Bioreactor Design and Operation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 952

3a 3 þ 1 p i

þ 1 þ p i
2

3 p

a 4 þ a 6

S 3 ¼ y 3 þ a 2

3a 3 ¼ x 3 a 5 x 3 þ a 2 3a 3 ¼ a 2

p

a 4 a 6 (18.85c)

3

2

where i is the imaginary unit,

p

1 i ¼ (18.85e)

6 0 or at least S 1 is of real value. There can be
multiple steady-state solutions besides the trivial solution. Also, there are regions where real-
istic steady-state solution does not exist at all. For example, when D is in the neighborhood of
m max d k d the right-hand side of Eqn (18.70) would be able to equal to 0. There is also potential
for coexistence of microbes in continuous culture because of the added flexibility in wall
attachment.
Fig. 18.15 shows the steady-state solutions of a continuous Enterobacter cloacae (formerly
Aerobacter cloacae) culture in a chemostat. The symbols are experimental data, while the lines
are drawn with surface adhesion of cells. There are three real solutions for the substrate
concentrations and only one has a value between 0 and S 0 . One can observe that the washout
region has a long trail before the biomass concentration drops to zero and the substrate
increases to feed concentration.

All three roots (S 1 , S 2 , S 3 ) can be real if a

1.4 2.5

1.2

2.0

1.0

1.5

0.8

0.6

1.0

0.4

0.5

0.2

0.0 0.0

0.0 0.5 1.0 1.5 2.0

D , h -1

FIGURE 18.15 Effect of surface adhesion of cells on the continuous culture of E. cloacae (formerly A. cloacae).
The parameters used for the lines are:

m max ,h 1

k d ,h 1

S 0 , g/L YF X/S , g/g K S , g/L K s X , L/g C s , g/L

2.5 0.8 0.014 0.53 0.018 7.7 0.1786

Data from Herbert D, Elsworth R, and Telling R. C., “The Continuous Culture of Bacteria; a Theoretical and Experimental
Study”, J. Gen. Microbiol. 14, 601 e 622 (1956).