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

The velocity and pressure profiles in the electrolyte due to a rotating disk electrode are determined by solving the two-dimensional (2D) Navier-Stokes equations employing axial symmetry. Most applications in the literature employ a one-term approximation of the series solution to von K\ arm\ an s one-dimensional (1D) 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%. © 2008 The Electrochemical Society.