Blotechnol. Prog. 1991, 7, 323-329
323
Enhancing Oxygen Transfer in Bioreactors by Perfluorocarbon Emulsions Lu-Kwang Ju' Department of Chemical Engineering, The University of Akron, Akron, Ohio 44325
Jaw Fang Lee and William B. Armiger' BioChem Technology, Inc., 100 Ross Road, King of Prussia, Pennsylvania 19406
This work aims to investigate the capability of perfluorocarbon (PFC) emulsions in enhancing oxygen transfer in bioreactors. Based on the penetration theory, a model has been derived for evaluating the potential oxygen transfer enhancement effects of PFC emulsions with very fine PFC particles. Defined as the ratio between the maximum oxygen transfer rates in systems with and without the emulsions, the enhancement factor achievable with dilute PFC emulsions can be estimated as the square root of the product of ratios of oxygen permeability and solubility in media with and without the emulsions. The effect of PFC emulsions on oxygen transfer in low-shear cultivation systems was further studied experimentally with direct measurements of volumetric oxygen transfer coefficients, k ~ a ,in bioreactors and with microbial fermentations conducted under low-shear conditions. It was found that significantly higher cell populations could be maintained at an aerobic state by using systems supplemented with the investigated emulsions. The experimentally determined values of oxygen transfer enhancement factor compare well with the theoretical values for emulsions with up to 1596 (v/v) PFC. The feasibility of enhancing oxygen transfer in bioreactors by introduction of adequate amounts of PFC emulsions was clearly demonstrated.
Introduction Oxygen supply has always been a central topic for design and scale-up of aerobic bioprocesses. Conventional fermentation equipment, designed to supply oxygen to microorganisms by vigorous agitation and/or air sparging, has been found unsuitable for cell culture (1-3). Shear forces associated with mechanical agitation and air bubbles tend to damage the fragile mammalian cell membranes, leading to metabolic changes and cell death (4). A pressing need exists for better oxygen supply techniques in lowshear cultivation systems. The difficulty in supplying enough oxygen to cells in cell culture, and other aerobic bioprocesses, results mainly from the fact that oxygen, unlike other nutrients, is only sparingly soluble in aqueous media. Therefore, it is feasible to improve the oxygen supply capability of a cultivation system by increasing the effective oxygen solubility of the medium through addition of upseudoerythrocytes", i.e., oxygen-carrying particles in the medium analogous to the erythrocytes in mammalian blood. There are two major types of products being developed that can imitate the high oxygen-carrying capability of red blood cells: hemoglobin solutions and perfluorochemicals. Hemoglobin is the primary protein component responsible for the oxygen-binding capacity of red blood cells. Prepared by isolatinghemoglobin from mammalian blood, the hemoglobin solutions can bind substantial quantities of oxygen. However, the oxygen is very tightly bound, and only a portion of it can be released from the solution to the cells. Another disadvantage of this approach is that it depends upon the availability of animal blood as the raw material. Since very large amounts of blood are needed to make useful quantities of purified hemoglobin, the raw material is subject to large price fluctuations due to commodity market conditions. 8756-7938/91/3007-0323$02.50/0
Perfluorocarbons (PFCs) are petroleum-based compounds synthesized by substituting fluorine for the hydrogen atoms of hydrocarbons. Lack of strong interactions between PFC molecules enables gaseous oxygen to enter the spaces between them. As shown in Table I, oxygen solubilities higher than 10-20 times that of pure water are found in several commercially available PFCs. PFCs are stable and virtually chemically inert due to the presence of very strong carbon-fluorine bonds (ca. 120 kcal/mol) (5). In addition, the fluorine atoms offer steric protection to the carbon groups. PFC formulations have several advantages compared to hemoglobin solutions. Whereas hemoglobin has a given number of receptor sites and can therefore bind only a finite amount of oxygen,the level of oxygen carried by PFCs is determined by the oxygen partial pressure in the gas with which the PFCs are in equilibrium. If necessary, oxygen-enriched gases can be used to further increase the oxygen supply to cells. In addition, since the oxygen is not bound to PFCs, as it is to hemoglobin, it is easily released to the cells. PFCs also have much higher solubilities for C02 than ordinary aqueous media (see Table I). Therefore, PFCs can carry carbon dioxide and handle the concomitant challenge of removing the C02 generated by cell metabolism. One mole of COz is produced per mole of oxygen consumed by the cells. This CO2 must be carried away from the living organisms and disposed of. So far, C02 removal has not proved to be a limtation in cell culture because COa can be reacted with componenb of the culture medium in order to fix it chemically. Nevertheless, C02derived ions raise the osmolality of the medium so that eventually cell functions would be impeded by adverse osmotic pressure across the cell membrane. PFC formulations have much higher potential to be used as oxygen carriers in bioprocesses, as compared to hemo-
0 1991 American Chemical Society and American Instltute of Chemical Engineers
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phase
liquid phase
0
0
0
0
0
I I.
