Approximate solutions to the shrinking core model and their interpretation

• Derivation and analysis of the shrinking core model • Approximate solutions obtained via the perturbation method • Perturbation solutions improve upon standard pseud-stady-state approximation • Accuracy of pertubration solutions tested with numerical solutions • Fitting procedure proposed using perturbation solutions The shrinking core model (SCM) describes the reaction of a solid particle with a surrounding fluid. In this work, we revisit the SCM by deriving it from the underlying physical processes and performing a careful non-dimensionalisation, which highlights the limitations of the commonly used pseudo-steady-state approximation, particularly in liquid-solid systems where fluid and solid densities are comparable. To address these limitations, we derive approximate analytical solutions using a perturbation method that improves upon the pseudo-steady-state model. We also obtain a small-time solution capturing early transient behaviour. A semi-implicit finite difference scheme is implemented to solve the full model numerically and benchmark the analytical approximations. We demonstrate that the perturbation solution provides significantly improved accuracy over the pseudo-steady-state model, especially in diffusion-limited regimes. Finally, we propose a simple fitting procedure combining the perturbation with the early-time solutions to estimate physical parameters from experimental data at minimal computational cost.