Biofilm kinetics
0.5
1
~ =t
partially efficient biofilm
fully efficient biofilm
1
~=X
L
Fig 5.3
The concentration distributions in a biofilm in which a first order reaction occurs.
Right: a biofilm in which the substance diffuses to the bottom. Left: a biofilm in which
the substance cannot penetrate to the bottom of the film.
From which we get the following solution:
(5.14)
(5.15)
where~, is the efficient part of the film. The concentration distribution in the film for
this case is also shown in Fig 5.3.
From Expression 5.14 it appears that the dimensionless parameter~ is an expression
of the relative length that a substrate can penetrate the biofilm. Hence ~ is called the
degree of penetration.
Hence, for the overall transport through the surface of the film we get:
r A = N = L ~, kovf = '1/2 kovf D 5 112
(5.16)
It is remarkable that while the zero order reaction in the fully efficient biofilm still
resulted in a reaction of zero order- independent of S- the zero order reaction in the
partially efficient film results in a half order reaction in the water outside the film.
For the surface area specific reaction rates of the material, of which the film forms a
part, we get:
148