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We consider basic and easily extendible transport formulations for lithiumbatteries consisting of an anode (Li-foil), a separator (polymer electrolyte),and a composite cathode (composed of electrolyte and intercalation particles).Our mathematical investigations show the following novel features: (i)\emph{complete and very basic description of mixed transport processes} relyingon a neutral, binary symmetric electrolyte resulting in a non-standard Poissonequation for the electric potential together with interstitial diffusionapproximated by classical diffusion; (ii) \emph{ upscaled and basic compositecathode equations allowing to take geometric and material features ofelectrodes into account}; (iii) \emph{the derived effective macroscopic modelcan be numerically solved with well-known numerical strategies for homogeneousdomains} and hence does not require to solve a high-dimensional numericalproblem or to depend on a computationally involved multiscale discretisationstrategies where highly heterogeneous and realistic, nonlinear, and reactiveboundary conditions are still unexplored. We believe that the here proposedbasic and easily extendible formulations will serve as a basic and simple setuptowards a systematic theoretical and experimental understanding of complexelectrochemical systems and their optimization, e.g. Li-batteries.

Basic and extendable framework for effective charge transport in electrochemical systems