for different values of substrate
modulus μ for external diffusion.
Figure 4.2 Rate of the inhibited
biocatalytic reaction, with α 0 =1 and
α 1 =1, (solid lines) and of the substrate
transport (dashed line) as a function of
the dimensionless substrate
concentration at the biocatalyst surface
for different α 2 values. Three steady-
states of the overall reaction are
possible for some values of βB, μ and
α 2 at βS1 and, βS2 and βS3.
1972). The response of the system to this perturbation will be an increase of the substrate
consumption rate while the diffusion rate, that is, the rate of substrate supply to the
surface, decreases. Since both effects tend to decrease βS, the surface concentration will
return to βS1. Therefore, the rate at βS1 is stable and can occur in practice. At βS2 both the
diffusion and reaction rates decrease when s is slightly increased. However, the decrease
in the reaction rate is greater than that in the diffusion rate resulting in a further increase
of the surface concentration and the system does not return to βS2, which is consequently
unstable. Similar considerations show that the rate at βS3 is stable.
Multiphase bioreactor design 98