| Issue |
EPL
Volume 154, Number 4, May 2026
|
|
|---|---|---|
| Article Number | 42002 | |
| Number of page(s) | 4 | |
| Section | Mathematical and interdisciplinary physics | |
| DOI | https://doi.org/10.1209/0295-5075/ae647a | |
| Published online | 13 May 2026 | |
Analytical time-dependent solutions of modelling of metal electrodeposits
Independent Researcher - Sydney, NSW 2033, Australia
Received: 23 March 2026
Accepted: 24 April 2026
Abstract
This work develops a rigorous analytical framework for electrodeposition transport incorporating diffusion, convection, electric-field–driven drift, and finite relaxation effects. The model is valid over a wide parameter range of dimensionless drift parameters 
and relaxation parameters (
[0, 1]). Unlike classical diffusion models, the formulation predicts finite-speed propagation and damped oscillatory transient responses. Explicit steady-state and full time-dependent solutions are derived via eigenfunction expansion. The results provide experimentally testable predictions for transient current response following perturbations, offering a pathway to validate finite-speed transport effects in electrochemical systems.
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