0 0 0
I.
Y
Figure 1. Schematicof a PFC emulsion near gas/liquid interface. Table I. Solubility of Oxygen and Carbon Dioxide in Perfluorocarbons (PFCs). mL of aas/lOO mL of PFCe PFCe oxygen carbon dioxide water 3.2 80.5 FC-72 65 248 FC-84 59 224 FC-77 56 214 FC-104 52 199 FC-75 51 209 FC-40 37 142 FC-43 36 140 FC-70 31 117 FC-71' 26 94 a At 1 atm and 25 "C (taken from Fluorinert Electronic Liquids, 3M Product Manual, 1987). Measured at 35 O C .
globin. Several studies on application of PFCs to cultivation of microbial (6-11) and mammalian (12-15) cells have been reported in the literature. A recent review on this topic is also available (16). While some used PFC emulsions as liquid microcarriers (12-14), most researchers took advantage of their high oxygen-carrying capability and circulated the pre- and/or reoxygenated PFCs or PFC emulsions through the cultivation system for supplying oxygen to cells (6-9, 15). Obviously, the latter required the modification of the bioreactors to incorporate an external oxygenation mechanism for the circulating PFCs or PFC emulsions. Since oxygen is transfered from the PFC to the aqueous phase, the efficiency of the process is directly related to the PFC-water interfacial area, which is determined by the droplet size of the PFC dispersed or emulsified in the media. Two previous studies addressed the possibility of using PFCs to enhance oxygen transfer rates in fermentation systems (IO,11). Pure PFCs were added and dispersed into droplets of 20-50 pm in diameter by the mechanical agitation employed in the fermentors. While higher oxygen transfer rates were shown to be achievable, several
disadvantages of applying pure PFCs in low-shear cell culture systems can be expected. PFCs have very high densities, e.g., ranging from 1.7 to 2.0 g/cm3. When applied in low-shear, gently mixed systems, pure PFCs will either settle to the bottom completely or be dispersed only partially into droplets of very large sizes. Accordingly, the efficiency of using pure PFCs as oxygen transfer enhancers in cell culture systems is unacceptably low. Furthermore, our experience of applying pure PFCs in cultures of human lymphocytes made in a column reactor with a suspended draft tube clearly identified the problem of protein stripping from the growth medium by the circulated PFCs (17). In this study, the oxygen transfer enhancement capability of FlurOz emulsions,stable PFC emulsions developed by BioChem Technology, Inc. (King of Prussia, PA), has been analyzed theoretically and studied experimentally with measurements of volumetric oxygen transfer coefficients, k ~ ain, bioreactors and with fermentations of Escherichiacoli K-12 conducted under low-shear conditions. With very fine PFC droplets (O
(2)
p=pG
fort>O,y=O
(3)
where p is oxygen partial pressure, k is oxygen solubility in terms of Henry's law constant, P is oxygen permeability (i.e., the product of the diffusion coefficient and the solubility), OCR is the rate of oxygen consumption by cells, and subscripts e, L, and G refer to the effective values in the heterogeneous system (in this case, the PFC emulsion),the liquid phase, and the gas phase, respectively. In a heterogeneous system, the discontinuity of oxygen concentration occurs at the boundary between different phases. The above equations have thus been expressed in terms of the oxygen partial pressure, which is a continuous property throughout the system. The general solution of this equation can be obtained by sequential transformations of the dependent and independent variables as described by Eckert and Drake (19). The average flux of oxygen through the gas-liquid interface, during the contact time 7, of a fluid element, follows from
N , = l p - P , [ YY]
Y-0
dt
re
The maximum flux occurs when p~ = 0, Le.
