Electrochimica Acta 112 (2013) 386–393 Contents lists available at ScienceDirect Electrochimica Acta jou rn al hom ep age: www.elsevier.com/locate/elec tacta Mathematical modelling of an enzymatic fuel cell with an air-breathing cathode M.H. Osman a , A.A. Shah b,∗ , R.G.A. Wills a , F.C. Walsh a a Electrochemical Engineering Laboratory, School of Engineering Sciences, University of Southampton, Highfield, Southampton SO17 1BJ, UK b School of Engineering, University of Warwick, Coventry CV47AL, UK a r t i c l e i n f o Article history: Received 28 March 2013 Received in revised form 6 August 2013 Accepted 6 August 2013 Available online 25 August 2013 Keywords: Enzymatic fuel cell Diffusional mediator Biological anode Two-substrate mechanism Modelling and simulation a b s t r a c t Multi-dimensional steady-state and dynamic models for an enzymatic fuel cell are developed. In the model system, the biocatalyst (glucose oxidase) is immobilized in a porous electrically conducting anode, while glucose and a mediator are supplied from a solution. A platinum air-breathing cathode and a Nafion membrane complete the cell unit. Detailed mass and charge balances are combined with a model for the ping-pong reaction mechanism in the anode, together with oxygen reduction in the cathode. The effects of enzyme oxidation by dissolved oxygen in the anode (a competing side reaction) are also included. The model is validated against experimental polarization and power curves, and the steady-state performance under different conditions is analyzed and discussed. The simulation results demonstrate some of the possible limitations of enzymatic fuel cells and provide insights into the spatial distributions of the reactants, potentials and current. © 2013 Elsevier Ltd. All rights reserved. 1. Introduction Biofuel cells have been defined as systems capable of direct chemical to electrical energy conversion via biochemical pathways [1–6]. Direct electrochemical conversion is a desirable feature since it avoids the thermodynamic limitations associated with combus- tion, in addition to being more environmentally friendly. Enzymatic fuel cells can yield low power densities as a conse- quence of slow rates of electron transfer from the enzyme active site to the electrode [7]. They can also suffer from short lifetimes as a result of poor stability of the enzyme when it functions in a foreign environment. Much of the current research is directed at alleviating these problems, with particular focus on new meth- ods and materials for enzyme-electrode (and possibly mediator) integration, often in highly ordered three-dimensional structures. Developments in the overall system design have also led to more efficient systems. For example, removing the separator membrane without a significant loss in the power output, and the emergence of single chamber, air-breathing systems using compact membrane electrode assemblies (MEAs). Mathematical models can reduce the burden on laboratory- based design, testing and characterization. At the cell level, models can capture the potential, reactant, and temperature distribu- tion, as well as global information such as the cell potential. For ∗ Corresponding author. Tel.: +44 023 8059 8520; fax: +44 023 8059 3131. E-mail address: Akeel.Shah@warwick.ac.uk (A.A. Shah). many important quantities, local information such as potential and current density profiles can only be gained from detailed and rig- orously validated models, particularly during in-situ operation. For these reasons, a great deal of effort has been invested in modelling polymer electrolyte membrane (PEM) and solid oxide fuel cells and solid-oxide fuel cells [8]. Numerical modelling of enzymatic and microbial fuel cells, on the other hand, is not a well-developed area [9,10]. With a few notable exceptions [11–13], models are highly simplified, neglecting crucial features such as transience, spatial non-uniformity, ion migration, fluid flow and heat transport. In this paper, a transient, two-dimensional model for a glucose-oxidase based fuel cell is developed. The ping-pong mechanism of the bio- catalyzed reactions is treated explicitly and the model is validated against experimental results. The approach can be applied to other biofuel cell systems and in a companion paper a model of a fully biological (anode and cathode) fuel cell is developed. 2. Fuel cell model 2.1. Reaction kinetics The system under consideration was reported by Fischback et al. [14] (see also [15,16]). The developed miniature fuel cell (12 mm × 12 mm × 9 mm) comprised a Nafion membrane/cathode electrode assembly (MCEA) stacked with an enzymatic (glucose oxidase) car- bon felt anode, as depicted in Fig. 1. Glucose oxidase was covalently attached to functionalized carbon nano-tubes (CNTs) before excess GOx was made to precipitate near the CNTs. Finally, a cross-linking 0013-4686/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.electacta.2013.08.044