Biomedical Engineering Reference
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C
A
= C
A0
C
A0
= C
A
+
-r
A
D
Bifurcation point
0
0
C
A0
FIGURE 16.6
Steady-state solution of C
A
as a function of feed concentration C
A0
for a fixed dilution rate D.
bifurcation phenomenon,
Figs. 16.6 and 16.7
show the variation of the steady-state solution
(C
A
) as a function of the feed parameters.
Fig. 16.6
shows that there are three values of C
A
when the feed concentration C
A0
is set
between the two bifurcation points. Therefore, there are three branches of the steady solution:
upper, middle, and lower branches. Based on our discussions in
x
16.1.2, both upper and
lower branches are stable, while the middle branch is not stable. Therefore, the middle
branch is not observable experimentally as any fluctuations would lead the operating point
to shift away to a new location. We can observe from
Fig. 16.6
that when the feed concentra-
tion is very high with a fixed dilution rate, the concentration of the reactant coming out of the
C
A0
-r
A
C
A0
-
C
A
D =
Bifurcation point 1
Bifurcation point 2
0
0
D
IG
D
EX
D
FIGURE 16.7
Steady-state solution of C
A
as a function of dilution rate D for a fixed feed concentration C
A0
.
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