurry to the above eye of the impeller for redistribution. The lower recycle stream lifts the suspension up to the bottom eye of the impeller. 4. Settling Characteristics. Suspension of solids in a liquid medium will mostly be achieved by the effect of liquid turbulence, namely, when the rising or falling velocity of the liquid phase equals or exceeds the terminal velocity of the particles. Terminal velocities of particles may be calculated from empirical correlations of drag coefficient and Reynolds number. 1990 American Chemical Society
Ind. Eng. Chem. Res., Vol. 29, No. 4, 1990 677 AGITATOR
LOAD CELL
/
SIDE
1
r
I
VIEW
TURBINE AGITATOR
L
TOP
VIEW
MOTOR
-
MOUNTING i
-dDb
/ r 1
r
k W
,BAFFLE
H
I
PADDLE
,o *D-
Figure 2. Types of impellers used in the experiments.
I Figure 1. Experimental apparatus.
An obvious condition affecting solids suspension is the density difference between solid and liquid. When all other factors are constant, the settling rate bears mostly a directly proportional relationship to this difference in density. Another major influence is the size and shape of the solid particles. In industrial applications, slurries normally involve a broad band of particle size, often extending from fractional centimeter size granules to the micrometer range. The following generalizations may be made concerning the effect of well-known variables on the terminal velocity of settling solids and hence on the fluid velocity required for the particles' suspension: (a) terminal rising velocity for floating solids increases with a decrease in the density and increase in the size of the discrete particle; for sinking solids, this velocity increases with the density and the size of the solid particle; (b) terminal rise velocity, for all solids, decreases with an increase in (i) irregularity or roughness of the particle surface, (ii) cross-sectional area of the particles, (iii) spread in the size range of the particles, (iv) concentration of the solids in the slurry, and (v) viscosity of the liquid. For floating solids, this velocity increases with the density of the liquid. 5. Vessel Geometry. The geometry of the vessel has to conform to the flow pattern in order to obtain a minimum impedence to the natural direction of stream flow. For the best design, a proper balance has to be achieved between the type of impeller and the vessel geometry for the particular slurry system. Usually more than one impeller type and vessel geometry configuration will work for a slurry system but the physical requirements of the process, plant, and power economic considerations usually limit the choice to one configuration. Important geometrical factors normally considered in the design of solids suspension systems are tank shape, baffles, tank-to-impeller diameter ratio, and impeller clearance from the tank bottom.
Experimental Section 1. Description of Equipment. A schematic diagram of the experimental apparatus is shown in Figure 1. The
Table I. Types and Dimensions of Stirrers dimension. m type of stirrer D Db Dd W turbine: 6-bladed 0.45 0.1125 0.225 0.0675 propeller: 3-bladed 0.38 paddle: 2-bladed 0.61 0.0915
~
2 0.076
vessel was a flat-bottomed cylindrical tank of 1.22-m diameter (2') by 1.22 m deep, fabricated from mild steel plate. The depth of the liquid (H)was maintained throughout a t 1.15 m. Four mild steel plate baffles of width 12.2 cm (10% of the tank diameter) were employed and fitted vertically over the side of the tank and secured in position by three mild steel bolts. Each baffle could be arranged to rest on the bottom of the tank or be raised to give a clearance of 0.305 m between the lower edge of the baffle and the base of the vessel. Agitation was provided by three impellers of standard geometrical configuration. These were a three-bladed propeller, a six-bladed disk turbine, and a simple paddle. Figure 2 shows the side and top views of the impellers, and their dimensions are listed in Table I. Each impeller was fabricated from mild steel plate, mounted on a 4.5-cmdiameter mild steel shaft. The impeller shaft was driven by a 2.54-kW motor through a variable-speed gear and a 3.98:l.O reduction gear to give a range of 1.06-12 rev/s of output rotational speeds. The entire drive assembly unit was vertically mounted on a thrust bearing. The impeller speed was measured with a hand-held electronic tachometer. Experiments were performed with impeller clearances ( c ) from the base of the tank of one-third and twothirds of the liquid depth. High-density square-shaped (aspect ratio of unity) white polyethylene chips of size range 1.40-3.35 mm and density of 925 kg/m3 (determined by a pygnometer) were used as the solids. Water was the liquid medium in all the experiments. Torque-Measuring Device. To determine the power consumed by the impellers, the torque on the motor was measured by using a thrust bearing connected by a me-
678
Ind. Eng. Chem. Res., Vol. 29, No. 4, 1990 NO. OF BAFFLES
r , -
ROTATION
BAFFLE
CONFIGURATION
v
ROTATION LOA C
4
T--Figure 3. Sketch of link mechanism for power measurement.
