identify the limiting substrate (substance), that is, the first one to reach zero concentration
(that is, to be completely consumed) within the biofilm. This depends on the mass
transfer and the reaction rates of the two components in the microbial layer. For the case
of intrinsic zero order kinetics, and taking into account the penetration depths (β), it can
be easily shown (Harremöes and Henze 1995) that:
Figure 10.7 Biofilm internal efficiency
as a function of the “dimensionless
observable modulus” ψ (equation 34).
i) the oxidant will be the limiting factor if:
(35a)
where the subscripts “ox” and “red” refer to the oxidant and reductant substance,
respectively, and Nox/red is the stoichiometric ratio between the two reactants;
ii) the reductant will be the limiting factor if:
(35b)
The previous equations apply to a flat biofilm. They can also be used when the biofilm is
formed around a particle, provided that the microbial layer is thin. In the case of thick
biofilms around small spherical supports or of microbial granules without any support
surface, a spherical geometry should be considered in the derivation of the model, and the
variable Lf in the Thiele modulus should be replaced by rpf/3 (rpf is the radius of the
spherical biofilm-particle). The reader should look in specialised textbooks on
heterogeneous catalysis for further modifications to the model equations when using
spherical or cylindrical particles.
Multiphase bioreactor design 310