Exploring the Impact of Concentration and Temperature Variations on Transient Natural Convection in Metal Electrodeposition: A Finite Volume Method Analysis

Abstract

A mathematical model was developed to accurately determine the current density, concentration, and velocity profiles in electrochemical reactors operating under natural convection conditions. The model considers the interplay of key variables, such as potential, concentration, and temperature linked to the hydrodynamics through the density field using the Boussinesq approximation. Thus, a comprehensive analysis under both laminar and turbulent flow conditions is provided. The computational algorithm that represents the model is implemented in OpenFOAM and it offers the ability to operate the reactor at a fixed cell potential difference or under potentiostatic and galvanostatic control. The model's accuracy was verified in different parallel-plate reactors using copper deposition as a test reaction from dilute and concentrated solutions, showing a strong agreement with the experimental results. This tool can be leveraged to optimize cell design and operating conditions in electrochemical systems that involve significant natural convection, such as in the electrowinning and electrorefining industries.

Modeling Electrode Shape Changes in Electrodeposition and Electrochemical Dissolution

“…The goal of choosing proper control is to minimize uneven current and potential distributions which can lead to irregular deposition, affecting coating thickness, appearance, morphology, and mechanical properties. [42][43][44] Galvanostatic mode is used in industrial settings for consistency and throughput. 45 Similarly, in anodization, maintaining steady voltage controls oxide layer growth and properties, while current control achieves desired coating thickness efficiently.…”

“…From the computational point of view utilized here, these modes results in a floating unknown potential (negative for the WE acting as an anode and positive when the WE acts as a cathode) at the CE when the WE potential is set to zero. This procedure employs a do-while loop 44 to maintain the reference potential during potentiostatic operation or the desired overall current during galvanostatic operation at each time increment. Thus, the do-while loop ensures that the specified electrical conditions are fulfilled at every time step.…”

“…Computational characteristics.-For each case analyzed in the present contribution, as depicted in Fig. 1, the final mesh was obtained after conducting a grid-independence study, 34,44,54 which involved comparing various parameters across five meshes of different sizes. These parameters included the ratios of the total current (for fixed cell potential difference), cell potential difference (for galvanostatic operation), the uniformity factor (UF) as per Eq.…”

“…1e, which serves as a focal point for shape evolution under the conditions detailed in Table III (columns 1 to 4). Copper deposition and dissolution at the plating surface, influenced by kinetic parameters and typical physical properties in such systems, 44 determine the local growth velocity.…”