chanical linkage to a load cell, as shown in Figure 3. The device consisted of a fixed base plate with a ball race on which was placed the whole motor assembly with the agitator shaft. The ball race was well greased so that the motor assembly could rotate on it with minimum friction. The torque exerted on the clockwise rotating impeller shaft produced an equal and opposite torque on the motor assembly, resulting in an anticlockwise rotation of the motor assembly. To prevent this anticlockwise motion of the motor assembly, the mechanical linkage was attached such that it transmitted the torque generated by the motor assembly to a hydraulic load cell. The force on the load cell was measured by a pressure gauge. 2. Techniques and Observations. For every series of experimental runs, the polyethylene solids were carefully weighed out and gently dropped down the side of the tank. The speed of the impeller was then gradually increased every 40 s until the solids were judged completely suspended. In order to establish a basis for experimental reproducibility, a criterion for determining complete solids suspension was devised. When a stagnant zone, even one containing as few as three to five floating solids, remained on the liquid surface for less than 4 s, the suspension was judged complete. Following this rule, the minimum suspension speed was judged with an accuracy of about 3% from repetitive experiments carried out by the same operator. Various baffle configurations were used for each solids concentration, impeller, and impeller clearance from the tank base. Figure 4 shows all 22 baffle configurations employed in the experiments. For each of these, the minimum suspension speed and associated power consumption were determined. Observations showed that the particle movement at the liquid surface varied according to the impeller type and size. For the disk turbine a t lower speeds, there existed small stagnant zones of floating solids in which the latter agglomerated due to surface tension effects. Stagnant zones were most prominent immediately behind the baffle(s) where the radial flow component was minimal. As the speed was gradually increased, more swirls, swells, and small turbulent vortices developed over the entire free liquid surface, breaking up the stagnant zones intermittently and sinking more solids. At higher speeds, much
1
3
.**I
-1
,
1
LOWERED RAISED
BAFFLE BAFFLE
Figure 4. Baffle configurations used in the experiments.
stronger, fewer swells, and deeper vortices ensued, with solids drawn down by the downward stream and vortices. A t a certain impeller speed, the stagnant zones of solids completely broke up, and all the solids were drawn down into the liquid. It was difficult to determine this point exactly and objectively because even a t higher impeller speeds some solid particles appeared and intermittently floated on the liquid surface. By use of this criterion, small groups of floating solids were usually observed in the region around the impeller shaft and behind the baffles. Also, when three or less baffles were used in any configuration, small stagnant clusters of solids existed near the tank wall, only to be swept away by a swell and almost immediately disappear in the resulting vortex formed. The time for which they were under the liquid surface was very much greater than that for which they remained floating, using a stopwatch, an average of about 20 s in suspension as opposed to about 3 s at the liquid surface. Since in most catalytic and
