Finite‐Difference Simulation of Multi‐Ion Electrochemical Systems Governed by Diffusion, Migration, and Convection: Implementation in Parallel‐Plate Electrochemical Reactor and Backward‐Facing Step Geometries

Abstract

A finite‐difference method for predicting the current‐density distribution in multi‐ion electrolytes was developed, then implemented to actual experimental systems and compared with other numerical methods, analytic solutions for limiting conditions, and experimental measurements in order to be tested. The method accounted for diffusion, ionic migration, laminar convection, and heterogeneous electrochemical reactions following Butler‐Volmer kinetics in two‐dimensional geometries under steady‐state conditions, and is applicable at high velocities as well. The finite‐difference method was applied to the acidic copper sulfate electrolyte with composition 0.01 M + 0.1 M and the alkaline potassium ferri/ferrocyanide electrolyte with composition 0.005 M + 0.01 M + 0.5 M NaOH, placed between two equally sized parallel‐plate electrodes fixed in a channel's walls at a separating distance being 3% of their length (PPER), under conditions of laminar parabolic flow. It was also applied to the ferri/ferrocyanide system placed in a similar configuration in which a backward facing step with height being 1.5% of the electrode length was introduced just before the cathode in the flow channel. The model computed concentration, potential, and current density distributions at Reynolds numbers Re = 230 and 1200 and applied cell voltage in the range −0.5 V ⩽ Vapp ⩽ −0.03 V for the first system; also at Re = 55, 180, 300, and 2100 in the PPER and Re = 55, 180, and 300 in the backward‐facing‐step geometry under limiting‐current conditions for the second. The computed local cathodic current density was compared to experimental data, multidimensional‐upwind‐method predictions, and the Léve⁁que analytic solution where applicable. Very good agreement was demonstrated, thus verifying the method's applicability to real cases.