Performance of Agitators in Liquid-Solid Chemical Systems A. W. HIXSONAND G. A. WILKENS. Columbia University, New York, N. Y. The purpose of this inzlestigation is the study of slow down the .fluid flow and are a hindrance to the the fundamental nature of the factors which affect dissolving process. The four-bafle system is exthe performance of agitaiion equipment for liquids amined with respect to the effects of stirrer speed and the development of a method f o r applying them and size of equipment. in problems of design. Comparisons of designs are made in a 20-gallon The comparison of intensities of agitation is vessel. aVlore effectice agitation is found in a made by the Hixson-Crowell cube root law velocity shallow vessel than in a deep one at the same stirrer constants for the liquid-solid dissolution system. speed. The rate of solution is greater in the free using benzoic acid tablets in water and seceral oils. rotational than in the bafled system at loui speeds Experiments were conducted in a series of geo- (100 to 300 r. p . m.). The freely rotating turbine metrically similar cylindrical vessels, ranging in is found io be more effective than the propeller under volume f r o m 0.73 to 353 gallons, with corresponding the same conditions. I n the higher range (300 stirrers of the propeller fype. I n free rotational to 500 r. p . nz.) fhe most effective agitation is obtained agitation the effects of the variables stirrer speed, f r o m the turbine operating in a fixed central desize of equipmeni, and fluid viscosity are very great. flecting ring. A general relation f o r the rate of solution in terms The power consumption per unit volume of liquid of composite z‘ariables is given. The transformation undergoing agitation increases rapidly as the size of free rotational into baffled agitation is shown by of the system is increased and as the free rotational the introduction of one to six rerfical bafles. Bafles jloul is modified by bafles.
T
H E purposes for which agitating, stirring, and mixing operations are used with solids, liquids, and gases are exceedingly numerous, and the machines and types of equipment in service are equally diversified. Outlines of the functions of agitation have been made by Seymour (18), by Wood, Whittemore, and Badger (e;),and by Hixson and Cram-ell (10); classifications of apparatus from the mechanical viewpoint have been made many times (6-8, 13, 16, 17, 20). An extensive illustrated compilation including recommendations for industrial selection is being made by Valentine and MacLean (22). The literature contains little of fundamental importance on the subject of agitation, and what there is has been examined by Hixson and Crowell (10). Since then Kambara, Oyamada, and hlatsui (11) have reported studies on thermostat stirrers, and White, Sumerford, Bryant, and Lukens (244) have studied the agitation of sand in water. The impracticability of a direct mathematical attack upon the study of agitation led to the employment of the indicating substance such as was employed by Hixson and Crowell (10). This method depends upon the use of a solid which dissolves in a liquid and which may be accounted for either by direct weight a t stated times or by estimation of the concentration in the liquid. The heterogeneous reaction velocity constant for such a diffusional process depends upon the surface area of the solid, upon the concentration of dissolved solid in the liquid, and upon the agitation. A general expression for this constant as a function of both concentration and surface was presented and termed the “cube root law,” which states the relation between the time and the cube root of the vieight of the dissolving solid a t that time. Special cases result in which (1) the initial weight of solid is that necessary for saturation, ( 2 ) the concentration change is negligible, and (3) the surface remains constant. Experimental verification of the law and its special cases were
shown to apply not only to free rotational agitation but also to many other types. The comparison of intensities of agitation by means of the heterogeneous reaction velocity constant for a given solidliquid dissolution system was employed in the present work. The constants were calculated in accordance with special case 2 of the cube root law ( I O ) , and the notation of the previous papers has been used here. I n this case the bulk concentration change has been kept negligible so that the rate of dissolution was proportional t o the surface and to the agitation. In the general case of the law, the rate of change of weight of the solid, d t c j d t , varies directly as the interfacial area of contact, S, together with the difference between the concentration a t saturation, C,, and the existing concentration, c; KS is a constant: dw/dt = -K,S(C,
