Comparison between CFD calculations of the flow in a rotating disk cell and the Cochran/Levich equations

Three CFD (Computational Fluid Dynamics) models (single-phase, VOF and Euler–Euler) are employed to simulate the flow in a finite, rotating electrode cell under different operative conditions. The main dimensionless groups are derived and their effect on the flow is investigated. Except very close to the rotating electrode (i.e. in the hydrodynamic layer), the results show a flow pattern considerably different from Cochran’s approximate analytical solution often used in electrochemistry. Historically, the Cochran equation was used to derive the Levich equation, which permits the calculation of the limiting current density on a rotating electrode. Despite the general inadequacy of Cochran’s analytical solution, however, we show that the Levich equation often retains its validity because, in many practical situations, the concentration boundary layer is considerably smaller than the hydrodynamic boundary layer. When bubbles are generated on the electrode and a certain critical void fraction is exceeded, however, the Levich equation also becomes inaccurate. We propose, therefore, an amended version of this equation, which provides results closer to the CFD calculations.