Biofilm kinetics
s
.... _ _yJ.
-vi- 5
0.5
0.1
0 '---....3o-'---'='--..... 0.01'------'-----'----+
0
0.5
1
0.1
10
~ = ~
Fig 5.2
The concentration distribution and efficiency factor for a biological film in which a
first order reaction occurs. The efficiency is reduced due to the limited transport
capacity of the diffusion.
transport through the surface of the film is proportional to the concentration just
outside the film.
For the reaction per surface area we get:
tanh a
fA= N =klVf LS. £ I £ = - -
a
and for the reaction rate per surface area we get:
where k1A is a reduced rate constant,£ is an efficiency factor.
(5.6)
(5.7)
In Fig 5.2 the efficiency factor is shown as a function of the dimensionless expression
a for film geometry and diffusion. It appears from the figure that for a < 1, £ - 1.0,
corresponding to a 100 per cent efficiency. The film is fully penetrated. The film is
considered to be thick. For a> 1 applies
~
1
k!Vf
£- - = - -
a
L
(5.8)
where.._) D has the dimension "length" and can be understood as the efficient
klVf
diffusion path.
(5.9)
for thick biofilms.
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