Investigation of the Optimum Operative Conditions for a Parallel Plate Electrochemical Reactor
Authors: Litrico Giuliana , Proulx Pierre 
Published: February 2020

A mathematical model of a parallel plate electrochemical cell has been developed, validated using well-known experimental data from the literature and applied to a simplified prototypical cell. This prototype of the electrochemical parallel plate reactor has been used extensively for electroplating; nevertheless the study can be easily extended to other configurations and other industrial applications such as chlor-alkali production. Despite the popularity of this type of cells, the mathematical models that can be used in order to simulate their behavior are scarce. Analytical models lack the capability to describe adequately the complexity of the flow, chemistry and electric potential interactions, while numerical models using CFD in commercial codes present “black box” solutions that allow little insight into the mathematical and numerical difficulties of the model. The objective of the present work is to develop a mathematical model allowing the user to fully analyze the critical and challenging strong coupling that characterizes each electrochemical system. The interconnection between different phenomena requires the simultaneous solution of an complex set of equations and boundary conditions. This is done using the well-known CFD open-source software: OpenFOAM. Its large user base crosses most areas of engineering and science, and thanks to its extensive range of features allows the user to implement new customized solvers for specific mathematical models. In the present work, a new solver using the OpenFOAM tools is developed for an electrochemical reactor model: POTisoFOAM. In details the solver uses the PISO algorithm, Pressure Implicit with Splitting of the Operator, for solving a single phase flow field under the assumption of incompressible. The momentum and continuity equations are part of a predictor corrector loop whose outcomes are the velocity and the pressure's fields. A second loop, undergoing the assumption of dilute solution, links the mass transport equation and the current conservation. The first takes into account advection, diffusion and migration as transport mechanisms. The second provides the electric potential field through a tertiary current density distribution, considering ohmic drops and concentration polarization. The presence of the migration term and the concentration polarization, respectively in the transport equation and in the charge conservation, enhances the coupling between the two equations. In addition to the partial differential equations involved, the boundary conditions increase significantly the complexity of the solution. The strongly nonlinear Butler-Volmer equation models the effect of the double layer close to the electrodes. Its inversion via a false position method retrieves the over-potential, essential parameter at the electrode/electrolyte interfaces. Alongside with a uniform distribution of the potential and the current density lengthwise the active boundaries, a constant concentration profile of the active species is desirable, since an uneven consumption of the electrodes can lead to poor performance of the reactor. To capture any uniformity POTisoFOAM features a dynamic mesh method that predicts the changes in the geometry of the active plates due to either deposition or consumption of the material. The model is used to identify the best trade-off between the minimum current needed and the maximum chemical production. The optimum operative conditions are found by performing a parametric study on the effects of both the flow rate (Reynolds number) and the cell potential. These two parameters are responsible of the transport of the active species, the first through the convective mechanism and the latter via the migration. The electrode process becomes mass transfer controlled at the limiting current density, a critical design parameter that determines the efficiency of the process. A homogeneous distribution of the limiting current density contributes as well to maximize the exploitation of the active plates, delaying their replacement, and lowering the maintenance costs. Results are presented and analyzed.