Active microrheology in active matter systems: Mobility, intermittency, and avalanches

We examine the mobility and velocity fluctuations of a driven particle moving through an active matter bath of self-mobile disks for varied density or area coverage and varied activity. We show that the driven particle mobility can exhibit nonmonotonic behavior that is correlated with distinct changes in the spatiotemporal structures that arise in the active media. We demonstrate that the probe particle velocity distributions exhibit specific features in the different dynamic regimes and identify an activity-induced uniform crystallization that occurs for moderate activity levels and is distinct from the previously observed higher activity cluster phase. The velocity distribution in the cluster phase has telegraph noise characteristics produced when the probe particle moves alternately through high-mobility areas that are in the gas state and low-mobility areas that are in the dense phase. For higher densities and large activities, the system enters what we characterize as an active jamming regime. Here the probe particle moves in intermittent jumps or avalanches that have power-law-distributed sizes that are similar to the avalanche distributions observed for nonactive disk systems near the jamming transition.

Figure 1

Particle locations for an active matter system with an externally driven probe particle (red). (a) Uniform liquid state at $\varphi =0.1885$ and $R_l=160$. The arrow indicates the direction of the probe driving force $F_d$. (b) Phase-separated cluster state at $\varphi =0.5$ and $R_l=160$ consisting of a high-density phase with local crystal ordering coexisting with a low-density liquid phase. (c) Uniform liquid phase at $\varphi =0.5$ and $R_l=1.0$.

Figure 2

(a) Mobility $\langle V_x\rangle$ of the probe particle vs run length $R_l$ for the system from Figs. 1 and 1 with $\varphi =0.5$. (b) Corresponding fraction of sixfold coordinated particles $P_6$ vs $R_l$. The $R_l=160$ point illustrated in Fig. 1, where the system is phase separated and the probe particle mobility is low, is marked $b$, while the $R_l=1$ point illustrated in Fig. 1, where the system is in a liquid state and the mobility is higher, is marked $c$.

Figure 3

(a) Plot of $\langle V_x\rangle$ vs $R_l$ for a system with $\varphi =0.801$. (b) Corresponding plot of $P_6$ vs $R_l$. Point $a$, in the crystalline phase where the mobility is low, is illustrated in Fig. 4. Point $b$, in the liquid phase where the mobility is high, is illustrated in Fig. 4. Point $c$, in the clump or phase-separated phase where the mobility decreases again, is illustrated in Fig. 4.

Figure 4

Voronoi construction images for the system in Fig. 3 with $\varphi =0.801$. The particle coordination numbers $z_i=5$ (dark blue), $z_i=6$ (white), $z_i=7$ (green), and $z_i\ge 8$ (light blue). The driven particle is marked with a red dot. (a) At $R_l=0.04$, labeled $a$ in Fig. 3, the system forms a crystallized state. (b) At $R_l=2.0$, labeled $b$ in Fig. 3, the system forms a disordered uniform liquid state. (c) At $R_l=160$, labeled $c$ in Fig. 3, the system forms a phase-separated state with high-density clusters and a low-density gas of particles.

Figure 5

(a) Mobility $\langle V_x\rangle$ of the probe vs run length $R_l$ for $\varphi =0.1885$, 0.3456, 0.5, 0.6273, 0.691, 0.754, 0.801, and $0.8482$, from top to bottom. (b) Corresponding $P_6$ vs $R_l$ for $\varphi =0.1885$, 0.3456, 0.5, 0.6273, 0.691, 0.754, 0.801, and $0.8482$, from bottom to top.

Figure 6

(a) Mobility $\langle V_x\rangle$ vs $\varphi$ for $R_l=1.0$ (circles) and $R_l=160$ (diamonds). The inset shows the corresponding $d\langle V_x\rangle /d\varphi$. (b) Plot of $P_6$ vs $\varphi$. The dashed line indicates the correspondence between the clustering onset and the mobility drop.

Figure 7

(a) Portion of a probe velocity time series $V_x\left(t\right)$ in the uniform liquid state at $\varphi =0.1885$ and $R_l=160$. The dashed line indicates the free probe velocity $V_0=F_d=0.5$. (b) Probability distribution of the velocity fluctuations $P\left(V_x\right)$ from (a). (c) Portion of $V_x\left(t\right)$ in the phase-separated state at $\varphi =0.5$ and $R_l=160$ where two-level fluctuations occur. (d) Plot of $P\left(V_x\right)$ from (c) showing peaks at $V_x=0.0$ and $V_x=V_0=0.5$.

Figure 8

(a) Portion of $V_x\left(t\right)$ in the active jamming phase at $\varphi =0.817$ and $R_l=160$ showing that the probe particle moves in discrete jumps or avalanches. (b) Plot of $V_x\left(t\right)$ in the uniform liquid state at $\varphi =0.817$ and $R_l=1.0$ where the probe moves continuously. (c) A log-linear plot of $P\left(V_x\right)$ from the time series at $\varphi =0.817$ with $R_l=160$ (circles) and $R_l=1.0$ (squares). The inset shows the log-log plot of $P\left(V_x\right)$ for the positive $V_x$ values at $R_l=160$. The solid line is a power-law fit with exponent $\alpha =-2.0$.