(17)
and is the Thiele modulus for a first order reaction for a flat plate:
(18)
The Thiele modulus represents the ratio between the reaction rate and the internal
diffusion rate. When the Thiele modulus has a small value, the biological reaction will be
the rate limiting step. For high values of , internal diffusion will control the rate of
substrate consumption. The more general expression of the Thiele modulus, which can be
applied to reactions of any order “n” is:
(19)knf is the rate constant for a reaction of order “n”.
The concentration profile in the biofilm (Figure 10.5), in the case of first order
kinetics, is:
(20)where y is the distance inside the biofilm (measured from the liquid-biofilm interface)
corresponding to the concentration Sf.
Figure 10.5 Dimensionless
concentration as a function
of the dimensionless distance inside
Multiphase bioreactor design 306