Mathematical modeling of processes in the microbial fuel cell membrane

Abstract

An important problem that limits use of the microbial fuel cell (MFC) is a scaling problem, e.g. the problem of choosing the optimal size. The main objective of the paper is to develop a mathematical model of the processes in the MFC, so that it allows solving the scaling problem analytically and by means of numerical experiments. The proposed in the paper MFC model includes the electrodiffusion processes equation for positive and negative ions in the anode chamber, the positive ions dynamic equation in the cathode chamber, the biological processes kinetics equation in the anode chamber, initial and boundary conditions. The model takes into account the residual charge dynamics in the anode chamber. The paper contains the comparison of the amperage dynamics in the MFC electrical circuit obtained from mathematical modeling and natural experiments conducted to confirm the correctness of the model. Qualitative agreement of the results of the natural and numerical experiments has been obtained for MFCs with different geometrical characteristics. In the natural and numerical experiments two surges of amperage have been revealed. The first surge of amperage does not depend on the geometry of the MFC chambers, it can be explained by the existence of the residual charge in the hinge of the sediments placed in MFS anode chamber. The second surge of amperage is caused by microbial processes in the MFC anode chamber; its amplitude is much larger than the amplitude of the first surge.