Abstract
We numerically investigate the self-diffusion coefficient and correlation length of the rigid clusters (i.e., the typical size of the collective motions) in sheared soft athermal particles. Here we find that the rheological flow curves on the self-diffusion coefficient are collapsed by the proximity to the jamming transition density. This feature is in common with the well-established critical scaling of flow curves on shear stress or viscosity. We furthermore reveal that the divergence of the correlation length governs the critical behavior of the diffusion coefficient, where the diffusion coefficient is proportional to the correlation length and the strain rate for a wide range of the strain rate and packing fraction Take across the jamming transition density.
Highlights
Transport properties of soft athermal particles, e.g., emulsions, foams, colloidal suspensions, and granular materials, are important in science and engineering technology [1]
If the packing fraction exceeds the jamming point, one observes yield stress at vanishing strain rate [19]. These two trends are solely determined by the proximity to jamming | φ| ≡ |φ − φJ| [3], where rheological flow curves of many types of soft athermal particles have been explained by the critical scaling near the jamming transition [4,5,6,7,8,9,10,11,12,13,14,15]
We show our numerical results of the selfdiffusion of soft athermal particles
Summary
Transport properties of soft athermal particles, e.g., emulsions, foams, colloidal suspensions, and granular materials, are important in science and engineering technology [1]. Another crossover from D ∼ γto D ∼ γ 1/2 was suggested by the studies of amorphous solids (though the scaling D ∼ γ 1/2 is the asymptotic behavior in rapid flows γ ≫ γc) [23,24,25] It was found in MD simulations of soft athermal disks that, in a sufficiently small flow rate range, the diffusivity changes from D ∼ γ (φ < φJ) to γ 0.78 (φ ≃ φJ) [26], implying that the crossover shear rate γc vanishes as the system approaches jamming from below φ → φJ. The size of rigid clusters ξ diverges as the shear rate goes to zero γ → 0 so that the power-law scaling ξ ∼ γ −s was suggested, where the exponent varies from s = 0.23 to 0.5 depending on numerical models and flow conditions [22, 28].
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