RICHARD
P.
RHODES and ELMER L. GADEN, Jr.
Department of Chemical Engineering, Columbia University, New York 27, N. Y.
Characterization of Agitation Effects in Shaken Flasks Though shaken flasks are commonly used in process studies, too little is known about performance. Experiments with rotary and reciprocating units provide needed data
A
WIDE VARIETY of industrially important reactions are carried out in agitated vessels. The problem of providing proper agitation in these cases falls into two parts: process requirements, or the degree of agitation necessary to achieve optimum results, and equipment performance, or the ability of the reactor mixing system to deliver agitation. The first must be determined individ- * ually for each reaction system. Usually this must be done experimentally, for few basic data are available. The second supplements the first, as a knowledge of power and flow characteristics of an agitator assembly will facilitate the design of a pilot unit and aid in interpretation and scale-up of results. So far the study of agitation effectspower, heat, and mass transfer-has been limited to mechanically stirred devices. Yet a great deal of development work is done in equipment which employs “rocking” or “shaking” agitation, particularly the shaken flask which is extremely popular for fermentation studies. Primarily because of their operational simplicity, convenience, and low cost, these test reactors are widely used. Nevertheless, little is known of their performance and examination of their agitation characteristics seems appropriate.
Agitation in Shaken Flasks Gas-liquid mass transfer, in terms of oxygen absorption coefficients, has been examined extensively in shaken flasks (7, 3, 7), with results about as expected. Little is known, however, about mass transfer within the liquid and between it and suspended cells. Measurements of this sort are inherently difficult to make and no system reported in the literature so far seems to be entirely satisfdctory. Most of the methods for determining
liquid-solid mass transfer rates involve measurement of the rate of solution of some material. Benzoic acid tablets (3, 5 ) and various slightly soluble crystals (6) have been used. There are a number of disadvantages to this method, the most obvious of which are: Density differences. The particle density is very different from that of water. Hence they do not move with the solution completely but through it, generating turbulence themselves. Shape factors as particles are usually not spherical, determination of surface area is difficult. Particle diameter changes during measurement, so that some mean value must be used. The accuracy of measurement of such data is often not great. The concentration driving force for dissolution involves the solubility of the substance and is therefore partially fixed at any temperature. T o improve this situation, a better technique for measuring liquid-solid mass transfer under agitated conditions is needed. One such is the exchange of a soluble ion between its solution and suspended particles of an ion exchange resin, previously developed in this laboratory ( 2 ) . Complementary to this would be some method for expressing the degree of “bulk mixing” produced in the fluid phase itself by agitation. A timehonored one is mixing time, the time required for a nonhomogeneous solution to become homogeneous. One method of estimating it is simply to drop a colored fluid-ink, for example-in the agitated liquid and note the time for complete dispersion of the color. This is rather subjective, and a more quantitative approach is desirable. A recent article (4) describes a similar, but better, technique, wherein the stirred liquid is a solution of dilute base with phenolphthalein indicator. Acid, in slightly greater quantity than
the stoichiometric requirement, is injected into the agitated base and the time for complete color disappearance is noted. Mass Transfer Coefficients by Ion Exchange
Exchange System. Rates of copper ion exchange between dilute solutions of copper sulfate and suspended particles of Amberlite IR-120 resin were used to characterize liquid-solid mass transfer. The essential process is: RH2
+ C u + + ZI? RCu + 2H+
This exchange system offers a number of advantages over dissolution measurements. Resin particles are nearly perfect spheres and size grading gives a fairly uniform diameter. Furthermore, particle size and shape do not change during the test. The density is much more nearly that of water, although it increases as copper is taken up. The resin system approaches much more closely the actually dimensional scale of suspensions of microorganisms. Benzoic acid pellets (3) cannot be prepared and handled very well in inch. sizes much under 3/32 to Resins, on the other hand, may be graded into narrow size ranges running down to small diameters. Mass Transfer Coefficients in Exchange. Two expressions concerning the transfer of copper from solution to resin particles may be written. The first is material balance :
xq
= V ( C , - C)
(1)
and the second is the rate equation for exchange : dg/dt = kdS(C
- C*)
(2)
whereX = weight of dry, hydrogenform resin used, grams V = total volume of copper solution, liters VOL. 49, NO. 8
AUGUST 1957
1233
t
FLASK : 500 m l . smooth Erlenmeyer LIQUID VOLUME: 2 0 0 m l . CuSO+ CONCENTRATION: 66 . 5 5 m m .//lliitteerr
-
0
-411 runs were made in 500-ml. Erlenmeyer flasks, creased and plain. Creased flasks were made with two vertical indentations opposite each other and roughly parallel. The creases were about 3 inches and '/z inch deep at the base of the flask. The resin used was first graded by sieving, with only the 18- to 22-mesh size range used in flask measurements. This corresponds to an average particle diameter of 850 microns (0.85 mm). Determination of Transfer Coefficients. The following experimental technique was finally employed.