- C)
(1)
I n the case where the bulk concentration change is negligible, the expression C, - c is a constant, and the rate is proportional to the surface. Since the surface is proportional to the two-thirds po-iver of the volume or weight of the dissolving solid, Equation 1 becomes: dw/dl = -K~W’I~
(2)
Integration gives Kt = ~ 0 ’ 1 3 - ~ ’ 1 3 (3) The dissolving solid used in these experiments was benzoic acid which had been formed into hard, compressed tablets. These weighed on the average 209 mg. and were cylindrically shaped m-ith curved ends, measuring 0.26 inch (6.35 mm.) in both diameter and height. These were unlike the usual compressed tablets which disintegrate readily in water. They were exceedingly hard and smooth and did not crush or break easily. Benzoic acid was selected as the indicating substance because it could be obtained easily in the pure state, It could also be estimated rapidly by titration with alkali. The tablet form provided a solid of greater uniformity
1196
INDUSTRIAL AND ENGINEERING CHEMISTRY
November, 1933
than would have been possible with a crushed and screened solid. The average weight of five lots of twenty tablets was 4.156 grams with an average deviation of 0.6 per cent. The average weight of sixteen tablets selected a t random was 0.209 gram with an average deviation of 2.6 per cent. In using this solid in experiments in which the sizes of vessels varied, it was necessary t o maintain a constant ratio of solid to liquid in order that the reaction velocity constants would be comparable. Throughout this work the ratio was maintained a t 5.740 grams of benzoic acid tablets per gallon (1.515 grams per liter) of liquid. This figure is the quantity w o used in Equation 3.
resting across two 4-foot (1.2-meter) diameter tanks in the laboratory. The beams were supported on rollers to provide flexibility of adjustment. The vessel in which an agitation experiment was conducted was placed upon a vertical stand, B (Figure l),which could be adjusted axially for height. The contents of the agitation vessel was maintained a t constant temperature (25.0" C.) by water in the surrounding tank, A , which was controlled by an electric thermostat of the Beaver type (1) (not shown), and agitated by means of a compressed air line (not shown). I n runs in two of the larger vessels (18 and 24 inches, or 45.7 and 61 cm.) in which the bulk of water was comparatively great, the thermostat was dispensed with and tank A was emptied. I n these runs the room teniperature was not more than 3" C. from the desired temperature of 25". The temperature of the liquid was adjusted to a few hundredths of a degree above 25" C. before the start of the run, and the temperature remained sufficiently constant (+0.05') for the duration of the run. The largest vessel used was tank A itself, in which case the stand was removed and the procedure followed was that for the larger sizes just mentioned. Experiments were conducted in a series of geometrically similar vessels with corresponding stirrers. The vessels were cylindrical and of circular cross section. The stirrers were of AGITATION
L: :1
'.
I
L
-, a 5
1197
I:::\
-
FIGURE 1. APPARATUS ASSEMBLY
The sampling in each vessel was done with devices comprising three glass tubes (2.5 mm. i. d., 3.5 mm. 0. d.) fitted through a glass stopcock to a common chamber. A rubber stopper and tube permitted suction to be applied for withdrawal of the sample o f liquid. The glass tubes were of such lengths that, when the device was dipped into the vessel, the tubes terminated respectively a t the midpoint of each third of liquid depth. The device was immersed midway between the agitator and the vessel wall. The method was employed in all free rotational agitation runs; in those runs in which baffles were used, the samples were dipped from the rising current midway between the stirrer and the vessel wall. The benzoic acid content of the samples of liquid was estimated by titration with sodium hydroxide using phenolphthalein as the indicator.
EQUIPNEXT The apparatus mas designed and arranged to permit operation over a range of stirring speeds from 100 to 500 r. p. m., and throughout a series of vessel sizes from 0.73 to 353 gallons (2.77 t o 1338 liters). The arrangement used is shown in Figure 1, wherein a Reeves' variable speed transmission was connected to a vertical shaft to which the stirrer was fastened by means of a coupling. The entire mechanism was mounted on two wooden beams ( i inches x 4 inches X 10 feet, or 10.2 em. X 10.2 em. x 3 meters) APP.4IlATUS AND
1
Reeves Pulley Company, Columbus, Ohio.
TABLE I . I. D. OF VESSEL( A ) Inches (Cn.)
