2. units of kla....................................................i.i...i

AGITATION-AERATION IN THE LABORATORY AND IN INDUSTRY

R. K. FINNDepartment of Chemistry and Chemical Engineering, University of Illinois, Urbana, Illinois

I. Oxygen Supply and Demand.............................................................1. The solubility of oxygen...............................................................2. Oxygen demand.......................................................................3. Measuring oxygen demand.............................................................4. Transport of oxygen to the enzyme....................................................

II. Supply-Side Resistances................................................................1. The absorption equation..............................................................2. Units of KLa....................................................I.I...I.......... ''I3. Methods for measuring KLa............................................................4. Individual resistances and KLa........................................................

III. Methods for Increasing the Total Rate of Gas Absorption................................1. Agitation.............................................................................2. Gas velocity..........................................................................3. Type of sparger........................................................................4. Increasing the driving force............................................................

IV. Demand-Side Resistances...............................................................1. Liquid film around cells or clumps....................................................2. Intracellular and intraclump resistance................................................

V. Practical applications ..................................................................1. Performance of equipment............................................................2. Criteria of sufficient aeration...........................................................3. Relations between respiration and product formation...................................4. Overagitation and overaeration ......................................................

VI. Summary...............................................................................

It is impossible to aerate all portions of aculture fluid without some degree of stirring, andtherefore agitation-aeration comprises a singletopic. As suggested by the title, this review willconcern the physical rather than the biochemicalaspects of oxygen uptake. Its aim is to drawtogether and to interpret for microbiologistsinformation which is now widely scatteredthrough the biological and engineering literature.Emphasis will be given to principles and tech-niques rather than to particular applications ofoxygen transfer. A point to be stressed is thatlaboratory workers as well as fermentationengineers should seek accurate definition of theaeration in a particular piece of equipment sothat experimental results may be readily re-produced in other laboratories. At present, manyof the same scientists who would shrink fromdescribing a culture medium as "strongly acid" or"moderately warm", are nevertheless content tocharacterize its aeration by such qualitativephrases as "intense" or "mild".Much of the current interest in aeration can be

traced to the changing character of the fermenta-

255255255257258258258259259260261261263263264265265266266266268268269270

tion industry itself. During the past decade,products of oxybiontic synthesis, antibiotics andthe like, have largely displaced in importancesuch classical anaerobic products as ethanol andbutanol. The trend is likely to continue, makingever more valuable our knowledge of cell respira-tion and aerobic tissue culture.The new era in fermentation was heralded by

the introduction in 1933 of a shake-flask tech-nique by Kluyver and Perquin (1). Developedinitially for culturing molds in the laboratory, the"Schuttelkultur" method was soon adapted to afactory scale by using horizontal rotating drums(2) or vertical deep-tank fermenters with spargersand mechanical stirrers to disperse the air. Thelatter type is now standard apparatus for thesubmerged production of vitamins and antibioticsfrom a variety of bacteria, molds, and acti-nomycetes. Its historical development has beenreviewed by Hromatka and Ebner (3).

In laboratory work the provisions for aerationhave usually been inadequate as shown by studiesof Rahn and Richardson (4). The neglect israther surprising, because the role of dissolved

254

AGITATION-AERATION IN LABORATORY AND INDUSTRY

oxygen in altering cellular metabolism and inpromoting growth has been known since thetime of Pasteur. Nevertheless, even recent bookson physiology (5, 6, 7) give scant attention to thematter of oxygen supply, owing perhaps touncertainty regarding its classification as a

physical or a chemical factor affecting growth.Allen (8) has summarized the situation by com-

menting that, "For the growth of bacteria thereare few data which are complete enough todeserve theoretical treatment, and which provideasurance that the investigator was measuringanything more significant than the rate of diffu-sion of oxygen into solution."

I. OXYGEN SUPPLY AND DEMAND

1. The solubilty of oxygen. Oxygen is a ratherinsoluble gas, water at 20 C and in an atmosphereof air holding only about 9 parts per million ofoxygen. As the temperature is raised, oxygen, likeany other gas, becomes Is8 soluble. At 37 C forexample, water in perfect contact with air con-

tains less than 7 ppm of oxygen. The solubilityof oxygen is substantially independent of the totalpressure and the presence of other gases. It is,however, directly proportional to the partialpressure of oxygen in the gas phase. This fact,known as Henry's law, may be written as

C* = HPo2 (1)

where H' is a Henry's law constant based on

molar concentration,' and the partial pressure isexpressed in atmospheres. The asterisk on Cdenotes concentration in the liquid at equilibrium.Henry's law predicts that in an atmosphere ofpure oxygen, water will dissolve about five timesas much oxygen as in air, where the partialpressure is only 0.21 atmospheres.

Umbreit, Burnis, and Stauffer (9) present dataon the effect of dissolved salts on oxygen solu-bility. These data and others in the literature are

often expressed in terms of a Bunsen coefficient, a.

The Bunsen coefficient should be multipliedby 1,000/22.4 to get H', which turs out to bemore convenient in aeration studies. For nutrient

1 Strictly stated the solubility should be ex-

pressed as a mole fraction, but for slightly solublegases there is little error in taking molarity as

proportional to the mole fraction. The units forH' as used here are liter-atmospheres/millimole02.

broth saturated with air at 25 C, C* is about0.20 mm per liter, so that H' is close to unity.

Since the respiratory enzymes are imbeddedwithin aqueous protoplasm, microorganisms canutilize only dissolved oxygen, even if grown at anair-water interface. Furthermore, oxygen is soinsoluble that there exists at any time only asmall reservoir of it in solution. Upon thisreservoir the microorganisms are continuouslydrawing, and into the reservoir there must flowa fresh supply of oxygen to balance the demand.Because the reservoir has such low capacity, andbecause the oxygen demand of microbial tissueis so high, the rate of supply must at least equalthe rate of demand in every portion of the culturefluid. Otherwise, there will be local or temporarydepletion which damages the respiring cells.Such damage was dramatically shown byHromatka, Ebner and Csoklich (10), who foundthat interruption of the air flow to Acetobacter for15 seconds caused death and disrupted metabo-lism.

Another consequence of low solubility is thelimit it imposes on the rate of oxygen supply tothe culture fluid. To see this restriction moreclearly let us revert again to the analogy of areservoir. Imagine that the supply comes from anocean of oxygen held at the same level as the topof the reservoir, and that transfer is accom-plished by some sort of siphon arrangement.The rate of inflow will then depend on the relativedepletion of the reservoir. Because the latter isso shallow (low solubility), no large driving forcecan ever develop, and even the maximum supplyrate is rather low.These considerations may seem very ele-

mentary; nevertheless they point up some com-mon misstatements of fact. One of these is thatthe culture fluid must be kept saturated with airat all times. Strictly speaking such a conditionis impossible with respiring cultures. Nor canoxygen be supplied at a rate faster than it isbeing consumed, for as the reservoir becomes fullthe rate of supply falls off to zero.

