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Rheological Properties of Fermentation Broths
Rheological Properties of Fermentation Broths FREDH. DEINDOERFER~ AND JOHNM. WEST The Squibb Znstitute for Medical Research, New Brunswick, New Jersey
Microorganisms in submerged culture fermentations thrive in a liquid environment which supplies them with the nutrients they need for biochemical activity. This liquid not only serves as a reservoir for the collection of metabolic end-products, but also absorbs the heat liberated by the reacting cell. The rate of transfer of heat and materials to and from the cells depends largely on the properties and motion of the fluid system in which the transport is carried out. Therefore, a knowledge of the rheological behavior of fermentation broths is an important prerequisite for an intelligent understanding of these transport processes. Rheological properties of most fermentation broths change appreciably during the course of a fermentation. The extent of these changes is related to the cellular concentration; in fermentations involving filamentous microorganisms it is related also to the nature of the mycelial network. Thus, in an analytical capacity, these properties provide information about growth of the microorganism. This paper has as its objective a review of the rheological properties of fermentation broths and an appraisal of the use of these properties in engineering and analytical correlations employed in fermentation practice.
Rheological Properties of Fluids Whenever a fluid is set in motion, shearing stresses are established within the fluid related to the velocity gradients in the flow regime. This is stated simply and concisely by Eq. (1). 7
=
f
(dU/dY)
C1)
Here 7 is the shearing stress, u is a skeamline velocity, and y is the normal distance from a point of reference to the streamline. The derivative, dv/dy, is then the velocity gradient. I n laminar flow, the nature of the functional relationship is characteristic of the behavior pattern or flow model assumed for the fluid. Newtonian JEuids.The simplest flow model is one in which there is a linear
* The School of Chemical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania. 265
266
FRED H. DEINDOERFER AND JOHN M. WEST
TABLE I V I S C O S I T Y O F COMMON FLUIDS Fluid
Viscosity a t 20°C. (centipoises)
Acetone Water n-Butanol 40% Sucrose solution Soybean oil 70% Sorbitol solution Glycerol Blackstrap molasses
0.33 1.oo 2.95 6.2 62 160 1500 6600
relationship between shearing stress and velocity gradient, as shown in Eq. (2) 7
= P
(dV/dY)
(2)
Equation (2) defines a Newtonian fluid, and the proportionality constant, p , is its viscosity. This one property characterizes the flow behavior for all shear stresses prior to the onset of turbulence. Table I lists viscosities of some familiar Newtonian liquids employed in the fermentation industry, illustrating the wide range of values this property has among different liquids. Non-Newtonian fluids. Any fluid which exhibits a nonlinear relationship between shearing stress and velocity gradient is called non-Newtonian. Such fluids have been classified according to their dependence on shear into a number of flow models. Fermentation broths which depart from Newtonian behavior, as will be shown later, follow closely the patterns of either of two non-Newtonian flow models generalized in Fig. 1. The curve representing a Newtonian fluid is a straight line passing through the origin, its slope being equal to the viscosity. The two non-Newtonian flow models represent fluids called plastic and pseudoplastic. Plastic fluids are the simplest type of non-Newtonian fluid to characterize. Their behavior is expressed by Eq. (3).
A definite yield stress, r Y, must be exceeded before the fluid will flow. Once flow begins, the shear stress is proportional to the velocity gradient, as in Newtonian fluids. The proportionality constant, q, is called rigidity to distinguish it from viscosity. Pseudoplastic fluids display a flow-curve which is concave downward, the rate of change of shear stress decreasing with increasing velocity gra-
FERMENTATION SYMPOSIUM : BROTH RHEOLOGY
dv/dy
267
Velocity gradient
FIG.1. Various fluid classifications
dient, and the curve asymptotically approaching a constant slope called the limiting consistency. A number of rheologists (11, 15) have assumed a n empirical power-law relationship such as Eq. (4) to describe this type of fluid behavior. T = K (dvldy)" (4) Metzner (11) has called K the consistency index and n the flow behavior index. The consistency index is somewhat analogous to viscosity and rigidity. For pseudoplastic fluids the flow behavior index lies between zero and one. If the value is one, the fluid is Newtonian. The closer this value approaches zero, the less the fluid displays a Newtonian behavior.
