Topic: Aeration and Agitation
Mobile No. : 8087464948
Dr. P. A Pawar Sir
Associate Prof. (Food Tech)
The majority of fermentation processes are
aerobic and therefore require the provision of
oxygen. The oxidation of glucose may be
C6H12O6 + 6O2 = 6H2O + 6CO2
It is not possible to provide a microbial culture with all
the oxygen it will need for the complete oxidation of
glucose in one addition. Therefore, a microbial culture
must be supplied with oxygen during growth at a rate
sufficient to satisfy the organisms demand.
The oxygen demand of an industrial fermentation
process is normally satisfied by aerating and agitating the
However, the productivity of many
fermentations is limited by oxygen availability and
therefore, it is important to consider the factors
which affect the fermenter’s efficiency in supplying
microbial cells with oxygen.
This chapter considers the requirement for
oxygen in fermentation processes, the
quantification of oxygen transfer and the factors
which will influence the rate of oxygen transfer
into the solution.
Stock Culture Raw Materials
Aeration and Agitation
Important factor in a fermenters
Provision for adequate mixing of its contents
Mixing in fermentation
to disperse the air bubbles
to suspend the cells
to enhance heat and mass transfer in
All relate to Gas-liquid mass transfer
Aeration and Agitation
Aeration refers to the process of introducing
air to increase oxygen concentration in
Aeration may be performed by bubbling air
through the liquid, spraying the liquid into
the air or agitation of the liquid to increase
Agitation – uniform suspension of microbial
cells in homogeneous nutrient medium
Structural components involved in
aeration and agitation
Aeration system (sparger)
View looking down into astainless steel
Achieve mixing objectives –
bulk fluid and gas-phase
mixing, air dispersion, oxygen
transfer, heat transfer,
suspension of solid particles
and maintaining uniform
Four baffles incorporated
into agitated vessels of all
sizes to prevent vortex
and to improve aeration
Metal strips roughly one-
tenth of vessel diameter
and attached radially to
growth on baffles and
Aeration system (sparger)
Introduces air into liquid of
Three basic types – porous
1. Orifice sparger – a
2. Nozzle sparger – an open or
partially closed pipe
3. Combined sparger-agitator
THE OXYGEN REQUIREMENTS OF
A culture's demand for oxygen is very much dependent on the
source of carbon in the medium. Thus, the more reduced the
carbon source the greater will be the oxygen demand.
From Darling~ ton's and Johnson's equations (Table 9.1) it may
be seen that the production of 100 grams of biomass from
hydrocarbon requires approximately three times the amount of
oxygen to produce the same amount of biomass from
However, it must be remembered that the high carbon content
of hydrocarbon substrates means that high yield factors (g
biomass g -1 substrate consumed) are obtained and the
decision to use such substrates is based on the balance
between the advantage of high biomass yield and the
disadvantage of high oxygen demand and heat generation.
However, it is inadequate to base the
provision of oxygen for a fermentation simply
on an estimation of overall demand, because
the metabolism of the culture is affected by the
concentration of dissolved oxygen in the broth.
The effect of dissolved oxygen concentration on
the specific oxygen uptake rate (Qo2' mmoles of
oxygen consumed per gram dry weight of cells
per hour) has been shown to be of the
Michaelis-Menten type, as shown in Fig. 9.1.
Fig. 9.1 it may be seen that the specific oxygen uptake rate
increases with increase in the dissolved oxygen concentration
upto a certain point(referred to as CCrit) above which no further
increase in oxygen uptake rate occurs.
Thus, maximum biomass production may be achieved by
satisfying the organism's maximum specific oxygen demand
by maintaining the dissolved oxygen concentration greater
than the critical level. If the dissolved oxygen concentration
were to fall below the critical level then the cells may be
metabolically disturbed. However, it must be remembered
that it is frequently the objective of the fermentation
technologist to produce a product of the micro-organism
rather than the organism itself and that metabolic
disturbance of the cell by oxygen starvation may be
advantages to the formation of certain products.
Equally, provision of a dissolved oxygen concentration
far greater than the critical level may have no influence on
biomass production, but may stimulate product formation.
Thus, the aeration conditions necessary for the optimum
production of a product may be different from those
favouring biomass production.