2. Oxygen demand. Happily for microbiologists,there is no need to keep cultures saturated withair. Cell respiration proceeds at a rate which isindependent of the dissolved oxygen concentra-tion so long as the latter remains above a criticalvalue. For unicellular organisms at least, C0rit isextremely low. Typical values are given in table 1.Below the critical oxygen level, respiration rate

25519541

26R. K. FINN

TABLE 1Typical values of Cg," in the presence of substrate

Temper- Equiva-Organism or Tissue ature Conit mm/liter lent s, Refer-

c Tension, ence

Luminous bac- 24 ca 0.010 ca 7.5 11teria

Azotobacter vine- 30 0.018-0.049 15-40 12landii

Escherichia coli 37.8 0.0082 7.5 1315.5 0.0031 1.9 13

Yeast 34.8 0.0046 4.0 1420.0 0.0037 2.5 14

Penicillium chry- 24 ca 0.022 ca 16 15sogenum

Kidney slices 37 ca 0.85 ca 760 16

falls off in hyperbolic manner. In a series ofbeautifully designed experiments with yeast cells,Winsler (14) demonstrated that at low oxygentension respiration rate is limited by unsaturationof the enzyme surfaces rather than by slow diffu-sion of oxygen into the protoplasm. He made useof the fact that carbon monoxide acts as a com-

petitive inhibitor, displacing oxygen from thecytochrome oxidase of yeast. With CO-02mixtures, a falling respiration rate was observedat oxygen tensions so high that diffusion of 02could not possibly have been rate limiting.Nevertheless such C-02 rate curves could besuperimposed upon the rate curve taken at low02 concentration with no CO if correction wasmade for competitive effects. Thus the under-lying mechanism for the decrease in respirationrate at low oxygen concentration was proved to beenzyme unsaturation. A similar mechanism

probably occurs in all unicellular microorganismsalthough a recent report of Longmuir (16a)reopens the whole question at least as regards thebacteria. Longuir, apparently unaware of the

pioneer work of Winzler, did not use the COtechnique. Rather he observed essentially thatC<it varied in regular fashion with the size of theorganism, larger bacteria exhibiting a highercritical oxygen level. Although these facts providecircumstantial evidence for diffusion-controlleduptake at low oxygen tension, the possibilityremains that all trends arose from differentoxygen affinities in the cytochrome systemstested. As pointed out by Smith (16b) the varia-tions in bacterial cytochromes are complex.

Diffusion of oxygen is more likely to becomerate lmiting in multicellular organisms or clumpsof cell tissue. Such possibilities are discussed byBerry (17) and by Stevenson and Smith (16)among others.Above the critical oxygen concentration where

neither diffusion nor unsaturation controls, it ispresumed that the rate at which reduced sub-strate can be supplied sets the pace of respiration.The respiratory "rebound" which occurs when airis readmitted to cells held anaerobic for a timeprovides evidence for this explanation (18).Alternatively, the quantity of oxygen trans-ferring enzyme may be rate limiting. These andother aspects of oxygen uptake by cells and tissuesare fully treated in reviews by Goddard (19),Tang (20, 21), and Kempner (22).

Surprisingly little is known about the peakoxygen demand of microbial cultures which areactively growing in a rich medium. While meas-urements of Qo, abound,2 these usually reflectthe behavior of cells under artificial conditionswhere there is no growth and where simplesubstrates are present in low concentration.Therefore, they cannot serve as a reliable indexof aeration requirements (23). Perhaps the mostcomplete study of oxygen uptake is that byClifton (24) who worked with enterobacteria.He showed that the uptake per cell is highest invery young cultures, and falls off as the cells age.A young culture, however has such a low cellconcentration that total demand is slight. Thepeak demand of a culture is reached duringthe phase of declining growth rate when theproduct of cell concentration and Qo2 is highest.In general one may write

Rate of demand = CeQo2 (2)

where C, is the cell concentration, and Qo, isthe specific respiration rate on a molar basis(Qos = Qo2/22.4). Some typical demand ratesare collected in table 2. These should not beconsidered the mmum possible rates since allvalues are strongly dependent on cultural condi-tions as well as on the particular strain of or-ganism used.Among the environmental factors that can af-

fect the total demand rates are:

2 Qo, is the commonly used quotient for oxygenuptake, defined as microliters 0s taken up permg dry weight of tissue per hour.

256 [VoL. 18


1. Concentration of sugar or other nutrient(affects C.).

2. Accumulation of toxic endproducts or lossof volatile intermediates (affects Ce).

3. Amount and nature of nitrogen sources,mineral salts, and accessory growth factors(affect primarily C. but also Qo,).

4. The supply of oxygen itself (affects pri-marily Cc, but also Qoa,)

The interplay of these factors is best illustratedin the work of those who have tried to preventany one condition from limiting the maximum

population (33, 49, 94a). For yeast, Maxon andJohnson (49, table 2) demonstrated that with a

poor medium (1% glucose) and inadequate aera-

tion the oxygen demand ranged from 15.0 to18.5 mM/(liter)(hr), whereas with a rich medium(10% glucose) and high aeration rates the de-mand rose to 296-342. The change to a superiorenvironment brought about a 10-fold increase incell concentration along with a doubling of spe-cific respiratory activity. Hixson and Gaden (26)reported a peak oxygen demand of only 10-15 forcultures of Saccharomyces cerevuiae. Aeration wasprobably adequate in their experiments, but sugarconcentrations were low and there may have beennutritional deficiencies because the Q02 was only2.5 as compared to an average of 7.7 for the cellsgrown by Maxon and Johnson. Differences in thestrains of yeast may also account for the loweroxygen demands observed by Hixson and Gaden.

3. Measuring oxygen demand. The net rate ofoxygen uptake by a cell suspension may belimited either by diffusion into the liquid or bythe demand of the organisms. When measuring

Qo2 the rate of supply must be eliminate as acontrolling factor, and for this reason Warburgtype respirometers are shaken rapidly so as toprovide a large gas-liquid interface. Umbreit,Burris, and Stauffer (9) have reviewed the effectof shaking. They note for example that one

hundred 2 cm strokes per minute are necessary ifthe respiration rate is as high as 300 microliters ofoxygen per hour.Another method for measuring oxygen demand

is variously described as polarographic, volta-mmetric or amperometric. It makes use of a

dropping-mercury electrode to measure directlythe concentration of dissolved oxygen in a cellsuspension. No assumption of "equilibration"with the gas is necessary. In fact, uptake dataare taken by cutting off the air supply to a cell

TABLE 2Peak oxygen demands of active cultures-

Estimations from published data,

TotalType of Culture Demand, Reference

(liter)(hr)

Activated sludge (domesticsewage) ................... 1-2 25

Escherichia coli, Aerobacteraerogenes.................. 5-8 24

Yeast.................... 10-15 14,26340 49

Streptomyces griseus (strep-tomycin) .................... 15 27,28

Ustilago zeae (ustilagic acid) 16 29PeniciUium chrysogenum

(penicillin).2030 15,30,31Aspergillus niger (citric

acid) .................... 28 29Aspergillus niger (a-amylase) 56 29Acetobacter sp............... 90 32Azotobacter vinelandii. 260 33

All the values of "oxygen uptake" reportedwere critically examined to make sure that theyrepresented the rate of oxygen demand and notmerely the rate of oxygen supply to a particularpiece of test equipment.

b A prolongation of exponential growth usually,but not always, brings about an increase in thepeak demand on a "per liter" basis, and some ofthe low values reported here undoubtedly reflectexperimental conditions that led to a low yield ofcells. For azotobacter and yeast (49),however, richnutrient solutions were used in an effort to getmaximum cell crops, and the oxygen demandswere correspondingly high. In fact, the data onyeast were obtained during a continuous fermenta-tion which provided somewhat higher cell popula-tions than would ordinarily be obtained in batchculture (49).

suspension and noting the course of depletion inthe oxygen reservoir. The rate of consuimption canusually be determined in 5 minutes or less, andtherefore the method is especially suited for usewith actively growing cultures.

Polarographic determinations depend uponthe fact that at an applied voltage of about 0.6the flow of a diffusion current to freshly formedmercury surfaces is proportional to the con-centration of dissolved oxygen. The mercuryelectrode is immersed in the test suspension,which in turn is connected through a salt bridge

2571954]

R. K. FINN

to a calomel half-cell. Galvanometer readings of aslide-wire circuit can be calibrated as a linearfunction of the oxygen concentration. Polarog-raphy was adapted for use in biology by Baum-berger (34), and its principles have been de-scribed briefly by Petering and Daniels (35)and by Umbreit, Burris, and Stauffer (9).Skerman and Millis (36) present a more completeand critical discussion, which should be consultedby anyone intending to use the method.