6.0 8.125 10.25
14.125 18.0 24.0 47.0
(15.24) (20.64) (26.04) (35.88) (45.72)
VOL. WHEN DEPTH= DI.411. Ga2.
0.73 1.82 3.67 9.57 19.85
(Liters)
(2.77) (6.90) (13.91)
(36.27) (75.23) (178.13)
4.71
6.0 S.0
A :VESSEL DIAMETER B:STIRRER SIZE
t :SHAFT DIAMETER D: QLADE WIDTH E: BOTTOM CLEARANCE
F: BAFFLE WIDTH
FIGURE 2. SPECIFICATIONS OF APPARATUS
the propeller type with four flat blades inclined a t an angle of 45' to the shaft axis. The vessels were provided with removable, narrow vertical baffles, which were held in place firmly by wooden wedges on the outside of the vessel (Figure 2). The vessels were of S o . 24 gage galvanized sheet iron; the stirrers were macle from steel drill rod to which blades of spring brass were attached by means of silver solder. The baffles were constructed of cold-rolled steel. The tank, A , was of wood lined with lead; the baffles were constructed of wood. All vessels, including tank .4, and all baffles and stirrers were given tn.0 coats of Bakelite varnish for protection against corrosion and for the assurance of surface uniformity throughout the series. The dimensions
SPECIFICATIONS OF APPa4RATUS
STIRRER LENQTH ( B ) Iwhes (Cn.) 2.0 (5.08) 2.71 (6.88) 3.42
BENZOIC AClD TABLET
STIRRER SHAFT
DIAM.(C)
Inch
(Cm.)
(8.69)
(11.96) (15.24)
(60.96) 47.0 (20.32) (119.38) 353 (133.8 1 15.7 (39.88) The width of the vertical baffles is the same as the blade width, D . b The series W E E planned so that all dimensions would be n definite fraction of the vessel diameter. F = 1/11 A; and E = 1/6 A .
B L A D E n OR B A F F L E WIDTH (D OR F )
Inches 0.50
0.678 0.855 1.18 1.50 2.0 3.93
CLEARANCE BOTTOM (E)b Inched 1.0
(Cm.)
(1.27) (1.72) (2.17) (3.00)
1.36 1.71
2.36
(3.81) (5.08)
(5.99)
3.0 (7.62) (10.16) 7.86 (19.83) 4.0
(9.98)
Thus (Figure 21, B =
(Cm.1 (2.54) (3.45) (4.34)
1s,'
A; C =
A; D =
INDUSTRIAL AND ENGINEERING CHEMISTRY
1198
of the vessels, stirrers, and baffles, and the assembly data are given in Table I, referred to Figure 2.
FREEROTATIONAL AGITATION(No BAFFLES) This series of experiments employed all vessels, including the 47-inch tank, with their respective stirrers. The depth of liquid was equal to the diameter of the vessel; the arrangement used is shown in Figure 1. 44
IO SO
IM
150 ZM) tm REVOLUTIONS PER MINUTE
m
350
FIGURE 3. EFFECT OF STIRRING SPEED FREEROTATIONAL AGITATIONIN DIFFERENT SIZESOF VESSELS
ON
EFFECTOF STIRRINGFREQUENCY. The runs mere conducted in the 6-, 8.125-, 10.25, 18-, and 24-inch vessels at 25.0" C. in water. The effect of variations in stirrer speed upon the rate of dissolution was studied from 89 to 356 r. p. m. The results are presented in Table I1 and Figure 3. TABLE11. EFFECTOF STIRRINQ FREQUENCY UPON RATE OF DISSOLUTION c
SPEED
6 in.
KO X 104 AT VESSELSIZE OF: 8.125 in. 10.25 in. 18 in.
24 in.
R . u m.
89 100 125 150 156 200 260 300 353 4
13.2 14.9 25.6
29:o 31.0 32.8
27.4 30.0 34.1
33:5
..
36:O
.. ..
29:2 35:O 37:5 30.9 33:3 37.8 4i:2 31.8 34.0 30:4 .. .. 33.3 .. .. 44.5 34.5 .. 38:4 This constant is from Equation 3 and is used throughout this work.
