Clogging and jamming transitions in periodic obstacle arrays

We numerically examine clogging transitions for bidisperse disks flowing through a two-dimensional periodic obstacle array. We show that clogging is a probabilistic event that occurs through a transition from a homogeneous flowing state to a heterogeneous or phase-separated jammed state where the disks form dense connected clusters. The probability for clogging to occur during a fixed time increases with increasing particle packing and obstacle number. For driving at different angles with respect to the symmetry direction of the obstacle array, we show that certain directions have a higher clogging susceptibility. It is also possible to have a size-specific clogging transition in which one disk size becomes completely immobile while the other disk size continues to flow.

Figure 1

(a) Average disk velocities $\langle V_x\rangle$, (b) fraction of disks in a cluster $C_l$, and (c) average contact number $Z$ versus time in simulation time steps for 2D bidisperse disks moving through a square periodic obstacle array with total disk density ${\varphi }_t=0.54$, lattice constant $a=3.0$, and constant external drive $F_d=0.025$ applied in the positive-$x$ direction. We illustrate three cases: steady-state flow (blue curve), full clogging (red curve), and partial clogging (green curve). (d) Distribution $P\left(\varphi \right)$ of local disk density $\varphi$ in $2\times 2$ spatial regions in the initial state (teal curve) and after reaching a clogged state (red curve), averaged over 40 clogged realizations.

Figure 2

Images of the obstacle locations (green circles) and the mobile disks (large disks, blue; small disks, orange) for the samples shown in Fig. 1 with $a=3.0$ and ${\varphi }_t=0.54$. (a) Initial configuration of the sample that clogs. (b) Final clogged configuration of the same sample. (c) Late-time configuration of the flowing sample. (d) Late-time configuration of the partially clogged sample.

Figure 3

(a) Clogging probability $P_c$ vs ${\varphi }_t$ for varied obstacle lattice constant $a=2.5$ (dark blue circles), 2.609 (light blue squares), 2.727 (light green diamonds), 2.857 (dark green up triangles), 3.0 (orange left triangles), 3.158 (red down triangles), and 3.33 (magenta right triangles). (b) Average value of $Z$ for realizations that clog vs $a$ increases monotonically. (c) Angles ${\theta }_s$ (red squares) and ${\theta }_l$ (blue diamonds) at which $x$-direction channeling is lost for the small and large disks, respectively, vs $a$. For driving angles falling within the green shaded region, size-dependent clogging can occur.

Figure 4

(a) $P_c$ vs $\theta$, the driving direction angle, in samples with ${\varphi }_t=0.5272$ and $a=2.857$. Here $P_c$ is enhanced for $\theta >{25}^{\circ }$. (b) $\langle V_x\rangle$ vs time in simulation time steps for the large disks only (red), the small disks only (blue), and all disks (purple) for a driving angle of $\theta ={20}^{\circ }$. We find a size dependence, with only the smaller disks becoming clogged while the large disks continue to flow. (c) Disk configuration in the clogged state at $\theta ={32}^{\circ }$ from (a). (d) Disk configuration for the size-dependent clogged state from (b).