(28)
Here, β corresponds to the biofilm internal efficiency (ηi) for a flat plate geometry and
zero order reaction.
bi) If the substrate fully penetrates through the whole microbial film (β>1),
the surface reaction rate will be given by:
(29)
or by;
(26)and the concentration profile will be:
(30)
In a fully penetrated biofilm, the reaction is of zero order throughout the whole biological
layer.
bii) When the substrate cannot fully penetrate the microbial film (β<1), then
the surface reaction rate is given by Equation (27), above (no external
mass transfer control):(27)
In this case, the overall process (also named as the “apparent” or “observable” reaction)
has a half-order dependency on the bulk substrate concentration. The concentration
profile (Figure 10.6) inside the biofilm in the partially penetrated film is then:
(31)The reaction rate constants for the first and zero orders are related by:
(32)where Ks is the affinity constant of the Monod model.
It can be shown (Harremöes and Henze 1995) that, by defining parameter as:
(33)Multiphase bioreactor design 308