The data show that a t low stirring speeds-for example, below 125 r. p. m.-the rate of dissolution increased rapidly with increasing stirrer frequency, rising from a rather low rate. This was due to the fact that the liquid was flowing gently with apparently little disturbance and could be compared with Hixson and Crowell's regime of curvilinear flow. As the speed of stirring was increased from 125 r. p. m., the rate of dissolving became approximately a straight-line function of the frequency. This rCgime was characterized by flow of greater vigor and turbulence as the higher speeds were reached. The vortex depression at 125 r.p.m. was scarcely noticeable, 'but, as the speeds were increased, it became deeper. Above 300 r. p. m. the agitator blades were uncovered. At greater speeds little increase in effectiveness of the stirrer was therefore to be expected. EFFECT OF SIZEMAGNIFICATION. The effect of absolute size of equipment (the stirrer and its vessel being considered together) in the free rotational type of agitation was investigated in the 6-, 8.125-, 14.125-, and 24-inch vessels, and the 47-inch t,ank, in water a t 25.0" C. The runs were made a t 200 r. p. m. and the depth of liquid was equal to the container diameter. The data obtained are given in Table I11 and Figure 4, curve 1. UPON TABLE111. EFFECTOF ABSOLUTESIZEOF EQUIPMENT RATEOF DISSOLUTION APPARATUS Srzm K x 104 APPARATUB SIZE K X 101 Inches 6 8.125 14.125
30.9 33.3 39.0
Inches 24 47
41.2 43.5
At 200 r. p.m. the r&gime of agitation was vigorous and turbulent, and the vortical depression was about half the
Vol. 25, No. 11
quiescent depth. The solid was in constant motion in the liquid swirl, and particles falling a t the vessel wall were instantly drawn up through the stirrer and discharged into the mass of water. The data show that for this system the velocity constant increased steadily throughout the 6-, 8.125, and 14.125-inch vessels, but that, from about this size on, there was little gain in the rate of dissolving. EFFECTOF FLUIDVISCOSITY. A demonstration of the effect of fluid viscosity requires that measured velocity constants, in order to be comparable for the different fluids, be brought t o a common denominator. This is essential for two reasons: The derivation of the velocity constant (Equation 3) expresses the driving force of the dissolution in terms of the solubility of the solid dissolving. Furthermore, in a diffusional process of this nature, the solute diffusivity represents the molecular movement through the film of quiescent liquid on the surface of the dissolving solid. This diffusion coefficient is expressed in Fick's law and is a specific characteristic of a solute in a given solvent. The diffusivity is nearly constant; it varies with concentration only a few per cent for variations in concentration of several hundred per cent (8.9) in the dilute range of these experiments. For the purposes of this work the constancy has been assumed. The experiments to show the effect of fluid viscosity were made in sperm (high-grade, bleached, and wintered oil), in cottonseed (bleached and deodorized oil of edible grade), and in rapeseed oil (refined, light straw oil). For these oils the following physical constants were determined: viscosity, solubility of benzoic acid, diffusivity of benzoic acid, and specific gravity (Table IV). Viscosity was determined at 25.0" C. by a Bingham viscometer calibrated with a known sucrose solution, and the procedure of Bingham (8)was followed closely. TABLEIV. PHYSICAL CONSTANTS OF FLUIDSAT 25.0' FLUID
S erm oil
2 ottonseed oil Rapeseed oil
0.995 0.0638 0,0382 0.0256
0.343 4.72 3.70 2.92
0.894" 26.59 47 93 69.50
Water
a
C.
SOL. OF SP. GR. ACID REFERRBD BENZOIC PER 100 GRAMS TO WATBR VISCO~ITY SOLN. DIFFUSITITY A T 25" c. Centiooises Grams Sq. cm./dau
1.000 0.880 0.917 0.910
From Bingham ( 8 ) .
The solubility measurements were made at 25.0' C. Benzoic acid tablets were left in contact with fluid in a flask for a long time (one day) in a thermostat (*0.05" C.). The flasks were shaken frequently until saturation was attained by detection of no further change in the acid content of the fluid. 40
35 30
t25 -T20 L I5
I
5
6
12
18
24
l 30
i
36
42
48
DlAMElLR OF VESSEL IN INCHES
OF SIZEMAGNIFIFIGURE 4. EFFECT CATION AT 200 R. P. M.
