A Comparison of Numerical Solutions for the Fluid Motion Generated by a Rotating Disk Electrode

Abstract

The velocity and pressure profiles in the electrolyte due to a rotating disk electrode are determined by solving the two-dimensional ͑2D͒ Navier-Stokes equations employing axial symmetry. Most applications in the literature employ a one-term approximation of the series solution to von Kármán's one-dimensional ͑1D͒ model for the rotating disk electrode. In this work, the finite-element method is used to solve the model equations rigorously within an electrochemical cell of practical dimensions, and the results are compared with the one-term approximate solution and a complete solution to the 1D model. The different hydrodynamic models are coupled with a mass-transport model for oxygen reduction reaction at the surface of the rotating ring disk electrode. The complete series solution is accurate to within four digits when compared to the 2D model, whereas the one-term approximation gives rise to an error as high as 4% in the limiting current values. Similar calculations on a ring disk electrode show that the one-term approximation underestimates the collection efficiency and the ratio of the ring and the disk currents of a sectioned electrode by 1-4%.

Characterization of the hydrodynamics inside a practical cell with a rotating disk electrode

“…4-6 show that the electrolyte near the electrode side wall flows upwards, which is in disagreement with that stated in Blurton and Riddiford [5]. Nevertheless, the same fluid flow pattern around the electrode obtained in the present work was also obtained in Dong et al [17], where two-dimensional axisymmetric numerical simulations of a cell with a rotating electrode were carried out. In that work, the electrode was submerged into the electrolyte and the entire cell was modeled.…”

Quantitative Kinetic Analysis of a PdAu3Alloy Catalyst for Oxygen Electro-Reduction

“…with I l from the Levich Equation 26. These results are depicted in Figure 2a in form of a Tafel plot.…”

“…26 Another approximation in the model is the neglect of surface roughness on the disk. But the overall quality of the data fit shows, that all the important reaction kinetics was included here.…”

Hydrodynamic Analysis of Electrochemical Cells

“…Mandin et al (Mandin, Fabian, & Lincot, 2006) show the significance of the submerged electrode side wall by means of two-dimensional numerical simulations of an electrochemical cell with a rotating cylinder electrode. Dong et al (Dong, Santhanagopalan, & White, 2008) carried out two-dimensional axisymmetric numerical simulations of a entire electrochemical cell with a RDE, where the electrode is partially submerged into the electrolyte. To include the existence of an air-liquid interface present in actual electrochemical cells, a slip wall was employed as boundary condition for the cell upper wall to represent numerically this interface.…”

“…To include the existence of an air-liquid interface present in actual electrochemical cells, a slip wall was employed as boundary condition for the cell upper wall to represent numerically this interface. The system modeled by Dong et al (Dong, et al, 2008) is schematically represented in Figure 6. In accordance with these authors, the simulated fluid velocity field and that obtained with the theoretical model proposed by von Kármán (von Kármán, 1921) and Cochran (Cochran, 1934) are in good agreement.…”