I
DONALD
H. PHILLIPS
and MARVIN J. JOHNSON
Department of Biochemistry, University of Wisconsin, Madison 6, Wis.
Oxygen Transfer in Agitated Vessels Oxygen absorption by sulfite in an agitated, spgrged fermentor seems to be controlled by a process quite different from that in an unsparged vessel T H E SULFITE METHOD (4)is used widely for evaluating performance of aerobic fermentors-the vessel is filled with sodium sulfite solution in the presence of copper ions as catalyst, and the rate at which sulfite is oxidized to sulfate is used to measure the efficiency of oxygen transfer to the liquid phase. However, confusion over interpretation of the results from such tests has arisen (8)e.g., opinion differs as to whether the reaction is controlled by resistance a t the interface (75), by the gas film (74),or by the liquid film (7, 72). Poor correlation has been reported (20) between the oxygen transfer rate with sulfite and that with an aqueous oxygen-free solution in sparged vessels. I t was assumed that much of the chemical reaction occurred in a liquid film surrounding the bubbles. O n the other hand, good correlation has been reported ( 3 ) between oxygen absorption rate with sulfite and that with oxygenfree solutions, also good correlation has been reported (74) between oxygen transfer rate with sulfite and maximum uptake in yeast fermentation under the same aeration conditions. T h e reason for this is not obvious. Oxygen uptake has been studied (77) using copper-catalyzed sulfite solutions with a n unsparged cylinder where oxygen could enter the liquid only through the horizontal air-liquid interface. Agitating, the gas phase did not increase the transfer rate ; therefore the reaction was not gas film-controlled. Also, agitating the liquid phase did not increase'.the transfer rate; in fact the transfer rate decreased at high liquid agitation rates. These results were surprising. Therefore, sulfite oxidation in an unsparged cylinder was investigated in an attempt to determine the nature of the rate-controlling process.
airtight pump (7) at approximately 80 ml. per minute. The oxygen partial pressure was measured with a Beckman oxygen analyzer (73) and recorded with a Leeds & Northrup Speedomax recorder. , The reaction vessel was a glass jar with a total capacity of approximately 4 liters; the operating liquid volume was 2 liters. T h e baffle was a.250-ml. Erlenmeyer flask cut longitudinally through its center. The liquid stirrer was a twobladed glass propeller. T h e temperature of the reaction vessels in all experiments was controlled a t 30' f 0.5' C. The p H of the sulfite solutions was approximately 9.2. The gas in the apparatus was maintained at a pressure slightly less than atmospheric so that any small leaks would not seriously affect the results. With the oxygen analyzer and the recorder, the transfer rate could be measured without disturbing the reaction vessel. Results. If oxygen absorption by sulfite solutions in the unsparged cylinder of Figure 1 were gas film-controlled or liquid film-controlled, agitation should increase the oxygen transfer rate. However, the turbulence provided by this system had no effect on the transfer rate (Figure 2), indicating that neither an ideal gas film nor an ideal liquid film
limited oxygen diffusion into the bulk of the liquid. Also, the oxygen transfer rate was not directly proportional to the oxygen partial pressure in the gas phase. T h e rate varied as the 1.5 power of oxygen partial pressure, indicating that transfer was limited bp a process other than simple diffusion. Obviously. a less naive approach was indicated. If the major resistance to oxygen transfer were in the gas phase or at the interface, the absorption rate would be independent of the nature of the oxygen-consuming chemical reaction. Since the absorption rate (Figure 3) is not independent of the nature of the oxygen-consuming reaction, the major resistance to oxygen transfer must be in the liquid phase. The curve for alkaline pyrogallol is incorrect, because the reaction rate was so rapid that the oxygen analyzer system did not respond rapidly enough for accurate measurement. The curve is included only to show that the rate was much higher than with sulfite.