The diffusivity of benzoic acid in the several fluids was determined by the method of Northrop (16) which has been carefully investigated and standardized by McBain and Liu (14). The solution is contained in a glass diffusion cell which may be an inverted funnel, across the bottom of which is cemented or fused a porous disk of alundum or sintered glass; a stopcock is attached to the stem of the funnel. The cells used in this work were constructed as follows:
November, 1933
INDUSTRIAL AND ENGINEERIKG CHEMISTRY
Alundum disks designated "RA 98" were reduced in thickness to about one millimeter by rubbing against one another; they were fastened to the cell by fused shellac. The cells were supported with the alundum disk in a level position by soft wire stirrups. The cell containing the solution dipped into pure solvent contained in a closely fitting beaker. The experiments were made in a thermostat at 25.0' C.; the procedure followed, with the necessary precautions, was that of Northrup (15) and of McBain and Liu (14). The cells were calibrated by means of 0.2 M potassium chloride solution in water. The specific gravities of the several oils were determined by pycnometer in a thermostat a t 25.0' C. and are expressed relative to water a t the same temperature. The agitation experiments on viscous oils were performed in the 10.25-inch vessel a t 25.0' C. The depth of liquid was equal to the vessel diameter and the stirring frequency was 200 r. p. m. The values for the velocity constants are given in Table V. The values of these constants brought to a common denominator by division by solubility and dsusivity are also given in Table V. TABLEV. FLUID Water
lo4
35.75 14.2 6.5 2.5 Read from Figure 3.
8 erm oil
2 ottonseed oil Rapeseed oil a
K X
AGITATION IN VISCOUS
Cd
K
x
104
104.5 55.9 46.0
33.4
1199
and the two composite variables are similar since u is equivalent to ND. A curve of the type of Figure 6 ( A ) expresses the agitation function for only the particular system which was used in its construction. This means that the factors of vessel shape, propeller design, location of stirrer, and surface roughness are considered part of the system. In spite of these restrictions the method is a simple one, and agitator design is able to proceed logically from model experiments. In this development the empirical equation for agitation has been expressed in terms of composite variables. Two systems undergoing agitation are dynamically similar when the unknown function of D2N/v is the same for each, provided that the systems are geometrically similar. It cannot be emphasized too strongly that the prerequisites of geo-
FLUIDS
KINEMATIC VISCOSITY VISCOSITY Centipoises/ Cenlipoises s p . gr. 0.894 0.894 26.59 30.21 47.93 52.25 69.50 76,42
I The data are shown graphically in Figure 5. This in22 26 30 34 38 42 46 50 54 dicates that the intensity of useful agitation, as expressed FIGURE6. EFFECT OF STIRRING SPEED,SIZE, in the K/C.d index, falls off as the viscosity of the fluid AND VISCOSITY IN FREEROTATIONAL AGITATION, AND IN IMPEDED ROTATIONAL AGITATION WITH increases. This is to be expected since viscosity is internal FOURBAFFLES friction acting in opposition to the motion of the fluid. FREEROTATIONAL AGITATIOX AND DYNANICAL SIMILARITY (4, 6). The dependence of agitation upon the fundamental metrical similarity must be extended to the smallest detail factors-size D , stirring frequency N , and kinematic vis- for two systems to be actually dynamically similar. Thus, cosity v-has been shown for each variable separately while two vessels which are not perfectly smooth must be prothe others have been held constant in Figures 3--5. These portionately rough. I n these experiments ideal dynamical similarity was not sought. It was considered of greater practical importance to maintain the same surface conditions throughout the experimental series. Also, true dynamical similarity demanded that the particle size of the dissolving solid should be in geometrical relation to the size of the vessel, Here again, the practical aspects of giving to different sized agitation systems proportional amounts of the same type of work to perform meant a departure from the theoretical demands for exact dynamical similarity. In this work no pretense was made to adherence to the requirements for rigorous dynamical similarity. In fact, such a procedure 0 would be utterly impractical and would deprive