An Integral Transform for Solving the Material Balance Equation

Abstract

The concentration of ions in a lithium cell plays an important role in predicting the charge-discharge cycle in a secondary battery. This is done by understanding the transportation processes in a lithium-ion cell during charge/discharge cycle. This paper presents the equations used in the mathematical modeling of a lithium cell. The model equations include the material balance equations, the Ohms Law and the flux equation for the porous electrodes in both the solution (electrolyte) and the solid phases.  These equations are then solved analytically, by means of Laplace transform, to give the concentration profile of the lithium ion with respect to the distance and time. The solutions to these equations are plotted in order to understand the profile of lithium ions concentrations during charge/discharge. These plots offer a clear view into how change in one variable interact with other variables and hence could help battery developers predict the performance of their batteries.