the biofilm (y+=y/Lf) for a flat biofilm
with first order kinetics at several
values of the Thiele modulus (ø) and
efficiency factor (ηi).
Sometimes, the observed reaction rate per unit area of biofilm (rA) is written as:
(21)
where η is the overall biofilm efficiency for a flat plate:
(22)Bi is the mass transfer Biot number which represents the ratio between the maximum
external mass transfer rate and the maximum internal mass transfer rate:
(23)
Equations (16) and (21) are simply two different forms of the same expression,
b) Zero order intrinsic reaction:
(24)
where;
(25)λ is a dimensionless variable that represents the ratio between the external mass transfer
rate and the internal coupled diffusion-reaction rate.
If the external mass transfer is the limiting step of the overall process, then:
(26)If the internal phenomena of diffusion and reaction are much slower than the external
mass transfer (consumption rate limited by internal processes), then:
(27)When applying the equations for zero order kinetics, two extreme situations can be easily
identified: either the biofilm is fully penetrated by the substrate or not. A new parameter
β, which represents the degree of substrate penetration in the biofilm, is related to the
reciprocal of the Thiele modulus for zero order intrinsic reactions:
Biofilm reactors 307