Hirose and Shibai's (1980) investigations of amino acid
biosynthesis by Brevibactelium flavum provide an
excellent example of the effects of the dissolved
oxygen concentration on the production of a range of
closely related metabolites. These workers
demonstrated the critical dissolved oxygen
concentration for B. flavum to 0.01 mg dm3 and
considered the extent of oxygen supply to the culture
in terms of the degree of 'oxygen satisfaction’, that is
the respiratory rate of the culture expressed as a
fraction of the maximum respiratory rate. Thus, a value
of oxygen satisfaction below unity implied that the
dissolved oxygen concentration was below critical
level. The effect of the degree of oxygen satisfaction on
the production of a range of amino acids is shown in
From Fig. 9.2 it may be seen that the production of
members of the glutamate and aspartate families of
amino acids was affected detrimentally by levels of
oxygen satisfaction below 1.0, whereas optimum
production of phenylalanine, valine and leucine
occurred at oxygen satisfaction levels of 0.55, 0.60 and
The biosynthetic routes of the amino acids are
shown in Fig. 9.3, from which it may be seen that the
glutamate and aspartate families are all produced from
tricarboxylic acid (TCA) cycle intermediates, whereas
phenylalanine, valine and leucine are produced from
the glycolysis intermediates, pyruvate and
An example of the effect of dissolved oxygen on
secondary metabolism is provided by Zhou et al. 's
(1992) work on cephalosporinC synthesis by
Cephalosporium acremonium. These workers
demonstrated that the critical oxygen concentration
for cephalosporin C synthesis during the production
phase was 20% saturation. At dissolved oxygen
concentrations below 20% cephalosporinC
concentration declined and penicillin N increased.
The biosynthetic pathway to cephalosporin C is
shown in Fig. 9.4, from which it may be seen that
there are three oxygen-consuming steps in the
FIG. 9.4. The biosynthesis of cephalosporin C, indicating the oxy-gen consuming steps:
(ii) deacetoxycephalosporin C synthase (commonly called expandase),
(iii) deacetyl cephalosporin C synthase (commonly called hydroxylase)
(i) Cyclization of the tripeptide, a-amino-
adipyl-cysteinyl-valine into isopenicillin N.
(ii) The ring expansion of penicillin N into
deace-toxycephalosporin C (DAOC).
(iii) The hydroxylation of DAOC to give
The oxygen demand of a fermentation largely
depends on the concentration of the biomass
and its respiratory activity, which is related to
the growth rate.
Oxygen is normally supplied to microbial cultures in
the form of air, this being the cheapest available
source of the gas. The method for provision of a
culture with a supply of air varies with the scale of
i. Laboratory-scale cultures may be aerated by
means of the shake-flask technique where the
culture (50 to 100 cm3) is grown in a conical flask
(250 to 500 cm3) shaken on a platform contained
in a controlled environment chamber.
ii. Pilot and industrial-scale fermentations are
normally carried out in stirred, aerated vessels,
Bartholomew et at. (1950) represented the
transfer of oxygen from air to the cell, during
a fermentation, as occurring in a number of
i. The transfer of oxygen from an air bubble
ii. The transfer of the dissolved oxygen
through the fermentation medium to the
iii. The uptake of the dissolved oxygen by the
The rate of oxygen transfer from air bubble to the liquid
phase may be described by the equation:
CL : is the concentration of dissolved oxygen in the
fermentation broth(mmoles dm3 ),
t : is time (hours)
dCL/dt : the change in oxygen concentration over a time
period, i.e. the oxygen-transfer rate (mmoles O2 dm-3 h-1),
KL : the mass transfer coefficient (cm h-1)
a : the gas/liquid interface area per liquid volume (cm2 cm-3),
C* is the saturated dissolved oxygen concentration (mmoles
KL may be considered as the sum of the
reciprocals of the resistances to the transfer
of oxygen from gas to liquid and (C* - CL) may
be considered as the 'driving force' across
the resistances. It is extremely difficult to
measure both KL and 'a' in a fermentation
and, therefore, the two terms are generally
combined in the term KLa, the volumetric
mass-transfer coefficient, the units of which
are reciprocal time (h-1).
The larger the KLa, the higher the aeration capacity
of the system. The KLa value will depend upon the
design and operating conditions of the fermenter
and will be affected by such variables as aeration
rate, agitation rate and impeller design. These
variables affect 'KL' by reducing the resistances to
transfer and affect 'a' by changing the number, size
and residence time of air bubbles.