- 0.2 - 0.4 -06-
c
-
1
- 1.0
Shaker r a t e
k s
Variance
--O-
240 cpn
0057
00051
--e-
190 c p m
0059
00091
kdS untti
L
I
0
0.5
o r e lcters/mfn(g)
I 10
I 2.0
I 1.5
L
Time (minutes)
Experimental data plotted for runs at two shaking rates on reciprocating shaker
S
specific surface of resin particles. sq. cm. per gram q = copper concentration in resin after exchange, meq. per gram C, = initial copper concentration of solution, meq. per liter C = solution concentration at any time. t C" = equilibrium concentration of copper ion for any particular resin concentration, q kd = mass transfer coefficient for transport between solution and resin particles in consistent units =
For this particular resin-ion (Amberlite I R 120-CUf+) system, the value of Ch is extremelv small comDared to C a t resin concentrations less than 40% of saturation. In these experiments all resins were essentially copper-free at the start and the total copper absorbed was small enough so that high resin concentrations were never approached. Hence the value of C* was assumed to be 0 in all calculations. By solving the two equations simultaneously and integrating. the folloiving relationship is obtained :
For any particular initial weight of resin, solution amount, and concentration, the term ( V In C,)X is a constant.
1234
The plot of ( V In C)X us. t is then linear with a slope of - kdS. '4 temperature correction may also be applied by first determining the ratio of kdS at any temperature T to that at 25' C. (designated by L ) . The relationship is ( 2 ):
Correction Factor,
Temp., 10
O
C.
L =
hdT/kd
26'
C.
0.70 0.79
15 20 25
0.89
30 35
1.12
1.00
1.26
In the region 22' to 28" C. the slope of the plot of correction factor L us. temperature is 0.0233 L / O C. Because (kdS)250 = k d S ) / L , Equation ( 3 ) can be rewritten to include the temperature correction as: t(kdS)z;'
=
V In C, XL
~
V In C XL
Experimental
Two shaker types were used: a reciprocating unit with a stroke amplitude of 13/, inches and frequency variable over the range 190 to 240 stroke cycles per minute,. and a rotary shaker with a 3/4 inch diameter circle of rotation. Rotation speed could be varied from 80 to 270 r.p.m.
INDUSTRIAL AND ENGINEERING CHEMISTRY
A small amount of wet resin, of known drv weight, is placed in the flask. Dry weight is determined by oven-drying a portion for 2 hours at 100' C. The resin, once dried, cannot be added directly to water, for the rapid expansion will cause many particles to break up. h-inety per cent of the desired liquid volume is added and shaking is begun. At time 0. the remaining 10% of the liquid volume is quickly injected as a concentrated copper sulfate solution. This brings the flask liquid to the proper level and copper concentration. The initial copper concentration, C,, in the flask, after the concentrate had been added to the water, was from 6.55 to 13 mmoles per liter, depending on conditions desired. Samples are withdrawn at half minu?e intervals by a hypodermic syringe. To prevent resin from being drawn up along with the sample, a fritted-glass tip was fitted on the syringe. Samples are analyzed as described below.
