Compression-driven jamming in porous cohesive aggregates

Abstract

I investigate the compression-driven jamming behavior of two-dimensional porous aggregates composed of cohesive, frictionless disks. Three types of initial aggregates are prepared using different aggregation procedures, namely, reaction-limited aggregation (RLA), ballistic particle-cluster aggregation (BPCA), and diffusion-limited aggregation (DLA), to elucidate the influence of aggregate morphology. Using distinct-element-method simulations with a shrinking circular boundary, I numerically obtain the pressure as a function of the packing fraction $φ$. For the densest RLA and the intermediate BPCA aggregates, a clear jamming transition is observed at a critical packing fraction $φ_{\rm J}$, below which the pressure vanishes and above which a finite pressure emerges; the transition is less distinct for the most porous DLA aggregates. The jamming threshold depends on the initial structure and, when extrapolated to infinite system size, approaches $φ_{\rm J} = 0.765 \pm 0.004$ for RLA, $0.727 \pm 0.004$ for BPCA, and $0.602 \pm 0.023$ for DLA, where the errors denote the standard error. Above $φ_{\rm J}$, the pressure follows $P \approx A {( φ- φ_{\rm J} )}^{2}$, which implies that the bulk modulus $K$ of jammed aggregates is proportional to $φ- φ_{\rm J}$. Rigid-cluster analysis of jammed aggregates shows that the average coordination number within the largest rigid cluster increases linearly with $φ- φ_{\rm J}$. Taken together, these relations suggest that the elastic response of compressed porous aggregates is analogous to that of random spring networks.

Figures (10)

• Figure 1: Schematics of elastic interaction models. (a) Unbreakable contact model. $F_{\rm e} = 0$ when the two particles are separated (black line). A contact is formed when the particles collide (red filled circle). Once a contact has formed, $F_{\rm e}$ is given by Equation (\ref{['eq:F_e']}) (red line). A repulsive force acts when the compression length is positive, whereas an attractive force acts when it is negative. In this model, a contact never breaks once it has formed. (b) Breakable contact model. $F_{\rm e} = 0$ when the two particles are separated (black line). A contact is formed when the particles collide (red filled circle). Once a contact has formed, $F_{\rm e}$ is given by Equation (\ref{['eq:F_e_break']}) (red line). In this model, the contact breaks when $\delta$ reaches $- 2 \delta_{\rm c}$ (black open circle).
• Figure 2: Three types of aggregates prepared using distinct aggregation procedures. Panels (a), (b), and (c) show the initial structures of DLA, BPCA, and RLA aggregates with $N = 16384$, respectively.
• Figure 3: Snapshots of a compressed aggregate obtained using a two-step numerical procedure. (a) Initial configuration of BPCA-16384-1. (b), (c) Configurations at $\phi = 0.694$ and $0.717$ during the first compression stage. (d), (e) Configurations at $\phi = 0.694$ and $0.717$ after relaxation. The red particles in panels (d) and (e) form the largest rigid cluster (see Section \ref{['sec:rigid']}).
• Figure 4: Normalized pressure $P/k$ after relaxation. The figure shows the relationship between ${\left( P / k \right)}^{1/2}$ and $\phi$ near the jamming transition. (a)--(c) Results for $N = 16384$. (d)--(f) Results for $N = 4096$. (g)--(i) Results for $N = 1024$. Data with positive $P$ are plotted using filled symbols, whereas data with negative $P$ are plotted as $- P$ using open symbols.
• Figure 5: System-size dependence of the jamming point $\phi_{\rm J}$. Symbol shapes (circle, triangle, diamond, square, and pentagon) correspond to those in Figure \ref{['fig:4']}. The solid lines represent the best fits obtained by least-squares fitting to Equation (\ref{['eq:phi_J_fit']}).