Behavior of Fermentation Broths Newtonian behavior. From theoret,ical considerations, only fermentation broths containing microorganisms of simple shape and in dilute solution should be expected to behave as Newtonian fluids. This would restrict Newtonian behavior to broths from yeast and bacterial fermentations, and to certain types of tissue culture where the microorganisms are nonfilamentous, not encapsulated, and do not form unusual cell agglomerates and chains. In these cases the viscosity is a function of the concentration and the individual cell's size and shape. More complicated broths, surprisingly enough, also show this behavior, as will be shown later. For fluids containing suspended solids of simple shape, the viscosity of the suspension depends on the concentration and the individual particle's
268
FRED H. DEINDOERFER AND JOHN M. WEST
shape and size. In colloidal suspensions this dependence is usually represented by equations of the form P S
f
= PL [1
CJ,
411
(5)
where p8 is the viscosity of the suspension, pL is the viscosity of the suspending liquid, f (J,4 ) is a function of the ratio of length to diameter, J, of the particles and their orientation due to Brownian motion, and the fractional volume, 4, occupied by the particles. For dilute suspensions of spheres, Einstein (5, 6) has shown that f (J,4 ) is equal to 2.5 4. For more concentrated suspensions of spheres, Vand (14) has extended Einstein's derivation to include particle interactions. The resulting equations are Einstein equation ~s
= PL
(1
+ 2.54)
(6)
= PL
(1
+ 2.5 4 + 7.25 4')
(7)
Vand equation
The latter equation agrees reasonably well for volume fractions of cells as high as 0.25. Equations of this type do not appear to have been applied in fermentation practice. Eirich et al. (7), however, investigated the viscosity of suspensions of yeast cells (presumably Saccharomyces cerevisiae) in water, and spores of the basidiomycete Lycoperdon bovista in tetrachloroethane. Figure 2 shows how well their measurements compare with values predicted by the Einstein equation at low volume fractions and how closely I
1.5
3 .n
-
1.4 .
0
.>
.
.-
-u
1.3
.
1.2
'
&
a
J
3 ?
0
A
0
2
Yeast cells Lycoperdon bovirtr spores
--
4 6 8 10 Volume of Suspended Spheres, X
12
14
FIG. 2. Effect of particle concentration on suspension viscosity (7).
269
FERMENTATION SYMPOSIUM: BROTH RHEOLOGY
TABLE I1 CHARACTER OF SEVERAL FERMENTATION BROTHS Process
Microorganism
Nystatin
Streptomyces noursei
Penicillin
Penicillium chrysogenum
Steroid hydroxylation Streptomycin
Coniothyriicm heltebor io Streptomyces griseus
Principal media ingredients Soybean meal, glucose Corn-steep liquor, Iactose Salts, glucose Soybean meal, glucose
Behavior Newtonian Pseudoplastic Plastic and pseudoplastic Newtonian and plastic
they follow the Vand equation as the volume fraction increases. Equations of this type should be applicable to a number of fermentation broths. Non-Newtonian behavior. Departure of fermentation broths from Newtonian behavior is due to the structural rigidity of three-dimensional mycelial networks or to long unidimensional particles having some degree of flexibility. A number of actinomycetes and molds impart structural rigidity because of their interlacing mycelial networks. Rheological properties reported for streptomycin broth by Karow et al. (lo), for water suspensions of an unidentified mold by Brown and Petsiavas @a), and for penicillin broth by Deindoerfer and Gaden (3) indicate that these fluids approximate plastic behavior. In recent studies reported elsewhere (4), rheological data were obtained on the several fermentations listed in Table 11. The pseudoplastic and plastic behavior of some of these broths was clearly evident at certain times during the course of their fermentations. Contrary to expectations, the nystatin broths (Streptomyces noursei) were Newtonian in character. Little is known about the quantitative relationship between rheological properties and cellular concentration in broths in which there are mycelial srtuctures. The problem is much more complex than in the case of unicellular microorganisms. The pseudoplastic behavior commonly associated with unidimensional particles, such as high molecular weight linear polymers, can be expected in bacterial fermentation broths in which the bacteria are encapsulated or form unusually long cellular chains. Rheological properties of broths of this nature do not appear to have been published. Rheological Properties in Engineering Correlations