Accordingly, the oxygen transfer enhancement factor, E, defied as the ratio between the maximum oxygen transfer rates (OTR) in systems with and without PFC emulsions, can be determined as
where a is the interfacial area per unit volume of the culture broth. In gas-sparged bioreactors, the effect of PFC emulsions on u depends on the surfactant systems used in the emulsions. Some foaming has been observed in gassparged systems containing FlurOz emulsions, leading to values of u,/uo larger than 1. Nevertheless, for surfaceaerated bioreactors, the influence of PFC emulsions on the gas-liquid interfacial area should be negligible. By further assuming an insignificant effect of PFC emulsions on the average contact time of an liquid element at the interface (or the surface renewal rate), i.e., 7, r0, the value of E in surface-aerated emulsions with low PFC volume fractions can be estimated as
-
(7) However, it should be noted that the true values of E obtainable in systems with higher volume fractions of PFC
can be much lower than those estimated by eq 7. Emulsification generally raises the system's viscosity, depending on the ratio of the volume fraction of dispersed to continuous phases, emulsion particle size, size distribution, and viscosities of pure dispersed and continuous phases (20-22). This may significantly decrease the surface-renewal rate of fluid elements and result in lower efficiency of oxygen transfer enhancement in emulsions with high PFC volume fractions.
Materials and Methods Formulation of FlurO2 Emulsions. The formation of a stable emulsion involves proper selection of surfactants, dispersed and continuous phases, emulsification equipment, and the emulsification process. A surfactant is a surface-activematerial with an amphipathic structure. One end of the molecule is lipophilic (nonpolar) and the other end is hydrophilic (polar). Accordingly, surfactant molecules tend to reside at the oil/water interface with the lipophilic end in the oil and the hydrophilic end in the aqueous phase, whereby they stabilizethe phase boundary. Choice of a specific surfactant system is generally based on the hydrophile-lipophile balance (HLB) number (2325). In many cases, mixtures of two or more surfactants are used to improve the emulsion stability and other physical characteristics, such as mobility of the interface, viscosity of the emulsion, etc. Nonionic surfactanta were used in the formation of FlurO2 emulsions. They are also known to be relatively nontoxic to biological systems. The emulsions investigated were made from two different PFCs, i.e., FC-40 and FC-77 Fluorinert electronic liquids (3M, St. Paul, MN) with various PFC volume fractions. Emulsification was performed with a Microfluidizer M-110 from Microfluidics Corp. (Newton, MA). The formed emulsions could be filter-sterilized by 0.2-pm filters at the PFC volume fractions lower than 15%. With such small particle sizes, the emulsions were found to be stable against dilution, moderate temperature changes, and reasonable storage time (e.g. 3-6 months). Measurement of Volumetric Oxygen Transfer Coefficient,kLu. The values of k ~ in u FlurO2 emulsions of different PFC volume fractions were assessed with the dynamic method proposed by Dang et al. (26) and improved by Ruchti et al. (27). Measurements were made at room temperature and atmospheric pressure in two surface-aerated bioreactors at different agitation speeds. One is a double-side-arm Celstir bioreactor (Wheaton Scientific, Millville, NJ) with a working volume of 700 mL; the other is a 5-L spherical bioreactor (BR-05,Techne, Inc., Princeton, NJ). Following a step change of the influent gas from nitrogen to a gas mixture of 5 % C02, 20% 02,and 75% N2 commonly used in cell culture, the variation in oxygen partial pressure of the liquid was measured by an oxygen electrode, recorded with computer data acquisition and analysis software (FERMAC software,BioChem Technology, Inc., King of Prussia, PA), and analyzed to generate a semilogarithmicplot of Y pvs time. Y p the , dimensionless oxygen partial pressure, is defined as Po - PL Y p= -
