Novel local fluctuation-preserving upscaling techniques for heterogeneous reaction-transport equation in porous media

Abstract

A body of research in the field of lithium-ion batteries is dedicated to the investigation of the influence on their behavior by the complex microstructure of their porous electrodes. Experimental and numerical studies reported the distinctly localized spatial fluctuations of overpotential and lithium ion concentration which are not observed in the simulation results based on a widely used lithium-ion cell’s DFN (Doyle-Fuller-Newman) model. Using a combination of perturbation technique and asymptotic analysis, we rigorously derived the analytical results that explain the fluctuation dynamics that was reported earlier in the microstructure-resolving simulations; importantly, it was theoretically demonstrated that the localized fluctuations generally do not disappear in the homogenization limit which is usually used to justify the use of DFN. We reported new numerical results that proves that the approximations made in our theoretical analysis are indeed applicable to the physical and chemical parameters corresponding to the real lithium-ion cells. Our ansatz may be of use for accurate derivation of DFN-like electrochemistry mathematical models beyond the narrow scope of this report, in particular for the models that accurately account for the cell degradation processes which are sensitive to the particle-scale local environment in the electrode.