Approximate solutions to the shrinking core model and their interpretation

TL;DR

This paper revisits the shrinking core model for spherical solid-fluid reactions, deriving improved analytical solutions and numerical methods to address limitations of traditional approximations, enabling better parameter estimation from experiments.

Contribution

It introduces a perturbation-based analytical solution that surpasses the pseudo-steady-state approximation and proposes a simple fitting method for experimental parameter estimation.

Findings

Perturbation solutions are more accurate than pseudo-steady-state models.

Numerical schemes validate analytical approximations effectively.

Method enables efficient parameter estimation from experimental data.

Abstract

The shrinking core model describes the reaction of a spherical 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 behavior. 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.