Biomedical Engineering Reference
In-Depth Information
species would be washed out as one can infer from
Fig. E16-7
. Therefore, only one
species would survive. As a result, the coexistence point is not realizable in
operations.
16.6.3. Interactions of Two Mutualistic Species
Species A produces P
A
as a by-product of growth, while species B produces P
B
. Organism
B requires P
A
to grow, while A requires P
B
. The feed to a chemostat contains all essential
nutrients except for P
A
and P
B
and A and B may compete for substrate, S, in the feed as
shown in
Fig. 16.20
.
Mass balances of species A and B, as well as the common growth-limiting substrate:
d
ð
X
j
V
Þ
d
t
Qð0X
j
Þþr
j
V ¼
(16.69)
d
ðP
j
VÞ
d
t
Qð0P
j
Þþr
Pj
V ¼
(16.70)
d
ð
SV
Þ
d
t
QðS
0
SÞþr
S
V ¼
(16.71)
Noting that
r
j
¼ðm
j
k
dj
ÞX
j
(16.72)
r
PA
¼
YF
P
A
m
A
X
A
m
B
X
B
(16.73)
YF
B=P
A
r
PB
¼ YF
P
B
m
B
X
B
m
A
X
A
YF
A=P
B
(16.74)
r
S
¼
m
A
X
A
YF
A=S
m
B
X
B
(16.75)
YF
B=S
Q, S = S
0
Feed
X
A
=
X
B
= 0
P
A
=
P
B
= 0
V
Q
Effluent
S
,
X
A
,
X
B
,
P
A
,
P
B
FIGURE 16.20
A mixed culture of A and B feeding on one common growth-rate-limiting substrate S in
a chemostat; A also feeds on the by-product produced by B while B feeds on the by-product produced by A.
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