Mathematical modelling of ionic transport in the electrolyte of Li-ion batteries

The ionic conductivity of the organic electrolyte in Li-ion batteries has been modelled. The classical one-dimensional Nernst–Planck approach results in a system of two non-linear parabolic second-order partial differential equations. It is shown that under electro-neutrality conditions this complex system of equations can be reduced to simple diffusion equations with modified diffusion coefficient, facilitating the efficient use of numerical methods. As a result, detailed information about transient and steady-state behaviour of the electrolyte is revealed, including potential gradients and the diffusion and migration fluxes for both Li+ and ions. Furthermore, an extension of the basic model is presented, taking into account salt dissociation in the electrolyte. The most characteristics of ionic transportation are illustrated with realistic examples of constant-current (dis)charging Li-ion batteries. Some of the numerical simulations are compared with recently reported experimental results.