Effect of variable viscosity and diffusivity as well as Schmidt number on the steady-state hydrodynamic and concentration fields near a rotating hemispherical electrode

The focus of this research is on the steady-state boundary layer that forms around a rotating iron hemispherical electrode in an electrochemical cell. Electrode’s material dissolution into the electrolyte solution, accompanied by the current passage through the circuit, generates a concentration boundary layer that is significantly thinner than the hydrodynamic boundary layer, primarily due to high Schmidt numbers typical for practical applications. The change of the solution composition inside this boundary layer leads to an increase in fluid viscosity near the electrode surface and a decrease in the electrolyte’s diffusion coefficient. Prior studies have indicated that radial velocity profiles are similar to those observed in electrolytes with constant viscosity and diffusivity, except for the spatial region near the electrode surface where the concentration boundary layer forms. This difference alters the velocity gradient at the wall, impacting the torque, mass flux, and ultimately the transport-limited current compared to solutions with constant properties. This research further explores the effects of the Schmidt number and the viscosity ratio of the electrolyte (the ratio of the viscosity at the electrode surface to the bulk-solution viscosity), along with the associated diffusivity variations prescribed by the Stokes-Einstein law. The Schmidt number plays an important role in determining the relative thicknesses of the concentration and hydrodynamic boundary layers, affecting the current flow due to electrode dissolution. The set of approximate equations, derived from the boundary layer concept, is solved using the Finite Volume Method in radial and polar-angle coordinates. This approach yields a set of algebraic equations for the discretized profiles of the three velocity components and the concentration at each polar angle. The approximation is valid at high Reynolds numbers for laminar flows, typically encountered in RHSEs, i.e. below the turbulent transition threshold This study is based on previous work where the same set of equations was solved using the power series method (Electrochim. Acta 450 (2023) 142236). The novelty of this study consists in the use of a different method to discretize and to solve the boundary layer equations, which allows for the exploration of a broader range of Schmidt numbers, viscosity ratios, and polar angles than was previously possible. The findings enhance the understanding of steady-state boundary layer dynamics around a rotating iron hemispherical electrode in an electrochemical cell and highlight the significant impact of Schmidt number and viscosity ratio on transport processes within these systems.