High Turbulence From the data presented thus far, it may be concluded that oxygen absorption by sulfite in an unsparged cylinder is probably controlled by a resistance in the liquid phase, but diffusion through
I
l o w Turbulence
Apparatus. The system used (Figure 1) to study oxygen transfer across a horizontal gas-liquid interface was completely closed except for an air-filled manostat which admitted air at a rate equal to the rate of oxygen absorption by the liquid in the reaction vessel. The gas was circulated through the system by an
Figure 1 . The system used to study oxygen transfer across a horizontal gas-liquid interface was completely closed, except for an air-filled manostat VOL. 11, NO. 1
JANUARY 1959
83
4
L io A 408
Figure 2. Effect of oxygen partial pressure on transfer rates. Turbulence had no effect
A 2000
360 930
v o
Liquid phase composition in moles per of copper sulfate ond 1.0 liter, of sodium sulfite
i '?,
i
T
s.15
rl
D4-
y/-,
SLOPE = 1.5
Figure 3. Effect of oxygen partial pressure on transfer rate. Liquid phase agitation
J
r" I
0.1
I
I
0.2
0.4
0.
a stagnant liquid film is not the rate-controlling step. T o explain the liquid phase resistance in the unsparged cylinder, it is necessary to consider in detail the liquid adjacent to the interface. For simplicity, it is assumed that the liquid adjacent to the interface was stagnant with respect to the interface (79). However, an assumption of surface renewal (5, 6 ) would result in the same conclusions. For the hypothetical instance Figure 4, A , the liquid turbulence is very low, and all of the oxygen is consumed by the chemical reaction in a film of liquid close to the interface. The portion of the stagnant film where the reaction occurs is called in this report the reaction film. Here, liquid agitation would not affect the transfer rate unless the edge of the stagnant liquid film advanced past the edge of the reaction film, in which event molecular diffusion would account for transfer in the film of oxygen that had not already reacted, and eddy diffusion would account for transfer in the bulk of the liquid (Figure 4, B ) . T h e concentration gradient is not constant throughout the film because a large portion of the chemical reaction occurs in the film. ' I n Figure 4, C, liquid turbulence has made the film so thin that most of the oxygen reacts in the bulk of the liquid, but the oxygen concentration in the bulk of the liquid is low because the volume of the liquid phase is large compared to the volume of the film. An equation has been derived to express oxygen transfer quantitatively when all of the oxygen is consumed in the stagnant liquid film.
Solution of pyrogallol contained 10% of both potassium hydroxide and pyrogallol (weight to volume); the sulfite solutions contoined 1 mole of sodium sulfite and 1 0 - 6 mole of either copper or cobalt sulfate
84
INDUSTRIAL AND ENGINEERING CHEMISTRY
Ea
0
Equation 1 is derived using assumptions as follows: T h e rate of the reaction follows the equation
All of the oxygen is consumed in the stagnant liquid film; its concentration in the liquid a t the interface is [ O ] , and remains constant. The sulfite concentration [SIin the liquid is constant throughout the liquid phase. Steady state conditions are maintained. T h e amount of oxygen entering the volume Adx in Figure 12 is AN,
=
5
2
order with respect to dissolved gas; rate of transfer of gas per unit area at interface; [O],, concentration a t interface of dissolved gas, in equilibrium with gas phase; [SI,concentration, in liquid phase, of the solute that reacts with
0 0.2
0
PO2,
0.4
0.6
ATM*
dissolved gas; and y, reaction order with respect to the above solute. The transfer rate is proportional to the square root of the reaction rate constant and to the ( n 1)/2 power of the oxygen partial pressure in the gas
+
2d[0] d2[0] - 2_ K [_ O]"d[O] dx dx2 Do dx
~~
but
Therefore d[(%?)'] dx
_ _2 K_ [_O _] " d [ O ] Do
dx
Upon integrating
or
[Ol - A D , -d dx
The amount of oxygen leaving this volume per unit time is since
The amount entering minus the amount leaving is equal to the amount of oxygen consumed in the volume.
d[Ol dx
and [ O ] approach zero a t
large values of x , L must equal zero. T h e rate of absorption is
or AD,
d2[0]dx - K [ O ] * Adx dx2
~
or
where A is area; Do diffusion coefficient for gas that reacts with solute; k , reaction rate constant; n, reaction
a
KOH + PYROGALLQL
d[OI Multiplying both sides by 2 __ dx
Therefore, when the reaction film is completely contained within the stagnant liquid film, the oxygen transfer rate is
