Tertiary Current and Potential Distribution Including Laminar/Turbulent Convection, Diffusion, and Migration by the Finite Volume Method Using OpenFOAM

Abstract

A numerical tool is presented under a finite volume framework, implemented in the open-source package OpenFOAM, to calculate concentrations and current and potential distributions in electrochemical systems composed of two-dimensional electrodes with a monopolar connection. The convection, diffusion, and migration of species in electrochemical systems are considered in coupling the potential and concentration fields together with the hydrodynamics under laminar or turbulent conditions. Multiple reactions with any kind of kinetic control (charge-transfer, mass-transfer, mixed, or special cases) are permitted at both electrodes. The algorithm allows calculations for a given local potential at the working electrode (potentiostatic control) or for a fixed cell potential difference and also for a current flowing through the cell (galvanostatic operation). The model was verified by using analytical expressions and simplified numerical implementations. Moreover, a new test reaction is proposed in order to study the effect of ionic migration and validate the model. A good match between experimental results and predicted calculations was obtained. This computational tool can be employed to optimize both cell stack design and system operation conditions. Furthermore, the algorithm can also be used to check, for a given geometrical configuration and reaction environment, the validity of some assumptions such as tertiary current distribution without migration, mass-transfer-controlled reactions, or primary-secondary current distributions.

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

“…3 the effect of turbulent flow on the migration contribution to the mass transfer flux has been disregarded as it was discussed by Colli and Bisang. 20 (ii) The heat equation according to…”

“…b Implementation in OpenFOAM.-For the boundary conditions a procedure similar to that described elsewhere was used. 20,27 Thus, considering a Robin BC, with the application of a Taylor series expansion to the right-hand sides of Eqs. 34 and 35, and neglecting higher-order terms results in…”

“…Further information can be found in previous works. 20,27 Figure 1 illustrates the control algorithm used in the proposed procedure. This algorithm employs a do-while loop to maintain the reference potential during potentiostatic operation or the desired total current during galvanostatic operation at each time step.…”

Modeling and Comparison of Typical Design of Filter-Press Flow Electrochemical Reactors

“…Equations – are known in the turbulent regime as a Reynolds-averaged Navier–Stokes model. , The Reynolds-averaged Navier–Stokes equations coupled with the low Re k –ε turbulent model were selected in this work.…”

A Simulation Framework for Electrochemical Processes with Electrolyte Flow

“…27 Litrico et al 28 applied Ridders method to invert a simplified Butler-Volmer equation that neglected mass transport effects on the exchange current density and the equilibrium electrode potential to simulate copper electrodeposition in a turbulent plug flow. Recently, Colli and Bisang 29 proposed a model for solving the tertiary current distribution in a parallel-plate electrochemical reactor with multiple reactions. The electrode kinetics was linearized to improve convergence in the iterative solver, but steady-state conditions for the electrolyte velocity and the species concentration were assumed.…”