A Simple Method to Compute the Response of Non-Homogeneous and Irregular Interfaces: Electrodes and Membranes

Abstract
We present a detailed numerical test of the coarse-graining method proposed by Sapoval to compute the flux through an irregular interface in the case where the local response is inhomogeneously distributed. It is shown, through comparison with detailed finite elements simulations, that this method permits to deduce the flux across an irregular interface from its topography only, as for example in the case of non-uniform polarizability in electrochemistry. The interest of the method lies in its computational simplicity. It then constitutes an essential step towards the understanding of the flux across irregular interfaces in non-linear regimes.