An ordinary differential equation model for simulating secondary battery reactions

Abstract Numerical simulation is a powerful approach for developing next-generation secondary batteries. The distance between the anode and cathode should be as small as possible in order to reduce the required voltage, which is typically designed to be less than 100 μm. In the present study, an ordinary differential equation (ODE) model for numerical simulation, which is applicable to batteries in which the anode–cathode distance is so small that the diffusion layers at both electrode surfaces are merged, is successfully developed. Quantitative comparisons of the approximation accuracy using the Newman model simulation based on partial differential equations revealed that the difference is less than 1% under typical experimental conditions. Remarkably, the proposed ODE-based model does not require that the system be a binary electrolyte that is a necessary condition for simulations based on the Newman model, indicating the wide-range applicability of the model.