Metachronal waves in a chain of rowers with hydrodynamic interactions

TL;DR

This study models a chain of hydrodynamically interacting beads, revealing conditions under which metachronal waves form, especially near boundaries, providing insights into microorganism surface wave phenomena.

Contribution

Introduces a simplified bead chain model to analyze the emergence of metachronal waves through hydrodynamic interactions and boundary effects.

Findings

Metachronal waves emerge with specific wavelengths near boundaries.

In bulk fluid, only transient synchronization occurs.

Synchronization depends on the curvature of the driving-force potential.

Abstract

Filaments on the surface of a microorganism such as Paramecium or Ophalina beat highly synchronized and form so-called metachronal waves that travel along the surfaces. In order to study under what principal conditions these waves form, we introduce a chain of beads, called rowers, each periodically driven by an external force on a straight line segment. To implement hydrodynamic interactions between the beads, they are considered point-like. Two beads synchronize in antiphase or in phase depending on the positive or negative curvature of their driving-force potential. Concentrating on in-phase synchronizing rowers, we find that they display only transient synchronization in a bulk fluid. On the other hand, metachronal waves with wavelengths of 7-10 rower distances emerge, when we restrict the range of hydrodynamic interactions either artificially to nearest neighbors or by the presence of a bounding surface as in any relevant biological system.