FEM Modelling of Diffusional Electrochemical Impedance Spectroscopy at a Channel Electrode
Bibliographic record
Abstract
Calculation of the electrochemical impedance spectroscopy for a diffusional process at a channel electrode with laminar flow necessitates the solution of the diffusion-convection equation with appropriate boundary conditions. Although the full equation has not been solved analytically, two sets of assumptions have been used previously, and the resulting equations were solved analytically: i) The axial diffusion is neglected and the Poiseuille flow is simplified as a Lévêque flow1,2. ii) Convection is neglected and it is solved as a simple diffusion process3. However, although the assumptions intuitively allow for solving the problem in a large parameter space, parameters for which these approximations are valid have not been determined. We demonstrate by using FEM software (Comsol Multiphysics™), that the full problem can be solved numerically. The solution obtained by FEM software is compared to experimental results and the two analytical solutions. The method shows good correspondence with the experimental results and a large flexibility, making it possible to solve more complex problems such as different diffusion coefficients4 and unconventional geometries. An example of a comparison between experimental results, numerical results using FEM software, and an analytical solution is shown in Fig. 1. The parameter space of the analytical solutions is investigated using two non-dimensional parameters, A and B, and a validity area is found where the analytical solutions are well-suited. The parameter A is a version of the Péclet number, A = 6vavh/D, and B is the ratio of electrode width and channel height, B = w/h. References: [1] B. A. Coles, R. G. Compton, J. Electroanal. Chem. 127,37 (1981). [2] R. G. Compton, G. R. Sealy, J. Electroanal. Chem. 145,35 (1983). [3] R. G. Compton, J. Winkler, J. Phys. Chem. 99,5029 (1995). [4] Y. Wang, J. G. Limon-Petersen, R. G. Compton J. Electroanal. Chem. 652,13 (2011). Fig 1: Nyquist plot of impedance spectroscopy at a channel electrode showing experimental values (blue boxes), values modelled in Comsol (blue line), values calculated analytically by neglecting axial diffusion and simplifying the flow (upward pointing black triangles), and values calculated by neglecting convection (downward pointing black triangles). Impedance values are dimensionless. Figure 1
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".