Common Packing Patterns for Jammed Particles of Different Power Size Distributions

Abstract

We introduce a model for particles that are extremely polydisperse in size compared to monodisperse and bidisperse systems. In two dimensions (2D), size polydispersity inhibits crystallization and increases packing fraction at jamming points. However, no packing pattern common to diverse polydisperse particles has been reported. We focused on polydisperse particles with a power size distribution $r^{-a}$ as a ubiquitous system that can be expected to be scale-invariant. We experimentally and numerically constructed 2D random packing for various polydisperse particles with different size exponents, $a$. Analysis of the packing pattern revealed a common contact number distribution for $a<3$ and a higher jamming point in $2<a<3$ than monodisperse systems. These findings demonstrate that the ambiguity of the characteristic length provides the common properties that leads to a novel classification scheme for polydisperse particles.

Figures (3)

• Figure 1: (a) Schematic of the experimental setup of polydisperse droplets confined in 2D space. (b) Microscopic image of the polydisperse droplets from the top (top) and the cross-sectional image along the dashed line (bottom). Scale bar is 100 $\mu$m. (c-h) Microscopic images (c, d), droplet radius distribution, $N(r)$ (e, g), and contact number distribution, $\nu(z)$ (f, h) for bidisperse system (c, e, f) and polydisperse system (d, g, h). Scale bars in (c, d) are 1 mm. Cumulative distributions of radius and contact number as represented by log-log graphs in (g) and (h), respectively; (g) $N(r)$ follows a power size distribution of $a\simeq3$ in the region of one order of magnitude.
• Figure 2: (a) Examples of numerically produced packing patterns for various polydisperse systems $r^{-a}$, and (b)-(f) corresponding cumulative contact number distribution $\nu(z)$. From left to right, $a=$1.5, 2, 2.5, 3, 3.5.
• Figure 3: (a) Dependece of pressure $P$ on the packing fraction $\phi$ for various $a$. For better visibility, the curves were shifted vertically. (b) Dependence of $\phi_{\rm c}$ on $a$.