O X Y G E N TRANSFER
DISTANCE L--t
DISTANCE
DISTANCE 4
A . LOW TURBULENCE
B. MEDIUM TURBULENCE
C. HIGH TURBULENCE
Figure
4. Concentration proflles
A. B.
l o w turbulence. All the oxygen i s consumed by the chemical reaction in a liquid film close to the interface Medium turbulence. Liquid agitation would not affect the oxygen transfer rate unless the edge of the stagnant liquid fllm advanced past the edge of the reaction film C. High turbulence. The fllm is so thin that most of the oxygen reacts in the bulk of the liquid
phase. Figure 2 indicates that transfer rate varied as the 1.5 power of the oxygen partial pressure. Since the degree of agitation used had no effect on the transfer rate in the unsparged cylinder, practically all of the oxygen must have been consumed in the film. Therefore, it can be concluded that the oxygen-consuming chemical reaction is second order with respect 1)/2 = 1.51. to oxygen [(n When only a negligible portion of the oxygen reacts in the stagnant liquid film and the oxygen concentration in the bulk of the liquid is very small (Figure 4,C), the transfer rate is
+
AN,
=
AD,--" LO1
where z is the depth of the stagnant liquid film. Here, the transfer rate is independent of the rate constant of the chemical reaction and proportional to the first power of the oxygen partial pressure in the gas phase. If enough interfacial turbulence could be achieved in a hypothetical vessel to decrease the depth of the stagnant liquid film and change the oxygen concentration profile from that represented by Figure 4,A to that represented by Figure 4, C, the transfer order with respect to oxygen should decrease from (n 1)/2 to 1.O. The transfer order is defined as the slope of the curve when the log of the transfer rate is plotted against the log of the oxygen partial pressure. If, when sulfite is oxidized in an unsparged vessel, the oxygen concentration profiles can be approximated by those shown in Figure 4, intense agitation should decrease the transfer order from l .5 to l .O. However, it is apparent from Figure 2 that the liquid turbulence provided with this vessel did not affect either the transfer rate or transfer order. Therefore, a reaction vessel was designed to provide very high liquid turbulence without bubble formation.
+
Apparatus. The reaction vessel used was similar to that in Figure 9 except that it was unsparged, the baffles were larger (approximately 4 X 9 cm.), and the operating liquid volume was 700 ml. The reaction vessel was operated in a closed system similar to that shown in Figure 1. Results. Experiments were m:de with copper-catalyzed sulfite as the oxygen absorbent; however, the results were not reproducible and the oxygen transfer rate with a consfant agitation rate increased with time. It appeared that the erratic behavior of the copper-catalyzed sulfite system was caused by random metal catalysis from the stainless steel components of the reaction vessel. Therefore, a solution containing sodium sulfite and Versene [ (ethylenedinitrilo) tetraacetic acid] was used. Versene made the regults more reproducible, probably by complexing the metal ions present as impurities. I t also lowered the observed oxygen transfer rate, probably by decreasing the reaction rate constant. With a lower reaction rate constant, oxygen would diffuse further into the liquid before it reacted, resulting in a deeper reaction film. Therefore, less turbulence would be required to change the concentration profile from that shown in Figure 4,A to that shown in Figure 4, C. I n Figure 5, the transfer rate is expressed as millimoles of oxygen per liter per minute because no correction was made for the effect of agitation on the area of the gas-liquid interface. I t is obvious that agitation changed the transfer order with respect to oxygen (Figure 6). At low agitator speeds, the transfer rate varied as the 1.5 power of the oxygen partial pressure, indicating that, according to the hypothesis made earlier, most of the oxygen was consumed in the stagnant liquid film, while at high agitator speeds, the transfer rate was proportional to the oxygen
partial pressure. This indicated that only a negligible portion of the reaction occurred in the film. T o determine whether the effect shown in Figures 5 and 6 was peculiar to the sulfite system, similar experiments were made with pyrogallol buffered at p H 6.8. The pyrogallol reaction is also second order with respect to oxygen and at low agitator speeds practically all of the reaction occurred in the film, whereas a t high agitator speeds practically all of the oxygen reacted in the bulk of the liquid. Oxygen Absorption from 6ubbles