Under these conditions sampling can be continued for 2 to 3 minutes. After that, solid diffusion of copper within the resin particle becomes important and external liquid-solid mass transfer is no longer rate-controlling. Determination of Copper. A simple, rapid procedure for copper determination was needed. I t was found that light absorption by copper ion in ammonia solution follows Beer's law. The concenrration range measured was from 0 to 20 mmoles per liter with ammonia concentrations of 3 to 7 M . For analysis, 1 ml. of the sample solution was placed in a dry Beckman spectrophotometer cell and an equal amount of concentrated ammonia added. The absorbance at 6350 A. was then measured. In some later experiments 2 ml. of copper solution and 0.75 ml. of ammonia were used to obtain a denser solution. The ratio does not matter, iT it is consistent within a given test, as only ratios rather than absolute values of copper concentration are needed. By measuring the absorbance of the solution (plus ammonia), initially and after various time intervals, the mass transfer coefficient can be calculated. These measurements need no? be
FERMENTATION E Q U I P M E N T & D E S I G N converted to concentration, but can be used directly in the equations, for they are proportional to concentration. Mixing Time Measurements. The mixing time measurement used by Fox and Gex (4) was adapted to shaken flasks in the following manner.
j/
For a total liquid volume of 50 ml., 45.5 ml. of water, 0.5 ml. of 2% phenolphthalein, and 2.0 ml. of 2M sodium hydroxide are added to the flask and shaking is begun, A hypodermic syringe is filled with 2.1 ml. of 2M hydrochloric acid and fitted with a fritted-glass diffuser tube. The diffuser tube is placed in the flask as it shakes. The tip is held just above the liquid surface as it is emptied, and is not dipped into the liquid. The diffuser is used so that the acid may be injected quickly, but with negligible velocity; additional stirring is avoided. At the same instant, the syringe contents are discharged into the flask and a times is started. The time for complete disappearance of the indicator color is recorded as the mixing time. As the volume is scaled u p or down, concentrations are maintained constanti.e., 1 ml. of indicator is used for 100-ml. total volume, and so on.
Results
1,
Mass Transfer Coefficients. Measurement, of mass transfer coefficients as described is subject to many errors and the data obtained exhibit a rather large variance. Time measurement is very critical with running times so short (about 2 minutes). The changes in absorbance are magnified by the log As a function used to calculate k$. result, many duplicate runs must be made and some statistical technique used in their evaluation. Experimental data were plotted for runs a t two different shaking rates, 190 and 240 cycIes per minute, on the reciprocating shaker. The flasks were smooth, 500 ml. Erlenmeyers containing 200 ml. of copper sulfate solution. Here the plot is actually 1nC
LX
The slope is then the intercept term,
Liquid-Solid Mass Transfer in Shaken Flasks Mass Transfer Coefficient, k d s , at Fluid Volume of 60 ml. 100 ml. 200 ml Smooth flasks Reciprocating shaker 190 c.p.m. 240 c.p.m.
0.042 0.060
0.046 0.058
0.059 0.057
Creased flasks 0.062 0.064 Rotary shaker, 268 r.p.m. 0.065 Reciprocating shaker 0.045 190 c.p.m. 0.059 240 c.p.m. For smooth flasks at any speed and crewed flasks below 250 r.p.m. on rotary shaker, resin distribution was inadequate and samples were considered unrepresentative. o.p.m. Stroke cycles per minute.
... ...
... ...
