In current work, the ionic transport limitations in the Li-ion battery liquid electrolyte with separator are studied by a finite element method. This theoretical approach is based on the Nernst–Planck equation. It is shown that instead of solving coupled PDE system for concentration and potential, it is sufficient to calculate only the concentration profile in a three-dimensional (3D) structure to obtain a full description of the diffusion–migration ionic transport in the electrolyte in the steady-state. Subsequently, the overpotential and electric field can be calculated by using the provided equations. It was found that diffusion and migration overpotentials are equal in the steady-state. Consequently, two algorithms exploiting electrolyte simulations are proposed and successfully used to calculate the limiting current for the simulated battery system. In the present study a single perforated layer of the separator is inserted into the electrolyte and the simulations are carried out by increasing the complexity of the membrane holes. The ionic transportation dependence on the pore shape was found to be local and limited by the spatial area around the perforated separator.
Zadin, V., Danilov, D., Brandell, D., Notten, P. H. L., & Aabloo, A. (2012). Finite element simulations of 3D ionic transportation properties in Li-ion electrolytes. Electrochimica Acta, 65, 165-173. https://doi.org/10.1016/j.electacta.2012.01.039