Instead of falling mercury droplets, a platinummicroelectrode may be used for voltammetricmeasurements provided the pH is above 5.0; insolutions which are more acid, hydrogen ionsdischarge onto the platinum. Polarization effectsmust be avoided, and therefore solid electrodesare usually rotated. A clever alternative hasbeen devised by Olson, Brackett, and Crickard(37), however, who impressed a square-wavepotential on the platinum electrode and thenarranged to take galvanometer readings onlyduring each half-cycle, thereby simulating theeffect of a mercury droplet. If such an instrumentcould be made more rugged and stable, it wouldfind application in industry for continuouslymonitoring dissolved oxygen content.

4. Transport of oxygen to the enzyme. In itspathway from the gas phase to an enzyme surface,oxygen encounters various resistances in series,the principal ones consisting of more or lessstagnant films. Through these the transport ismainly by diffusion. Consider first the supply-side resistances i.e., those which slow downthe rate at which oxygen can enter solution orat which it can "flow into the reservoir". Thereare two films, one between the bulk of the gasand the gas-liquid interface, and the otherextending from the interface to the bulk of theliquid. Such films may be anywhere from micronsto millimeters thick, depending upon the degreeof turbulence and the physical properties of thefluids. At the interface itself one can also postulatea barrier since only those molecules which possesufficiently high energy can penetrate into theliquid phase. The remainder suffer reflection backinto the gas phase (38).

Concentrations in the bulk of the gas phase andin the bulk of the liquid phase are assumed to beuniform. This is simply another way of statingthat there is negligible resistance in the bulkphases. Of course in stagnant pools of liquid or

gas or in agar medium, one cannot make such anassumption. However, even mild mechanicalagitation provides rapid mixing of dissolvedsolutes (39), and the stirring provided by risingair bubbles is usually sufficient to dispel allgradients, even those within the bubbles (26, 40).On the demand side of the oxygen reservoir,

the resistances are: (a) the liquid film aroundindividual cells or cell clumps; and (b) intra-cellular and intraclump resistances. Insofar asthese are significant, the measured values ofQo, will misrepresent the enzymatic behavior ofcells. Discussion will be deferred until later inthis review because our major concern is withsupply-side resistances, over which the investi-gator has more control.The foregoing picture of oxygen transfer

represents a special case of gas absorption, whichis one of the so-called unit operations studiedintensively by chemical engineers (41). Some ofthe first applications to biology were made byRoughton (42, 43) whose special concem was thegaseous exchange of red blood cells in aqueoussuspension. More recently Bartholomew et al.(27), Hixson and Gaden (26), and Wise (44) haveapplied the concepts to microbial respiration.

II. SUPPLY-SIDE RESISTANCES

1. The absorption equation. It has already beenstated that the rate of dissolution of oxygen isproportional to the depletion of dissolved oxygenin the liquid. The rate is also proportional to theinterfacial area, a, and therefore one may writefor a unit volume of culture fluid,

Rate of absorption = KLa (C* - CL) (3)

where CL is the actual concentration of oxygenin the liquid. The proportionality constant, KL,may be looked upon as an over-all conductance.Its reciprocal, 1/KL, an over-all resistance, isequal to the sum of the separate resistancesresiding in the gas film, the interface, and theliquid film. When these resistances are large, KLis small and vice versa.

Neither KL nor a can be evaluated directly asa rule, but the product KLa can be found in-directly by measuring CL (voltammetrically), C*(by Henry's law), and the rate of absorption.Since, in a steady state, the rate of absorptionmust exactly equal the rate of demand, the lefthand member of the above equation is given by

258 [VOL. 18


COQO2 from Equation 2. An explicit equation forKLa in terms of known or measurable quantities is

C0QKa=(0C -CL)(4

where C,, = cell concentration, mg/ml or g/literQo'2 = specific rate of oxygen uptake,

AM/(hr) (mg dry wt) or mm/(hr)(gm dry wt)

C* = equilibrium concentration of dis-solved oxygen, pM/ml or mm/liter ;-

CL = actual concentration of dissolvedoxygen, mM/ml or mm/liter

KLa = absorption rate, mm/(hr)(liter)(unitconcentration difference), or 1/hr.

Over short time intervals C., Qo0, and CL aresubstantially constant. Even when these quan-tities vary during fermentation, however,KLa remains nearly fixed. It is unlikely thatgases leaving the fermentation unit are appre-ciably depleted in oxygen, but if so an averageC* should be used (27).The product KLa provides an over-all measure

of the gas absorbing capacity of any fermenter.It is in fact the only satisfactory way to char-acterize the performance of laboratory or in-dustrial devices. Olson and Johnson (45) wereperhaps the first to recognize this when theyused KLa values to describe the degree of aerationin shake flasks and in a small stirred fermenter.High values of KLa denote an efficient oxygenat-ing device whereas low values, an inefficient one.

2. Units of KLa. Before considering thefactors which affect KLa it is worthwhile toreview the units of measure, because variousinvestigators have not been consistent in thisregard.

Cooper, Fernstrom, and Miller (46) in afamous study of oxygen absorption in stirredtanks reported their results in terms of a Kvwhich was based on English units and a partialpressure difference rather than the equivalentconcentration difference. Stir other systems wereused by Hixson and Gaden, Bartholomew et al.,and Wise. A comparxison of these is made intable 3. Not included in table 3 are Streeter's"reaeration coefficient", K2 (47), and Adeney's"escape coefficient", f (48) which appear oc-casionally in the literature on sewage treatment.The choice of nomenclature for this reviewresults from the author's conviction that when-

TABLE 3Comparison of units for absorption capacity

Factor forSymbol Units Investigator Conversion

to KLaa

KY lb moles/(cu Cooper, Fern- 1.68 X 10'ft) (hr) strom, Miller(atm) (46)

kd 1/hr Hixson and 1Gaden (26)

kd g moles/(ml) Bartholomew 1.05 X 106(hr) (atm) et al. (27)

s'L 1/min Wise (44) 60KLa 1/hr This review 1

a At C* = 0.2 mm/liter - 6.4 ppm).

ever possible coinage of new symbols should beavoided; the term KLa is accepted in the en-gineering literature (41).

Another source of confusion in the agitation-aeration literature arises in the following way.Instead of using the absorption rate constantdirectly, a number of workers (29, 31, 45, 49)have chosen to multiply it by C*. This is quiteall right; the units then become mM/(liter) (hr)or some equivalent set which signifies the max-imum rate of absorption. But a recent article byKarow, Bartholomew, and Sfat (50) proposesthat the kd factor of Bartholomew et al (seetable 3) be multiplied by P, the total pressure.This is inconsistent with the prior practice andtends to confuse the casual reader, who is leftwith a feeling that the subject matter is in-herently difficult.

3. Meds for measuring KLa. There are threemethods generally used to measure KLa. Twoof these involve the polarograph and are describedby Wise (44) as the "sampling method" and the"gassing-out method".In the sampling method, a value of CL is

obtained by quickly placing a sample from theactual fermentation in a polarographic cell andthen noting the concentration of dissolvedoxygen at various times. A graph of the results isextrapolated to zero time, i.e., the time ofsampling. Knowing CL and Qo, (from the slopeof the above-mentioned plot), Equation 3 isused to find KLa. In a modified procedure,Hixson and Gaden (26) sampled with a nitrogen-flushed hypodermic syringe which also containeda small amount of phenol to "kill" the respi-

2591954]

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R. K. FINN

ration. Initial readings on the polarograph thengave CL directly.Wise (44) considers that the gassing-out

technique is more accurate than the one justdescribed, though not so convenient, because thefermentation vessel must be held out of produc-tion during a test. Either broth or a dilute saltsolution is placed in the fermentation vessel, andafter a preliminary gassing-out with nitrogen,aeration is begun at constant flow rate. Atconvenient intervals thereafter, the value ofCL is measured voltammetrically by a samplingtechnique. The time rate of increase in theconcentration of dissolved oxygen may bewritten dCL/dG, and therefore equation 3 be-comes

dCL - La(C* -CD)do

This means that the unsteady-state absorption ofoxygen follows a logarithmic course, for uponintegration equation 5 yieldsln (C* - CL) = -KLaO + constant of

integration (6)

To evaluate KLa it is convenient to plot log(C* - CL) against the time, 0, whence

KLa = -2.303 (slope of straight line) (7)

In using this gassing-out method Bartholomewet al. (27) located the dropping-mercury electrodewithin the fermentation vessel, thereby increas-ing the speed of manipulation.A third method of measuring KLa is indirect.