Ind. Eng. Chem. Res., Vol. 29, No. 4,1990 679 mass-transfer processes a “dead” time of 3 s for a very small proportion of solids would not seriously effect the efficiency of the entire process, the particles were assumed to be fully suspended for these processes. This criterion corresponds to bottom and corner fillet suspension states for dense solids, although our method should be considerably less subjective than the fillet state. The propeller produced a strong vertical current as it was pumping downward. This agitator drove the liquid down to the bottom of the tank, where the stream spread radially in all directions toward the tank wall, flowed upward along the wall, and returned to the eye of the propeller from the top. At the free liquid surface, the stream was seen as swells behind each baffle, on the right side, where the radial flow component was maximum. Solids accumulated in the resultant shallow vortices, disappearing in the surrounding rotating liquid, and were thus suspended. Also, suspension was further achieved when the swells became so strong that they splashed against one another, thereby sinking more solids in their wake. Even though the swells were continuously produced, their volume and force fluctuated. As a result, some parts on the liquid surface remained almost still, with a few solids floating on the top. However, even though these floated intermittently for longer than 5 s before being drawn into the turbulent liquid, drawdown was deemed complete as the solids comprised a very small proportion of the total amount in suspension. The simple paddle produced a strong tangential flow pattern with a negligible vertical current when no baffle was used. As the speed was slowly increased, the gross vortex deepened much faster and was wider than those developed by the other impellers. In every case, when one or more baffles were employed to create more turbulence in the liquid, the load cell indicator needle fluctuated considerably, making it difficult to accurately make a reading; these fluctuations were more violent and frequent as the paddle speed was increased. Suspension was mainly achieved by adjacent swells splashing together and sinking the solids floating in the calm between them. Furthermore, a small, turbulent, intermittently produced vortex suspended the bulk of the solids for all the baffle configurations cited. Results a n d Discussion A discussion of the results will focus on the effects of the following variables on the minimum drawdown speed and associated power input: namely (a) solids concentration; (b) type of impeller; (c) height of stirrer above the tank bottom; (d) baffle configuration. Solids Concentration. Disk Turbine. Experiments were conducted for increasing concentrations of solids from 0.75% to 3.75% w/w increments of 0.75%. At an impeller clearance of one-third of the liquid depth from the tank base, the turbine could not a produce complete suspension for X = 0.75-3.00% w/w for baffle configuration 1,even a t the highest speeds allowable. For this case, the limitating agitator speed was taken to be the one at which the liquid vortex produced reached the impeller, causing severe mechanical vibration due to entrainment of air into the liquid by the spinning impeller. Solids drawdown was only attained for X = 3.75% w/w. Nmin was measured for all the other baffle configurations and solids concentrations. The results are rather extensive, and only plots of the minimum suspension speed (Nmin) versus X for representative baffle configurations are presented in Figure 5 for c = H / 3 . It is seen that an increase in X has a negligible influence on Nmk In fact, for all practical purposes, “in may be taken to be independent of X,for any baffle
TURBINE
B
zool I60
,161 141
o
-*
-
= I
1
I
1
2
3
I
4
x (%)
D 200
80
t
L
Figure 5. Plots of Nmh versus X for the turbine for different baffle configurations. PROPELLER
1601
A
0
I20
280
I6O
80
1
I
I
I
I
2
3
4
x ( %1
1
t
C
D
I
1
1
I
Figure 6. Plots of Nh versus X for the propeller for different baffle configurations.
configuration. For the turbine, Nmin is seen to be approximately constant a t 120 rpm for all the cases cited. Propeller. The results are presented in Figure 6 for the propeller at c = H / 3 above the tank base. For all the
680 Ind. Eng. Chem. Res., Vol. 29, No. 4, 1990
280 "I"
240
200
-
B
A
-
I
60 -
280
c I
"I"
240
r
200
r
I60
r
C
I - 1 1 1 Figure 7. Plots of Nmin versus X for the paddle for different baffle configurations.
