Upscaling mass and electric charge transport in porous electrodes: A formal derivation of Newman’s model

Modeling species mass and electric charge transport in porous electrodes has been a subject of intense research over several decades using many different approaches. On the one hand, there are postulated models dedicated to specific empirical use. On the other hand, there are models derived using robust upscaling techniques. The postulated model derived by Newman’s work group is nowadays the standard starting point when performing simulations in porous electrodes. Derived upscaled models using techniques such as volume averaging or homogenization have some points in common, such as sharing similar closure problems, although they do not always lead to the same final macroscopic equations. The resulting variety of models does not provide a clear path to make a well-founded model choice for a particular application. The purpose of this work is to conciliate the use of upscaling techniques and Newman’s model by providing a detailed formal derivation of a macroscopic model using the volume averaging method and show how it coincides with Newman’s heuristic model. Connections and similarities with other previous upscaling efforts are also pointed out throughout the derivations. The present contribution helps to identify points of improvement of this well-known model to enhance its predictive capabilities in future works.