It is convenient to use KLa as a yardstick of
fermenter performance because, unlike the oxygen-
transfer rate, it is unaffected by dissolved oxygen
The dissolved oxygen concentration reflects the
balance between the supply of dissolved oxygen by
the fermenter and the oxygen demand of the
organism. If the KLa of the fermenter is such that the
oxygen demand of the organism cannot be met, the
dissolved oxygen concentration will decrease below
the critical level (Ccrit).
If the KLa is such that the oxygen demand of
the organism can be easily met the dissolved oxygen
concentration will be greater than Ccrit and may be
as high as 70 to 80% of the saturation level. Thus,
the KLa of the fermenter must be such that the
optimum oxygen concentration for product
formation can be maintained in solution throughout
Determination of KLa
Determination of KLa in a fermenter is important in
to establish its aeration efficiency and quantify
effects of operating variables on oxygen supply.
It is important to remember at this stage that
dissolved oxygen is usually monitored using a
dissolved oxygen electrode which records dissolved
oxygen activity or dissolved oxygen tension (DOT)
whilst the equations describing oxygen transfer are
based on dissolved oxygen concentration.
Thus, to translate DOT into concentration the
solubility of oxygen in the fermentation medium
must be known and this can present difficulties.
A number of different methods are available
1. The Sulphite oxidation technique
Measures the rate of conversion of a 0.5m solution of sodium sulphite to
sodium sulphate in the presence of a copper or cobalt catalyst
Na2SO3 + 1/2 O2 Na2SO4
Oxidation of sulphite is equivalent to the oxygen-transfer rate.
The dissolved oxygen concentration, for all practical purposes, will be
zero and the KLa may then be calculated from the equation:
(where OTR is the oxygen transfer rate)
Disadvantages i) slow,
ii) effected by surface active agents
iii) Rheology of solution not like media
Cu++ or Co++
2. Gassing out techniques
Estimation of KLa by gassing out involves measuring
the increase in dissolved O2 of a solution during
aeration and agitation
The oxygen transfer rate will decrease during the
period of aeration as C L approaches C* due to the
decline in the driving force (C* - CL).
The oxygen transfer rate, at one time, will be equal
to the slope of the tangent to the curve of values of
dissolved oxygen concentration against time of
aeration, as shown in Fig. 9.5.
2. Gassing out techniques: This involve initially lowering the oxygen
value to a low level. Two methods have been employed to achieve
this lowering of the dissolved oxygen concentration - the static
method and the dynamic method.
(i) Static Method
O2 concentration of the solution is lowered by gassing out with
The deoxygenated liquid is then aerated, agitated and increase in
dissolved O2 is monitored with oxygen probe.
The integration of equation (9.1) yields:
Thus, a plot of In (C* - CL) against time will yield a straight line of
slope -KLa, as shown in Fig 9.6.
It is very rapid than sulphite method (15 mins).
May utilise fermentation medium and dead cells.
Use of a membrane-type electrode, the response time of
which may be inadequate to reflect the true change in the rate
of oxygenation over a short period of time.
Use for small scale vessels, there are severe limitations to its
use on large scale fermenters which have high gas residence
The air supply to such a vessel is resumed after deoxygenation
with nitrogen, the oxygen concentration in the gas phase may
change with time as the nitrogen is replaced with air.
(ii) Dynamic Method:
Taguchi and Humphrey (1966) utilized the respiratory activity of
a growing culture in the fermenter to lower the oxygen level
prior to aeration.
Complex nature of fermentation broths the probe used to
monitor the change in dissolved oxygen concentration must be
of the membrane-covered type which may necessitate the use
of the response-correction factors referred to previously.
The procedure involves stopping the supply of air to the
fermentation which results in a linear decline in the dissolved
oxygen concentration due to the respiration of the culture, as
shown in Fig. 9.7.
In Fig. 9.7 the slope of the line AB is a measure of the
respiration rate of the culture.
At point B the aeration is resumed and the dissolved oxygen
concentration increases until it reaches concentration X.
BC, the observed increase in dissolved oxygen concentration
is the difference between the transfer of oxygen into solution
and the uptake of oxygen by the respiring culture as
expressed by the equation:
where x is the concentration of biomass
Qo2 is the specific respiration rate (mmoles of oxygen g -1
biomass h-1 ).
The term xQo2 is given by the slope of the line AB in Fig. 9.7.