values of X and baffle configurations cited, the plots again indicate the independence of Nminon X. I t is seen that Nminstays at about 220 rpm for all the conditions. However, there is quite a bit of scatter in the graphs for baffle configurations 2 and 3, as shown in Figure 6A. In particular, as the speed was increased for X = 2.25% and 3.00% w/w, it was rather difficult to decide objectively when complete solids drawdown was attained. The reason for this behavior was that, since one baffle was employed in both configurations, solids were mostly drawn into the liquid by the gross vortex near the center of the liquid surface. However, to get to the center of the vortex, most floating particles had to travel around the tank periphery until the rising swell produced immediately behind the baffle directed them into the vortex. Nminwas then decided upon when the solids took less than 3 s to travel around the circumference of the tank and into the vortex. To determine this stage precisely proved rather difficult as some stagnant clusters of solids still remained floating for longer than 3 s immediately in front of the baffle and along the side of the tank. Paddle. Figure 7 shows the results obtained for the paddle positioned at c = H / 3 above the tank base. For each value of X , the corresponding value of N- is smaller for the turbine and propeller. However, the efficiency of the suspension, defined here as the ability to sustain the suspension of the solids with a minimum of stagnant floating solid zones appearing on the liquid surface, is lowest for the paddle and highest for the propeller. Even though the load needle fluctuations were the most erratic of all the impellers employed, Nminfor the paddle was determined with good reproducibility. For all the configurations tested, plots of Nminversus X were found to be horizontal, within experimental error. The value of Nfor the paddle is seen to be about 100 rpm. This once again demonstrates the independence of Nminwith solids con-
centration for all the impellerlbaffle configurations tested in this work. Type of Impeller. The impellers tested are shown in Figure 2 and their dimensions are listed in Table I. From Figures 5-7, for the baffle configurations considered, Nwas found to be about 130, 220, and 100 rpm for the turbine, propeller, and paddle, respectively. Thus, based on this work, it may be concluded that Nminis strongly dependent on the type of stirrer, which generates the desired flow patterns in the liquid for drawing floating solids down into the liquid, with or without the use of baffles. Height of Stirrer above the Tank Bottom. For this set of experiments, the impeller clearance (c) was varied at two positions, namely, at one-third and two-thirds of the liquid depth above the tank base. For X = 3.75% w/w, N,,, was determined at both values of c for all 22 baffle configurations considered. Table I1 compares the power consumption (PI V ) and Nminfor representative baffle arrangements. No comparison could be made for the simple paddle; it could not readily be mounted a t a height of 2H/3. The results obtained for the other two impellers indicate there is a slight influence of the impeller clearance above the bottom on N,,,. For the turbine, the values of Nminand P/ V for c = H / 3 are higher than those for c = 2H/3 by factors of approximately 1.2 and 1.7, respectively. As the number of baffles increases from 1 to 4, the ratios of N,, and P / V at the two clearances considered increased by 10% and 34%, respectively. Thus, there is a substantial influence of impeller clearance on the power required for suspension; this effect approximately doubles for the turbine as the number of baffles is increased from 1to 4. The effect of impeller clearance from the tank base on both the minimum drawdown speed and associated power consumption is least when two oppositely placed baffles in the raised position are utilized. For the propeller, from the five baffle configurations considered, the values of Nminand those of power consumption for c = H/3 are higher than those for c = 2H/3 by factors of 1.15 and 2.3, respectively. Also, as the number of baffles increases, the ratio of N- decreases from a value of 1.3 (one baffle) to 1.08 (four baffles), a fall of 17%. The required power, which is proportional to the stirrer speed cubed, decreases by 2.5, which is more than the expected 1.173in this case. The reason for this discrepancy is because the power number (Po)for the stirrer in the high position is lower for all baffle configurations tested. Joosten et al. (1977) also predicted the power number for the stirrer in a high position as lower than in a low position, and the slight influence of the height of the stirrer above the tank bottom on Nmin.A minimum effect of c on N,, and P/ V occurs when three equally spaced baffles in the lowered position are used. The lower Po determined at the higher impeller clearance is most likely due to the air entrained from the surface of the liquid. Not only do these air bubbles enhance turbulence in the liquid, thus prolonging solids suspension, but the power required by the impeller to pump the solid-liquid-gas mixture, as opposed to a solid-liquid slurry, to achieve complete drawdown of solids is reduced. Baffle Configuration. From Figures 5 to 7, no dependence of N- on baffle configuration is evident for each impeller. Power numbers were calculated at the minimum stirrer speed required for solids drawdown. For each impeller used, at both values of impeller clearance c, it was found that Po generally increased with number of baffles. Values of Po are given in Table 111 for X = 3.75% w/w, for both clearances, and baffle configurations (2), 13),and
Ind. Eng. Chem. Res., Vol. 29, No. 4,1990 681 Table 11. Comparison of Power Consumption ( P l V )and Minimum Suspension Speed at Two Clearances
1/ 3)/Nmin(2/ 3) (P/V) (1/3) / (PiV) (2/ 3)
"in(
2
3
1.18 1.52
1.21 1.75
configuration 6 13
4
Turbine 1.00 0.94
1.12 1.39
1.17 1.47
16
17
22
1.21 1.74
1.44 2.70
1.32 2.31
1.03 1.15
1.10 1.70
1.05 1.19
Propeller
Table 111. Values of Power Numbers at the Minimum Drawdown h e e d for c = H/3O stirrer turbine propeller paddle
1 baffle 2 raised 3 lowered 2.4 (2.5) 2.2 (2.4) 0.8 (0.5) 0.8 (0.4) 1.3 (nd) 1.3 (nd)
4 baffles 17 raised 22 lowered 4.0 (4.4) 4.7 (4.7) 1.0 (0.8) 1.1 (1.0) 1.5 (nd) 1.8 (nd)
( ) determined at c = 2H/3. nd = not determined.