Engineering design and successful scale-up of fermentation processes require an understanding of the rheological properties of their fluids sys-
270
FRED H . DEINDOERFER AND JOHN M. WEST
tems. Such common fermentation unit operations as flow in pipes, agitation, mass transfer, and heat transfer, as well as bubble and particle dynamics, all are influenced greatly by broth rheological properties. Because of the complexity of many of these relationships, they are expressed most frequently in dimensionless equation form. Some important chemical engineering correlations which illustrate the need for rheological data are listed in Table 111. Brown and Petsiavas (2a), Metzner and Otto f12), and Calderbank (2b) have developed correlations from which the power requirements for mixing non-Newtonian fluids can be predicted. The correlation of Brown and Petsiavas was developed based on plastic behavior, while the latter two correlations apply to pseudoplastic fluids. Almost exactly analogous methods are employed in designing pipelines and estimating the pumping requirements for transporting non-Newtonian fluids. These were developed by Hedstrom (9) for plastic fluids, by Metzner and Reed ( 1 3 4 for pseudoplastic fluids, and by Weltman (15) for both plastic and pseudoplastic fluids. The effect of increased broth consistency on oxygen transfer during a fermentation has been reported by a number of investigators. Unfortunately, in many cases, no rheological characterization of the broth has been made. Chain and Gualandi (2c) observed a 57% reduction in the oxygen transfer capacity coefficient in the presence of 13.5 gm. (dry)/liter of Penicillium chrysogenum mycelium. Bowers ( l a ) simulated mycelki using shredded paper pulp and suspended it in sulfite solutions to observe its effect on the sulfite index. When 2 % pulp was added to solutions in various equipment, decreases in the sulfite index of from 96 to 43% were experienced, the decrease being lessened by increased turbulence in the system. Brierly and Steel (2b) found as high as a 90% reduction in the oxygen transfer capacity coefficient when 20 gm (dry)/liter of filamentous Aspergillus niger mycelia was suspended in aqueous salt solution, and an 85% reduction when shredded paper pulp was suspended a t the same concentration level. Using sago pellets to simulate smooth mold pellets, they found no significant change in the capacity coefficient. This is as expected, since these spherical particles impart only a slight increase in viscosity to the suspension a t the 3 % concentration a t which they were added. Deindoerfer and Gaden ( 3 ) and more recently Solomons and Perkins (13b) measured oxygen transfer capacity coefficients and rheological properties of the broths as well. These investigators, using Penicillium chrysogenum and an Aspergillus species, respectively, showed marked decreases in the capacity coefficient due to the increase in broth consistency with increase in mycelial concentration. In the penicillin fermentation, rigidities as high as 200 centipoises reduced the oxygen transfer capacity coefficient about 85%. This corresponded to a mycelial concentration of 13.5 gm
FERMENTATION SYMPOSIUM: BROTH RHEOLOGY
271
TABLE 111 IMPORTANT RHEOLOGY-DEPENDENT ENGINEERING CORRELATIONS I N FERMENTATION Empirical relationships Dimensionless correlation with other groups Engineering problem
Agitation in baffled tank Drag on particles Mass transfer Heat transfer 5
Dimensionless group
Newtonian
Non-Newtonian Plastica
Pseudoplastica
* = pN3D6 -P AP& C D = ~__
3p vz KLD S h = __ D, hD NU = k
Numbers in parentheses refer to references.
