The criterion for the oxygen limitation of substrate uptake in microbial film fermenters is expressed in terms of diffusion coefficients, utilization coefficients, and the free solution concentrations of substrate and oxygen. It is proposed that the ideal film thickness in such fermenters is equal to the penetration depth of the limiting substrate. The ideal film thickness is calculated, in terms of the parameters contained in the criterion for oxygen limitation, for three separate kinetic rate expressions. It is found that for the air–glucose–microbe system a simplified kinetic rate expression can be used and the region of dependence on two substrates is shown to be very limited. This is not true for other systems. Maximum uptake rates are calculated for a range of concentrations. Finally, it is shown that the procedure used can be generalized to determine the limiting substrate in a multisubstrate system and to calculate ideal film thickness and uptake rates for any pair of substrates where the kinetics of substrate uptake are known for the individual microorganism.
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Howell et al. (1976) studied this question.
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