Abstract
A mathematical model for microbial fuel cells (MFC) which integrates macro-scale time-dependent mass balances for solutes and biomass in the anodic liquid with a micro-scale individual-based two-dimensional biofilm model is developed. Computational fluid dynamics and Nernst–Plank mass and charge balances with diffusion, electromigration, convection and electroneutrality in the biofilm are combined to calculate spatial pH distribution and solutes speciation. Soluble redox mediators are the electron shuttle between microbial cells and the electrode. The model describes the generally observed variations of pH, solute concentrations and electrical current produced over time from electroactive biofilms. Numerical simulations also show the effect of bicarbonate buffer and mass transfer through the proton exchange membrane on the microbial population within a mixed anaerobic digestion sludge consortium of methanogenic and electrogenic microorganisms. In addition, the new modeling approach opens the way to study the influence of fluid flow and any two- or three-dimensional biofilm and electrode geometry on the MFC output parameters. Hydrodynamic calculations show that porous bio-electrodes with greater specific surface area do not necessarily produce more current, as long as convection through the pores is absent. An innovative model solution strategy combines in a very efficient and flexible way MATLAB, COMSOL finite element and Java codes.