Nomenclature for Table I I I : CD CP
D D”
f
9
sc
h
K k
KL
Drag coefficient Specific heat Diameter Diffusivity Fanning friction factor Acceleration of gravity Conversion factor in Newton’s law of motion Coefficient of heat transfer Consistency index Thermal conductivity Coefficient of mass transfer in the liquid phase
L n N Nu P Sh
v
9
P P
A TY
9
Length Flow behavior index Number; revolutions per minute Nusselt number Power; pressure Sherwood number Velocity Rigidity Viscosity Density Difference, finite Yield stress Power number
(dry)/liter. A similar reduction was noted in suspensions of the Aspergillus mycelia by the latter workers. Unfortunately, they do not mention what their cellular concentrations were, and it appears that the viscosities reported (as high as 10,000 cps.) were obtained from extrapolation of their shear diagrams to shear stresses which are too low to yield a meaningful broth characteristic.
272
FRED H. DEINDOERFER AND JOHN M. WEST
Probably the severest criticism of fermentation practice that can be made is that all its published design and scale-up correlations are based on Newtonian characteristics, despite the fact that many fermentations yield non-Newtonian broths.
Analytical Use of Rheological Data One of the more apparent uses of fermentation broth rheological properties is the characterization of growth in the broth. Figure 3 shows how rigidity magnifies the growth curve in a penicillin fermentation. Small changes in cellular concentration appear as large changes in rigidity. Sincy many fermentations are carried out in media containing various suspended solids (which prohibit accurate determination of cell weight), the use of a rheological property is particularly useful as a measure of growth. Harris et al. ( 8 ) used torque (proportional to the shearing stress) at a prescribed cup speed (proportional to velocity gradient) measured in a MacMichael viscosimeter to characterize the growth of Streptomyces garyphalus in a medium containing soybean meal, glucose, and calcium carbonate, as used in the production of cycloserine. Studies of Deindoerfer and West (4) illustrated interesting changes in the rheological behavior of nystatin and streptomycin broth which appear to characterize the course of these fermentations. These changes in rheological properties undoubtedly indicate changes in the complexity and/or concentration of cellular material. Thus, the analytical nature of rheological data can provide useful information about cellular
0
I2
24
36
48
Age, houn
60
12
04
PI
FIG.3. Broth rigidity as an index to characterize mycelial development in a penicillin fermentation (3).
FERMENTATION SYMPOSIUM : BROTH RHEOLOGY
273
development in fermentations. Also, in continuous fermentatmiomwhere process measurement and control lags must be minimized, rheological properties should be very suitable indices of growth. Future Work
One of the objectives of this symposium is to predict areas in which future investigations should prove fruitful. There are two avenues of research along rheological lines which appear ripe for further study. One is the development of suitable design and scale-up correlations based on non-Newtonian properties, for there are many fermentations in which the broths are non-Newtonian in character. The other is the correlation of rheological properties with cellular concentration and mycelial structure. -4s has been shown, rheological properties provide a sensitive analytical means for observing cellular changes. Such studies may, perhaps, even furnish an important link between cellular structure and biochemical activity.
REFERENCES l a . Bowers, R. H. (1955). J. A p p l . Chem. 5 , 542. Ib. Brierly, M. R., and Steel, R. (1959). A p p l . Microbiol. 7, 57. 2a. Brown, G. A., and Petsiavas, D. N. (1954). Am. Inst. Chem. Engrs. Meeting,
New York. 2b. Calderbank, P. H. (1959). Trans. I n s t . Chem. Engrs. (London) 37, 26. 2c. Chain, E. B., and Gualandi, G. (1954). Rend. ist. super. sanitd 17, 5. 3. Deindoerfer, F. H., and Gaden, E. L. (1955). A p p l . Microbiol. 3, 353. 4. Deindoerfer, F. H., and West, J. M. (1959). J. Microbiol. Biochem. Technol. & E n s . In press. 5. Einstein, A. (1906). Ann. Physilc [4] 19, 289. 6. Einstein, A. (1911). Ann. Physik [41 34, 591. 7. Eirich, F. et al. (1936). Kolloid 2. 74, 276. 8. Harris, D. A. et al. (1955). Antibiotics & Chemotherapy 5 , 183. 9. Hedstrom, B. 0. A. (1952). I n d . Eng. Chem. 44, 561. 10. Karow, E. 0. et al. (1953). J . Agr. Food. Chem. 1, 302. 11. Metsner, A. B. (1956). Advances in Chem. Eng. 1. 79. 12. Metzner, A. B., and Otto, R. E. (1957). A.I.Ch.E. Journal 3, 3. 13a. Metzner, A. B., and Reed, J. C. (1955). A.1.Ch.E. Journal 1, 434. 13b. Solomons, G. L., and Perkins, M. P. (1958). J. A p p l . Chem. (London) 8, 251. 14. Vand, V. (1948). J. Phys. & Colloid Chtm. 52,277. 15. Weltman, R. N. (1956). I n d . Eng. Chem. 48, 386.