Wise (20) observed that the oxygen transfer rate from bubbles in an u11agitated cylinder was greater with copper-catalyzed sulfite than with an aqueous, oxygen-free solution. He concluded that when bubbles rise through a sulfite solution, a large portion of the reaction occurs in a film surrounding the bubble. However, other investigators ( 3 ) found a good correlation between the oxygen transfer rate with sulfite and the rate in an aqueous, oxygen-free solution, indicating that only a negligible portion of the oxygen reacts in the film surrounding the bubbles. According to the hypothesis made earlier, if a considerable portion of the reaction occurs in the film, the transfer order with respect to oxygen should be greater than unity. However, Myamoto (75)observed that oxygen absorption by sulfite in a sparged vessel was directly proportional to the oxygen partial pressure. Therefore, some factors involved in sulfite oxidation in sparged vessels were investigated. The ancillary apparatus used to study oxygen absorption from bubbles was similar to thgt shown in Figure 1. The reaction vessel is shown in Figure 7. The bubbles were allowed to rise from a single orifice approximately 33 cm. VOL. 51, NO. 1
JANUARY 1959
85
+
0.04
E‘
Figure 5. Effect of oxygen partial pressure on the transfer rate in an unsparged vessel
2 Y
I
0.02
B
Solution composition per liter, 1 .O mole of sulfite and 0.1 mole of boric acid with 1 gram of verrene; pH, 9.2
w^ H
2
0.01
E
2 $
6 8
b
0.008
0.003 0.1
.--
Figure 6. Agitation changed the transfer order with respect to oxygen in an unsparged vessel 0.5
0.2
POa,
1.0
ATM.
below the meniscus. The size of the bubbles was determined from photographs, and their areas and volumes were calculated on the assumption that they were oblate spheroids (70). T h e total volume of gas as bubbles was calculated from the increase in liquid head in tube A in Figure 7. T h e liquid level was measured with a cathetometer. T h e oxygen transfer rate from bubbles rising through a copper-catalyzed sulfite solution was found to vary as the first power of oxygen partial pressure in the gas phase (Figure 8), indicating that only a negligible portion of the chemical reaction occurs in the liquid film. T h e transfer rates observed in these experiments agree fairly well with those observed by Hammerton and Garner ( 7 7 ) for bubbles of the same size in aqueous, oxygen-free solutions. There-
GAS Y-PASS
GAS FROM t PUMP
Figure 7. Reaction vessel for studying oxygen absorption. Bubbles were allowed to rise from a single orifice approximately 33 cm. below the meniscus
86
. L o -
fore, it appears that oxygen transfer in this instance is limited by the same process that limits transfer from bubbles in aqueous, oxygen-free solutions. T h e transfer rate a t high oxygen partial pressures was greater in an unsparged cylinder than it was from bubbles (Figure 8). T h e reason for this is not obvious. Oxygen Absorption in a Sparged Agitated Fermentor
The sulfite method is widely used to evaluate efficiency of oxygen transfer in aerobic fermentors and many investigators have observed a good correlation between the oxygen transfer rate with sulfite and the maximum oxygen utilization rate in nonviscous fermentations. If the physical differences between sulfite solutions and bacterial suspensions are neglected and the same process limits oxygen uptake in both solutions, the observed correlation would be expected. I t was concluded previously that when bubbles rise through a coppercatalyzed sulfite solution, oxygen transfer is limited by the same process that limits transfer from bubbles in an aqueous, oxygen-free solution. If the same process limits oxygen transfer when a sparged vessel is agitated, the transfer rate should vary as the first power of the oxygen partial pressure and within limits should be independent of the reaction rate constant Apparatus. A closed system was not used for studying oxygen transfer in a sparged, agitated fermentor (Figure 9), because gas leakage at the impeller shaft bearing on the head of the fermentor was very great at high agitator speeds. Mixtures of oxygen and nitrogen were used as the gas phase. The flow rates were controlled with reducing valves and orifices.. During a n experiment, oxygen contents of the influent and effluent gases were recorded periodically. The total flow rate was measured with a rotameter and controlled manually a t 950 ml. per minute.