(17), (22). A lower Pois found if baffles are raised to 0.25D from the tank base in any one configuration. However, the effect of raising or lowering of baffles is seen to be small. Of the three impellers tested, the propeller consumed the least power, while the turbine required the highest power for achieving complete solids drawdown. As shown in Table 11, the most significant power saving (highest P/V value) occurs when four baffles in the lowered position are used with the turbine positioned at c = 2H/3, whereas for the propeller, a single baffle and the same impeller clearance gave the highest reduction in power. The ratio of Nmin generally increases with baffle number for the turbine impeller; for the propeller, the converse is true. Hence, based on this work, two preferred stirrer/baffle configurations have been experimentally determined, within experimental error, for attaining complete solids drawdown with a minimum power input. These are (1) one baffle (three-bladed propeller at c = W / 3 ) and (2) four baffles (six-bladed turbine, also at c = 2H/3).
Conclusions and Recommendations for Future Work On the basis of the experimental results and observations, there is a small effect of solids concentration on the agitator speed required for complete suspension. This agrees with the findings of Joosten et al. (1977), who did not even include a concentration term in their experimentally deduced correlation. The type of stirrer used strongly influences the minimum drawdown speed. Of the three stirrers used, the propeller requires the highest speed, while the paddle requires the least. The trend of the results indicates there is only a slight influence of the impeller clearance above the tank bottom on the minimum speed required for solids drawdown. It was found that the baffle configuration does not effect the minimum stirrer speed. However, it strongly influences the power input to just attain complete suspension. The power number increases as the number of baffle increases. A lower power input is required if baffles are raised in any particular configuration. The propeller consumed the least power, while the turbine required the highest power input for achieving complete suspension. For complete drawdown of floating particles, two stirrer/baffle configurations recommended here are (1)one baffle (three-bladed propeller at c = H/3) and (2) four baffles (six-bladed turbine, also at c = 2 H / 3 ) .
Regarding the effects of factors such as baffle width, baffle wetted depth, impeller blade widthlpitch ratio, and inclined blade turbines, though interesting, work was not carried out in these areas. For future work in this subject, these factors should be considered. Further aspects that can also be looked into are (1)use of stream-lined and inclined baffles, as well as baffles cut off at the top to allow a swirling flow pattern to develop at the surface; (2) variation of the baffle clearance from the side of the tank; (3) use of screw impellers such as the one designed by Litz (1985); (4)use of very fine wetting solids to enchance the accuracy by using an optical probe technique for determining complete suspension; (5) variation of the density difference between solids and liquid; (6) effect of particle size; (7) use of a transparent tank to observe the homogeneity of the suspension; (8) use of a helical coil to investigate suspension of floating solids in heated agitated vessels; (9) use of inclined impellers; (10) use of a draught tube in a baffled vessel; and (11) use of high-impeller clearances from the tank base.
