# Hydrodynamic synchronization and collective dynamics of colloidal particles driven along a circular path

## TL;DR

This paper theoretically investigates the collective behavior of colloidal particles driven along a circular path by an optical vortex, revealing synchronization phenomena and dynamic rearrangements that align with experimental observations.

## Contribution

It derives phase equations considering hydrodynamic and repulsive interactions, providing new insights into the collective dynamics of colloidal particles on a circular trajectory.

## Key findings

- Particles synchronize and form doublets that move faster than singles.
- Periodic rearrangements of particle groups occur for certain numbers of particles.
- The system exhibits oscillating or stable synchronized states depending on initial conditions.

## Abstract

We study theoretically the collective dynamics of particles driven by an optical vortex along a circular path. Phase equations of N particles are derived by taking into account both hydrodynamic and repulsive interactions between them. For N = 2, the particles attract with each other and synchronize, forming a doublet that moves faster than a singlet. For N = 3 and 5, we find periodic rearrangement of doublets and a singlet. For N = 4 and 6, the system exhibits either a periodic oscillating state or a stable synchronized state depending on the initial conditions. These results reproduce main features of previous experimental findings. We quantitatively discuss the mechanisms governing the non-trivial collective dynamics.