Analytical time-dependent solutions of modelling of metal electrodeposits

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 (Vₛ = O(1-10)) and relaxation parameters (Θ = τ D/L ²\,∈ [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.