Conduction-based modeling of the biofilm anode of a microbial fuel cell

The biofilm of a microbial fuel cell (MFC) experiences biofilm-related (growth and mass transport) and electrochemical (electron conduction and charger-transfer) processes. We developed a dynamic, one-dimensional, multi-species model for the biofilm in three steps. First, we formulated the biofilm on the anode as a "biofilm anode" with the following two properties: (1) The biofilm has a conductive solid matrix characterized by the biofilm conductivity (κ_bio). (2) The biofilm matrix accepts electrons from biofilm bacteria and conducts the electrons to the anode. Second, we derived the Nernst-Monod expression to describe the rate of electron-donor (ED) oxidation. Third, we linked these components using the principles of mass balance and Ohm's law. We then solved the model to study dual limitation in biofilm by the ED concentration and local potential. Our model illustrates that κbio strongly influences the ED and current fluxes, the type of limitation in biofilm, and the biomass distribution. A larger κ_bio increases the ED and current fluxes, and, consequently, the ED mass-transfer resistance becomes significant. A significant gradient in ED concentration, local potential, or both can develop in the biofilm anode, and the biomass actively respires only where ED concentration and local potential are high. When κ_bio is relatively large (i.e., ≥10^-3 mS cm ^-1), active biomass can persist up to tens of micrometers away from the anode. Increases in biofilm thickness and accumulation of inert biomass accentuate dual limitation and reduce the current density. These limitations can be alleviated with increases in the specific detachment rate and biofilm density.