Microorganisms in submerged culture fermentations thrive in a liquid environment which supplies them with the nutrients they need for biochemical activity. This liquid not only serves as a reservoir for the collection of metabolic end-products, but also absorbs the heat liberated by the reacting cell. The rate of transfer of heat and materials to and from the cells depends largely on the properties and motion of the fluid system in which the transport is carried out. Therefore, a knowledge of the rheological behavior of fermentation broths is an important prerequisite for an intelligent understanding of these transport processes. Rheological properties of most fermentation broths change appreciably during the course of a fermentation. The extent of these changes is related to the cellular concentration; in fermentations involving filamentous microorganisms it is related also to the nature of the mycelial network. Thus, in an analytical capacity, these properties provide information about growth of the microorganism. This paper has as its objective a review of the rheological properties of fermentation broths and an appraisal of the use of these properties in engineering and analytical correlations employed in fermentation practice.
Rheological Properties of Fluids Whenever a fluid is set in motion, shearing stresses are established within the fluid related to the velocity gradients in the flow regime. This is stated simply and concisely by Eq. (1). 7
=
f
(dU/dY)
C1)
Here 7 is the shearing stress, u is a skeamline velocity, and y is the normal distance from a point of reference to the streamline. The derivative, dv/dy, is then the velocity gradient. I n laminar flow, the nature of the functional relationship is characteristic of the behavior pattern or flow model assumed for the fluid. Newtonian JEuids.The simplest flow model is one in which there is a linear
* The School of Chemical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania. 265
266
FRED H. DEINDOERFER AND JOHN M. WEST
TABLE I V I S C O S I T Y O F COMMON FLUIDS Fluid
Viscosity a t 20°C. (centipoises)
Acetone Water n-Butanol 40% Sucrose solution Soybean oil 70% Sorbitol solution Glycerol Blackstrap molasses
0.33 1.oo 2.95 6.2 62 160 1500 6600
relationship between shearing stress and velocity gradient, as shown in Eq. (2) 7
= P
(dV/dY)
(2)
Equation (2) defines a Newtonian fluid, and the proportionality constant, p , is its viscosity. This one property characterizes the flow behavior for all shear stresses prior to the onset of turbulence. Table I lists viscosities of some familiar Newtonian liquids employed in the fermentation industry, illustrating the wide range of values this property has among different liquids. Non-Newtonian fluids. Any fluid which exhibits a nonlinear relationship between shearing stress and velocity gradient is called non-Newtonian. Such fluids have been classified according to their dependence on shear into a number of flow models. Fermentation broths which depart from Newtonian behavior, as will be shown later, follow closely the patterns of either of two non-Newtonian flow models generalized in Fig. 1. The curve representing a Newtonian fluid is a straight line passing through the origin, its slope being equal to the viscosity. The two non-Newtonian flow models represent fluids called plastic and pseudoplastic. Plastic fluids are the simplest type of non-Newtonian fluid to characterize. Their behavior is expressed by Eq. (3).