Equation (9.4) may be rearranged as:
Thus, from equation (9.5), a plot of CL versus dCL/dt +
xQo2 will yield a straight line, the slope of which will equal
-1/KLa, as shown in Fig. 9.8. This technique is convenient
in that the equations may be applied using DOT rather
than concentration because it is the rates of transfer and
uptake that are being monitored so that the percentage
saturation readings generated by the electrode may be
The occurrence of oxygen-limited conditions during
deoxygenation may be detected by the deviation of
decline in oxygen concentration from a linear
relationship with time, as shown in Fig. 9.9.
When the oxygen demand of a culture is very
high it may be difficult to maintain the dissolved
oxygen concentration significantly above Ccrit during
the fermentation so that the range of measurements
which could be used in the KLa determination would
be very small. Thus, it may be difficult to apply the
technique during a fermentation which has an
oxygen demand close to the supply capacity of the
Both the dynamic and static methods are also
unsuitable for measuring KLa values in viscous
systems. This is due to the very small bubbles
(< 1 mm diameter) formed in a viscous system
which have an extended residence time
compared with 'normal’ sized bubbles.
Thus, the gassing out techniques are
only useful on a small scale with non-viscous
• Can determine KLa during an actual fermentation
• Rapid technique
• Can use a dissolved oxygen probe of the membrane type
• Limited range of dissolved oxygen levels can be studied
• Must not allow oxygen levels to fall below Ccrit
• Difficult to apply technique during a fermentation with a
high oxygen demand
• Relies on measurements taken at one point
3. The oxygen-balance technique
The KLa of a fermenter may be measured during a
fermentation by the oxygen balance technique which
determines, directly, the amount of oxygen transferred into
solution in a set time interval. The procedure involves
measuring the following parameters:
i. The volume of the broth contained in the vessel, VL (dm3).
ii. The volumetric air flow rates measured at the air inlet
and outlet, Qi and Qo' respectively (dm3 min-1).
iii. The total pressure measured at the fermenter air inlet
and outlet, Pi and Po, respectively (atm. absolute).
iv. The temperature of the gases at the inlet and outlet, Ti
and To, respectively (K).
v. The mole fraction of oxygen measured at the inlet and
outlet, Yi and Yo' respectively.
The oxygen transfer rate may then be determined from the
following equation (Wang et al., 1979):
where 7.32 X 105 is the conversion factor equalling (60 min h-1)
[mole/22.4 dm3 (STP)] (273 K/1 atm).
The ideal gaseous oxygen analyser is a mass spectrometer analyser
which is sufficiently accurate to detect changes of 1 to 2%. The KLa
may be determined, provided that CL and C* are known, from
The oxygen-balance technique appears to be the
simplest method for the assessment of KLa.
It can measure aeration efficiency during a
The balance method is the most desirable
technique to use and the extra cost of the
monitoring equipment involved should be a
Fluids may be described as Newtonian or non- Newtonian
depending on whether their rheology (flow)
characteristics obey Newton's law of viscous flow.
Consider a fluid contained between two parallel
plates area A and distance x apart. If the lower plate is
moved in one direction at a constant velocity, the fluid
adjacent to the moving plate will move in the same
direction and impart some of its momentum to the 'layer'
of liquid directly above it causing it, to move in the same
direction at a slightly lower velocity.
Newton's law of viscous flow states that the viscous
force, F, opposing motion at the interface between the
two liquid layers, flowing with a velocity gradient of
du/dx, is given by the equation:
where is the fluid viscosity, which may be considered
as the resistance of the fluid to flow.
Equation (9.7) may be written as:
F/ A is termed the shear stress (T) and is the applied
force per unit area, du/dx is termed the shear rate (y)
and is the velocity gradient. Thus:
Equation (9.8) conforms to the general relationship:
where K is the consistency coefficient.
n is the flow behaviour index or power law index.
For a Newtonian fluid n is 1 and the consistency
coefficient is the viscosity which is the ratio of shear
stress to shear rate.
Thus, a plot of shear stress against shear rate, for a
Newtonian fluid, would produce a straight line, the
slope of which would equal the viscosity. Such a plot
is termed a rheogram (as shown in Fig. 9.10).
A plot of shear stress against shear rate for a
non-Newtonian liquid will deviate from the
relationship depicted in Fig. 9.10, depending on
the nature of the liquid.
Several types of non-Newtonian liquids are
recognized and typical rheograms of types
important in the study of culture fluids are given
in Fig. 9.11, and their characteristics are
Some of the following fluid rheology:
1. Binghamplastic rheology
2. Pseudoplastic rheology
3. Dilatant rheology
4. Casson body rheology
1. Bingham plastic rheology
Bingham plastics are similar to Newtonian liquids apart
from the fact that shear rate will not increase until a
threshold shear stress or yield stress or yield value, is
exceeded. A linear relationship of shear stress to shear
rate is the yield stress is exceeded and the slope of this
line is termed the coefficient of rigidity or the plastic
Thus, the flow of a Bingham plastic is described by the
where n is the coefficient of rigidity.
is the yield stress.