PG-PN where the subscripts G, L, and N represent the gas mixture, liquid, and nitrogen, respectively. On the basis of a linear model that accounts for the gas residence time and the serial resistances of oxygen transfer through the liquid diffusion film and the electrode membrane, the time needed for the value of Y pto drop to
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Bbtechml. Frog., 1991, Vol. 7, No. 4
Table 11. Composition of Medium for E. coli K-12 Fermentation component concn K2HPO4 4.8 g/L KHiPO4 2.95 g/L (NHi)aSO4 1.05 g/L MgSO4 0.10 g/L FeSO4.7H20 0.3 mg/L Ca(NO&4H20 7.1 mg/L thiamine hydrochloride 1.0 mg/L
Table 111. Experimental Results of lrrs of FlurOz Emulsions in Surface-Aerated Biomactors PFC agitation kLa x 109, volume fraction bioreactor rate, rpm min-1 (kLa)./(kLda 0 Celstir 100 16.43 1.00 04 14.98 1.00 15 14.29 0.87 15 14.93 0.91 25 7.41 0.45 25a 4.57 0.30
l/e, tile, is equal to the sum of several time constants (27,
04 BR-05 200 34.45 1.00 25O 13.58 0.39 a The aqueoue phase of them system is Dulbecco's modified Eagle's medium (DME) with glutamine and high glucose (Mediatech, Washington, DC); that of the others is water.
%), i.e.
where TEand TFare time constants for the electrode and 15% and 25 % PFC, respectively. Viable cell counts of the liquid film and TGis the mean gas residence time. The samples taken during the fermentations were performed value of TE+ TFcould be evaluated experimentally from periodically. The final sample of each bioreactor was taken the response curve of the electrode to a step change of 5 min after the dissolved oxygen content dropped down liquid-phase oxygen partial pressure. In order to achieve to zero. the step change, the electrode was first placed in a nitrogensparged external solution to obtain a steady value Of p ~ . Results and Discussion It was then moved quickly into the bioreactor agitated at the studied speed and saturated with the gas mixture used Volumetric Oxygen Transfer Coefficient. Experimental results of kLa in two different surface-aerated in the study. The switching time was approximately 2 s. bioreactors containing emulsions of different PFC volume The value of TE + TFwas assessed by subtracting the a to fractions are listed in Table 111. Values of k ~ appear switching time from the time needed for the value of a dimensionless oxygen partial pressure, similarly defined decrease with increasing volume fraction of PFC. This to drop to l/e. Since values of t l / , in low-shear as Y,,, can be at least partly attributed to the increase in the systems are large, say, >30 min, a slight error in estimation emulsion viscosity with increasing PFC volume fraction, which slows down the surface-renewal rate of liquid of the switching time is tolerable. Finally, TG can be estimated by dividing the headspace volume by the volelements. A similar effect of viscosity on oxygen transfer umetric gas flow rate. The value of k ~ acan then be in fermentation systems has been reported in the literature (29-31). Viscosities of FlurOz emulsions having various calculated by using eq 9. PFC volume fractions,prepared by dilution of an emulsion Escherichia coli Fermentations. To investigate the influence on cell growth and metabolism by the surfacfrom the same batch with different amounts of distilled tants and different PFC volume fractions used in FlurOz water, are shown in Figure 2. The emulsion viscosity was emulsions, fermentations of E. coli K-12 were first made found to increase exponentially with the PFC volume in shaker flasks a t 37 "C. The studied systems included fraction. With a further increase in its PFC volume two different surfactants and emulsions of 15% and 25 % fraction, the emulsion would eventually turn into a creamPFC, respectively. The base medium composition emlike semisolid. ployed in the fermentations is listed in Table 11. All In order to achievethe optimal effect of Flu02 emulsions chemicals used were purchased from Sigma Chemical Co. on oxygen transfer enhancement, the increase in emulsion (St. Louis, MO). Efforts were made to ensure the same viscosity should be minimized. Since the viscosityincrease nutrient composition and inoculated cell concentration in is a very strong function of the particle size distribution, the aqueous phase of the medium in each flask. Experit is essential to produce emulsions with size