A definite yield stress, r Y, must be exceeded before the fluid will flow. Once flow begins, the shear stress is proportional to the velocity gradient, as in Newtonian fluids. The proportionality constant, q, is called rigidity to distinguish it from viscosity. Pseudoplastic fluids display a flow-curve which is concave downward, the rate of change of shear stress decreasing with increasing velocity gra-
FERMENTATION SYMPOSIUM : BROTH RHEOLOGY
dv/dy
267
Velocity gradient
FIG.1. Various fluid classifications
dient, and the curve asymptotically approaching a constant slope called the limiting consistency. A number of rheologists (11, 15) have assumed a n empirical power-law relationship such as Eq. (4) to describe this type of fluid behavior. T = K (dvldy)" (4) Metzner (11) has called K the consistency index and n the flow behavior index. The consistency index is somewhat analogous to viscosity and rigidity. For pseudoplastic fluids the flow behavior index lies between zero and one. If the value is one, the fluid is Newtonian. The closer this value approaches zero, the less the fluid displays a Newtonian behavior.
Behavior of Fermentation Broths Newtonian behavior. From theoret,ical considerations, only fermentation broths containing microorganisms of simple shape and in dilute solution should be expected to behave as Newtonian fluids. This would restrict Newtonian behavior to broths from yeast and bacterial fermentations, and to certain types of tissue culture where the microorganisms are nonfilamentous, not encapsulated, and do not form unusual cell agglomerates and chains. In these cases the viscosity is a function of the concentration and the individual cell's size and shape. More complicated broths, surprisingly enough, also show this behavior, as will be shown later. For fluids containing suspended solids of simple shape, the viscosity of the suspension depends on the concentration and the individual particle's
268
FRED H. DEINDOERFER AND JOHN M. WEST
shape and size. In colloidal suspensions this dependence is usually represented by equations of the form P S
f
= PL [1
CJ,
411
(5)
where p8 is the viscosity of the suspension, pL is the viscosity of the suspending liquid, f (J,4 ) is a function of the ratio of length to diameter, J, of the particles and their orientation due to Brownian motion, and the fractional volume, 4, occupied by the particles. For dilute suspensions of spheres, Einstein (5, 6) has shown that f (J,4 ) is equal to 2.5 4. For more concentrated suspensions of spheres, Vand (14) has extended Einstein's derivation to include particle interactions. The resulting equations are Einstein equation ~s
= PL
(1
+ 2.54)
(6)
= PL
(1
+ 2.5 4 + 7.25 4')
(7)
Vand equation
The latter equation agrees reasonably well for volume fractions of cells as high as 0.25. Equations of this type do not appear to have been applied in fermentation practice. Eirich et al. (7), however, investigated the viscosity of suspensions of yeast cells (presumably Saccharomyces cerevisiae) in water, and spores of the basidiomycete Lycoperdon bovista in tetrachloroethane. Figure 2 shows how well their measurements compare with values predicted by the Einstein equation at low volume fractions and how closely I
1.5
3 .n
-
1.4 .
0
.>
.
.-
-u
1.3
.
1.2
'
&
a
J
3 ?
0
A
0
2
Yeast cells Lycoperdon bovirtr spores
--
4 6 8 10 Volume of Suspended Spheres, X
12
14
FIG. 2. Effect of particle concentration on suspension viscosity (7).