It involves the carrying out of a sulfite oxidationin the fermentation apparatus. In the presence ofcopper or cobalt sts, which act as catalysts, thereaction with oxygen or air proceeds rapidly andirreversibly to completion in the liquid phase.The reaction rate is not only much more rapidthan the absorption rate, but it is independent ofsulfite ion concentration at molarities above0.015. These features attracted Cooper, Fern-strom, and Miller (46) to the use of sulfiteoxidation as a test system for evaluating gas-liquid contactors. To find KLa it is necessaryonly to titrate the sulfite solution with iodine atintervals during aeration. The rate of absorptionfound in this manner iS KLaC* since CL, theconcentration of dissolved oxygen, is zero at alltimes.

Unfortunately, the absorption of air by

sulfite solutions is not so simple as it seems. Infact, considerable confusion has arisen over theinterpretation of results from such tests, andmany of the issues are still unsettled. Miyamoto(38), one of the early investigators, becameconvinced that the absorption rate into sulfitewas limited primarily by resistance at the inter-face, a view that has recently been accorded freshattention (51). On the other hand, some workers(44, 46) have referred to the liquid film as thesite of rate limiting diffusion. Wise (52), forexample, has accounted for differences betweenthe polarographic and sulfite methods of measur-ing KLa by assung finite reaction rates in astagnant liquid film. Just recently Maxon andJohnson (49) made the unusual claim thatabsorption in sulfite was gas-film controlled.They offered no supporting arguments other thanthat the chemical reaction was extremely rapidand of zero order. The complexity of the chem-istry involved becomes evident from the fact thatin a review by Abel (53) over 100 references arecited.To use the sulfite method in the presence of

broth or cells, Bartholomew et al. (27) found itnecessary to measure the back-pressure of oxygenpolarographically because anticatalysts werepresent. Apparently Shu (29) did not make thiscorrection, but his results were consistent none-theless. The sulfite method of finding KLa orKLaC* is certainly a convenient one since itinvolves no special instruments. Results must beinterpreted with caution, however, if the vesselunder test is to be used for fermentation insteadof for sulfite oxidation (52).

4. Individual resistanes and KLa. The rate-controlling step in oxygen absorption cannot bethe gas film. This was proved by Bartholomewet al. (27) who measured temperature effects ofabsorption by sterile fermentation broth. Notonly did KLa increase as the temperature wasraised from 27 C to 32 C, but the thermalincrement or activation energy for the over-allprocess was 4,200 calories per mole, a valuecharacteristic of diffusional processes throughwater. If diffusion through a gas film had beencontrolling, KLa would vary as the square root ofthe absolute temperature, and this was notobserved.For a slightly soluble gas like oxygen the

concentration driving force across the gas film isso much greater than the driving force across the

260 [voL. 18


liquid film that the latter is almost certain tooffer more resistance. Also, since the diffusioncoefficient of oxygen through water is les thanthrough air by a factor of about 10,000, air filmswould have to be enormously thicker than liquidfilms in order to become controlling. Even thislast possibility is made unlikely by the relativelylow viscosity of air compared to water (roughly1:50).Maxon and Johnson (49) have suggested that

while a liquid film may be rate limiting in theabsorption of oxygen by sterile broth, a gas-filmresistance sets the rate for actively respiringyeast cultures. They noted a correspondencebetween the oxygen uptake by yeast and bysulfite solutions. However, Miyamoto and hisco-workers (54) have shown rather conclusivelythat absorption into sulfite cannot be gas-filmcontrolled. The Japanese investigators used pureoxygen so as to eliminate any gas film, and theyalso observed temperature coefficients whichwere much too high to fit a gas-film hypothesis.Perhaps for yeast as for sulfite solutions, a majorresistance is at the interface.

It is of more than theoretical interest to ex-amine the individual resistances. If a gas film doesfix the pace, then our present fermentation

80

7C

60 .

* 5C

T 40:,dC-il. I

o _r

20*

10

I I I I I

I I I I I0 2 4 6 8 10 12 14

MYCELIAL CONCENTRATION- G./L.

Figure 1. Effect of mycelial concentration ofPenicillium chrysogenum on the absorption rateof a typical 5 liter stirred fermenter. (Replottedfrom a curve in Deindoerfer's unpublished thesis.)

equipment should be redesigned so as to createmore turbulence in the gas phase and thereby toreduce film thickness. If, on the other hand, amajor resistance is at the interface, stirring willbe of little account except as it creates moreinterfacial area.The factors which affect KLa are listed by

Hixson and Gaden (26) as the area of gas-liquidcontact, the time of contact, and the agitationintensity. These in turn depend upon the designand operation of the equipment and upon suchphysical properties of the culture fluid as viscosityand surface tension. Hixson and Gaden observedthat after six hours the absorption rate constantfor a small yeast propagator almost doubles itsinitial value. This variation in KLa they ascribedto the noticeable physical changes in the mediumwhich occurred during the course of growth. Insome recent work from Gaden's laboratory thesechanges are further elucidated (unpublishedresults of F. Deindoerfer). For example, figure 1shows how rapidly KLa decreases as the con-centration of mold mycelium increases. Theeffect is undoubtedly caused by changes in theviscosity of the fermentation mash.

M. METHODS FOR INREING TH TOTAL RATEOF GAS ABSORPTION

The rate at which oxygen goes into solutioncan be increased either by improving K1La or byraising the partial presure of oxygen in the gasso as to create a larger driving force, C* - CL.These methods will now be discussed. The operat-ing and design variables which affect KLa areagitation, type of sparger, and gas velocity.

1. Agation. A general review of the literatureon agitation up to 1944 was given by Hixson(55) as part of an engineering symposium on thesubject. More recent developments have beencovered in a series of annual reviews which haveappeared since 1946 in the January issues ofIndutrial and Engineering Chemistry. Of greaterutility perhaps to the microbiologist who wishesa quick survey, are articles by Rushton (56) andby Mack and Uhl (57). Agitation acts to improveKLa in three ways: First, by chopping up the airstream into small bubbles, agitation increases theinterfacial area, a. Second, by circulating theliquid in swift eddies, it delays the normal escapeof bubbles. Lengthening the time of contact inthis manner has the effect of increasing the inter-facial area (58). Third, agitation creates turbulent

1954] 261

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R. K. FINN

shear which reduces the thickness of the liquidfilm. Insofar as diffusion through the liquidcontrols, such shear increases KL.Because these three effects cannot be separated,

we resort to empirical correlations between thedegree of agitation and the absorption rateconstant. Cooper, Fernstrom, and Miller (46)found that in a well designed system KLa isalmost directly proportional to the power inputper unit volume

KLa c (power/volume)095 (8)

This relationship, which is valid for both labora-tory and plant-scale equipment, was confirmedby Karow, Bartholomew, and Sfat (50).Power input per unit volume is a reliable index

of the degree of agitation only if there is fullydeveloped turbulence within the fermenter andno loss of power due to swirling or vortexing ofthe liquid. The criterion of turbulence is adimensionless quantity, called the Reynoldsnumber, which is defined as

NRe -L'Np (9)

where L is impeller diameter, N is revolutions ofimpeller per unit time, p is fluid density, and M,is fluid viscosity. If the Reynolds number isabove 106, the following general equation can beused to relate the horse-power to operatingvariables

Power/volume = cN' L6P (10)

The constant c depends upon the particularimpeller design. Equation 10 holds at all valuesof NRe in the range of fully developed turbulence.Note that under these conditions the power inputis independent of viscosity. Power input measure-ments are difficult to make, especially on largeequipment, but the relative effects on KLa ofchanging the rpm and impeller diameter can bepredicted from equations 8 and 10.

