Figure 10.6 Dimensionless
concentration as a function
of the dimensionless distance inside
the biofilm (y
+=y/Lf) for a flat biofilm
with zero order kinetics at several
values of the Thiele modulus (ø): (A)
biofilm partially penetrated by the
substrate; (B) biofilm fully penetrated
by the substrate.
only first order or zero order reactions (and no half-order apparent reaction) can exist
when α<2. If the concentration is low and the biofilm is thin (1st order process) or if the
concentration is very high and the biofilm is totally penetrated (zero order process),
diffusional limitations will not affect the order of the overall process; that is, an intrinsic
zero order reaction in the biofilm will yield an apparent overall zero order reaction
(process), and an intrinsic first order reaction will yield an apparent first order reaction.
For α>2, the apparent (or observable) “half-order” process will predominate for
intermediate values of the substrate concentration, although the intrinsic order is zero.
The half-order case emphasises the existence of strong diffusional limitations inside the
biofilm.
Figure 10.7 shows the internal efficiency factor as a function of a “dimensionless
observable modulus” (ψ) for two different geometries, spheres and slabs. The new
modulus ψ is defined as:
(34)
Limiting substrateMany biological degradation processes involve at least two nutrients or, more precisely, a
nutrient/substrate and an electron acceptor: they are of the oxidation-reduction (redox)
type. In order to use the diffusion-reaction model described above, it is essential to
Biofilm reactors 309