INDUSTRIAL AND ENGINEERING CHEMISTRY
T h e fermentor had a total capacity of approximately 900 ml. ; its operating liquid volume was 500 nil., and its cross-sectional area was approximately 72.3 square cm. The eight-bladed turbine impeller had a diameter of approximately 6 cm. and each blade had an area of approximately 3 square cm. Each of the four baffles was approximately 12 cm. long and 1.5 cm. wide. Results. It was previously observed that cobalt-catalyzed sulfite gave approximately 5 times the uptake rate observed with copper-cacalyzed sulfite in an unsparged vessel. However, both cobalt-catalyzed and copper-catalyzed sulfite gave the same transfer rate in an agitated, sparged fermentor and the transfer rate varied as the first power of the oxygen partial pressure (Figure 8). Therefore, according to the hypothesis made earlier, it appears tha[ all of the chemical reaction occurs in the bulk of the liquid and that the oxygen tension in the bulk of the liquid is negligible. The observed transfer rate is the maximum rate a t which oxygen can be transferred from the gas phase to the bulk of the liquid under the aeration conditions employed. However, when a fermentor was evaluated with 10% potassium hydroxide and 107, pyrogallol, the transfer was much greater than with sulfite, probably because a large portion of the reaction occurred in a liquid film surrounding the bubbles. Therefore, it appears that with pyrogallol, the observed oxygen transfer rate is much greater than the maximum rate at which oxygen can be transferred from the gas phase to the bulk of the liquid. Using sulfite solutions in a n agitated, sparged fermentor; Pirt and others (76) observed a much greater uptake rate with 0.005M cobalt than with 0.005M copper as catalyst. Perhaps with O.OO5,M cobalt,, some oxygen reacted in the film. Effect of Sulflte Concentration on Oxygen Transfer Rates
Fuller and Crist ( 9 ) studied the effect of sulfite concentration of the oxygen transfer rate in a sparged, agitated
OXYGEN TRANSFER Figure 9. An open system was used for studying oxygen absorption in an agi-1 tated, sparged fermentor
z
4
'
v 0.04
0.04
IN
., 0IN2
FERMENTOR
'
/
UNSPARGED CYLINDER SLOPE = 1 . 5 1
0.1
0.4
1.0
ATM. Figure 8. Effect of oxygen partial pressure on the transfer rate in a sparged vessel and an unsparged cylinder liquid phase composition per liter, 1 .O mole of sodium sulfite and 10' mole of copper sulfate; average major axis and minor axis of bubbles in the sparged vessel were 2.6 and 1.6 mm., respectively
vessel. They observed that the transfer rate was independent of sulfite a t high concentrations and concluded that this was due to changes in pH. However, if, when sulfite is oxidized in an agitated, sparged vessel, practically all of the oxygen reacts in the bulk of the liquid and the oxygen tension in the bulk is negligible, the observed oxygen transfer rate should, according to the hypothesis made earlier, be independent of the chemical variables, including sulfite. If sulfite were oxidized in an unsparged vessel, the transfer rate should depend on the maximal reaction velocity, provided practically all of the chemical reaction occurs in the stagnant liquid film. The maximal reaction velocity should depend on the sulfite concentration. Apparatus. The apparatus used to study the effect of sulfite concentration on the oxygen uptake rate in an agitated, sparged fermentor was similar to that shown in Figure 9. The influent gas contained only 5.2% oxygen because with air the sulfite was depleted too rapidly to allow accurate measurements. The gas flow rate was 950 ml. per minute and agitator speed 2200 r.p.m. The ancillary apparatus used to study the effect of sulfite concentration on the transfer rate in an unsparged vessel was similar to that shown in Figure 9. The reaction vessel was a square glass vessel, 25.3 cm. wide, 34 cm. long, and 4.2 cm. deep containing 1 liter of liquid. Air was passed from a single G mm. orifice over the surface of the liquid a t 144 ml. per minute.