All fermentation vessels, even the simplestlaboratory ones, should be adequately baffled.Unless this is done it is meaningle to cite astirrer speed since the relative velocity betweenliquid and impeller changes with the extent of theswirl. At a given speed it has been found thatadding, baffles causes a rapid increase in powerconsumption up to a point, but the addition ofstill more baffles does not increase the power

consumption very much. Several "fully baffled"arrangements are described by Mack and Kroll(59); a standard one consists of four baffles eachY0 to K2 of the tank diameter, and extending thefull depth of the tank.The following broad statements concerning the

design of stirred tanks are intended primarily asa guide for microbiologists who desire to constructtheir own small fermenters. Turbines or paddleshaving a radial flow pattern are generally pre-ferred to propellers, which produce axial flow.The impeller is located from a half to one di-ameter above the bottom of the fermenter, andits diameter is about one-third of the tankdiameter although for viscous mashes theimpeller diameter is often increased beyond theone-third ratio. Air is admitted through asparge ring having a diameter about three-fourthsthat of the impeller; at air rates less than 150ft/hr, however, a single center inlet directlybeneath the impeller gives equally good results.Multiple impellers are separated on the shaft bya distance of one impeller diameter, and theheight of liquid is approximately one tank di-ameter in the "standard" arrngement. Figure 2illustrates a typical stirred tank with "closed"turbines, i.e., with turbines having a disc orbaffle transverse to the plane of the blades.

In scale-up from laboratory to factory theusual procedure (46, 50) is to insure geometricsimilarity of the fermenters and equal powerinput per unit volume. Not all dynamic andgeometric factors can be kept the same, however,(e.g., tip velocity of the impeller is not heldconstant in the above method), and large ex-trapolations of the data are unwise. Enoughpower must be available to run the impellers inungassed culture fluid, but during the spargingmuch less than rated power is drawn owing to thelow density of the bubbly mixture (46, 48).At high gas rates, power input may be only one-fourth of the ungassed value.When agitation is defined only in terms of

power input per unit volume, no account is takenof how the power is distributed within thefermenter. The inadequacy can be illustrated bycomparing a small high-speed stirrer with alarge, slow-moving one operating at the samepower. The former may effectively disperse theair stream into fine bubbles, but it fails to cir-culate these through the mash. A slow mixer, onthe other hand, is unable to shear off the air

262 [VOL.. 18


Dt

Figure 2. Typical dimensions of a stirred fer-menter: Z/Dt = 1.0; D/Dt = 0.34; A/D = 0.8 to1.0; B/D = 1.0 to 1.2; Wb/D = 0.08 to 0.10.

bubbles even though it provides good pumping

action. Just what compromise to arrive at inthe optimum design of tank and impellers wouldhave to be worked out separately for each typeof fermentation, and no rational approach is yetavailable. Added refinements in design will

depend ultimately upon a better understanding oftransfer resistances and the mechanics of bubbles.

2. Gas velocity. For stirred tanks it has beenfound that KLa varies as Vy.67 (46), where V. isthe superficial gas velocity (e.g., cm/sec or ft/hrbased on the total cross-sectional area of thevessel). Small laboratory fermenters may exhibit

a slightly different characteristic in which theexponent of V8 is 0.4 to 0.5 (46, 49), but other-wise the relationship appears to be quite general.For an unstirred propagator Hixson and Gaden(26) found the exponent to vary from 0.33 to0.82 depending on the fineness of air dispension,and elsewhere in the literature a value of 0.74is reported for apparatus which is not stirred(60). Mechanical effects of the air bubbles causethese variations, more turbulence being createdby larger bubbles as V8 is increased.At high air rates, flooding or "loading" of the

impeller occurs. Cooper, Fermstrom, and Miller(46) reported that above a superficial velocity ofabout 400 feet per hour their vaned-disc impellerseemed to be unable to disperse the air. By-passing of the impeller is accompanied by escapeof the gas in large bubbles around the shaft,and above the loading velocity KLa does notincrease much with further increases in gas rate.Open-type turbines or paddles load at low airvelocities because the gas can more readily riseup through the slow-moving central part of theturbine. For example, Cooper, Fernstrom, andMiller observed loading of a paddle stirrer at avelocity of only 70 feet per hour.

Lee (61) has listed several methods whichhave been used for reporting the degree ofaeration, but it should be emphasized that ofthese, only the linear velocity, V., is appropriate.The commonly used "volumes of air per volumeof medium per unit time" is wholly unrelated togas holdup or KLa (44); with such a measure ofaeration, experimental results cannot be repro-duced by other investigators who employ "theame gas rate".3. Type of sparger. Comminution of air may be

achieved by methods other than high-speedagitation, and as pointed out by Hixson andGaden (26), unstirred vessels may offer economyof operation if the breakup of cell clumps is notdemanded. A review of fine-bubble aeration by deBeeze and Liebmann (62) describes the manyingenious devices which have been used for thispurpose.The effect of such factors as orifice diameter,

gas velocity, and surface tension on bubble sizeand bubble velocity is under study both in thiscountry (63, 64) and in England (65, 66). Mostof the work concerns the mechanics of a singlestream of gas bubbles and is not immediatelyuseful for practical aeration problems. For

26319541

R. K. FINN

bubbles from a single orifice, bubble volumeis directly proportional to orifice diameter andsurface tension, and it is inversely proportional tothe density of the liquid (67). Neither gaspressure, temperature, nor liquid viscosity isreported to have much effect on bubble size, butunfortunately no work has been done withsystems exhibiting non-Newtonian viscosity(plastic flow) such as occurs in mold cultures(50).Mass transfer from a stream of single bubbles

was reported by Coppock and Meiklejohn (67)in terms of KL values since the interfacial areawas accurately known. The absorption coefficientwas found to vary directly with bubble velocity,and it was immaterial whether oxygen or air wasused in the gas phase. Values of KL ranged from100 to 200 cm/hr for absorption into deaeratedwater. These values were some five times smallerthan those estimated from data by Pattle (68).There is general agreement that coalescence ofbubbles occurs mostly by head-on rather thansideways colion, and that a bubble may bepushed into the slipstream of another bubbleimmediately ahead of it, thereby causing suchcontact. Small amounts of the same materialswhich promote foaminess inhibit coalescence.

Observations on swarms of bubbles (69) showthat the gas holdup increases as expected withincreasing gas rate, but that in unstirred vesselsthe initial linear relation is interrupted at somecritical rate which corresponds roughly to theloading point for stirred vessels. Bubble size isalways larger than the pore size by a factor of 10to 100 for porous spargers. Surface-active agentswhich are present in most complex mediareduce the bubble size, and one might supposethat the resulting increase in interfacial areawould cause higher values for KLa. On the otherhand, tiny bubbles which are unable to createmuch turbulence in their passage through thebroth would be surrounded by rather thickliquid films, and these in turn would adverselyaffect KL. It has also been suggested (27, 70)that the presence of large organic molecules atthe gas-liquid interface interferes with the pasageof oxygen gas, but others (51, 54) discount suchan effect. One can state only that the influenceof surface-active agents on mass transfer is notyet clear. Bartholomew et al. (27) found thatsurface-active materials tended to lower theabsorption rate of water, while Hixson and

Gaden (26) observed an opposite effect onKLa during the growth of yeast. The performanceof porous ceramic and porous carbon spargershas been described in general terms by Ungeret al. (71), and more quantitatively by Anderson(72) and King (73) who used sulfite absorptiontests. Such spargers are used for aerating sewageand for yeast production despite their tendencyto clog and become less efficient during longperiods of service.

