Analytical modeling of solution-phase diffusion in porous composite electrodes under time-dependent flux boundary conditions using Green’s function method

Abstract

Mathematical modeling of species transport in a Li-ion cell is important for understanding and optimizing the performance of Li-ion cells in a wide variety of energy conversion and storage processes. Specifically, solid- and liquid-phase diffusion in the electrodes is an important process that governs cell performance. Most analytical and numerical models developed in the past have focused on a constant current boundary condition. However, time-dependent boundary conditions may be important in many applications, where the applied charging or discharging current changes with time. This paper presents an analytical solution for the solution-phase diffusion limitation problem for a composite electrode operating under time-dependent flux boundary condition and arbitrary initial conditions using the Green’s function approach. Results based on the analytical solution show good agreement with past work for constant current boundary conditions, as well as numerical simulation results. The results are used to predict the concentration distribution for linear, periodic, and step-function variations in current density as a function of time. Results from the step-function boundary condition address practical applications where sudden changes in the magnitude and direction of the imposed current may occur. Results derived for periodic functions are also of practical significance since other current profiles can be represented by series comprising periodic functions. This work expands the theoretical understanding of diffusion in Li-ion cells, and provides the basis for understanding and optimizing important charge/discharge processes in Li-ion cells.