Biomedical Engineering Reference
In-Depth Information
TABLE 11.6
Typical Values of m
max
and K
S
for Various Organisms and Substrates at Optimum Growth
Temperature
m
max
,h
L1
Microorganism
Limiting substrate
K
S
, mg/L
Escherichia coli at 37
C
Glucose
0.8
e
1.4
2
e
4
E. coli at 37
C
Glycerol
0.87
2
E. coli at 37
C
Lactose
0.8
20
Saccharomyces cerevisiae at 30
C
Glucose
0.5
e
0.6
25
Candida tropicalis at 30
C
Glucose
0.5
25
e
75
Candida sp.
Oxygen
0.5
0.045
e
0.45
Hexadecane
0.5
Klebsiella aerogenes
Glucose
0.85
9
Aerobacter aerogenes
Glucose
1.22
1
e
10
Source: H.W. Blanck and D.S. Clark, Biochemical Engineering, 1996, Marcel Dekker, Inc: New York.
and a general product formation rate of
r
P
X
¼
m
P
max
S
K
P
þ S
m
P
¼
(11.22)
This is the most commonly used microbial growth model. As we have discussed in
11.4, it
performs well in pseudosteady state (or balanced growth) cases.
Table 11.6
shows typical
values of
x
m
max
and K
S
.
In Chapters 8, 9 10 and
11.4, we learned that the rate form may be taken on any individual
step in particular when the mathematical forms are similar. To show Monod equation is truly
an approximation to microbial growth, we further consider the effect of external diffusion (or
mass transfer) on the growth rate. In this case, the equation of mass transfer rates is different
mathematically from the enzymatic reaction rate. More extensive coverage on the mass trans-
fer effects is found in Chapter 17. Let us consider that the bulk medium contains S g/L of
substrate and the substrate concentration in the medium just outside of the cell membrane
is S
c
. The substrate concentration just outside of the cell membrane is the concentration that
the cell can make use of. Therefore:
x
r
X
X
¼
m
max
S
c
m
G
¼
(11.55)
K
S
þ S
c
The substrate uptake rate is thus given by
r
X
YF
X=S
¼
X
YF
X=S
m
max
S
c
K
S
þ S
c
r
S
¼
(11.56)
Mass transfer flux between the bulk medium and the microbial cells is given by
X
r
cell
ðS S
c
Þ
N
S
c
¼ k
L
a
c
(11.57)
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