distributions iments were run in duplicate with each flask having a as narrow as possible through a tight control on the working volume of 40 mL. The rotating speed of the shaker emulsification process. was set a t 250 rpm. Samples were taken periodically and E. coliFermentations. Experimental results of E. coli plated in petri dishes containing agar for viable cell counts. fermentations conducted in shaker flasks with media E. coli fermentations were also conducted simultacontaining different surfactants and FlurOz emulsions of neously in three identical Celstir bioreactors in order to various PFC volume fractions are shown in Figure 3. For demonstrate the oxygen transfer enhancement capability meaningful comparison, the live cell concentrations shown of FlurOz emulsions in actual biological processes. Each in the figure have been adjusted to the basis of aqueous bioreactor was equipped with one pH electrode (Model phase volume. No apparent effects of the surfactants and A320, Ingold Electrodes, Inc., Wilmington, MA) and one the emulsions on cell growth were observed. galvanic dissolved-oxygen electrode (Model A316, AssoTo demonstrate the enhancement in the oxygen transfer rate in actual biological processes via introduction of FlurOl ciated Bioengineering and Consultant, Inc., Lehigh Valley, PA). The agitation speed was 100 rpm and the temperemulsions,fermentations of E. coli K-12were further made ature was controlled at 37 f 0.1 "C. The operating in three identical Celstir bioreactors, simultaneously. The conditions, such as the rate and mechanism of agitation time profiles of dissolvedoxygen and live cell concentration and aeration, the reactor configuration, etc., used in the in the fermentations are shown in Figure 4. The dissolved fermentations were purposely chosen to be similar to those oxygen content was found to decrease much more slowly in cell cultures. The oxygen transfer enhancement effects in systems supplemented with FlurOz emulsions than in of FlurOz emulsions demonstrated in these E. coli ferthe control. Qualitatively, the oxygen transfer enhancementations are thus more or less representative of those ment effect of the FlurOz emulsions has been clearlyshown. potentially obtainable in cell cultures. Oxygen Transfer Enhancement Factor. In the The medium in one reactor was the base medium current study the effect of enhancing oxygen supply in described in Table 11. The medium in the others contained bioreactors by addition of FlurO2 emulsions, quantified
BkMchd. Rug., lQQl, Vol. 7, No. 4
327 U
P / /
151 13
>
9 i
’1
z 3.0
W
/
31 l0
7 I
//
(45
>
is 4.0 1
5
10
15
20
25
30
2
35
”
’,W M
*
A
40 i
PFC VOLUME FRACTION (%)
Figure 2. Viscosity of a studied PFC emulsion as a function of PFC volume fraction.
W
m
2
9.2
Figure 5. Oxygen transfer enhancement factor as a function of PFC volumefraction in the studied FlurO2 emulsions. (i)Results predicted from the mathematical model; (-), FC-77, and (- - -), FC-40. (ii)Experimental data obtained from k ~ measurements a for emulsions of FC-77; +, Celstir at 100 rpm, and *, BR-05at 200 rpm. (iii) Experimental data from E. coli fermentation in Celstir bioreactor, agitated at 100 rpm; 0 , FC-40,and A, FC-77.
2
average rule, i.e.
IJ 8.8 W
0
k , = k f o + ~PFJPFC
w 8.4
2 -1
or
v
C3 8.0
0,
7.6
TIME (HOURS)
Figure 3. Experimental results of aqueous-phase live cell
concentrations in E. coli fermentationsmade in shaker flasks. A, Control; i r , surfactant A; 0 , surfactant B;0,emulsion with 15% FC-77; X, emulsion with 25% FC-77.
k,/ko 1 + ~ P F C ( ~ P F C-/1)~ ~ where f is the volume fraction. In a previous study (32),measurements of oxygen permeability in pure PFCs and emulsions of various PFC volume fractions were made a t room temperature and 1 atm with a polarographic oxygen electrode (YSI Model 5750 probe, Yellow Springs Instrument Co., Inc., Yellow Springs, OH). It was concluded that the effect of interfacial surfactant molecules on oxygen transport through the PFC-water phase boundary is minimal in the developed FlurOz emulsions. In addition, the oxygen permeability of FlurOz emulsions can be assessed reasonably well from Maxwell’s equation (331, when f p ~ :C 0.1, i.e.
and from Meredith’s equation (34),when f p ~ :1 0.1, i.e.
