Periodic Orbits of Active Particles induced by Hydrodynamic Monopoles

TL;DR

This paper develops a theoretical framework for understanding the periodic orbits of active particles like Volvox, emphasizing the role of hydrodynamic monopoles and gravitational effects in their oscillatory behavior.

Contribution

It introduces a Hamiltonian-based model for active particle dynamics near planes, accounting for monopolar flows and gravity, explaining observed oscillations and dancing behavior.

Findings

Limit cycle oscillations are governed by a Hamiltonian system.

Reflected flow and gravity influence the stability of oscillations.

The theory explains the dancing Volvox phenomenon.

Abstract

Terrestrial experiments on active particles, such as Volvox, involve gravitational forces, torques and accompanying monopolar fluid flows. Taking these into account, we analyse the dynamics of a pair of self-propelling, self-spinning active particles between widely separated parallel planes. Neglecting flow reflected by the planes, the dynamics of orientation and horizontal separation is symplectic, with a Hamiltonian exactly determining limit cycle oscillations. Near the bottom plane, gravitational torque damps and reflected flow excites this oscillator, sustaining a second limit cycle that can be perturbatively related to the first. Our work provides a theory for dancing Volvox and highlights the importance of monopolar flow in active matter.