the method KINLMPTIC VISCOSITY (= CENIlwlXS/SP G R ) of usefulness in the solution of practical design problems. OF FLUID VISCOSITY FIGURE 5. EFFECT A curve of the type of Figure 6 ( A ) can be obtained for a IN FREE ROTATIONAL AGITATION particular system from experiments in small vessels with conditions chosen so that several points are sufficient to variables have been combined and expressed in terms of a establish the curve. For any value of the abscissa, log general relation. Here the agitation index, K/C,d, multi- D 2 N / v , can be read the corresponding value of K D / C d from plied by the size, D , is expressed as a function of the com- which the agitation index may be obtained. posite variable, D2N/v. The data used in making the plot were obtained from all of the free rotational agitation runs R ~ G I MMODIFICATION E BY BAFFLES at speeds above 125 r. p. m. where the flow was fully turbulent. The flow encountered in the free rotational type of agitaThe relation is shown in Figure 6, curve A . Here the length ( D ) is in inches, the stirring frequency ( N ) in r.p.m., the tion is modified considerably by the introduction of narrow specific gravity is referred to water a t 25' C., viscosity in vertical baffles a t the wall of the agitation vessel. The use centipoises, solubility (C,) in per cent, and diffusivity in of baffles in this manner is commonplace in industry so that square centimeters per day. The quantity D2N/v corre- this investigation included a study not only of the effect of sponds to the Reynolds number which is used in the expression the number of baffles in a given vessel, but also the behavior for the resistance to the flow of fluids through pipes. This of the effect when the size of the agitating system is varied. number is Duslz; the symbols u, s, and z are, respectively, The experiments were conducted in the 6-, 10.25-, 18-, and the average fluid velocity, specific gravity, and viscosity. 24-inch vessels, and in the 47-inch tank in water a t 25.0' C. In agitation the velocity factor appears in the stirring speed, The frequency of stirring was 200 r. p. m. and the depth of
'
1200
Vol. 25, No. 11
INDUSTRIAL AND ENGINEERING CHEMISTRY
ON RATE OF liquid was equal to the vessel diameter. The results are TABLEVIII. EFFECTOF SIZE OF EQUIPMENT SOIAJTION presented in Table VI and Figure 7. VESSELSIZE K x 104 VESSELSIZE K x 104 Inches Inches TABLEVI. EFFECTO F NdRROW VERTICAL RAFFLES ON RATE 24 6 11.1 33.6 OF SOLUTION 10.25 18.5 47 40.8 VESSEL K X 104 WITH FOLLOWING BAFFLES: 18 28.6 SIZE 0 1 2 3 4 5 6
Inches 6 10.25 18 24 47
30.9 33.9 37.8 41.2 43.5
28.3
26.7 27.5
.. ..
38.9
32.0 34.8
35.1
..
15.2 20.4 .. ..
..
11 1 18:5 28.6 33.6 40.8
12.5
20.9 .. .. ..
1717 28.4 34.6
..
The baffles have been described in the text, in Figure 2, and in Table I. The introduction of one baffle interrupted the circular swirl of water and displaced the vortical depression somewhat to the side of the stirrer away from the baffle. This depression was less pronounced than that encountered in the free rotational r6gime. The baffle served to set up a vertical stream before it; behind it an eddy formed. The further addition of baffles up to six, with even spacing in all cases, served to multiply the effect of one baffle on the modification of flow. The vortical depression disappeared entirely after two or more baffles had been introduced. A strong upward current flowed before each baffle; behind each baffle a locality of slowly moving, eddying water appeared. Near the stirrer shaft periodic eddies formed and disappeared. The meeting of the upward streams with the general circular flow produced what appeared to be a high degree of turbulent mixing. The data for these runs show that the introduction of baffles into a free rotational regime is accompanied by a diminution in the rate of dissolving. The magnitude of this decrease is proportional approximately t o the number of baffles introduced and is in inverse ratio to the size of the agitating system. I n the small vessels (6 and 10.25 inches) the falling off of the rate of solution (about 60 and 44 per cent, respectively) is most marked, whereas this is less in the 18and 24-inch vessels; finally in the 47-inch tank this decrease amounts to only 6 per cent in the four-baffle r6gime. The introduction of baffles in excess of four appears not to influence the rate of solution; this is shown by the curves of Figure 7.
