Active particles in tunable crowded environments

TL;DR

This work demonstrates that a 2D colloidal bath with tunable mechanical properties, controlled by an external AC field, can strongly modulate active swimmer dynamics. The swimmers’ speed scales as $v \\propto E^2$ while persistence time $\\tau$ decreases with bath stiffness, leading to a viscous-to-viscoelastic transition in the environment’s influence on motion. At large propulsion and stiffness, a lever-arm torque from asymmetric dipolar interactions yields spontaneous chiral helical trajectories, a phenomenon captured by a coarse-grained Fokker-Planck/Boltzmann framework that predicts a density-dependent swim speed $v(\\rho)$ and a net angular drift $\\langle \\dot{\\theta} \ angle$. The combination of particle-resolved experiments, simulations, and theory provides a general mechanism for tuning active trajectories via environmental compressibility and anisotropic interactions, with potential applications in microrheology, micro-swimming, and targeted delivery. The results extend understanding of active matter in viscoelastic-like media by showing that chirality and reorientation can be controlled in situ without changing particle geometry or bath composition.

Abstract

Active particles affect their environment as much as the environment affects their active motion. Here, we present an experimental system where both can be simultaneously adjusted in situ using an external AC electric field. The environment consists in a two-dimensional bath of colloidal silica particles, whereas the active particles are gold-coated Janus spheres. As the electric field orthogonal to the planar layer increases, the former become stiffer and the latter become faster. The active motion evolves from a viscous like to a viscoelastic like behavior, with the reorientation frequency increasing with the particle speed. This effect culminates in the spontaneous chiralization of particle trajectories. We demonstrate that self-sustained reorientations arise from local compressions and interaction asymmetries, revealing a general particle-level mechanism where changes in the mechanical properties of the environment reshape active trajectories.

Figures (8)

• Figure 1: Active particles in tunable colloidal environments. Snapshots of active Janus particles cruising in colloidal monolayers of Brownian microspheres under applied electric fields (a) $\rm E=42$$\rm V/mm$ and (b) $\rm E=108$$\rm V/mm$ (packing fraction, $\phi=0.48$). The active particle trajectories for the last $12$ minutes are reported as a red lines. The scale bar corresponds to $20$$\rm \mu m$ in both microscopy images.
• Figure 2: Tuning the structure of the environment. (a) Experimental (red solid lines) and numerical (black dotted lines) pair correlation functions $\rm g(r)$ for colloidal monolayers with packing fraction $\phi=0.48$ subjected to electric fields of different magnitude (as shown in the graph). The experimental data are an average over $1000$ independent realizations. (b) Mean absolute value of the hexagonal order parameter $|\Psi_6|$ as a function of the applied electric field. Experiments and simulations are denoted by solid and empty symbols, respectively. The dotted line connecting the numerical results is a guide for the eye. (c-e) Maps of the phase $\varphi$ of $\rm \Psi_{6,n}$ for experiments at (c) $\rm E=42$$\rm V/mm$, (d) $\rm E=75$$\rm V/mm$ and (e) $\rm E=108$$\rm V/mm$. The color indicates the orientation of the crystalline domain, as shown below in the panel. The scale bar is $20$$\rm \mu m$.
• Figure 3: Quenching colloidal environments by changing the electric field amplitude. (a) Mean hexagonal bond order parameter $\rm \left| \Psi_{6} \right|$ plotted as a function of the electric-field strength $\rm E$ for colloidal monolayers with packing fraction $\phi=0.15$ (green), $\phi=0.35$ (blue), $\phi=0.48$ (red) and $\phi=0.64$ (orange). The filled symbols are obtained by experiments while the empty symbols (connected by dotted lines) correspond to numerical results. (b) Experimental dynamical orientational correlation $\rm g_6(\Delta t)$ as a function of the normalized delay time $\rm \Delta t / \tau_{B}$ for different packing fractions and electric fields. (a) and (b) share the same legend with colors corresponding to different packing fractions $\phi$. Note that in (b) we only report the curves at $\rm E=48$$\rm V/mm$, $\rm E=75$$\rm V/mm$ and $\rm E=108$$\rm V/mm$ for clarity. At all $\phi$, the decay of $\rm g_6(\Delta t)$ is slower for larger electric fields (as schematically indicated by the arrows).
• Figure 4: Swimming in crowded environments. (a) Mean swimming velocities (black) $v_0$ and (red) $v$ plotted as a function of the electric-field strength squared $\rm E^2$ for active particles swimming 'freely' ($\phi=0$) or cruising in colloidal environments of packing fraction $\phi=0.48$. The solid lines are linear fits crossing the origin. The error bars are calculated as standard deviations. (b) Ratio between the effective viscosity $\rm \eta_{eff}$ of the colloidal environment and the water viscosity $\rm \eta_0$ calculated as described in the text. (c-d) Normalized histograms of the instantaneous speed $\left | \dot{\mathbf{x}} \right |$ under an applied electric field (c) $\rm E = 42$$\rm V/mm$ and (d) $\rm E = 108$$\rm V/mm$.
• Figure 5: Reorienting in crowded environments. (a-c) Trajectories of active particles cruising in colloidal environments of packing fraction $\phi=0.48$ under applied electric fields (a) $\rm E=42$$\rm V/mm$, (b) $\rm E=75$$\rm V/mm$ and (c) $\rm E=108$$\rm V/mm$. The scale bar is 'dynamic' and corresponds to $\left ( v \tau_{\rm R} \right )$ for all trajectories, where $v$ is the average swimming velocity and $\rm \tau_R$ is the rotational Brownian time (defined in the text). The color indicates the time: from $\rm t=0$ (white) to $\rm t=500$$\rm s$ (red). (d) Time autocorrelation functions of $\dot{\mathbf{x}}$ for the trajectories shown in (a-c). The solid lines are linear fits. (e) Mean persistence times $\tau$ (red symbols, $\phi=0.48$) and $\tau_0$ (black symbols, $\phi=0$) plotted against $v$. The filled symbols are obtained from experiments while empty symbols (linked by the dotted line) are from numerical simulations matching the experimental values of $v$. The error bars are calculated as standard deviations.