Kinetic and hydrodynamic implications of 1-D and 2-D models for copper electrodeposition under mixed kinetic-mass transfer control

Numerical analysis of the hydrodynamics and kinetics of copper deposition on a copper rotating disk electrode during voltammetry at a scan rate of 100 mV s−1 is conducted to determine the impact of fitting for the system parameters using a 1-dimensional model when the process operates under transition (1000 rpm) and turbulent (1500 rpm) velocity flow conditions. The 1-dimensional model is based on solution of the transient mass transport equation for Cu(II) utilizing the well-known series solution by von Karman and Cochran for the fluid velocity. The suitability of using this model is assessed by comparison to an axially symmetric 2-dimensional model of the system. In the 2-dimensional model, the Reynolds-averaged Navier–Stokes (RANS) equations are solved first for the pressure and the fluid velocity components which are then used in the transient mass transport equation. The turbulent viscosity is estimated using the k–ɛ model. In both models, transport of Cu(II) by diffusion and convection is coupled to the flux associated with its reduction at the cathode surface. The velocity obtained from the 1-dimensional model is found to be accurate only at locations within a distance of ∼1.4 × 10−5 m from the electrode. Although no significant differences are found for the fitted kinetic parameters obtained using the two models, the diffusion coefficient of Cu(II) fitted using the 1-dimensional model exceeds that obtained from the 2-dimensional model by approximately 44%. The model with the fitted parameters can accurately predict the experimental behavior at a different CuSO4 concentration, although larger deviations arise when the scan rate is reduced to 5 mV s−1.