Cooperative Self-Propulsion of Active and Passive Rotors

TL;DR

This paper models hydrodynamic interactions between passive and active rotors at low Reynolds number, revealing that active rotors can also exhibit cooperative self-propulsion due to higher-order interactions.

Contribution

It introduces a unified framework for passive and active rotors, showing active rotors can self-propel cooperatively through octupolar hydrodynamic interactions.

Findings

Passive rotors exhibit dipolar azimuthal interactions (~1/r^2).

Active rotors lack dipolar interactions due to torque balance.

Active rotors can self-propel via octupolar interactions (~1/r^4).

Abstract

Using minimal models for low Reynolds number passive and active rotors in a fluid, we characterize the hydrodynamic interactions among rotors and the resulting dynamics of a pair of interacting rotors. This allows us to treat in a common framework passive or externally driven rotors, such as magnetic colloids driven by a rotating magnetic field, and active or internally driven rotors, such as sperm cells confined at boundaries. The hydrodynamic interaction of passive rotors is known to contain an azimuthal component \sim 1/r^2 to dipolar order that can yield the recently discovered "cooperative self-propulsion" of a pair of rotors of opposite vorticity. While this interaction is identically zero for active rotors as a consequence of torque balance, we show that a \sim 1/r^4 azimuthal component of the interaction arises in active systems to octupolar order. Cooperative self-propulsion, although weaker, can therefore also occur for pairs of active rotors.