Emergent Synchronization and Defect Dynamics in Confined Chiral Active Suspensions

Abstract

Hydrodynamic interactions can generate rich emergent structures in active matter systems. Using large-scale hydrodynamic simulations, we demonstrate that hydrodynamic coupling alone can drive spontaneous self-organization across a hierarchy of spatial and temporal scales in confined suspensions of torque-driven particles at moderate Reynolds numbers. Spinners first self-assemble into dimers, which crystallize into a hexatic lattice and subsequently undergo a collective tilting instability. The resulting tilted dimers rotate and synchronize through hydrodynamic repulsion, which can be tuned by the Reynolds number. Upon synchronization, the polar director develops splay and bend deformations and nucleates topological defects with charges of $\pm1$. These defects induce long-wavelength concentration gradients and drive crystal vortex dynamics spanning hundreds of particle diameters. Our results reveal a purely hydrodynamic route to synchronization and defect-mediated dynamics in chiral active matter, without explicit alignment rules or interparticle forces.

Figures (4)

• Figure 1: Multiscale self-organization of confined spinners. (a) Schematic of the system. (b) Schematic representation of the streamlines generated by a spinner at $\mathrm{Re} \sim 10$. (c) Simulated flow field of an isolated spinner at $\mathrm{Re} \approx 7$ confined between walls separated by $W \approx 5R$. A recirculating flow arises due to the confinement, as indicated by the streamlines. The color map shows the pressure field, with low-pressure regions appearing near the spinner surface. (d) Example of spinner pairing and the surrounding streamlines of a stable vertical dimer under confinement ($W \approx 5R$). (e) Schematic illustrating the crystallization of tilted dimers and rotational synchronization. Black lines (magnified $\times 4$) represent the alignment $\mathbf{L}_p$, calculated as the projection of the vector connecting the centers of two paired spinners onto the plane perpendicular to the spinning axis. (f) Right: Time series of snapshots showing the evolution of tilted dimer configurations. At early times, the dimers are vertical ($L_p\approx 0$). Spontaneous tilting ($L_p > 0$) emerges and spreads across the system. The color map indicates the spatial distribution of $L_p$. Left: Zoom-in view of the boxed area in the right panel. Black lines show the alignment of the dimers given by $\mathbf{L}_p$ (magnified $\times 4$). Darker regions highlight defect locations, where vertical pairing persists ($L_p\approx 0$). Simulation corresponds to $N=30720$ spinners at $\mathrm{Re} \approx 10$, confined within a computational domain of $5R\times 480R\times 480R$. (g) Time evolution of the hexatic order parameter $\Psi_6$ and the Kuramoto order parameter $K$. (h) Time evolution of the total number of defects $N_D$.
• Figure 2: Active defects. (a) Instantaneous orientation structures around a $+1/-1$ defect. (b) Probability distribution of defect lifetimes. (c) Example of a short-lived $+1/-1$ defect pair undergoing spontaneous nucleation, movement, and annihilation. (d) Probability distribution of defect speeds.
• Figure 3: Vortex dynamics. (a) The average number of defects $N_D$ decreases with increasing volume fraction of a local domain $\phi$. (b) Regions with high (black) or low (white) local volume fractions exhibit slow vortical motion. The black-and-white shading indicates the local volume fraction. The motion of the dimer centers is represented by streamlines, color coded by the observed speed.
• Figure 4: Rotational synchronization driven by hydrodynamic interactions. (a) Spatial fields of dimer orientation angle $\alpha$ and local synchronization parameter $K$. (b) Schematic of the minimal model describing rotational dynamics of dimers arranged on a hexatic lattice. Each dimer is represented by a rotating vector, and hydrodynamic interactions are modeled via transverse $f_t$ and repulsive $f_r$ forces. (c) Mean Kuramoto order parameter $\langle K \rangle$ as a function of Reynolds number $\mathrm{Re}$. Results from both hydrodynamic simulations and the minimal model show a consistent increase in synchronization with $\mathrm{Re}$.