Approximate Solution Methods for Solid-State Diffusion in Phase-Change Electrodes

Approximate solution methods have been developed for solid-state diffusion in phase-change electrodes, which, when incorporated into a porous electrode battery model, would provide a computational advantage over the exact rigorous solution without sacrificing accuracy. A shrinking core approach has been used to describe the phase boundary movement in a spherical electrode particle, where a shell of one phase covers a core of the other phase. Two approximations have been developed in this work, which account for diffusion in the shell while taking into account the moving phase interface. It is assumed that there are no concentration gradients in the core at any time. The validity of the approximations has been tested by solving the governing diffusion equation with the moving boundary using the arbitrary Lagrangian-Eulerian application mode in COMSOL Multiphysics. One of the approximations (order-2) is seen to perform very well over a wide range of discharge currents in predicting the positions of the moving interface, surface concentrations, concentration profiles, etc. The order-2 approximation is also seen to capture scenarios where diffusion continues in a single-phase particle after the core has been completely consumed. (C) 2009 The Electrochemical Society. [DOI: 10.1149/1.3237142] All rights reserved.