Quadratic voltage profiles in lead acid cells during slow, steady processes

Abstract

It is standard lore that the voltage profile varies linearly in space within the electrolyte of a lead acid cell under slow, steady discharge. However, this hypothesis has never been put to the test. A recent theory predicts a uniform, non-zero charge density in the bulk of the electrolyte, an electric field that varies linearly across the cell and a voltage prose that varies quadratically. To test this theory, experiments were performed, using platinum reference electrodes to read the voltage probes during periods of charge and discharge. Such experiments revealed quadratic voltage probes, but of a specific form that has not yet been explained. Perhaps more interesting than the quadratic voltage profiles under slow, steady charge and discharge was our observation of (different) quadratic voltage profiles in the zero current state. This can be explained within the context of the theory as due to the non-current-carrying (non-faradaic) reactions. As a test of the experimental set-up, voltage-jump readings were measured in the electrolyte at the onset and discontinuation of charge and discharge processes, revealing the expected linear voltage-jump probes across the cell.