Modeling Steady-State Biofilms with Dual-Substrate Limitations

This Technical Note presents a systematic analysis of a steady-state biofilm model for the simultaneous utilization of an electron donor and an electron acceptor. It shows that the flux of the electron donor is balanced by the flux of the electron acceptor and the concentrations of the two substrates linearly depend on each other in a steady-state biofilm. An analytical solution can be derived for the substrate fluxes into the biofilm as direct functions of the bulk substrate concentrations. This analytical solution, not much more complicated than the one given by the classic single-substrate biofilm model, eliminates the need to identify the rate-liming factor from the two substrates prior to using it. Comparing the single-substrate and the dual-substrate biofilm models shows that the difference between the two for predicting the flux of the limiting substrate of a deep biofilm can be significant when the bulk concentration of the nonlimiting substrate becomes comparable with or less than its Monod half-saturation constant.