Dynamic Clustering in Active Colloidal Suspensions with Chemical Signaling

In this Letter, we explore experimentally the phase behavior of a dense active suspension of self-propelled colloids. In addition to a solidlike and gaslike phase observed for high and low densities, a novel cluster phase is reported at intermediate densities. This takes the form of a stationary assembly of dense aggregates—resulting from a permanent dynamical merging and separation of active colloids—whose average size grows with activity as a linear function of the self-propelling velocity. While different possible scenarios can be considered to account for these observations—such as a generic velocity weakening instability recently put forward—we show that the experimental results are reproduced mathematically by a chemotactic aggregation mechanism, originally introduced to account for bacterial aggregation and accounting here for diffusiophoretic chemical interaction between colloidal swimmers.

Figure 1

Top: (left) Schematic representation of the experimental system and (right) normalized surface density profiles $\rho /{\rho }_{\max }$ as a function of the position $z$ along the cell—with (blue line) and without (red dotted line) ${\mathrm{H}}_2{\mathrm{O}}_2$. Solid lines are fits with a tangent hyperbolic function. Bottom: picture of the 2D sedimented particles: left, passive colloids in water; right, active colloids (SPCs) in a solution of $0.1\%$ of ${\mathrm{H}}_2{\mathrm{O}}_2$. The effective gravity, $g\sin \theta \simeq 2\times {10}^{-2}\mathrm{m}·{\mathrm{s}}^{-2}$, is indicated by the arrow.

Figure 2

Structure factors $S(k)$: Nonactive SPCs in water in the solid phase are indicated by the dashed line. The bottom arrows point to the first vectors in the reciprocal space for a triangular lattice. Active SPCs (in ${\mathrm{H}}_2{\mathrm{O}}_2=0.1\%$) for the solid phase (light green line), the intermediate zone (dark blue line), and the gas phase (red dotted line). Inset: same plots in logarithmic scales, zooming in on the small $k$ behavior.

Figure 3

Dynamic clusters of SPCs observed in a horizontal geometry for $\varphi \approx 5\%$ and $C_{{\mathrm{H}}_2{\mathrm{O}}_2}=0.1\%$. The images are obtained in the transmission mode with a $63\times$ objective. For the chronophotography of the clusters, see the Supplemental Material [29] for movies. (a) Illustration of the dynamics between clusters. (b) Dynamics inside a cluster. Marked particles show exchanges between clusters, a dynamic exchange of SPCs between the gas phase and the cluster, and internal reorganization of the cluster.

Figure 4

(a) Mean cluster size $N^{*}$ vs the average velocity of the particles in the gas phase, measured in the experiments (with SPC surface fraction $5\%$). The point at $V=0$ is measured for zero activity. The dashed line is a linear fit, $N(V)=1.6V+1.4$ ($V$ in $\mu \mathrm{m}·{\mathrm{s}}^{-1}$). (b) Schematic representation of the aggregation mechanism (top view): two SPCs, moving with phoretic velocity ${\overrightarrow{V}}_1$ and ${\overrightarrow{V}}_2$, create a monopole of concentration $c$ (for instance, ${\mathrm{H}}_2{\mathrm{O}}_2$, ${\mathrm{O}}_2$) around them. This gradient induces a diffusiophoretic motion of the SPCs toward each other with a drift velocity $V_{DP}\propto \nabla c$. For the sake of simplicity, only the gradient of chemical for the bottom SPC is represented.