Examples of these fluids include toothpaste and clay.
2. Pseudoplastic rheology
The apparent viscosity of a pseudoplastic liquid
decreases with increasing shear rate. Most polymer
solutions behave as pseudoplastics.
The flow of a pseudoplastic liquid may be described
by the power law model, equation (9.9), i.e.:
The flow-behaviour index is less than unity for a
pseudoplastic liquid, the smaller the value of n, the
greater the flow characteristics of the liquid deviate
from those of a Newtonian fluid.
Equation (9.9) may be converted to the logarithmic
3. Dilatant rheology
The apparent viscosity of a dilatant liquid
increases with increasing shear rate. The value
of the flow-behaviour index is greater than 1,
the greater the value the greater the flow
characteristics deviate from those of a
Example is liquid cement slurry.
4. Casson body rheology
A type of non-Newtonian fluid, termed a Casson
body, which behaved as a pseudoplastic in that
the apparent viscosity decreased with increasing
shear rate but displayed a yield stress and,
therefore, also resembled a Bingham plastic.
The flow characteristics of a Casson body may
be described by the following equation:
where Kc is the Casson viscosity.
FACTORS AFFECTING KLa VALUES IN
A. The effect of air-flow rate on KLa
1. MECHANICALLY AGITATED REACTORS
2. NON-MECHANICALLY AGITATED REACTORS
i. Bubble columns
ii. Air-lift reactors
3. THE RELATIONSHIP BETWEEN KLa AND POWER CONSUMPTION
4. THE RELATIONSHIP BETWEEN POWER CONSUMPTION AND OPERATING
B. The effect of medium and culture rheology on Kla
1. MEDIUM RHEOLOGY
2. THE EFFECT OF MICROBIAL BIOMASS ON KLa
i. Agitator design for non-Newtonian fermentations
ii. The manipulation of mycelial morphology
3. THE EFFECT OF MICROBIAL PRODUCTS ON AERATION
C. The effect of foam and antifoams on oxygen transfer
A. The effect of air-flow rate on KLa
1. MECHANICALLY AGITATED REACTORS
The effect of airflow rate on KLa values in
conventional agitated systems is illustrated in
The quantitative relationships between aeration
and KLa for agitated vessels are considered in
the subsequent section on power consumption.
If the impeller is unable to disperse the
incoming air then extremely low oxygen
transfer rates may be achieved due to the
impeller becoming 'flooded'.
Flooding is the phenomenon where the
air-flow dominates the flow pattern and is due
to an inappropriate combination of airflow rate
and speed of agitation.
The flooding could be avoided if:
where FS is the volumetric airflow rate at the
pressure conditions of the lower stirrer (m 3 sec-1)
N is the stirrer speed (sec-1),
D is the stirrer diameter (m),
g is the gravitational acceleration(m sec-2).
The different flow patterns produced by a disc
turbine that occur under a range of aeration
and agitation conditions (Fig. 9.13).
Figure 9.13 A shows the flow profile of a non-
aerated vessel and Figs 9.13 B to F the profiles
with increasing airflow rate. As air-flow rate
increases the flow profile changes from one
dominated by agitation (Fig. 9.13 B)to one
dominated by air flow (Figs9.13 D to F) until
finally the air flow rate is such that the air
escapes without being distributed by the
agitator (Fig. 9.13 F).
2. NON-MECHANICALLY AGITATED REACTORS
Bubble columns and air-lift reactors are not mechanically
agitated and, therefore, rely on the passage of air to both
mix and aerate.
i. Bubble columns
The flow pattern of bubbles through a bubble column
reactor is dependent on the gas superficial velocity(cm sec-1).
At gas velocities of below 1-4 cm sec-1 the bubbles will rise
uniformly through the medium and the only mixing will be
that created in the bubble wake. This type of flow is referred
to as homogeneous. At higher gas velocities bubbles are
produced unevenly at the base of the vessel and bubbles
coalesce resulting in local differences in fluid density. The
differences in fluid density create circulatory currents and
flow under these conditions is described as heterogeneous
as shown in Fig. 9.14.
