On the interchangeability of potentiostatic and galvanostaticboundary conditions for fuel cells

This paper addresses the importance of the boundary conditions for the charge conservation equationin the modeling of fuel cells. In this context, we analyze the charge transport in an electric conductor,aiming to determine whether constant current and constant potential boundary conditions can be inter-changed without disturbing the local current density distribution in the cell. Their interchangeability canbe described with a dimensionless number, referred to as the interchangeability number, which cap-tures the relevant operating, geometrical and material parameters. The effect of the interchangeabilitynumber is further explored in a model for non-isothermal two-phase flow in a proton exchange mem-brane fuel cell, for which is it verified that the interchangeability number should be much less than 3, inorder to ensure that the prediction for the local current density distribution at the catalyst layers remainsthe same regardless of galvanostatic or potentiostatic boundary conditions.