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 PF6− 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.