Theory and Experiment of the Limiting Current in Impinging Jet Electrodes
Authors: Schneemann Christian , Trägner Jakob , Tang Bo , Dietzel Andreas , Köhler Jürgen , Oezaslan Mehtap 
Published: August 2024

Recently, flow cells with a confined impinging jet type have emerged as a promising hydrodynamic electrochemical setup for non-conventional square model electrodes that cannot be measured in the commonly used rotating disk electrode (RDE) setup1. Due to the complex hydrodynamic flow profiles, these flow cell types usually rely on computational fluid dynamics (CFD) simulations for the description of the local current density profiles and overall current-potential characteristics2. In this work, we present an advanced analytical model of the limiting current in confined impinging jet electrodes and validate the model with experimental data and corresponding CFD simulations.
Around 350 parameter sets of the confined impinging jet electrode arrangement were analyzed by varying the inlet diameter (d), distance between inlet-nozzle and electrode (H), electrode radius (RIII), and volume flow rate (V0). Figure 1 shows the proposed analytical solution which separates the electrode into three different diffusion regions: (i) wall-tube region (blue rectangle), (ii) wall-jet region (green rectangle), and finally (iii) radial channel-flow region (orange rectangle). The approach allows predicting the limiting current characteristics for a broad variety of impinging jet electrodes, including the confined impinging jet electrode type. The flow line profiles obtained by CFD simulations are in excellent agreement with the analytically determined regimes with radii RI and RII and flow regime transitions. Very importantly, for the construction of ideal wall-tube electrodes the transition point RI can now be described by our analytical model in high accuracy and requires no more in-depth numerical or experimental studies3. We determined an average relative error over all parameter points compared to the numerical CFD simulations to be 7.8 %. In contrast, the analytical formula for free wall-jets4 to the entire electrode is in the range of 29 %. Furthermore, using a 3D-printed flow cell geometry (H = 0.7 mm; d = 0.5 mm) with the confined impinging jet type, the obtained experimental data confirm the here developed analytical model. The experimental data for different electrode radii (1 mm < R < 3 mm) using the ferrocyanide/ferricyanide redox pair ([Fe(CN)6]4-/[Fe(CN)6]3-) also show good agreement to the analytical model with an average deviation of 6 %.
In summary, we have developed an analytical model that allows an accurate prediction of the limiting current for different geometries of the impinging jet electrode. Based on numerical and experimental approaches, our model shows an accuracy of below 10 %, which is very remarkable compared to the current models reported in the literature. The results of this study help to improve the design and construction of electrochemical flow cells based on this electrode type as an alternative to the classic RDE setup.
References
[1] S. E. Temmel et al., Rev. Sci.
Instrum., 87(4), 45115 (2016). [2] J. Fuhrmann et al., Electrochim.
Acta, 55(2), 430–438 (2009). [3] A. Hadj Ahmed et al., Electrochim. Acta, 403, 139521 (2022). [4] J. Yamada et al., J. Electroanal. Chem. Interf. Electrochem., 44(2), 189–198 (1973).

Figure 1