  We consider basic and easily extendible transport formulations for lithium
batteries 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} relying
on a neutral, binary symmetric electrolyte resulting in a non-standard Poisson
equation for the electric potential together with interstitial diffusion
approximated by classical diffusion; (ii) \emph{ upscaled and basic composite
cathode equations allowing to take geometric and material features of
electrodes into account}; (iii) \emph{the derived effective macroscopic model
can be numerically solved with well-known numerical strategies for homogeneous
domains} and hence does not require to solve a high-dimensional numerical
problem or to depend on a computationally involved multiscale discretisation
strategies where highly heterogeneous and realistic, nonlinear, and reactive
boundary conditions are still unexplored. We believe that the here proposed
basic and easily extendible formulations will serve as a basic and simple setup
towards a systematic theoretical and experimental understanding of complex
electrochemical systems and their optimization, e.g. Li-batteries.
