The influence of an additional mass transfer resistance at the liquid/solid interface must be considered for the case of low (kLa) values (Fig. 7.6, curve V). The required oxygen uptake rate can only be guaranteed for sinking concentrations cO at z = 0.
The boundary condition, Eq. (7.7a), must be replaced by:
After consideration of Eq. (7.7b) as well as:
which is called the Biot number as a relation of:
mass transfer rate liquid/solid diffusion rate inside the biofilm then Eq. (7.19) can be rewritten in dimensionless form:
Now, ç is influenced by three numbers:
and it is very difficult to present the field of results using only one figure. Therefore, we will not discuss these results in detail. Notice that, with decreasing Biot number (decreasing concentration c0 as a result of decreasing mass transfer rate liquid/solid), the process is controlled more and more by liquid/solid mass transfer and the efficiency coefficient ç decreases. Finally, the problem corresponds to that of Section 7.4.3. Also, the problem corresponds to that of Section 7.4.5 for high Bi numbers; and this follows from a high (kLa)L and biofilm thickness L.
Results for a spherical particle filled with bacteria or enzymes were published by Fink and Schultz (1973).
164 | 7 Aerobic Treatment with Biofilm Systems 7.4.7
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