Flooding in a bubble column is the situation when
the airflow is such that it blows the medium out of
the vessel. This requires superficial gas velocities
approaching 1 m sec-1 which are not attainable on
The relationship derived for non-coalescing, non-
viscous, large bubbles (6 mm diameter)will give a
reasonably; accurate estimation for most non-
c is the superficial air velocity corrected for
However, viscosity has an overwhelming
influence on KLa in a bubble column which
where π is the liquid dynamic viscosity (N s m-2 ).
The practical implication of this equation is that
bubble columns cannot be used with highly
ii. Air-lift reactors
The difference between a bubble column and an
air-lift reactor is that liquid circulation is
achieved in the air-lift in addition to that caused
by the bubble flow.
A given air-lift reactor and medium KLa varies
linearly with superficial air velocity on a log-log
scale over the normal range of velocities.
Thus, the KLa obtained in an air-lift will be less
than that obtained in a bubble column at the
same superficial air velocity, i.e. less than
The degree of agitation has been demonstrated to
have a profound effect on the oxygen-transfer
efficiency of an agitated fermenter.
The agitation assisted oxygen transfer in the
i. Agitation increases the area available for oxy-
gen transfer by dispersing the air in the culture
fluid in the form of small bubbles.
ii. Agitation delays the escape of air bubbles from
iii. Agitation prevents coalescence of air bubbles.
iv. Agitation decreases the thickness of the liquid
film at the gas-liquid interface by creating
turbulence in the culture fluid.
The degree of agitation may be measured by the
amount of power consumed in stirring the
vessel contents. The power consumption may be
assessed by using a dynamometer, by using
strain gauges attached to the agitator shaft and
by measuring the electrical power consumption
of the agitator motor.
3. THE RELATIONSHIP BETWEEN KLa AND POWER
A large number of empirical relationships have
been developed between KLa, power consumption
and superficial air velocity which take the form of:
Where Pg is the power absorption in an aerated
V is the liquid volume in the vessel
Vs is the superficial air velocity
K, x and y are empirical factors specific to the sys-
tem under investigation.
The KLas of a number of agitated and aerated vessels
(up to a volume of 66 dm3 ) containing one impeller,
using the sulphite oxidation technique, and derived
the following expression:
Thus, it may be seen from equation (9.15) that the
Kla value was claimed to be almost directly
proportional to the gassed power consumption per
The KLa of an aerated, agitated vessel is affected
significantly by the consumption of power during
stirring and, hence, the degree of agitation.
Quantitative relationships between power
consumption and operating variables may be
i. Estimating the amount of power that an
agitation system will consume under certain
circumstances, which could assist in
ii. In providing similar degrees of power
consumption (and, hence, agitation and,
therefore, KLas in vessels of different size.
4. THE RELATIONSHIP BETWEEN POWER CONSUMPTION
AND OPERATING VARIABLES
The relationship between power consumption and
operating variables in baffled, agitated vessels using the
technique of dimensional analysis. The power absorption
during agitation of non-gassed Newtonian liquids could be
represented by a dimensionless group termed the power
number, defined by the expression:
where Np is the power number,
P is the external power from the agitator,
ρ is the liquid density,
N is the impeller rotational speed,
D is the impeller diameter.
Thus, the power number is the ratio of external force
exerted(P) to the inertial force imparted (ρ N 3D5) to the
liquid. The motion of liquids in an agitated vessel may be
described by another dimensionless number known as the
Reynolds number which is a ratio of inertial to viscous
where NRc is the Reynolds number and
is the liquid viscosity.
Another dimensionless number, termed the Froude
number, relates inertial force to gravitational force and is
given the term:
where NFr is the Froude number and
g is the gravitational force.
The power number was related to the Reynolds
and Froude numbers by the general expression:
where c is a constant dependent on vessel
geometry but independent of vessel size
x and y are exponents.
In a fully baffled agitated vessel the effect of
gravity is minimal so that the relationship
between the power number and the other
dimensionless numbers becomes:
Therefore substituting from equations (9.16 and
Values for P at various values of N,D, ρ and may
be determined experimentally and the Reynolds
and power numbers for each experimental
situation my then be calculated. A plot of the
logarithm of the power number against the
logarithm of the Reynolds number yields a graph
termed the power curve is shown in Fig.9.15.
