Mathematical modelling of biofilm systems in biological wastewater treatment-a review

The bioprocessing community has traditionally focused on fermentation technology or cell culture methods (e.g., the bioreaction step) as opposed to downstream processing operations (e.g., product recovery and purification). In recent years, however, an interest in integrated biomanufacturing has emerged, while also considering the overall environmental impact of bioprocessing schemes. In this new context, it is imperative for a bioprocessing platform to be conceived beyond the final product itself. A further focus should be on effluent and/or side stream reutilization and/or abatement. One such option is the use of biofilm systems, which can be understood by employing appropriate and implementable modelling approaches. In this paper, we advocate for the adoption of a zero-dimensional biofilm modelling approach, which does not describe biofilm structures at all, but which instead correctly describes the macrokinetic behaviour of biofilm systems. We elaborate on the various attempts to model the biofilm system in a technical scenario, considering the evolution of modelling approaches from zero-dimensional to three-dimensional approaches. Additionally, we discuss relevant kinetic principles - that is, Fick's laws of diffusion, the Monod model of reaction and the combination of both in the diffusion-reaction equation. We then briefly outline the content of relevant selected literature. Finally, we evaluate both zero-dimensional and higher-dimensional biofilm modelling approaches, offering practical recommendations for selecting the most suitable framework under various engineering and research conditions. (c) 2025 Society of Chemical Industry (SCI).