Editors' Choice—Coupling k Convection-Diffusion and Laplace Equations in an Open-Source CFD Model for Tertiary Current Distribution Calculations

Abstract

A mathematical model to calculate tertiary current distributions in electrochemical reactors is presented taking into account the potential and concentration fields together with the hydrodynamics under laminar or turbulent conditions. Multiple reactions with different kinetic controls are considered at both electrodes. The computational algorithm solving the model was implemented in OpenFOAM. It allows the 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 validated by using the reduction of ferricyanide and the oxidation of ferrocyanide from dilute solutions as main test reactions and hydrogen and oxygen evolution as secondary ones, in a modified hydrocyclone. A close agreement between experimental and predicted current distributions was obtained. The hydrocyclone presents a promising electrochemical performance being the mass-transfer conditions in its cylindrical part better than in the conical region. The computational tool developed in this paper can be employed to optimize both cells stack design and system operation conditions. Likewise, the algorithm can also be used to check, when limiting current studies are needed, whether the desired reaction is under mass-transfer or charge-transfer control for a given geometric configuration.

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

“…An interesting case of concentration and potential distributions occurs when the reactant interacts with the supporting electrolyte or it participates in homogeneous reactions in the solution bulk. This situation was analyzed by Hauser and Newman 42 considering four cases: (i) the deposition of gold in a KAuC1 4 -KC1 electrolyte, (ii) the reduction of copper and simultaneous generation of chloride ions from cuprous chloride in a supporting potassium chloride electrolyte, (iii) the deposition of zinc in alkaline solutions where the reduction of Zn(OH) 4 2− takes place, and (iv) the nitrate reduction in acidic nickel nitrate. Hsueh and Newman 43 considered the effect of bisulfate ions on copper deposition, and Van Den Bossche et al 44 reported the case of silver reduction from a nitrate-thiosulfate solution.…”

“…Primary, secondary, and tertiary current distributions refer to diverse approximations that apply depending on the relative significance of fluid resistance, electrode kinetics, and mass-transfer. 2 Several cases, in increasing order of complexity, can be performed under the tertiary current distribution approach, i.e., (i) considering electrochemical reactions under mass-transfer control, 3 (ii) a combined mass-and charge-transfer kinetic control requiring the calculation of the potential distribution in the fluid phase, 4 and (iii) the same as the latter but including the migration term in the mass-transfer of each ion.…”

“…In the design of electrochemical reactors with an excess of a supporting electrolyte, the contribution of migration to the mass-transfer can be disregarded, solving a diffusionconvection problem. 4 However, the working conditions for electro-synthesis of some products in special electrochemical reactors can deviate from the previous situation and the masstransfer could be influenced by migration, affecting the reactor performance. This situation occurs in the production of periodate from iodate, 16 persulfate, 17 electrodeposition of manganese, 18 organic electrochemistry, 19 electrophoresis, 20 electrodialysis, 21 electrochemical treatment of wastes and effluents, or molten salt electrochemical process.…”

A multi‐region and open‐source computational fluid dynamic tool for electrochemical systems with three‐dimensional electrodes

“…The knowledge of the hydrodynamic behavior is necessary in Equation () in order to calculate the concentration distribution of each species. For the most general case, the Navier–Stokes equations must be solved under laminar or turbulent flow conditions by means of CFD, which can be performed by using the open‐source software OpenFOAM as it was previously reported 42–44 …”

“…The usual boundary conditions to attend hydrodynamic calculations for a general case were outlined in our previous contributions 42,44 …”