The sulfite concentration in both reaction vessels was determined iodometrically ( 4 ) a t high sulfite concentrations, but at low concentrations it was d e t e r d n e d by another method. The rate of oxygen absorption us. time could be calculated easily from the data recorded with the oxygen analyzer. The rate was then plotted against time, the curve was integrated with a planimeter and the total quantity of oxygen absorbed was plotted against time. Since practically all of the oxygen absorbed oxidized sulfite to sulfate, the sulfite concentration at any time could be calculated. Results. In the sparged fermentor, the transfer rate was independent of sulfite concentration down to approximately 0.008M, whereas in the unsparged vessel, it was dependent on sulfite concentration up to 0.2M (Figure 11) ; this indicated qualitatively the relative independence in an agitated, sparged fermentor of the oxygen absorption rate on chemical variables. I n the fermentor, the transfer rate varied as the first power of the sulfite concentration below 0.002M, indicating that the reaction is first order with respect to sulfite. This was also observed by Fuller and Crist (9). Because it has been concluded that the sulfite reaction is first order with respect to sulfite, Equation 1 predicts that the transfer rate should vary as the 0.5 power of the oxygen partial pressure in the unsparged vessel. However, it is apparent that below 0.01 5Msulfite the transfer rate varied as the first power of the sulfite concentration in this vessel. This would be expected if sulfite diffusion as well as oxygen diffusion limited the oxygen absorption rate. Above O.015M sulfite, the oxygen absorption rate seemed to approach a cons.tant value, indicating that a factor other than sulfite was limiting the velocity of the chemical reaction ( 2 ) . Discussion and Conclusions
When sulfite was oxidized in an unsparged cylinder, all of the chemical reaction appeared to occur in a film of liquid adjacent to the gas-liquid interface.
The absorption rate was limited by diffusion into a liquid film, and the transfer rate is given by Equation 1. When all of the reaction occurred in the film, the oxygen transfer rate was independent of liquid agitation. When sulfite was oxidized in an agitated, sparged fermentor, in the presence of copper or cobalt ions as catalyst, practically all of the chemical reaction seemed to occur in the bulk of the liquid, and the oxygen content of the bulk was negligible. Here, the transfer rate was relatively independent of the reaction velocity constant and was independent of sulfite over a wide range of concentrations. T h e observed oxygen uptake rate appeared to be the maximal rate at which oxygen could be
R. P.M. Q 2
3
4500
-
1
A200
/1800 -/ / /
0. 0
/8
1000
/
- /*
600
I
0'
C U +SULFITE 0
Co+SULFITE
0
0.1 0.05 p'2
>
0.2 ATM
0.6
Figure 10. Transfer rate vs. oxygen partial pressure using cobalt and copper as catalysts in evaluating a sparged fermentor. Temperature was controlled with a thermistor-activated control and cooling coils Sulflte solutions contained per liter 1.0 mole of sodium sulfite and 10-6 mole of either cobalt or copper sulfate
VOL. 51, NO. 1
JANUARY 1959
87
Figure 11. Effect of SUIfite concentration on the transfer rate in both an unsparged and an agitated sparged vessel Liquid phase contained 10mole of copper sulfate per liter
n
=
Ai,
=
Nz
=
N(,+d,)
+
[0] = [O], = 10.1
10-2
SULFITE CONCENTRATION IN MOLES PER LITER
INTERFACE X+
dx
EDGEOF EDGEOF REACTION STAGNANT FILM LIQUID FILM
transferred from the gas phase to the bulk of the liquid under the aeration conditions employed. Since aerobic microorganisms rely primarily on the oxygen dissolved in the bulk of the liquid, the oxygen absorption rate with sulfite in an agitated, sparged fermentor is the maximum rate at which oxygen becomes available to microorganisms under the same aeration conditions, neglecting the physical differences between the solutions. For the sulfite oxidation method to be valid for evaluating aerobic fermentors, practically all of the chemical reaction must occur in the bulk of the liquid, and the oxygen content of the bulk of the liquid must be negligible. With a valid sulfite evaluation, the transfer rate is independent of the reaction rate constant, within limits (Figure 10) and the transfer rate varies as the first power of the oxygen partial pressure-e.g., the transfer rate is 4.67 times greater with pure oxygen than with air. When a shaken flask is