Jamming with Tunable Roughness

We introduce a new model to study the effect of surface roughness on the jamming transition. By performing numerical simulations, we show that for a smooth surface, the jamming transition density and the contact number at the transition point both increase upon increasing asphericity, as for ellipsoids and spherocylinders. Conversely, for a rough surface, both quantities decrease, in quantitative agreement with the behavior of frictional particles. Furthermore, in the limit corresponding to the Coulomb friction law, the model satisfies a generalized isostaticity criterion proposed in previous studies. We introduce a counting argument that justifies this criterion and interprets it geometrically. Finally, we propose a simple theory to predict the contact number at finite friction from the knowledge of the force distribution in the infinite friction limit.

Figure 1

Schematic picture of the surfaces of two particles. The solid lines represent the surfaces of particles, while the dashed lines represent the surfaces of the references disks. The solid and dashed arrows represent the minimal paths connecting the surfaces of particles and reference disks, respectively.

Figure 2

(a) $f(\theta )/\mu$ for $ϵ=0.1$ and several $n$. The number of minima increases with $n$. (b) $f(\theta )$ for $n=2$ and several $ϵ$. The triangle wave is recovered when $ϵ=0$. (c) Schematic pictures of a particle shape. The shape deviates from the reference disk with $\mu$, and the surface becomes rougher for larger $n$.

Figure 3

$\mu$ dependence for fixed $ϵ=0.1$ of (a) the contact number per particle at the jamming transition point $z_J$ and (b) the jamming transition point ${\phi }_J$. The data for the Coulomb friction model were taken from Ref. [42].

Figure 4

$\mu$ dependence for fixed $n={10}^4$ of (a) the contact number per particle at the jamming transition point $z_J$ and (b) the jamming transition point ${\phi }_J$. Markers denote the numerical results, while the dashed line denotes the theoretical prediction; see main text.

Figure 5

(a)–(c) Cumulative distributions of $|f_n/\mu f_t|$ for $n={10}^4$ and $ϵ=0.25$, 0.1, and 0.01, respectively. (d) Cumulative distribution of $|f_n/f_t|$ for $n={10}^4$ and $ϵ=0.01$.

Figure 6

Relation between $n_m$ and $z_J$ for $n={10}^4$. Markers denote numerical results. The solid line denotes the theoretical prediction $n_m=z-3$ corresponding to generalized isostaticity.