A FE2 Framework for Ionic Transport Modeling in the Electrolyte of a Battery Cell

Abstract

An electrolyte is an indispensable component in any battery as it saturates the porous structure of battery separator and electrodes to transport ions. The pore size in battery separator and electrodes is usually two to three orders of magnitude smaller than the typical size of a battery cell [1]. It is therefore computationally infeasible to resolve this problem at the microstructural level for a full scale simulation. To obtain the field variable profiles at the battery cell level, we formulate a FE2 framework for the calculation of ionic concentration and electrostatic potential at the macro cell level from computations at the micro pore scale. The FE2 framework consists of solving governing equations at two (macro and micro) scales and managing the information exchange between them. The macroscale governing equations describe the balance of charge (with the electroneutrality assumption) and the mass conservation of ionic species [2]; the macroscopic electric current and mass flux are obtained from the solution of the microscale boundary value problem, which is defined on a representative volume element (RVE). The microscale governing equations also describe the balance of charge and the mass conservation of ionic species, but the time variation of the ionic concentration is neglected within the microstructural domain due to the small RVE size [3]. The electric current and mass flux at the micro scale are derived from Nernst-Plank's equations and Faraday’s law of electrolysis. The macroscopic variables (ionic concentration and its gradient, and electrostatic potential and its gradient) at each macroscale integration point are transferred to the microscale problem as boundary conditions, while the averaged current and mass flux are transferred back for the macroscopic computation. The current FE2 framework can be used to calculate effective transport properties of porous battery separator and electrodes, especially when the microstructure changes in time and space. Moreover, it will be extended to a multiscale simulation of a full battery cell that will allow the prediction of the battery electrochemical performance and in turn provide practical guidelines for battery microstructure design.