| The mathematical analysis of mass transport in chemical systems usually involves the method of averaging to obtain system level information from the microscopic domain. In many cases, reactions in such systems are usually assumed to be occurring in the bulk (homogeneous reactions). However, in electrochemical systems (Batteries or Fuel Cells), the reactions are heterogeneous and they usually occur on catalytic surfaces.;In this thesis, a diffusion-reaction model is developed to study concentration distributions and the behavior of the system within the porous anode catalyst layer of Direct Formic Acid Fuel Cells (DFAFCs) as an example of electrochemical applications. Furthermore, an area-average approach is implemented to obtain macroscopic concentration distributions within the domain, i.e., porous cavity. To analyze the role of averaging, this work is organized based on different cases of electrochemical kinetics. Firstly, the linearized form of the Butler-Volmer (concentration independent) kinetics is analyzed followed by classic Butler-Volmer (concentration dependent) type of kinetics. The system parameters varied are geometric (aspect ratio) and kinetic parameters. From this thesis, it is inferred that the averaging technique is valid for the linearized form of Butler-Volmer kinetics at all conditions. However, for the case the of the general Butler-Volmer kinetics, the area-averaging technique has certain limitations: For example, longer pores (with respect to cross-sectional area) and low over potentials promote agreement of the area-averaging predictions with those from analytical approaches. Also, the percentage of error, calculated using two methods, i.e. area-averaging and analytical-based is also reported for different cases of Butler-Volmer kinetics to assess, illustrating the limitations.;In this thesis, a diffusive-kinetic-based model is also developed and then applied for the porous anode catalyst layer of DFAFCs to study mass transfer and kinetic limitations by using an effectiveness factor and Thiele modulus approach. The study involved the assessing of the effectiveness factor (an area-averaging approach) by using an analytical solution for the same case. |