Nomenclature c = impeller clearance from the tank bottom, m D = stirrer diameter, m Db = blade length, m H = depth of liquid, m Nmin= minimum drawdown speed of stirrer, rpm P = power consumption, kW Po = power number T = tank diameter, m V = liquid volume, m3 X = solids concentration, w / w % W = blade width, m z = blade pitch, m
Literature Cited Aeschbach, S.; Bourne, J. R. The Attainment of Homogeneous Suspension in a Continuous Stirred Tank. Chem. Eng. J. 1972, 4 , 234-242. Baldi, G.; Conti, R.; Alaria, E. Complete Suspension of Particles in Mechanically Agitated Vessels. Chem. Eng. Sci. 1978, 33 (8), 21-25. Edwards, M. F.; Ellis, D. I. The Drawdown of Floating Solids into Mechanically Agitated Vessels. Proc. Fluid Mixing II; Institute of Chemical Engineering Symposium Series 89; Institute of Chemical Engineering: Bradford, England, 1984; pp 1-13. Ellis, D. I.; Godfrey, J. C.; Majidian, N. A Study of the Influence of Impeller Speed on the Mixing of Floating Solids in a Liquid. Proc. Fluid Miring III; Institute of Chemical Engineering Symposium Series 108; Institute of Chemical Engineering: Bradford, England, 1986; pp 181-194. Harnby, N.; Edwards, M. F.; Nienow, A. W. Mixing in the Process Industries; Butterworths: Toronto, 1985. Hemrajani, R. R.; Smith, D. L.; Koros, R. M.; Tarmy, B. L. Suspending Floating Solids in Stirred Tanks - Mixer Design, Scale-up and Optimization. Proc. 6th European Conference on Mixing, Pavia, Italy; AIDAC and BHRA: Milano, Italy, and Cranfield, Bedford, England, 1988; pp 259-265. Joosten, G. E. H.; Schilder, J. G . M.; Broere, A. M. The Suspension of Floating Solids in Stirred Vessels. Trans Inst. Chem. Eng. 1977, 55, 220-222.
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Ind. Eng. C h m . HPS 1990, 29, 682-690
Litz, L. M. A Novel Gas-Liquid Stirred Tank Reactor. Chem. Eng. Prog. 1985, 36-39. Mann, R. Gas-Liquid Contacting in Mixing Vessels. Industrial Research Fellowship Report; The Institution of Chemical Enpineers: Rugby, England, 1983; 108 pp. Musil, L.; Vlk, J. Suspending Solid Particles in an Agitated Conical-Bottom Tank. Chem. Eng. Sei. 1978, 33 ( 8 ) , 1123-1131. Narayanan, S.; Bhatia, V. K.; Guha, D. K.; Rao, M. N. Suspension of Solids by Mechanical Agitation. Chem. Erzg. Sei. 1969, 24 (21, 223-230. Nienow, A. W.Suspension of Solid Particles in Turbine Agitated Baffled Vessels. Chem. Eng. Sci. 1969, 23 (121, 1453-1459. Rieger, F.; Ditl, P. Suspension of Solid Particles in Agitated Vessels. Proc. 4th European Conference on Miring; BHRA Fluid Engineering: Cranfield, Bedford, England, 1982; paper H1.
Schwartzberg, H. G.; Treybal, R. E. Fluid and Particle Motion in Turbulent Stirred Tanks. Ind. Eng. Chem. Fundam. 1968, 7, 1-12. Ulbrecht, J. J., Patterson, G. K., Eds. Mixing of Liquids by Mechanical Agitation. Chemical Engineering; Concepts and Reviews Series; Gordon and Breach Science Publishers: New York, 1985; Vol. 1. Weisman, J.; Efferding, L. E. Suspension of Slurries in Mechanical Mixers. AIChE J. 1960, 6, 419-429. Zwietering, T. N. Suspending of Solid Particles in Liquids by Agitators. Chem. Eng. Sei. 1958, 8 ( 3 ) ,244-253.