Air is dispersed in another method by itsintroduction at acoustical velocity as proposedby Achorn and Schwab (74). These investi-gators found that with an orifice 0.00312 inchesin diameter in an air tube 0.156 inches in di-ameter, many bubbles were less than 10 micronsin diameter provided the pressure drop across theorifice was 13 pounds per square inch. In theirlaboratory apparatus they observed more violentagitation than was obtainable with porous media.

Perforated pipes have been widely used eitheralone or in conjunction with mechanical stirring.The pipe spargers are usually in the form of ringsor crosses, with drilled holes ranging in size from0.03 to 0.13 inches. Pressure drop along a pipemanifold causes nonuniform emission of air, andideally finer holes should be drilled close to theair source (75, 76). Plugging of some of the holes,which is bound to occur in time, causes unevendistribution of air or perhaps local flooding of animpeller if the tank is stirred. A number offermentation plants now prefer open or slightlyconstricted pipes for introducing the gas, andthey depend upon intense agitation to give smallbubbles and favorable transfer rates (27).

If air is sparged at high velocity through fineorifices, it does mechanical work on the fermenta-tion mash, and power input from this sourceshould be added to that from the agitator itselfwhen scale-up of equipment is being consideredor when equation 8 is used. Bartholomew et al.(27) describe the calculation of work done by theair stream.

4. Increasing the ring force. One obviousmeans of increasing the rate of oxygen supply toa culture medium is to raise the solubility, C*,by increasing the partial pressure of oxygen. Thismay be done by using either oxygen-enriched airor air under pressure. Except for (a) the sweepingeffect of the nitrogen, (b) the concomitantincrease in carbon dioxide solubility as P israised, and (c) a possible failure to supply enough

264 [VOL. 19

AGITATION-AEltATION IN LABORATORY AND INDUSTRY

carbon dioxide along with the pure oxygen, thetwo methods for increasing C* are equivalent.Microorganisms are not injured by pressures upto 5 atmospheres (77) which is about the limit ofpractical operation. Oxygen or air under pressurehas been found especially beneficial in gluconicacid (78) and citric acid (29, 79) fermentationswhich are characterized by unusually highoxygen demand.Harmful effects of high oxygen tension have

been noted many times, and no simple explan-ation will fit all cases; Bean (80) has exhaustivelyreviewed the literature up to 1945. On the onehand, poisoning may be reversible; if so, oxygenand reduced substrate compete for the same siteon the enzyme (81), or else sulfhydryl groups onthe enzyme itself are reversibly oxidized. On theother hand, continued exposure results inpermanent damage to the respiratory enzymes.The cytochromes appear to be rather resistant,(82) and although flavoprotein activity increaseswith oxygen tensions up to 760 mm (83), higherpressures do cause damage (84) perhaps owingto accumulation of peroxide. The ease of poison-ing depends upon the particular organism, andindeed with its environmental and nutritionalstatus (85). Poisoning by oxygen has been notedin the production of yeast (86), acetic acid (32),and penicillin (30).

each cell offers negligible resistance. Furtherproof comes from a calculation such as thefollowing.

Consider a yeast cell 5 microns in diametersuspended in an infinite quantity of stagnantfluid. It has been shown theoretically andexperimentally (41) that under such conditions

kLDe = 2D,r (11)

where kL is the absorption coefficient for a liquidfilm, D. is the diameter of the yeast cell, andD, is the diffusivity of oxygen. Since D, =1.8 X 10- cm:/sec, kL is 0.072 cm/sec. The ratioD,/kL can be considered a "film thickness",which here is equal to the cell radius. If the truerate of* oxygen uptake is about 0.08 g/(hr)(g DW), as found by Hixson and Gaden (26),and if 25 per cent dry weight is assumed, eachyeast cell consumes 4.1 X 10" mm 02/hr.The maxmum concentration difference betweenthe bulk of the fluid and the cell wall is, byanalogy with equation 3,

(CL - OW) _rate of consumption

kL a(12)

where Cw is the concentration of 02 at the cellwall. For a 5 micron yeast cell a is 7.86 X 107cm2, and the maximum concentration differenceis therefore

(CL -W) = 1 0.072 7.86 X 10- 3,600 |

= mm 0 | secaec cell hr ml(hr)(cell) cm cm | sec liter

- 2.0 X 10- mm O/liter.IV. DEMAND-SIDE RESISTANCES

1. Liquid film around cels or clumps. Forsingle cells at least, a liquid film at the cell walloffers no appreciable resistance to the diffusionof oxygen. Occasionally though, microbiologistsraise the question of such a resistance andexpres their concern over it. For example,Marshall et al. (87) state, "The rate of aerationemployed in these studies was sufficiently rapidto maintain high extracellular 0, tension.Limited diffusion of 02 into the cell, however,cannot be excluded." The fact that above acritical oxygen concentration the uptake bymicroorganisms is independent of CL may betaken as evidence that a liquid film surrounding

This difference in concentration is negligiblysmall compared to the level of CL ordinarilymaintained in the liquid (e.g., C* for air is about0.2 mm/liter). The liquid film is of even lessimportance for celLs smaller than yeast becauseCL - Cw varies roughly as D0'.Quite apart from the foregomg, one can

predict that agitation in excess of what is re-quired to suspend the single cells uniformly willnot markedly improve the oxygen tranfer fromliquid to cell wall. The reason is that the thicknessof the liquid film surrounding each cell can bereduced only by increasing the relative velocitybetween the cell and the fluid. Now the cells areso small and their specific gravity is so close to

1954] 265

R. K. FINN

that of the culture medium that they possessinsufficient inertia to attain an appreciablevelocity relative to the medium. In other words,the particles tend to follow the fluid streamlines,even though the latter may turn sharply andwhirl about in swift eddies.3 Despite all theseconsiderations, studies on the liquid filmsaround cells continue to be made, and these havebeen reviewed by Gaden (88). Most investigatorsare probably observing side-effects of agitationwhen they report improved growth rates and thelike. For example, stirring will relieve super-saturation of CO2 in the culture medium.For cell clumps, such as occur in submerged

mold fermentations, the liquid films may assumeimportance. Here, however, relative motionbetween the clump and its surrounding fluid ismore likely. Furthermore, the intraclumpresistance transcends that of the liquid film.

2. Intracelular and intraclump res?itances.The most complete reviews on diffusion throughdeep layers of respiring tisue are those ofGerard (89), Jacobs (90), and Rashevsky (91).Calculations show that clumps of tisue must beless than about 1 mm in diameter if anaerobicconditions at the interior are to be avoided. Thecritical size depends, of course, on the Qo2 ofa particular tissue and on the presence or absenceof an enclosing membrane of low permeability(92).No quantitative information is available on

the degree of agitation which is necessary tobreak down cell clumps although cell physi-ologists have made preliminary investigations onthe effects of shear on tissues of higher plantsand animals (93). Perhaps the most satisfactoryprogress, both in the theory and technique, isbeing made by those who are studying paperpulp suspensions. The work of Mason (94) andhis associates, for example, is especially pertinentfor those who are interested in the filamentousfungi.

