Hydrodynamic bound states of rotating micro-cylinders in a confining geometry

TL;DR

This paper investigates the complex hydrodynamic interactions of rotating micro-cylinders in confined spaces, revealing the formation of stable bound states due to the interplay of cylinder interactions and boundary effects.

Contribution

It introduces analytical and numerical analysis of hydrodynamic bound states of rotating micro-cylinders in confinement, highlighting four distinct stable configurations.

Findings

Four non-trivial hydrodynamic bound states identified

Hydrodynamic interactions depend on relative positions within confinement

Confinement influences the formation of stable cylinder pairs

Abstract

Many micro-swimmers propel themselves by rotating micro-cylindrical organelles such as flagella or cilia. These cylindrical organelles almost never live in free space, yet their motions in a confining geometry can be counter-intuitive. For example, one of the intriguing yet classical results in this regard is that a rotating cylinder next to a plane wall does not generate any net force in Newtonian fluids and therefore does not translate. In this work, we employ analytical and numerical tools to investigate the motions of micro-cylinders under prescribed torques in a confining geometry. We show that a cylinder pair can form four non-trivial hydrodynamic bound states depending on the relative position within the confinement. Our analysis shows that the distinct states are the results of competing effects of the hydrodynamic interactions within the cylinder pair and between the active cylinders and the confinement.