Active phase separation: role of attractive interactions from stalled particles

Abstract

Dry active matter systems are well-known to exhibit Motility-Induced Phase Separation (MIPS). However, in wet active systems, attractive hydrodynamic interactions mediated by active particles stalled at a boundary can introduce complementary mechanisms for aggregation. In the work of Caciagli et al. (PRL 125, 068001, 2020), it was shown that the attractive hydrodynamic interactions due to active particles stalled at a boundary can be described in terms of an effective potential. In this paper, we present a model of active Brownian particles, where a fraction of active particles are stalled, and thus, mediate inter-particle interactions through the effective potential. Our investigation of the model reveals that a small fraction of stalled particles in the system allows for the formation of dynamical clusters at significantly lower densities than predicted by standard MIPS. We provide a comprehensive phase diagram in terms of weighted average cluster sizes that is mapped in the plane of the fraction of stalled particles ($α$) and the Peclet number. Our findings demonstrate that even a marginal value of $α$ is sufficient to drive phase separation at low global densities, bridging the gap between theoretical models and experimental observations of dilute active systems.

Figures (4)

• Figure 1: Panel (a) shows a schematic diagram of motion of free (blue) and stalled particles (yellow) in the $xy$-plane. The stalled particles have no self-propulsion in the plane while free particles can freely self-propel. (b) shows that the stalled particles acts as sites of attraction in the system. See Eq.\ref{['eq:HI_pot']} for the functional form of effective inter-particle attractions mediated by stalled particles.
• Figure 2: Active phase separation with a fraction of stalled particles ($\alpha$) for the case of $\lambda\rightarrow\infty$ and area fraction $\phi=0.3$. (a) Phase diagram in terms of weighted average cluster size $m$ in the plane of $\alpha$ and Péclet number Pe. (b) Plot of $m$ as a function of $\alpha$. We obtain clustering at Pe=$10$ as $\alpha$ is increased, a region where clustering is not possible from usual MIPS. Interestingly, at Pe=$100$, cluster size first decreases on increasing $\alpha$. Thus, suppressing MIPS due to reduction in number of particles self-propelling in the plane. But on further increasing $\alpha$, we again get pronounced aggregation due to dominance of attractions mediated by stalled particles. (c) Snapshots from steady state at different values of Péclet number Pe and $\alpha$. It should be noted that we get phase separation at any value of Pe and $\phi$ on increasing $\alpha$ beyond a threshold.
• Figure 3: Panel (a) contains plots of the structure factor $S(\mathbf k)$ at corresponding values of Pe and $\alpha$, while the contribution from $\mathbf k=0$ is discarded. There is no clustering at $\alpha=0$ and Pe = 10. (b-c) shows the growth of weighted average cluster size $M$. (b) shows growth solely due to effective attraction from potential of Eq.\ref{['eq:HI_pot']} as $\alpha=0.3$ and Pe=10. (c) shows growth through MIPS alone as $\alpha=0$ and Pe=130.
• Figure 4: Active phase separation with a fraction ($\alpha$) of stalled particles for the case of $\lambda=0$. Here, the total area fraction is $\phi=0.3$. (a) Phase diagram in terms of weighted average cluster size $m$ in the plane of $\alpha$ and Péclet number Pe. We get phase separation at any value of Pe and $\phi$ on increasing $\alpha$ beyond a threshold. (b) Plot of $m$ for two different Pe as a function of fraction of stalled particles. (c) Snapshots from steady state at different values of Péclet number Pe and $\alpha$.