Figure 4. Experimental results of dissolved oxygen profiles (-) and live cell concentrationsin E. coli fermentationssupplemented
with FlurOz emulsions, made in Celstir bioreacton- &, control; A, 15% FC-77; 0 , 25% FC-77.
as the oxygen transfer enhancement factor, can be assessed in three ways: (i) the theoretical model, (ii) kLa measurements, and (iii) experimental results of E. coli fermentations. (17 Theoretical Model. As described in eq 7, the oxygen transfer enhancement factor, E, of dilute FlurOz emulsions can be estimated as the square root of the product of ratios of oxygen permeability and solubility in systems with and without the emulsions. Since the interaction between aqueous and PFC phases in the emulsions occurs only a t the interface, which accounts for minimal volume when compared to the bulk, the molecular structures of the main body of both aqueous and PFC phases remain unaltered in the emulsified systems. Therefore, the effective oxygen solubilities of PFC emulsions can be estimated by using the volume-
where K , = P,/Po, Kppc = PPFC/P~,and fpFC is the volume fraction of the PFC phase. By using eqs 7 and 10-12, the values of E for the studied FlurOz emulsions have been calculated. Results are plotted against the PFC volume fraction, up to 30%, in Figure 5. (11’) h a Measurements. As mentioned earlier, the overall oxygen transfer rate in a low-shear culture system is controlled by the liquid-film resistance of mass transfer through the gas-liquid interface. Accordingly, the oxygen transfer rate, OTR, is generally expressed as = kLak& - P L ) (13) where Co2* is the saturation concentration of dissolved oxygen at the gas-liquid interface and Co2is the dissolved oxygen concentration in the bulk liquid phase. The maximum oxygen transfer rate, (OTR),,, achievable in
&technol. Prog., lQQl, Vol. 7, No. 4
328
a system is thus, when p~ = 0 (OTR),, = kLakp0 (14) Consequently, the oxygen transfer enhancement factor, E, defined as the ratio of the maximum oxygen transfer rates attainable in the bioreactor with and without the introduction of PFC emulsions, can be determined as (15)
where subscripts e and o represent the effectiveand original values with and without the emulsions, respectively. The values of E for the PFC emulsions studied in the k ~ measurements a have been determined by multiplication of the experimental results of (k~a),/(k~a), listed in Table I11and the values of k,/ k, calculated by eq 10. The results are shown in Figure 5. (ih')ResultsofE. coliFermentation. The maximum oxygen transfer rate achievable in a bioreactor is reached when the dissolved oxygen content in the culture medium drops to zero, Le., CoZ= p~ = 0. By assuming the pseudosteady state that oxygen transfer rate is equal to the oxygen consumption rate, the maximum oxygen transfer rate, (OTR),,, can be estimated as the product of specific oxygen demand of the microorganisms and the viable cell concentration at CO,= p~ = 0. Since no apparent effect of FlurO2 emulsions on cell growth was observed in fermentations of E. coli K-12 in shaker flasks, the assumption of the same specific oxygen demand of cells in media with and without FlurO2 emulsions seems to be reasonable. With this assumption, the oxygen-transfer enhancement factor, E, in a system containing FlurO2 emulsion can be calculated as the ratio between the viable cell concentration in samples taken from bioreactors with and without the emulsion, when the dissolved oxygen content dropped down to zero. For example, the value of E for the system containing 15% PFC was calculated as 7.9 x 10' cells/mL = 2.55 E= 3.1 X lo7 cells/mL where 3.1 X lo7and 7.9 X lo7 cells/mL were the live cell concentrations in the last samples taken from the control and the emulsion-supplemented system, respectively, as shown in Figure 4. Values of E thus determined from several runs of E. coli fermentation are summarized in Figure 5, together with the values derived from the theoretical model and from a For the studied FlurO2 emulsions the k ~ measurements. made from two different PFCs with