Abstract A mathematical model is formulated describing the mechanism of substrate removal by a microbial slime over which a film of liquid, containing the substrate as dissolved biodegradable material, is flowing. It is assumed that a lack of either organic carbon, oxygen, or both simultaneously, can limit the overall rate of the process. Basic chemical engineering principles of interfacial mass transfer, diffusion and biochemical reaction are used in the formulation of the model and the resulting set of equations is solved by digital computer using typical kinetic parameters taken from the literature. Predictions of whether organic carbon, oxygen, or both simultaneously, limit the process, the substrate removal rate, and the active depth of the biofilm are made. Data were obtained in support of the model by measuring substrate removals on a vertically mounted experimental biofilm reactor over a range of hydraulic and organic loadings typical of industrial-scale operation. Good agreement between the experimental results and the model predictions was obtained with the exception of the data pertaining to hydraulic loadings approaching the minimum wetting rate. These data deviated from the predicted values at high substrate concentrations indicating that under conditions of low hydraulic load the model is less satisfactory for describing the system. Conversely it may be that at low hydraulic loads and high applied substrate concentrations experimental accuracy is poor.
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