Dynamics and interactions of active rotors

TL;DR

This paper models and analyzes the hydrodynamic interactions of self-rotating objects in a fluid, revealing how pairs of rotors can induce translation or rotation, with implications for controlled self-propulsion.

Contribution

It provides a detailed analytical and numerical study of the coupled dynamics of rotor pairs, highlighting their potential for controlled self-propulsion in low Reynolds number fluids.

Findings

Same-sense rotors rotate around each other with constant angular velocity.

Opposite-sense rotors translate with a separation-dependent constant velocity.

Hydrodynamic interactions enable pairs of rotors to move despite isolated rotors being stationary.

Abstract

We consider a simple model of an internally driven self-rotating object; a rotor, confined to two dimensions by a thin film of low Reynolds number fluid. We undertake a detailed study of the hydrodynamic interactions between a pair of rotors and find that their effect on the resulting dynamics is a combination of fast and slow motions. We analyse the slow dynamics using an averaging procedure to take account of the fast degrees of freedom. Analytical results are compared with numerical simulations. Hydrodynamic interactions mean that while isolated rotors do not translate, bringing together a pair of rotors leads to motion of their centres. Two rotors spinning in the same sense rotate with an approximately constant angular velocity around each other, while two rotors of opposite sense, both translate with the same constant velocity, which depends on the separation of the pair. As a result a pair of counter-rotating rotors are a promising model for controlled self-propulsion.