Biofilters
(5.3)
The characteristic equation of this second order homogenous differential equation
with constant coefficients is:
The complete solution for real values of a is
The constants A and B are determined by these limiting conditions:
~=1
SVf =1
asVf
- = 0
a~
from which the complete solution is obtained:
svf = cosh a ~ - tanh a sinh a ~
By using the addition formulas, we get:
svf = cosh( a (1 - ~)) , a= ~ klVtL
2
cosha
D
(5.4)
(5.5)
The concentration distribution for different values of the dimensionless expression
of the geometry and diffusion of the biofilm is shown in Fig 5.2.
The transport through the surface of the biofilm is
N = _ n(a Svtl = _ Q(a sv£ 1 5
ax =O
Ll a~ ~=O
By differentiation of 5.5 and substitution, we get:
D
N =L (a tanh ex)
tanh a
S=k1VfL--S
(X
from which it can be seen that a first order reaction in the biofilm can be interpreted as
a corresponding first order reaction in the water outside the biofi.lm. The reaction as a
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