A simplified mathematical model to calculate the current distributions in bipolar electrochemical reactors is proposed. The current distributions are deduced from a combination of the voltage balance in the reactor with a voltage balance including the electrolyte inlet and outlet. Thus, equations to predict the effect of geometric and operational variables on the current distributions at the electrodes are reported. The parameters acting upon the current distributions were lumped into two dimensionless variables and their effects on the current distributions are discussed. The primary current distributions are obtained as a limiting case. Comparisons between calculated and experimental primary current distributions are reported. List of symbolsA transverse section of the electrolyte manifold (m 2 ) b i constant in the Tafel equation of the ith reaction (i= a or c) (V) C 1 constant given by Equation 7 (V) C 2 constant given by Equation 13 (V) d r mean relative deviation (%) e interelectrode distance (m)

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.

This work presents numerical simulations, with validation considering analytical expressions and experimental results, of masstransfer in electrochemical reactors under laminar and turbulent flows in ducts of rectangular and tubular shape. Sudden expansion at the reactor inlet and segmented electrodes are also analyzed. Computational fluid dynamics (CFD) simulations were performed solving the laminar or RANS equations with the Shear Stress Transport (SST) k-ω turbulence model using the open source code OpenFOAM in steady-state. For mass-transfer simulations, the averaged diffusion-convection equation was implemented and solved. A good agreement between mass-transfer simulations with experimental data and analytical results were attained for both laminar and turbulent flow. Discussions about the segmented electrode technique in order to obtain local mass-transfer data in laminar and turbulent flow are also performed.