From Fig. 9.15 the power is divisible into three
clearly defined zones;
i. The laminar or viscous flow zone where the
logarithm of the power number decreases
linearly with an increase in the logarithm of the
ii. The transient or transition zone, where there is
no consistent relationship between the power
and Reynolds numbers.
iii. The turbulent flow zone, where the power
number is a constant, independent of the
Reynolds number so that the value of x is zero
and the value of the Reynolds number is in
If the values of the exponent, x are substituted into equation
(9.21) for the zones of viscous and turbulent flow then the
following terms are given:
Power consumption on the small scale may be represented as:
And on a large scale as:
Where the subscripts sm and L refer to the small and large scale
respectively. Maintaining the same power input per unit
Where V is the volume. Assuming the vessels to
be geometrically similar then c will be the same
regardless of scale and as the same broth would
be employed p would remain the same for both
For geometrically similar vessels
Therefore substituting for Dsm/DL in eq. (9.26)
A number of workers have produced correlations of gassed
power consumption, ungassed power consumption and
operating variables, that of being widely used:
where Q is the volumetric airflow rate.
The following correlation from 248 sets of published data:
where Q is the volumetric airflow rate,
g is the acceleration due to gravity,
W is the impeller blade width.
Using dimensional analysis:
where Na is the aeration number and equals Q/ND
T is the vessel diameter.
B. The effect of medium and culture
rheology on KLa
The rheology of a fermentation broth has a marked
influence on the relationship between KLa and the degree
of agitation. The objective of this section is to discuss the
effects of medium and culture rheology on oxygen transfer
during a fermentation.
The rheology of the broth is affected by the composition of
the original medium and its modification by the growing
culture, the concentration and morphology of the biomass
and the concentration and rheological properties of the
Therefore, fermentation broths vary widely in their
rheological properties and significant changes in broth
rheology may occur during a fermentation.
1. MEDIUM RHEOLOGY
Fermentation media contain starch as a carbon source
which may render the medium non-Newtonian and
relatively viscous. As the organism grows it will degrade the
starch and thus modify the rheology of the medium and
reduce its viscosity.
The study of the growth of Streptomyces aureofaciens on a
starch-containing medium. Before inoculation, the medium
displayed Bingham plastic characteristics with a well-
defined yield stress and an apparent viscosity of
approximately 18 pseudopoise; after 22 hours the
organism's activity had decreased the medium viscosity to
a few pseudopoise and modified its behaviour to that of a
Newtonian liquid; from 22 hours onwards the apparent
viscosity of the broth gradually increased, due to the
development of the mycelium, upto a maximum of
approximately 90 pseudopoise and the rheology of the
broth became increasingly pseudoplastic in nature.
2. THE EFFECT OF MICROBIAL BIOMASS
i. Agitator design for non-Newtonian
The biomass concentration and its morphological
form in a fermentation has been shown to have a
profound effect on oxygen transfer. However, the
highly viscous non-Newtonian broths of fungal
and streptomycete fermentations present major
difficulties in oxygen provision, the productivities
of many such fermentations being limited by
The difference in the pattern of oxygen uptake
between unicellular and mycelial fermentations as
illustrated in Fig. 9.16. In both unicellular and
mycelial fermentations the pattern of total oxygen
uptake is very similar during the exponential growth
phase, up to the point of oxygen limitation.
However, during oxygen limitation, when arithmetic
growth occurs, the oxygen uptake rate remains
constant in a unicellular system whereas it
decreases in a mycelial one.
The only possible explanation for such a decrease is
the increasing viscosity of the culture caused by the
increasing mycelial concentration.
Figure 9.17 illustrate the effect of Penicillium
chrysogenum mycelium on KLa. The KLa decreased
approximately in proportion with the square root of the
broth viscosity, i.e.:
ii. The manipulation of mycelial morphology
The biomass of mycelial organisms grown in
submerged culture may vary from the
filamentous type, in which the hyphae form a
homogeneous suspension dispersed through
the medium, to the 'pellet' type consisting of
compact, discrete masses of hyphae. The
filamentous form tends to give rise to a highly
viscous, non-Newtonian broth where as the
pellet form tends to produce an essentially
Newtonian system with a much lower viscosity
making oxygen transfer much easier.
The KLa attained in the lovastatin
Aspergillus terreus fermentation was 20h-1
with a filamentous culture and 80 h-1 with
a pelleted one at the same power input.