269
FERMENTATION SYMPOSIUM: BROTH RHEOLOGY
TABLE I1 CHARACTER OF SEVERAL FERMENTATION BROTHS Process
Microorganism
Nystatin
Streptomyces noursei
Penicillin
Penicillium chrysogenum
Steroid hydroxylation Streptomycin
Coniothyriicm heltebor io Streptomyces griseus
Principal media ingredients Soybean meal, glucose Corn-steep liquor, Iactose Salts, glucose Soybean meal, glucose
Behavior Newtonian Pseudoplastic Plastic and pseudoplastic Newtonian and plastic
they follow the Vand equation as the volume fraction increases. Equations of this type should be applicable to a number of fermentation broths. Non-Newtonian behavior. Departure of fermentation broths from Newtonian behavior is due to the structural rigidity of three-dimensional mycelial networks or to long unidimensional particles having some degree of flexibility. A number of actinomycetes and molds impart structural rigidity because of their interlacing mycelial networks. Rheological properties reported for streptomycin broth by Karow et al. (lo), for water suspensions of an unidentified mold by Brown and Petsiavas @a), and for penicillin broth by Deindoerfer and Gaden (3) indicate that these fluids approximate plastic behavior. In recent studies reported elsewhere (4), rheological data were obtained on the several fermentations listed in Table 11. The pseudoplastic and plastic behavior of some of these broths was clearly evident at certain times during the course of their fermentations. Contrary to expectations, the nystatin broths (Streptomyces noursei) were Newtonian in character. Little is known about the quantitative relationship between rheological properties and cellular concentration in broths in which there are mycelial srtuctures. The problem is much more complex than in the case of unicellular microorganisms. The pseudoplastic behavior commonly associated with unidimensional particles, such as high molecular weight linear polymers, can be expected in bacterial fermentation broths in which the bacteria are encapsulated or form unusually long cellular chains. Rheological properties of broths of this nature do not appear to have been published. Rheological Properties in Engineering Correlations
Engineering design and successful scale-up of fermentation processes require an understanding of the rheological properties of their fluids sys-
270
FRED H . DEINDOERFER AND JOHN M. WEST
tems. Such common fermentation unit operations as flow in pipes, agitation, mass transfer, and heat transfer, as well as bubble and particle dynamics, all are influenced greatly by broth rheological properties. Because of the complexity of many of these relationships, they are expressed most frequently in dimensionless equation form. Some important chemical engineering correlations which illustrate the need for rheological data are listed in Table 111. Brown and Petsiavas (2a), Metzner and Otto f12), and Calderbank (2b) have developed correlations from which the power requirements for mixing non-Newtonian fluids can be predicted. The correlation of Brown and Petsiavas was developed based on plastic behavior, while the latter two correlations apply to pseudoplastic fluids. Almost exactly analogous methods are employed in designing pipelines and estimating the pumping requirements for transporting non-Newtonian fluids. These were developed by Hedstrom (9) for plastic fluids, by Metzner and Reed ( 1 3 4 for pseudoplastic fluids, and by Weltman (15) for both plastic and pseudoplastic fluids. The effect of increased broth consistency on oxygen transfer during a fermentation has been reported by a number of investigators. Unfortunately, in many cases, no rheological characterization of the broth has been made. Chain and Gualandi (2c) observed a 57% reduction in the oxygen transfer capacity coefficient in the presence of 13.5 gm. (dry)/liter of Penicillium chrysogenum mycelium. Bowers ( l a ) simulated mycelki using shredded paper pulp and suspended it in sulfite solutions to observe its effect on the sulfite index. When 2 % pulp was added to solutions in various equipment, decreases in the sulfite index of from 96 to 43% were experienced, the decrease being lessened by increased turbulence in the system. Brierly and Steel (2b) found as high as a 90% reduction in the oxygen transfer capacity coefficient when 20 gm (dry)/liter of filamentous Aspergillus niger mycelia was suspended in aqueous salt solution, and an 85% reduction when shredded paper pulp was suspended a t the same concentration level. Using sago pellets to simulate smooth mold pellets, they found no significant change in the capacity coefficient. This is as expected, since these spherical particles impart only a slight increase in viscosity to the suspension a t the 3 % concentration a t which they were added. Deindoerfer and Gaden ( 3 ) and more recently Solomons and Perkins (13b) measured oxygen transfer capacity coefficients and rheological properties of the broths as well. These investigators, using Penicillium chrysogenum and an Aspergillus species, respectively, showed marked decreases in the capacity coefficient due to the increase in broth consistency with increase in mycelial concentration. In the penicillin fermentation, rigidities as high as 200 centipoises reduced the oxygen transfer capacity coefficient about 85%. This corresponded to a mycelial concentration of 13.5 gm
FERMENTATION SYMPOSIUM: BROTH RHEOLOGY
271
TABLE 111 IMPORTANT RHEOLOGY-DEPENDENT ENGINEERING CORRELATIONS I N FERMENTATION Empirical relationships Dimensionless correlation with other groups Engineering problem
Agitation in baffled tank Drag on particles Mass transfer Heat transfer 5
Dimensionless group
Newtonian
Non-Newtonian Plastica
Pseudoplastica
* = pN3D6 -P AP& C D = ~__
3p vz KLD S h = __ D, hD NU = k
Numbers in parentheses refer to references.
