Approximate solutions to the shrinking core model and their interpretation
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912515583115264 |
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| author | Moreno-Pulido, Cristian Olwande, Rachael Myers, Tim Font, Francesc |
| author_facet | Moreno-Pulido, Cristian Olwande, Rachael Myers, Tim Font, Francesc |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21042 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximate solutions to the shrinking core model and their interpretation Moreno-Pulido, Cristian Olwande, Rachael Myers, Tim Font, Francesc Other Condensed Matter 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. |
| title | Approximate solutions to the shrinking core model and their interpretation |
| topic | Other Condensed Matter |
| url | https://arxiv.org/abs/2507.21042 |