Hydrodynamically synchronized states in active colloidal arrays

TL;DR

This study investigates how active colloidal particles in fluid environments synchronize their motion, revealing that the collective states depend on eigenmode structures and spatial configurations, with distinct synchronization patterns for different arrangements.

Contribution

The paper demonstrates that the collective dynamical states of active colloids can be predicted from eigenmode analysis and spatial configuration, providing new insights into synchronization mechanisms.

Findings

Two-particle and polygonal arrays synchronize in anti-phase.

Three equally spaced colloids synchronize in-phase.

The dominant eigenmode determines the stable dynamical state.

Abstract

Colloidal particles moving in a fluid interact via the induced velocity field. The collective dynamic state for a class of actively forced colloids, driven by harmonic potentials via a rule that couples forces to configurations, to perform small oscillations around an average position, is shown by experiment, simulation and theoretical arguments to be determined by the eigenmode structure of the coupling matrix. It is remarkable that the dynamical state can therefore be predicted from the mean spatial configuration of the active colloids, or from an analysis of the fluctuations near equilibrium. This has the surprising consequence that while 2 particles, or polygonal arrays of 4 or more colloids, synchronize with the nearest neighbors in anti-phase, a system of 3 equally spaced colloids synchronizes in-phase. In the absence of thermal fluctuations, the stable dynamical state is predominantly formed by the eigenmode with longest relaxation time.