Solution Phase Limited Diffusion Modeling in a Li-ion Cell Subject to Concentration-Dependent Pore Wall Flux

Mathematical modeling of ionic transport in a Li-ion cell is critical for understanding and predicting key performance parameters such as cell voltage. Past work on solution phase limitation modeling of a Li-ion cell has assumed constant and uniform pore wall flux, which is valid only under certain conditions. It may be more appropriate to assume, similar to chemical reactions in general, that the pore wall flux is proportional to the local ion concentration. This paper presents a theoretical model for solution phase limited ionic diffusion in a separator-electrode stack under the assumption of the pore wall flux being linearly proportional to the local concentration. The resulting non-linear governing equation is linearized and solved using Laplace transformation technique. Concentration field in the two-layer stack is calculated as a function of space and time in a parameter space of practical interest. A comparison of results with past work based on constant, uniform reaction rate indicates that the assumed nature of concentration-dependence of the pore wall flux plays a significant role in determining the concentration distribution. This work advances the theoretical understanding of ionic diffusion in a Li-ion cell, and may contribute towards understanding and optimizing the performance of Li-ion cells.