V. PRACTICAL APPI.CATIONS

The practical aspects of agitation-aeration arecovered in reviews on fermentation publishedeach year in September in Induial and En-

3 It should be stated of course that each particlerotates at an angular velocity which does increasewith the degree of turbulence and which is in-dependent of the size and specific gravity of theparticle.

gineering Chemistry. No complete survey will beattempted here, especially since the data areoften too fragmentary to be useful.

1. Performance of equipment. For aerobicprocesses carried out in pilot-plant or full-scaleindustrial equipment, power input may varyanywhere from 0.1 to 1.0 horsepower per 100gallons, and air velocities from 50 to 200 feet perhour, depending upon the tendency to clump andto foam as well as upon the oxygen needs of theculture. Some typical values of KLa for shake-flasks and other types of apparatus are collectedin table 4. Smith and Johnson (94a) have re-cently presented a similar tabulation of effectiveaeration rates for the types of equipment used intheir laboratory. They found that KLa values forshake-flasks could be increased fourfold byindenting the sides of the flasks.

It appears that if shake-flask contain only ashallow layer of culture medium, they aresuperior to simple bubbling devices. Stirredfermenters give the best aeration. One cannotrely, however, on the absolute values of KLashown in table 4 because undesignated factorscome into play. For example, if shake-flasksdevelop a head of foam much of their effectivenessis lost (97).Only a small per cent of the oxygen supplied

to a fermenter is actually absorbed. Oxygenefficiency seldom exceeds 2 per cent underordinary operating conditions, and it is oftenbelow 1 per cent. Low efficiency is not so seriousbecause sterile air, while not free, is a relativelycheap raw material. Special devices can some-times accomplish efficiencies of 30 per cent ormore- (68), but such high values are attained atthe expense of a large pressure drop and lowthroughput of air.On the other hand, a high oxygen efficiency

may dictate the choice of a tall fermentationvessel rather than a short one. To illustrate thisdifference, let us suppose that a new fermenter isto be built with double the capacity of a presentone. If the present vessel is of standard dimen-sions, with liquid height equal to the tankdiameter, two possibilities which arise are: (a)the new vessel may be scaled up by a linearfactor of -'2 so as to have twice the volume, or(b) it may be made twice as tall as the presentone without any change in the diameter. For thelatter case, Cooper, Fermstrom, and Miller (46)found that KLa is increased by a factor of about

266 [voL. 18


TABLE 4Typical values of KLaa for various types of apparatus

Type of Fermenter

A. Shake type1. Respirometer vessel, 25 ml con-

taining 3 ml (1 mm liquid depth)2. Erlenmeyer flask 300 ml/one liter

flask3. Erlenmeyer flask 75 ml/250 ml



flaskB. Bubblers-unstirred

1. Model of sewage aerator (porousplate in a tank)

2. Glass column, 5 cm diameter (1 in.coarse sintered disc)

3. 2 liter glass vessel, 6 in. diameterSingle orifice, 0.060 in. diameter

Fritted stainless steel, 2% in. di-ameter, 65 A openings

4. Single orifice (uniform stream ofsingle bubbles, 3 mm diametereach)

C. Bubblers-stirred1. 6 in. diameter vessel, standard

design

2. 6 in. diameter vessel, standarddesign'

3. 6 in. diameter vessel, standarddesign

4. 36 in. diameter vessel, standarddesign(120 gallon working capacity)

5. 15,000 gallon vessel

2.4 cm throw150/min7 cm throw9/min12 in. eccentric220 rpm1X6 in. eccentric210 rpm1 in. eccentric253 rpm

None

None

None

None

None

Single impeller3 in. diameter 500 rpm(0.5 HP/100 gal)Single 4 in. impeller500 rpm750 rpm

1,680 rpmSingle 4 in. impeller740 rpm

Single 10 in. impeller300 rpm

0.2 HP/100 gallon

150

60120601200.065

60

60606065

50

175

ca

420

3251,0002,650420

600

370

95

44

15

29

45

73

44

26

26

67

27

49

15

96

46, 50

^ Values are only approximate since often they were obtained by interpolation from published di-agrams. Most experimenters used sulfite method of evaluation.

b This value seems exceedingly low. The experimental technique may have been subject to largeerrors.

o With mycelium present.d Based on area of sparger. A superficial velocity cannot be calculated. Air rates 3 to 4 times as high

are used in activated sludge tanks.e Depends on the permeability rating of the porous plate. The sulfite method used to find KLa was

not well conducted.f Liquid height only % of vessel diameter. If height of liquid had been equal to diameter of vessel,

KLa would have been only about 60% of values shown.

1954] 267

R. K. FINN

1.4 at a given linear gas velocity. Therefore thetwo schemes compare as follows if superficial gasrate and power input are held constant duringthe scale-up:

Factor of increase usingScheme A Scheme B

KLa.................. 1.0 X 1.4 XTotal power........... 2.0 X 2.0 XVolumetric gas rate..... 1.6 X 1.0 XOxygen efficiency....... 1.26X 2.8 X

Less total air is required if the tank is made taller(scheme B), because the air is being scrubbedmore thoroughly in its pasage through themash. Any improvement in KLa from stillfurther increases in height is not large, and thereare in addition engineering limitations on theuse of very tall tanks. It might be supposed thatthe increase in gas pressure due to hydrostatichead would favor the solution of oxygen, butsuch an effect is almost cancelled by the smallerbubble size (50). In tall tanks where more thanone impeller is necesary, it has been suggtedthat better absorption is possible if each impelleris gased individually (50). More studies areneeded on the effect of impeller position and D/Dtratio before such suggestions can be accepted asfinal.

2. Criteria of 8ufficient aeration. The only wayto be sure that the aeration is sufficient in aparticular setup is to measure the concentrationof dissolved oxygen. If a microbial culture fails torespire more rapidly as CL is increased, then itmay be safely aumed that the critical oxygenconcentration has been exceeded and all is well.

Indirect methods of asessing CL fail to givereliable information. Two examples of this willbe cited. In a pilot-plant study of penicillinfermentation, Stefaniak and his asociates(30) observed that beyond an aeration rate of 1volume per minute per volume of culture, therewas little increase in the rate of respiration, andthey concluded that, "At aeration rates in excesof 1 volume per minute, available air was nolonger the chief factor limiting oxidation rate."Such a conclusion may be correct, but an al-ternative explanation is that air in excess of 1volume per minute was largely wasted. Thelatter possibility is strengthened by noting thatthe impeller was probably loaded at the limitingair rate of 200 liters per minute. Although nodiameter was given for the 100 gallon tank, the

superficial gas velocity must have been about 100feet per hour. This exceeds the loading velocity ofan open type impeller (46), and it is thereforenot surprising that further increases in air ratewere without effect.Another example concerns the use of Warburg

apparatus. It is commonly assumed that if morerapid shaking fails to increase the oxygen uptake,then diffusion into the liquid is no longer ratelimiting. Such an argument presupposes thatKLa increases without limit as the shaking isintensified. Winzler (14), who used both amanometric and a polarographic technique,showed quite clearly that diffusion could berate limiting even though the Warburg cup wasshaken to excess. Wiliams and Wilson (97a)made similar observations in their experimentswith Azotobacter vinelandii.

3. Relation betueen respiration and productformation. Throughout this review respirationrate has been looked upon as a primary measureof the effectiveness of aeration. We must nowexamine how respiratory activity correlates withother properties of microorganisms such as theirability to grow and to manufacture useful orinteresting products.

