Diffusion in jammed particle packs

TL;DR

This study uses simulations to analyze how diffusion behaves near the jamming transition in sphere packings, revealing two regimes of normal diffusion and how contact networks influence long-term transport properties.

Contribution

It demonstrates the scaling laws of diffusion recovery time and diffusivity near the jamming point, linking them to particle contact networks and mean first passage times.

Findings

Normal diffusion regimes are separated by an anomalous regime.

Long-time diffusivity scales as (phi - phi_c)^{0.5}.

Recovery time scales as (phi - phi_c)^{-0.5}.

Abstract

Using random walk simulations we explore diffusive transport through monodisperse sphere packings over a range of packing fractions, $\phi$, in the vicinity of the jamming transition at $\phi_{c}$. Various diffusion properties are computed over several orders of magnitude in both time and packing pressure. Two well-separated regimes of normal, "Fickian" diffusion, where the mean squared displacement is linear in time, are observed. The first corresponds to diffusion inside individual spheres, while the latter is the long-time bulk diffusion. The intermediate anomalous diffusion regime and the long-time value of the diffusion coefficient are both shown to be controlled by particle contacts, which in turn depend on proximity to $\phi_{c}$. The time required to recover normal diffusion $t^*$ scales as $(\phi-\phi_c)^{-0.5}$ and the long-time diffusivity $D_\infty \sim (\phi - \phi_c)^{0.5}$, or $D_\infty \sim 1/t^*$. It is shown that the distribution of mean first passage times associated with the escape of random walkers between neighboring particles controls both $t^*$ and $D_\infty$ in the limit $\phi \rightarrow \phi_c$.