Multiscale modelling of diffusion and enzymatic reaction in porous electrodes in Direct Electron Transfer mode

Abstract

h i g h l i g h t sA macroscopic model for enzymatic porous electrode operating in DET mode is derived. The upscaled model is validated with pore-scale direct numerical simulations. Macroscopic model predictions are validated by comparisons with experimental data.

Numerical tools for the simulation of enzymatic bio porous-electrodes operating in DET mode

“…A new macroscopic model, based on a rigorous upscaling procedure was derived for diffusion and electrochemical enzymatic reaction involved in a porous electrode operating in direct elctron transfer (DET) mode [1] . This model does not make any specific assumption on the macroscopic shape of the electrode, nor on its microstructure.…”

“…Upon assuming that the microstructure of the material is pseudo-periodic, a representative elementary volume is identified, that can be restricted to a unit cell of the periodic pattern forming the porous structure. Typically, for real materials as those considered in [1] (see also [ 2 , 3 ]), a face-centered cubic (FCC) structure can be used (see Fig. 1 for more details on the geometry).…”

“…Nevertheless, the latter is not supposed to be performed routinely and does not constitute the core of the method reported here. Indeed, this method leads to a powerful numerical tool for predicting the behavior of bio porous-electrode with a considerable speed-up compared to direct numerical simulations [1] , and for the electrode's design in the sense of [ 3 , 4 ]. Voltammetry experiments, carried with several gold porous-electrodes with different thicknesses, functionalized with a bilirubin oxidase reported in [1] , serve as illustrative data for the modeling procedure.…”

“…Indeed, this method leads to a powerful numerical tool for predicting the behavior of bio porous-electrode with a considerable speed-up compared to direct numerical simulations [1] , and for the electrode's design in the sense of [ 3 , 4 ]. Voltammetry experiments, carried with several gold porous-electrodes with different thicknesses, functionalized with a bilirubin oxidase reported in [1] , serve as illustrative data for the modeling procedure. The macroscopic equations solved with COMSOL Multiphysics are directly coupled with a parameter identification procedure, carried out in Matlab, in order to determine the unknown electrochemical parameters involved in the experiments.…”

“…In addition, direct numerical simulation (DNS) of the 3D pore-scale model, providing the pore-scale concentration fields, can be performed with another COMSOL Multiphysics code to compute the current delivered by the electrode. This solution, once averaged, may be compared to that of the macroscale problem to validate the upscaled model, as reported in [1] .

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