IMPEDED ROTATIONAL AGITATION, FOURBAFFLES These experiments were designed to demonstrate the effects of the variables, stirring frequency and absolute size in the regime of impeded rotational agitation with four baffles. EFFECTOF STIRRING FREQUENCY. The runs were conducted in the 18- and 24inch vessels in water a t 25.0" C. The effect upon the rate of dissolution was studied for variations in r. p. m. from 112 to 350. The depth of mater was equal to the diameter of the vessel. The results are presented in Table VI1 and Figure 8. TABLEVII. EFFECTOF STIRRIYG FREQUEXCY K X 104 FOR VESSEL K x 1 0 4 FOR VESSEL STIRRIKG SIZEOF: SPEED 18 in. 24 in. R. p . m 112 125 200
17.0
28:6
25:2 33.6
STIRRING SPEED
R. p .
SIZEO F : 18 in. 24 in.
The effect of size of equipment upon the dissolving performance is seen to be more marked in the smaller sizes than in the larger. 40 35
-
q-
0
30 25
21)
15
IO 5 0
1
2
3
4
5
6
NUMBER OF BAFFLES
FIGURE7 . EFFECTOF BAFFLESos FREER O T 4 T I O S A L AGIT-ATION .4T 200 R . P. M.
IMPEDED ROTATIONAL AGITATIOK AND DYNAMICAL SIMILARITY. The effects of the variables stirring speed and size
of equipment in four-baffle, impeded rotational agitation have been shown separately for each variable in Figures 4 and 8. The general relation which was used in free rotational agitation in Figure 6, curve A , has been employed for the data in impeded rotational agitation with four baffles. This relation is shown in curve B of Figure 6. The general function which expresses the factors in terms of t x o composite variables appears to be of general application since it has been shown t o hold for these two very different types of agitation. COMPARISON OF DESIGNS A number of the more commonly used types of agitation systems for liquids have been examined with a view to making comparisons of effectiveness in promoting the dissolving process. The tests were made in water a t 25.0' c. in the 18inch vessel. The performance has been determined over a range of stirring speeds. The types of equipment include the free rotational and the impeded rotational (four-baffle) agitation with propeller stirrers, which have been described but are included here for comparison. The effect of liquid depth in the vessel
40
0 0
30
r
m.
275 350
40.1
45.4
43.5 49 6
I n this regime the effect of stirring frequency is shown to be a straight-line function up to about 300 r. p. m. where the effect becomes less pronounced. Throughout this range of speeds the mode of flow appears to suffer little variation so that a relation of this sort is not entirely unexpected. EFFECT OF SIZEOF EQUIPMENT. The effect of this variable was demonstrated in runs made in the 6-, 10.26, 18-, and 24-inch vessels, and in the 47-inch tank. The runs were made in water a t 25.0" C. and 200 r. p. m. The data are given in Table VI11 and in curve 2, Figure 4.
