Diffusion in Jammed Particle Packs

Using random walk simulations we explore diffusive transport through monodisperse sphere packings over a range of packing fractions φ in the vicinity of the jamming transition at φc. 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 φc. The time required to recover normal diffusion t* scales as (φ-φc)^-0.5 and the long-time diffusivity D_∞~(φ-φc)0.5, or D_∞~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_∞ in the limit φ→φc.