evaluated with sulfite, the evaluation may not be valid unless a proper catalytic system is chosen. Consequently, the validity of evaluation of unsparged fermentors should be determined before correlations are made. In a fermentor containing facultative bacteria, the oxygen concentration in the bulk of the liquid is high when the population is low, and the oxygen transfer rate is limited by the maximum rate at which the microorganisms can use the dissolved oxygen. As the population increases, the oxygen concentration in the bulk of the liquid decreases, but the oxygen utilization rate of a cell is independent of the oxygen concentration in the bulk of the liquid until very low values are reached. Therefore, no change in growth rate is observed until the oxygen tension in the bulk of the
88
Figure 12. This represents a volume of liquid adjacent to the interface in an unsparged cylinder. Agitated liquid phase contains an oxygen absorbent
liquid approaches 0.01 atm. (8). If oxygen were uniformly distributed in the bulk of the liquid, anaerobic metabolism would begin when the oxygen tension fell below approximately 0.01 atm., and the transfer rate in the fermentation would be the same as the transfer rate with sulfite. neglecting the physical differences between the solutions. However, in a practical fermentor, a uniform oxygen distribution would not be expected, and anaerobic metabolism may, begin when only a fraction of the bulk of the liquid is devoid of oxygen, even though most of the bulk has sufficient oxygen for aerobic metabolism. The quantitative correlation between the oxygen transfer rate with sulfite and the absorption rate a t which anaerobic metabolism begins in nonviscous fermentations appears to depend primarily on the uniformity of the oxygen distribution in the bulk of the liquid and the ability of the cells to traverse the regions of low oxygen tension without exhibiting anaerobic metabolism. The oxygen transfer rate with a valid sulfite procedure is the maximum rate a t which oxygen becomes available to microorganisms under the same aeration conditions. Acknowledgment
The authors are grateful to Jerome S. Schultz for the derivation of Equation 1. The Shemood and Pigford text (78) was a valuable aid. Nomenclature
A Do
k
K L
INDUSTRIAL AND ENGINEERING CHEMISTRY
area diffusion coefficient for oxygen in liquid = reaction rate constant = k[S]Y which is constant = constant of integration = =
reaction order with respect to oxygen rate of transfer of oxygen per unit area at the interface rate of transfer of oxygen per unit area at a distance x from the interface = rate of transfer of oxygen per dx unit area at a distance x from the interface concentration of dissolved oxygen concentration at the interface of dissolved oxygen in equilibrium with gas phase sulfite concentration in liquid phase time distance within the stagnant liquid film reaction order with rewect to sulfite thickness of ideal liauid film \\.hen only a negligible portion of the reaction occurs in the film
[SI
=
t
=
x
=
1’
=
I
=
Literature Cited (1) Bartholomew, I$’. H., Karow, E. O.,
Sfat, M. R., FYilhelm, R. H., IND.ENG. CHEW42, 1801 (19.50‘). (2) Bassett, H., Parker, M 7 . , J . Chern. SOC. 1951, p. 1540. (3) Chain, E. B., Gualandi, G., Rend. ist.
sujer. sanita. 1 7 , 1 3 (1954). (4) Cooper, C. M., Fernstrom, G. A , Miller, S. A , , IND.ENG.CHEM.36, 504 (1944). (5) Danckwerts, P. V., Ibid., 43, 1460 (1951). (6) Danckwerts. P. V.. Kennedv. A. M.. Trans. Inst. Ch‘em. Engrs (Londo;) suppl. 1; 549 11954). ,(7) Davey, V. F., Johnson, M. ,J., Apfii. Microbial. 1, 208 (1953). (8) Finn, R. K., Bacterid. Reu. 18, 254 (1954); (9) Fuller, E. C., Crist, R. H., J . Am. Ciiem. SOC.6 3 , 1644 (1941). (10) Garner, F. H., Hammerton, D., Chem. E n g . Sci. 3, 1 (1954). (11) Hammerton, D., Garner? F. H., Trans. Inst. Chem. Engrs. (London) suppl. 1, 518 (1954). (12) Hixon, A . W.,Gaden, E. L., TND. ENG.CHEM.42, 1792 (1930). (13) Hoover, S. R., Jasewicz, L., Porges, N., Instr. and Automation 27, 774 (1954). (14) Ivlaxon, W.D., Johnson, M. J., IND. END.CHEM.45, 2554 (1953). (15) Myamoto, S., other, Bull. (:hem. Sac. J a j a n 5 , 125, 229, 321 (1930); 6, 9 (1931); 7, 8 (1931). (16) Pirt, S. J., Callow, D. S., Gillett, W. A., Chem. 3 h d . (London) 1957, p. 730. (17) Schultz, J. S., Gaden, E. L., IND. ENG.CIIEM.48, 2209 (1956). (18) Sherwood, T. K., Pigford, R. L., “Absorption and Extraction,” 2nd ed., p. 322, McGraw-Hill, Xcw York, 1952. (19) Whitman, W.G., Cizem. @ M e t . I
