Sustainability and Stability - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 842

Therefore, the washout condition for the predator (while prey is not washed out) is

D k dp þ m p max YF b=S S 0

(16.92)

K p þ YF b=S S 0

All washout (both prey and predator are washed out) condition can be obtained by first
setting X p ¼ 0 (prey washed out). Eqn (16.88) indicates that if prey is also being washed
out

d X b
d t < 0 ,

> m b max S
K b þS

D (16.93)

0.50

0.25

0

1.5

1.0

0.5

0

8

6

4

2

0

0 2 4 6 8 10

Time, days

12 14 16 18 20

FIGURE 16.21 Oscillations of the concentrations of substrate (glucose), prey (E. coli), and predator
(D. discotideum) with time in a continuous culture. Predictions based on Eqns (16.87) through (16.89) (lines),
superimposed on experimental data (symbols), for continuous culture with a residence time of 16 h or D ¼ 0.0625/h
at 25 C. The kinetic parameters are given by k dp ¼ 0, m pmax ¼ 0.24/h, K p ¼ 4 10 11 E. coli/L, m bmax ¼ 0.25/h, K b ¼ 5
10 4 g/L, YF p/b ¼ 7.14 10 4 D. discoideum/E. coli,YF b/S ¼ 3 10 12 E. coli/g. Replotted from H. M. Tsuchiya, J. F.
Drake, J. L. Jost, and A. G. Fredrickson, “Predator-Prey Interactions of Dictyostelium discoideum and E. coli in Continuous
Culture”, J. Bacteriology. 110(3): 1147-1153, 1972.