Empirically there is good correlation. Increasesin KLa give rise to parallel increases in pro-ductivity, at least up to a point beyond whichsome process other than gas absorption becomescontrolling.4 Data on the formation of yeastcelLs (45, 98), bacterial cells (33, 94a), penicillinand streptomycin (27, 44, 50), organic acids(29), and mold amylase (29) all follow such acourse. However, Calam, Driver, and Bowers(31) point out that the relationship is not arigid one. They found, for example, that yields ofpenicillin cannot be predicted from knowledge ofthe respiration rate alone because each particularstrain of mold, each type of fermentation ap-paratus, and each medium have a characteristicinfluence on the correlation. To emphasi theindependence of respiration, growth, and pen-icillin formation, they cite the different temper-ature coefficients which they observed for theserate processes in Peniilium chrywgenum.Thermal increments, ,u, were: for growth ofmycelium, 8,230 g-cal;. for respiration, 17,800

'Alexander and Wilson (33) and Smith andJohnson (94a) have emphasized that when aerationis adequate, the normal levels of sugar and min-erals may be insufficient for optimum growth.

268 [voL. 18


g-cal; for penicillin formation, 26,800 g-cal.Peculiar temperature breaks were also observed.

Other investigators have made simil ob-servations. In their studies on ustilagic acidformation, Sallans, Roxburgh, and Spencer(96) found that to achieve the same productivityin shake-flasks withKLa = 90 (29) and in stirredfermenters, the latter had to be operated atKLa - 600. The values given for KLa in table 4must therefore be interpreted cautiously whenapplied to product formation rather than tooxygen uptake.Even with a given organism, apparatus, and

culture medium a lack of correspondence existsbetween respiration and the formation of prod-ucts. The point at which yield or rate of prod-uction reaches a maximum may not be alwaysthe same as C,rit for oxygen uptake. In shake-flask experiments, Shu (29) found that withcitric acid (A&pergillu niger) and ustilagic acid(Uilago zeae) maximum production did indeedcoincide with maxmum respiration. But the rateof mold amylase formation reached its peakwhen the oxygen needs of the organism (A.niger) were still unsatisfied. Presumably thesame would be true for enzymes like nitratase(99) and hydrogenase (100) which depend uponlow oxygen tension for their formation andfunction. Still a third posibility is that aerationwould have to be far in excess of that requiredfor full respiration. Such a situation might ariseif the formation of product demanded a highoxidation-reduction potential. One rather clear-cut example is available from the work ofRolinson and Lumb (101) who, working withspore inoculated cultures of PeniciUium chryso-genum, found that lard oil was attacked inpreference to lactose provided very high aerationrates were used.

In their studies on facultative anaerobesDagley, Dawes, and Morrison (e.g., 102) em-phasize that oxygen acts in complex ways tocontrol the utilization of substrates. Thus, aerobicrather than anaerobic deaminases are formed athigh oxygen tension, and the type of deaminein turn may alter the course of growth andproduct formation. Gale (103) has reviewed someof the earlier work on such directive effects ofoxygen.Many fermentation proceses of industrial

interest are characterized by a long delay betweenthe growth and respiration phase and the

product forming phase. During the latter, oxygensupply is seldom limiting because the rate ofrespiration is relatively low. Rolinson (15)observed that failure to meet the peak oxygendemand of P. chrysogenum during its growthphase caused permanent damage which wasmanifested later when penicillin was beingsynthesized by the mold. Upon maturity,oxygen starved cells had a lower level of respi-ration and lower productivity. There appears tobe adaptive development of respiratory enzymessimilar to that reported in facultative micro-orgaisms. Moss (104) who presents data on theadaptive cytochrome system of Escherichia colisummarizes the work which has been done in thisfield which continues to be actively investigated(104a).

4. Overagitation and overaeration. From time totime there are reports that too much agitation(105, 106, 107) or too much aeration (45, 108) hasinterfered with the yield of a particular fermen-tation product. A direct relationship, however,between cause and effect is not always proved.To mustrate the difficulties of interpretation, letus consider an example where increased aerationcauses evaporative cooling of the fermentationmash. It would seem that any deleteriouseffect should be charged to lack of temperaturecontrol rather than to excessive aeration. Adirect measure of the temperature within thefermentation vessel is especially necessary whenhigh-speed stirring is used because all themechanical power supplied is ultimately dis-sipated as heat. Also, under vigorous aerationthe fermentation may proceed so rapidly thatpH changes or degradative reactions are ac-celerated. If tests of productivity are made onlyat a stated time, say 60 hours after inoculation, afalse impression may be gained of the efficacy ofaerating. Still another type of artifact associatedwith high air rates is the loss of volatile inter-mediates such as acetaldehyde (49) or the loss ofC02 (109). An interesting example, in which thecause of adverse results was traced, is suppliedby the work of Pfeifer and his associates. In anearly study (105) it was believed that poorresults in the riboflavin fermentation were causedby high air rates.. Later work (110), which wasdone on a different fermentation proces, demon-strated that excessive amounts of antifoam agentcould account for the low yields.There are, of course, harmful effects from over-

1954] 269

R. K. FINN

agitation or overaeration. The complex effects ofoxygen have already been mentioned, but moreshould be said concerning the damage to cellsfrom stirring. Outright rupture of the cells isappreciable only when there are abrasive particlespresent (111) or when there is cavitation (112).In the ordinary fermentation apparatus, cavita-tion is not severe even with rapid stirring. In theauthor's experience a 5 minute treatment in theWaring blendor failed to disrupt young mold cells.Aged cells are so much more fragile, however,that high-speed agitation may well influence theirlysis. It would be desirable to know the limits ofshear both for breakdown of cell clumps and forcell rupture; a start in this direction has beenmade by Ackerman (113) who provided quanti-tative comparisons of cell fragilities. The abilityto withstand sonically induced cavitation appearsto bear no relation to cell size. Thus E. coli andT-2 phage have about the same fragility, whereasbaker's yeast is not always broken even in intenseacoustical fields.

VI. SUMMARY

To provide quantitative descriptions of theefficiency of aeration, KLa values should bemeasured, preferably with the aid of a polaro-graph and under conditions which closely simu-late an actual fermentation. If a polarograph isnot available, KLa can be estimated by themethod of Cooper, Fernstrom, and Miller (46)in which a 0.5 M sodium sulfite solution containinga copper or cobaltiquinolate catalyst replaces thefermentation medium. The rate of oxygenabsorption is measured by titrating iodometri-cally the unoxidized sulfite ions after a 3 to 20minute period of aeration. Results are expressedas millimoles of 02 absorbed per liter per hpur,which is KLaC* in the nomenclature used here.Replicate determinations should agree to withinabout 5 per cent. Because oxygen may not havethe same solubility in a fermentation mash as inthe sulfite solution under test (e.g., fermentationmay be carried out under pressure), it is desirableto report KLa values rather than KLaC*. Iftests are made with air at 25 C, C* for 0.5 m

sodium sulfate is about 0.20, and thereforeKLa = 5KLaC*.To illustrate the application of KLa data,

suppose that it is desired to grow E8cherid&ia coliin nutrient broth at 37 C (C* = 0.17) usingshake-flasks with a measured KLa of 25 hr-'.

The rate at which oxygen will be supplied to thecells is

Rate of supply = KLa (C* - CL). (13)

If 10 per cent of saturation is set as a lower limitfor CL in order to have a safe margin of dissolvedoxygen, equation 13 becomes

Rate of supply = 25 (0.17 - 0.017)= 3.8 mm 02/(liter) (hr)

Reference to table 2 shows that the calculatedrate of supply may not satisfy the peak demand ofan active E. coli culture, and therefore lessculture fluid should be used in the shake-flasks orthey should be shaken more violently so as toraise KLa.The following is a check-list of suggestions for

those who work with aerated cultures:1. Measure KLa for all aeration devices.2. Report the linear velocity of air flow, but

also include dimensions of the fermentationvessel so that a volumetric air rate can be cal-culated.

3. Check to see that air rates do not exceed400 feet per hour for closed impellers, 70 feet perhour for open or paddle impellers.

4. Provide adequate baffling in stirred tanks.5. To be sure that aeration is adequate, make

a direct determination of the dissolved oxygenwithin the medium.

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2. units of kla....................................................i.i...i

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