Nomenclature for Table I I I : CD CP
D D”
f
9
sc
h
K k
KL
Drag coefficient Specific heat Diameter Diffusivity Fanning friction factor Acceleration of gravity Conversion factor in Newton’s law of motion Coefficient of heat transfer Consistency index Thermal conductivity Coefficient of mass transfer in the liquid phase
L n N Nu P Sh
v
9
P P
A TY
9
Length Flow behavior index Number; revolutions per minute Nusselt number Power; pressure Sherwood number Velocity Rigidity Viscosity Density Difference, finite Yield stress Power number
(dry)/liter. A similar reduction was noted in suspensions of the Aspergillus mycelia by the latter workers. Unfortunately, they do not mention what their cellular concentrations were, and it appears that the viscosities reported (as high as 10,000 cps.) were obtained from extrapolation of their shear diagrams to shear stresses which are too low to yield a meaningful broth characteristic.
272
FRED H. DEINDOERFER AND JOHN M. WEST
Probably the severest criticism of fermentation practice that can be made is that all its published design and scale-up correlations are based on Newtonian characteristics, despite the fact that many fermentations yield non-Newtonian broths.
Analytical Use of Rheological Data One of the more apparent uses of fermentation broth rheological properties is the characterization of growth in the broth. Figure 3 shows how rigidity magnifies the growth curve in a penicillin fermentation. Small changes in cellular concentration appear as large changes in rigidity. Sincy many fermentations are carried out in media containing various suspended solids (which prohibit accurate determination of cell weight), the use of a rheological property is particularly useful as a measure of growth. Harris et al. ( 8 ) used torque (proportional to the shearing stress) at a prescribed cup speed (proportional to velocity gradient) measured in a MacMichael viscosimeter to characterize the growth of Streptomyces garyphalus in a medium containing soybean meal, glucose, and calcium carbonate, as used in the production of cycloserine. Studies of Deindoerfer and West (4) illustrated interesting changes in the rheological behavior of nystatin and streptomycin broth which appear to characterize the course of these fermentations. These changes in rheological properties undoubtedly indicate changes in the complexity and/or concentration of cellular material. Thus, the analytical nature of rheological data can provide useful information about cellular
0
I2
24
36
48
Age, houn
60
12
04
PI
FIG.3. Broth rigidity as an index to characterize mycelial development in a penicillin fermentation (3).
FERMENTATION SYMPOSIUM : BROTH RHEOLOGY
273
development in fermentations. Also, in continuous fermentatmiomwhere process measurement and control lags must be minimized, rheological properties should be very suitable indices of growth. Future Work
One of the objectives of this symposium is to predict areas in which future investigations should prove fruitful. There are two avenues of research along rheological lines which appear ripe for further study. One is the development of suitable design and scale-up correlations based on non-Newtonian properties, for there are many fermentations in which the broths are non-Newtonian in character. The other is the correlation of rheological properties with cellular concentration and mycelial structure. -4s has been shown, rheological properties provide a sensitive analytical means for observing cellular changes. Such studies may, perhaps, even furnish an important link between cellular structure and biochemical activity.
REFERENCES l a . Bowers, R. H. (1955). J. A p p l . Chem. 5 , 542. Ib. Brierly, M. R., and Steel, R. (1959). A p p l . Microbiol. 7, 57. 2a. Brown, G. A., and Petsiavas, D. N. (1954). Am. Inst. Chem. Engrs. Meeting,
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