Thus, the morphological form of a mycelial
organism in submerged culture has a major
effect on the broth rheology and may,
therefore, be expected to influence
3. THE EFFECT OF MICROBIAL PRODUCTS
The product of a fermentation contributes
relatively little to the viscosity of the culture
broth. However, the exception is the
production of bacterial polysaccharides,
where the broths tend to be highly viscous
Normally, microbial polysaccharides tend to
behave as pseudoplastic fluids, although some
have also been shown to exhibit a yield stress.
The yield stress of a polysaccharide can make the
fermentation particularly difficult because, beyond
a certain distance from the impeller, the broth will
be stagnant and productivity in these regions will
be practically zero.
Thus, bacterial polysaccharide fermentations
present problems of oxygen transfer and bulk
mixing similar to those presented by mycelial
An air-lift loop reactor is designed incorporating a
pump to circulate the highly viscous broth.
C. The effect of foam and antifoams on
The high degree of aeration and agitation required in a
fermentation frequently gives rise to the undesirable
phenomenon of foam formation.
In extreme circumstances the foam may overflow from
the fermenter via the air outlet or sample line resulting in
the loss of medium and product, as well as increasing the
risk of contamination.
The presence of foam may also have an adverse effect on
the oxygen-transfer rate.
Thus, it is desirable to break down a foam before it
causes any process difficulties and this may be achieved
by the use of mechanical foam breakers or chemical anti-
All antifoams are surfactants and may,
themselves, be expected to have some effect on
oxygen transfer. Antifoams tend to decrease the
oxygen-transfer rate, it also cause the collapse of
bubbles in foam but they may favour the
coalescence of bubbles within the liquid phase,
resulting in larger bubbles with reduced surface
area to volume ratios and hence a reduced rate
of oxygen transfer.
THE BALANCE BETWEEN OXYGEN
SUPPLY AND DEMAND
This section attempts to bring these two aspects
together and considers how processes may be
designed such that the oxygen uptake rate of the
culture does not exceed the oxygen transfer rate of
The volumetric oxygen uptake rate of a culture is
described by the term, Qo2x, where Qo2 is the
specific oxygen uptake rate (mmoles O2 g-1 biomass
h-1 ) and x is biomass concentration (g dm-3 ). Thus,
the units of Qo2x are mmoles oxygen dm-3 h-1 .
It is necessary that the oxygen-transfer rate of
the fermenter matches the oxygen uptake rate
of the culture whilst maintaining the dissolved
oxygen above a particular concentration. A
fermenter will have a maximum KLa by balancing
the supply and demand. This may be achieved
i. Controlling biomass concentration.
ii. Controlling the specific oxygen uptake rate.
iii. A combination of (i) and (ii).
i. Controlling biomass concentration
The highest biomass concentration (termed the critical
biomass or xcrit ) which can be maintained under fully
aerobic conditions in a fermenter of known KLa. Thus, xcrit
is the biomass concentration which gives a volumetric
uptake rate (Qo2Xcrit) equal to the maximum transfer rate
of the fermenter, i.e. KLa (C* - Ccrit). If Ccrit is defined as the
dissolved oxygen concentration when:
Qo2 = 0.99Qo2max
then the volumetric oxygen uptake rate when the
dissolved oxygen concentration is Ccrit will be:
0.99Qo2max 'xcrit .
If the oxygen transfer rate were equal to the uptake
rate when the dissolved oxygen concentration equals
Equation (9.29) may be used to calculate xcrit for a
fermenter with a particular KLa value:
Equation (9.30) may also be modified to calculate
biomass concentration which may be maintained
fixed dissolved oxygen concentration above Ccrit:
This is shown graphically in Fig. 9.20.
The upper graph represents the relationship
between the dissolved oxygen concentration
and the volumetric oxygen transfer rate
achievable in three fermenters (plots 1, 2 and 3
represent fermenters of increasing KLa values)
while the lower graph represents the
relationship between biomass and the
volumetric oxygen uptake rate of the culture.
ii. Controlling the specific oxygen
Very few commercial fermentations are operated in
continuous culture, fed-batch culture is widely used in
industrial fermentations and provides an excellent tool for
the control of oxygen demand.
The most common way in which the technique is applied
to control oxygen demand is to link the nutrient addition
system to a feed-back control loop using a dissolved
oxygen electrode as the sensing element. If the dissolved
oxygen concentration declines below the set point then
the feed rate is reduced and when the dissolved oxygen
concentration rises above the set point the feed rate may
These techniques are particularly important in
the growth-stage of a secondary metabolite
mycelial fermentation prior to product
production when the highest growth rate
commensurate with the oxygen transfer rate of
the fermenter is required.