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.

中文翻译：

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可变黏度和扩散率以及施密特数对旋转半球电极附近稳态流体动力学场和浓度场的影响


这项研究的重点是在电化学电池中围绕旋转铁半球电极形成的稳态边界层。电极的材料溶解到电解质溶液中，伴随着电流通过电路，产生一个浓度边界层，该边界层比流体动力学边界层薄得多，这主要是由于实际应用中典型的高施密特数。该边界层内溶液成分的变化导致电极表面附近的流体粘度增加，电解质的扩散系数降低。先前的研究表明，径向速度曲线与在粘度和扩散率恒定的电解质中观察到的曲线相似，除了形成浓度边界层的电极表面附近的空间区域。与具有恒定特性的解决方案相比，这种差异会改变壁面的速度梯度，从而影响扭矩、质量通量，并最终影响传输极限电流。这项研究进一步探讨了施密特数和电解质粘度比（电极表面的粘度与本体溶液粘度的比值）的影响，以及斯托克斯-爱因斯坦定律规定的相关扩散率变化。施密特数在确定浓度层和流体动力学边界层的相对厚度方面起着重要作用，它会影响由于电极溶解而引起的电流。从边界层概念推导出的一组近似方程使用有限体积法在径向和极角坐标中求解。 这种方法为三个速度分量的离散轮廓和每个极角的浓度生成了一组代数方程。该近似值在层流的高雷诺数下有效，通常在 RHSE 中遇到，即低于湍流过渡阈值本研究基于以前的工作，其中使用幂级数法 （Electrochim.Acta 450 （2023） 142236）。这项研究的新颖之处在于使用不同的方法来离散化和求解边界层方程，这允许探索比以前更广泛的施密特数、粘度比和极角。这些发现增强了对电化学池中旋转铁半球电极周围的稳态边界层动力学的理解，并强调了施密特数和粘度比对这些系统内传输过程的重大影响。