Use of dynamically adaptive grid techniques for the solution of electrochemical kinetic equations. Part 14: extension of the patch-adaptive strategy to time-dependent models involving migration–diffusion transport in one-dimensional space geometry, and its application to example transient experiments described by Nernst–Planck–Poisson equations

Abstract

The finite-difference patch-adaptive strategy for electrochemical kinetic simulations, introduced in Part 5 and extended in Part 10 of this series of papers, is further extended to time-dependent models involving migration–diffusion transport in one-dimensional space geometry. The extensions include: spatial discretisation of generalised second spatial derivative expressions typical of migration–diffusion equations; allowance for the dependence of boundary conditions on displacement current; support for an a posteriori calculation of the displacement current as one of the model responses; optional calculation of steady-state initial conditions; the ability to use enhanced precision of floating point calculations. The extended strategy is used to simulate four examples of transient experiments, represented by Nernst–Planck–Poisson equation systems: coulostatic charge injection at an ideally polarised planar electrode; a voltage step for a thin layer asymmetric electrochemical cell; chronopotentiometry for an electrolyte|membrane|electrolyte system; and chronopotentiometry for a bipolar membrane. The strategy provides fairly reliable solutions, but its automatism and efficiency are less satisfactory compared to models without electric migration, owing to the need for model-dependent tuning of the method parameters, and increased computational cost necessary for the exact adaptive determination of the electric potential profiles.