Porous electrodes with high specific surface area have been efficiently applied to design miniaturized electro-devices such as bio-batteries, bio-captors, etc. Such electrodes may provide much higher electrical current than classical flat electrodes of the same macroscopic size . In a previous work , a multi-scale model of diffusion and electrochemical reaction in porous electrodes has been developed for a simple oxygen reduction reaction so that oxygen is reduced to hydrogen peroxide by directly consuming electrons at the cathode. In order to improve the efficiency of such devices, redox reactions may be catalyzed by enzymes which are immobilized within a polymer layer in the vicinity of the solid surface . In the present work, we develop a multi-scale model of coupled transport and electrochemical reaction in porous electrodes operating in the enzymatic Direct Electron Transfer regime where complex reactions induced by the enzymes together with their mass balance are taken into account.
At the microscopic pore-scale, an electrochemical model for complex redox enzymatic reactions at the solid-fluid interface is developed, considering the oxygen reduction reaction which is catalyzed by the bilirubin oxidase enzyme (BOD) at the cathode. In this scenario, the Butler-Volmer equation is used to relate the potential and reaction rates with the current. This electrochemical model is further coupled with the mass transfer of oxygen governed by Fick's law and the mass balance of enzymes to form the microscopic coupled model in transient regime. By making use of the volume averaging method , the above mentioned microscopic problem is upscaled to obtain a macroscopic model. This model is characterized by a macroscopic coupled diffusion-reaction equation in the porous electrode involving an effective diffusion coefficient that can be computed from the solution of an intrinsic closure problem. Using a model pore geometry, 3D direct numerical simulations of the microscopic model are carried out and compared to 1D numerical simulations of the macro-model. Excellent agreement between the oxygen concentration profiles within the electrodes obtained from the two models is observed while a speed-up of about 21600 is achieved with the 1D macro-model illustrating the capability of the multi-scale approach. Such a model is capable of providing an accurate estimation of the electrical current density with respect to the pore-space architecture providing a useful tool for electrode microstructural optimization. A successful comparison between the model and experiments is also reported.
Keywords: Porous electrode, Diffusion, Reaction, Volume averaging, Enzyme.
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