O n this basis the data plotted are taken to mean that there is no significant difference in the mass transfer coefficient between the particles and surrounding fluid due to the increase in shaking rate shown. Similar data for a number of other flask and liquid volume combinations on both rotary and reciprocating shakers are collected in the Table. No values are given for smooth flasks, or for creased flasks at speeds below 268 r.p.m., on the rotary shaker, because the distribution of resin was very poor in those cases. A good part, most of it at low speeds, lay on the flask bottom instead of being suspended as intended. Mixing Time. Determination of mixing time is simple and satisfactory. Again, the timing measurements are extremely sensitive, for the periods are very short-from a few seconds up to half a minute. The best practice seems to be to take an average of several readings made on different occasions. Mixing time data for a number of flask liquid combinations on both shaker types are presented in the second table. Experimental values under 2 seconds have been reported as “instantaneous”;
any attempt a t closer reckoning seems unrealistic.
Discussion and Interpretation The transfer coefficient (kdS) data indicate that the shaken flask is a poor agitator so far as mass transport between liquid and fine suspended solids is concerned. For the reciprocating shaker liquidsolid mass transfer appears to be independent of shaker rate. Even when a baffled (creased) flask is used, there is no great improvement in mass transfer. In contrast, similar measurements in mechanically agitated vessels show a great increase in mass transfer coefficient with stirrer speed ( 2 ) . This sharp contrast between the mass transfer coefficients in shake flasks and stirrer-agitated devices is shown clearly in Figure 1. The resin does not remain suspended in the tank at a stirrer speed much below 40 r.p.m.; thus kdS of 0.04 to 0.05 corresponds almost to stagnant diffusion. Bulk mixing for the reciprocating shaker, according to the mixing index, was almost instantaneous.
Mixing Times for Shaken Flasks
lnC, LX us.
Mixing Time, Sec., at Fluid Volume of
kdS
7. Subtraction
‘2,
of
simply brings
all lines together at t = 0 for easier comparison. In interpreting these data it is assumed h a t the variance of the first data point ( k = 0) is small compared to that of the other values. This is a good assumption, for the starting solution concentration can be determined many times over if desired. The variance of the slope and hence kJ from the mean, can readily be calculated by using the slope of a line from the starting point to any individual data point as the random variable.
Smooth flasks Rotary shaker 90 r.p.m. 176 r.p.m. 268 r.p.m. Reciprocating shaker 190 c.p.m. 240 c.p.m. Creased flasks Rotary shaker 90 r.p.m. 176 c.p.m. 268 c.p.m. Reciprocating shaker 190 c.p.m. 240 c.p.m.
+
100 ml. asbestos
50 ml.
100 ml.
200 ml.
6
7 10
23 16 11,
52 20 16
... ...
2 2
2
2
Inst.
Inst.
... ...
2 3 4
3 2.5 2
12.5 2.5
27 24 11
Inst.
4
‘2.5
3
Inst.
Inst.
Inst.
VOL. 49, NO. 8
1%
6 3
AUGUST 1957
1235
0.161
I
I
I
I
I
I
I
1
I
L
I
i
t
P ‘ /‘
/*/
/”
I
L
500ml. SMOOTH FLASKS
-
RECIPROCATING SHAKER
-
0 50d.fluid volume 0-103 ’ ” 0-2m ,I 11
0
I
0
I
40
I
I
80
I
I
I
I20
I
I
160
-
I
180
I
I
220
I
2
AGITATOR SPEED RPM SHAKING RATE STROKE CYCLES/MIN.
-
Figure 1.
Mass transfer coefficients in shake flasks and stirrer-agitated devices
From these experimental observations it can be concluded that for the reciprocating shaker the scale of turbulence was large, with considerable gross flow and good bulk mixing. The introduction of baffles contributes little. This is reasonable, for turbulence is generated a t the baffle only when a high velocity fluid strikes the discontinuity. In the case of the rotary shaker, the fluid vortexed and was largely in laminar flow. Bulk mixing was so poor in some cases that the ion exchange technique could not be used because of the difficulty in drawing a representative sample. When vortexing occurred, the fluid rode the flask walls in a heavy layer with very little flow perpendicular to the wall. When baffles were introduced, the vortex broke and turbulence was generated as shown by the marked reduction in mixing time. Liquidsolid mass transfer rates were substantially the same as for the reciprocating shaker. The effect of liquid volume and shaking rate on flask agitation follows the expected pattern. Reducing the volume or increasing the shaking rate results in more effective bulk mixing.
