Generic Conditions for Hydrodynamic Synchronization

TL;DR

This paper derives the fundamental conditions under which hydrodynamic interactions lead to synchronization of oscillating biological structures like cilia and flagella, with implications for understanding biological systems and microfluidic device design.

Contribution

It provides the first comprehensive set of necessary and sufficient conditions for synchronization of rotors with arbitrary shapes and driving forces, including a novel time-dependent phase shift pattern.

Findings

Derived conditions for synchronization in various geometries

Identified a new synchronized pattern with time-dependent phase shift

Enhanced understanding of hydrodynamic interactions in biological systems

Abstract

Synchronization of actively oscillating organelles such as cilia and flagella facilitates self-propulsion of cells and pumping fluid in low Reynolds number environments. To understand the key mechanism behind synchronization induced by hydrodynamic interaction, we study a model of rigid-body rotors making fixed trajectories of arbitrary shape under driving forces that are arbitrary functions of the phases. For a wide class of geometries, we obtain the necessary and sufficient conditions for synchronization of a pair of rotors. We also find a novel synchronized pattern with a time-dependent phase shift. Our results shed light on the role of hydrodynamic interactions in biological systems, and could help in developing efficient mixing and transport strategies in microfluidic devices.