IO
I 1W
I
I IS0 ZOO 250 30 REVOLUTIONS P € R MINUTE
350
FIGURE 8. EFFECT OF STIRRIUG SPEEDIN IMPEDED ROTATIONAL A4GITATIOiV WITH FOUR BAFFLES
has been studied with a series of runs using the propeller in a depth of liquid equal to half the diameter of the vessel. A commercial machine of the turbine type has been studied, both with and without a central deflecting baffle ring. This is shown in Figure 9. The rotor measures 6 inches (16.24 cm.) in diameter and 1.625 inches (4.13 cm.) in average
I N 1) U S T 11 I A 1. A N El
'Vove,niber, 1933
E N G 1 N 13 1': I< I N G C 1-1 f?,M 1 S 'T !I Y
1201
In 1880 Uiiwio (21) made a tliorougli iuvestigatioii of the resistsiice offered by surrvumliiig water to rotating disks rangiiig Srorn 10 to 20 inclios in diameter. The rosistarice of disks of different diiunetors, but otlienvise similar, varied as tlie 4.85 power of the iliitmeter. Thoinmn l i d found tliis variatioii as tlie fifth wiwer. Uirwin showed that the rouglinass of tlie siirfiicc of the divk was exceedingly important rind varied to :in extent quite 5s great. as in the i:xp&ncnts of I h u d e , Zalirn, and others, on flrit plates a i d boards. Tlie friction was found to increase aitli the size of tlic chamber in which the disk was rotat.ed. Uiiwin Sound also thnt roughening the surface of the chamber in wliicii the disk was rotatcd increased tlie resistance con-
tiiickiiess, ami is cuniparable in size nnd location aitli tlie propeller stirrer. The deflecting ring [9.625 inches (24.45 cm.) over-all] is sliowii tiy itsclS in Figure 10, and witli tlie turbine rotor ~6 they are used togetlicr in Figure 9. Tlie yerforniance dntn are given i n Table IY and the characteristic curvcs in Fircure 11.
ll? 200
275 330
4
170
300
4011
40.0 41.7 45.0 58.4
'rwhirio % v i C l w i t centrnl r i n ~ iiiiuid . depth equal tu verso1 diarnetor
26.6 42.5 58.2
T a i b i i l o K i L l i rontrrii l i i l P , iinuid depth eilunl to veanel dinmeter
89
5
107 140 200 283 * S e e Figure 11. b Rend from IGgure 3 .
46.3 47.1
The data skrv t h t tlie cfyect. of vuriatioii of .stirring freqoerrcy is inucli niore gronounced in the Ls%d systems than in those m i wliich tire agitation is of tlie free rotat.imril type. The curve of tlie propeller, iising four baffles, rises rapidly frolll a lorn rate of dissolution until about 275 r. p. sn., wlicn the rate inerenses lcss rapidly. The performa~rieeof the turbine xitli central baffle i n rrlace, IUIV' C 4 of Figure 11, approsiniates quite dosely ixrve 2; however, it continues to risc steiidily to 400 r. 11. ill.,m l i i c l i wa hryond this point \THS chipixi1 arid fracturt:il from impact. wit11 the baffle ring, T i i c free rotaiional agitation sptearis, curvos 1 , 3, tli alii1 5 , show a s i i i n l l c r rate of change of dissolving variatiiiiis in the stirriug speed. At the s l o w x spc 100 to 250 r. p. ni.-tlbc ru11 with liquid dcptli equal t tlie vessel dianieter sho~vcdthe advant.a .o be gtliiied by the sl~allowerform. Curve 5 for tliis e1ii is situated iines (1 and 3). above timsc uf the otlrer free rotational In the run a t half-depth tire agitator was completely wcorcrrd at. 250 r. g. m.,so t,liat l i t t l e gain \>-as to be espccted lxyoiid tliis jioini. T!E t11r1,ine u;it,lioiit, it,s eeiitml defleot.ing l,aflle, r e p r c ~ e i i i e i ilig &ve 3, sho~vedbetter perfoririancc tluiin the plain, f~iilr-blnddpropi:ller of curve 1. Kilt only does the rate of dissolution esreed tlmt of tlic latter at all s1mds of tile test, but it s i i o w IIII s i g i i iiffalling off up to ;io0 r. 11. in. vliieh is :is fnr as tlie study \Tent. ( ~ O K s U ~ l I P T l O KOF
I'oWBX
s t i d i d , pdiaps, who measured the reaction 011 the conI. This di?vice ivus later u tig Frouile i n lice
US rotatiiig disks
W ~ L Sfirst
(2;))
his fluid dynanioiirr~icr. TAllLE
-_ 18~Ih.l'"vrarm--No .-. 1:our heffier bnKler IC. p. +n. W & r / l o o gal." 212 13.6
240 271
28.2
303 332 374
57.0 96.1 125 150 178
RB9 412 0
44.8
100 m l l u e e
-
I t . 18.
,n.
253 282 618 389 413
iB4
379 litria.
__~
x.
...
(.F.>%I,,,,.
286
125
310 328
108
159
I < l X O t Y PI.