Received for review December 2, 1988 Revised manuscript received August 2, 1989 Accepted November 20, 1989
Determination of Activity Coefficients via Microdroplet Evaporation Experiments Theresa M. Allen, Daniel C. Taflin, and E. James Davis* Department of Chemical Engineering, BF-10, University of Washington, Seattle, Washington 98195
It is demonstrated that activity coefficients of binary miscible solutions can be determined by means of microdroplet evaporation experiments in which a microdroplet is suspended in an electrodynamic balance. Weight loss and light-scattering measurements were used to determine the size and composition as functions of time. The light-scattering measurements include phase functions (scattering intensity as a function of the angle) and optical resonance spectra. The latter are extremely sensitive to the size and refractive index of the microdroplet. T h e microdroplet technique was applied t o binary pairs consisting of 1-bromododecane, 1,8-dibromooctane, hexadecane, and heptadecane t o obtain the activity coefficients of each component from the data. These results are compared with application of the Gibbs-Duhem equation to test the thermodynamic consistency of the experimental results. The design of processes for the production, separation, and purification of petrochemicals, natural products, pharmaceuticals, food products, and other chemicals requires accurate phase-equilibrium data. Techniques have been and are being developed to predict multicomponent thermodynamic properties from information on binary pairs, but as pointed out by Donohue et al. (19851, accurate data are needed for the development of new theories. Frequently infinite-dilution activity coefficients are used to fit binary vapor-liquid equilibrium data to expressions for the excess Gibbs energy, but traditional methods for determining such activity coefficients are of questionable quality (Lobein and Prausnitz, 1982). Measurement of activity coefficients by classical vapor-liquid equilibrium techniques is exceedingly time consuming if wide ranges of composition, temperature, and pressure are involved, so in recent years two techniques have been developed to measure infinite-dilution activity coefficients. For binary pairs in which both species are volatile, differential ebulliometry is particularly useful (Nicolaides and Eckert, 1978; Lobein and Prausnitz, 1982). The gas chromatographic technique used by Donohue and his co-workers to study alkane-alkane, alkane-aromatic, and aromatic-aromatic pairs is more suitable when the solvent is relatively nonvolatile compared to the solute. The development of the electrodynamic balance for the study of microdroplets has made it possible to develop a new method of measuring thermodynamic properties, and several investigators have used it to measure activities of water in electrolyte salt solutions. Rubel (1981) studied aqueous solutions of phosphoric acid, and Richardson and his colleagues examined aqueous solutions of LiBr (Rich0888-5885/90/2629-0682$02.50/0
ardson and Kurtz, 1984), of LiI (Kurtz and Richardson, 1984), of (NH,)$O, (Richardson and Spann, 1984), and mixed solutions of (NHJ2S04and NH4HS04(Spann and Richardson, 1985). By operating an electrodynamic balance under vacuum, Richardson et d. (1986) measured the vapor pressure of sulfuric acid over concentrated aqueous solutions for the temperature range 263-303 K. Cohen et al. (1987a,b) measured water activities for several singleand mixed-electrolyte solutions. Tang and his co-workers measured the water activities of NaCl-H20 and KCl-H20 systems (Tang et al., 1986) and obtained vapor-liquid equilibrium data for dilute nitric acid solutions (Tang et al., 1988). In all of these studies, the aqueous solutions were brought into contact with humid air, and the equilibrium state of the droplet was determined by weighing it, using the dc voltage required to levitate the droplet to determine the weight. Nonequilibrium experiments can also be used to measure thermodynamic properties of microdroplets. Rubel (1981) used an electrodynamic balance to measure the evaporation rates of multicomponent oil droplets, obtaining an “effective vapor pressure” of the mixture. The first electrodynamic experiments with binary organic microdroplets designed to obtain thermodynamic information were made by Ravindran and Davis (1982), who showed that the evaporation of submicrometer droplets of dioctyl phthalate and dibutyl phthalate followed ideal solution behavior. Their results were substantiated by Rubel (1982) using droplets of the order of 100 pm. Ravindran and Davis selected the dioctyl/dibutyl phthalate system with the expectation that it would show ideal solution behavior because of the similarity of the C 1990 American Chemical Society