various PFC volume fractions, experimental results from both E. coli fermentations and k ~ measurements a are shown to agree fairly well with the theoretically derived values for emulsions containing up to 15% PFC. On the other hand, experimental data of E obtained in emulsions of 25 % PFC were found to be much lower than those in emulsions of 15% PFC. This is believed to be primarily caused by the significant increase in medium viscosity due to the presence of high concentrations of FlurO2 emulsions. Since the change of surface-renewal rate due to addition of FlurO2 emulsions is not considered in eq 7, overestimation of E in systems with high volume fractions of PFC can be reasonably explained. Nevertheless, the feasibility of enhancing oxygen transfer in bioreactors by introduction of adequate amounts of FlurO2 emulsions is clearly demonstrated. Another factor that may play an important role in the oxygen transfer enhancement effect of FlurOz emulsions
is the significant increase in bulk density of the medium. Pure PFCs have very high densities, e.g., ranging from 1.7 to 2.1 g/cm3, when compared to ordinary aqueous media. Addition of FlurO2 emulsions into aqueous solutions would thus result in marked increases in the effective density of the systems, normally unattainable in aqueous media. In which way and to what degree this density increase influencesthe application of F l u 0 2 emulsions in biological systems certainly warrants more research work in the future.
Conclusions In this study the ability of FlurO2 emulsions to improve oxygen supply capability of bioreactors has been analyzed theoretically and investigated experimentally with k ~ a measurements and E. coli fermentations made under lowshear conditions similar to those in cell culture. The theoretical model, derived on the basis of the penetration theory, indicated that the oxygen transfer enhancement factor in surface-aerated systems with low PFC volume fractions can be estimated as the square root of the product of ratios of oxygen permeability and solubility in media with and without the emulsions. The ratio of oxygen permeability can be assessed from Maxwell's and Meredith's equations and the solubility ratio from a volumeaverage rule. The predicted values of the enhancement factor were supported by the experimental results of k ~ measurea menta and of E. coli fermentations for systems with up to 15% PFC. However, a further increase in PFC volume fraction to 25% generally led to a poorer enhancement effect. This was attributed mainly to the exponential increase in medium viscosity with increasing PFC volume fractions. Nevertheless, the feasibility of enhancing oxygen transfer in bioreactors by addition of adequate amounts of FlurO2 emulsions was clearly demonstrated.
Notation CO* E
dissolved oxygen concentration, mol/L oxygen transfer enhancement factor, defined in eq
f K
volume fraction relative oxygen permeability oxygen solubility, in terms of Henry's law constant, mol/(L.atm) volumetric oxygen transfer coefficient, 5-1 average oxygen flux, mol-cm/(L.s) oxygen consumption rate by cells, mol/(L.e) oxygen transfer rate, mol/(L.s) oxygen permeability, mol-cm2/(Lwatm) oxygen partial pressure, atm electrode time constant, s liquid film time constant, s mean gas residence time, s time, s the time needed for Y pto drop to l/e, s dimensionless oxygen partial pressure, defined in eq 8 distance from the gas/liquid interface, cm gas/liquid interfacial area per unit volume of the culture broth, cm-1 contact time of a liquid element with gas phase, s
6
k kLa
N OCR OTR P P
TE TF TG t
til,
YP Y a 1
Subscripts e effective value in a heterogeneous system G gas phase
Bktechnol. Rog., 1991, Vol. 7, No. 4
L max N 0
PFC
liquid phase maximumvalue nitrogen original value perfluorocarbon
Acknowledgment T h i s research was sponsored by NASA under Contract
NAS9-17812 administered by the Lyndon B. Johnson Space Center. Literature Cited
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Accepted April 9, 1991. Registry No. FC-40,51142-49-5; FC-77,52623-00-4; 02,778244-7.