1 236
The 50-ml. flask volume on the rotary shaker appears to be an exception to this, however, as mixing time increases slightly with shaker speed. This is not unreasonable, for this small volume in an unbaffled flask forms only a “thick film” on the walls. The faster it is swirled, the more the liquid is spread and the poorer the mixing. Baffles practically eliminate this effect. Mass transfer data show essentially the same performance under all conditions, so long as adequate bulk mixing is achieved. The slight decrease in kdS values a t some of the lower flask volumes for the reciprocating shaker is not considered significant. Air is entrapped under these conditions and may very well “blanket” a part of the resin surface, causing a reduction in kdS through S, the interfacial (particle) area. Shake-Flask Agitation. I n a shaking device, mass transfer between liquid and suspended particles i s considerably poorer than in a mechanically stirred system. Two factors contribute to this. First, the energy (power) input per unit volume is mechanically limited in the shaker; it is not possible with conventional equipment to increase power input to the levels obtainable with a mechanical
INDUSTRIAL AND ENGINEERING CHEMISTRY
agitator. Secondly, the energy input is distributed throughout the fluid volume in the case of the shaker rather than being concentrated in smaller reginm as in the stirred device. Even when discontinuities are intro. duced into the flask, the intensity of turbulence is still so low that no effect on mass transfer rates is seen. In the absence of zones of high fluid shear, such as those produced around the impeller and baffles in a mechanically agitated tank. suspended ion exchange particles simply ride with the fluid, and effective solid-liquid mass transfer is indifferent to shaking conditions over the range attainable. For the rotary shaker, bulk mixing in unbaffled flasks was so poor that representative samples could not be drawn for mass transfer measurements. Baffles improve the agitation and bring the performance of the rotary into line with that observed for the reciprocatin5 shaker. Gas-Liquid Transfer. The experimenu reported here were not concerned with gas-liquid mass transfer. Yet, in many cases, gas absorption, and not the transfer processes in the liquid phase or between it and suspended solids, seems to be the rate limiting step. Under such conditions shaken flasks can be made to perform very well, giving results comparable with those in mechanically stirred fermentation vessels. In fermentations which develop thick, viscous cell suspensions, on the other hand, the liquid-solid mass transfer phenomena studies here can-and apparently do-become the controlling ones. Baffling also markedly improves gasabsorption rates in shaken Erlenmeyer flasks (3, 7). If cleaning problems and the like are not excessive, creased or indented flasks can be profitably employed on rotary shakers. literature Cited
(1) Auro, M. A,, Hodge, H. M., Koth, iV. G., IND. ENG. CHEM.49, 1237 (1957). ( 2 ) Bieber, H., Ph.D. thesis, Columbia University, 1957. (3) Dayan, S.: Gaden, E. L., Jr., Ahstracts, 128th Meeting ACS, Minneapolis, Minn., 1955, p. 32A. (4) Fox, E. A . , Gex, V. E., .4bstracts, 48th Annual Meeting, American Institute of Chemical Engineers, Detroit, 1956. ( 5 ) Hixson, A. W.: Baum, S. J.. IND.ENG. CHEM.33. 474 11941) (6) Hixson, A h., Crowell, J. H., Ibid., 23, 924, 1002 (1931). (7) Smith, C. G., Johnson, M. J., J . Bacterid. 68, 346 (1954). RECEIVED for review November 20, 1956 ACCEPTED May 21, 1957 Division of Agricultural and Food Chemistry, Fermentation Subdivision, Symposium on Fermentation Process and Equipment Design, 130th Meeting, ACS, Atlantic City, N. J., September 1956.
