Biomedical Engineering Reference
In-Depth Information
12.1.2. The Ideal Chemostat
An ideal chemostat is the same as a perfectly mixed continuous-flow reactor or CSTR.
Most chemostats require some control elements, such as pH and dissolved oxygen (DO)
control units, to be useful. Fresh sterile medium is fed to the completely mixed and aerated
(if required) reactor, and cell suspension is removed at the same rate. Liquid volume in the
reactor is kept constant.
Figure 12.3
is a schematic of a simplified chemostat. The culture volume in the reactor is
maintained by withdrawing the effluent from an overflowing side device. Amaterial balance
on the cell concentration around the chemostat yields
d
ðVXÞ
d
QðX
0
XÞþr
X
V ¼
(12.1)
t
where
Q
is the volumetric flow rate of nutrient solution (L/h),
V
is the culture volume (L)
(assumed constant),
X
is the cell concentration (g/L), and
r
X
is the net production rate of
biomass. At steady state, nothing changes with time and this includes
d
ðVXÞ
d
¼ 0
(12.2)
t
Dividing
Eqn (12.1)
by reactor volume
V
and substituting in
Eqn (12.2)
, we obtain the cell
mass balance equation for an ideal chemostat:
DðX X
0
Þ¼r
X
(12.3)
where D is
dilution rate
and D
Q/ V
. D is the reciprocal of space time.
Figure 12.4
shows
a schematic of cell mass balance on the cell mass concentration vs cell growth rate plane.
Clearly, the mass balance is a straight line. The intercept(s) are the solutions for the chemostat
for the given cell growth curve.
The net growth rate can be expressed as
¼
r
X
¼ m
net
X
(12.4)
Q
Feed
S
0
,
X
0
= 0,
P
0
= 0
Q
S
,
X
,
P
Effluent
Air sparger
FIGURE 12.3
A schematic of a chemostat.
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