On a simple model that explains inversion of a self-propelled rotor under periodic stop and release operations

TL;DR

This paper introduces a simple mathematical model that explains how a self-propelled rotor on a liquid surface can invert its rotational direction under periodic stop-and-release cycles, aligning well with experimental observations.

Contribution

The model incorporates surface concentration, hydrodynamics, and asymmetry to qualitatively reproduce experimental inversion phenomena and analyze factors influencing inversion probability.

Findings

Model accurately predicts inversion probability based on stop duration.

Rotor asymmetry and noise significantly affect inversion likelihood.

Hydrodynamic flow and camphor transport compete to determine rotation direction.

Abstract

We propose a simple mathematical model that describes the time evolution of a self-propelled object on a liquid surface using such variables as the object location, the surface concentration of active molecules and the hydrodynamic surface flow. The model is applied to simulate the time evolution of a rotor composed of a polygonal plate with camphor pills at its corners. We have qualitatively reproduced results of experiments, in which the inversion of rotational direction under periodic stop-and-release operations was investigated. The model correctly describes the probability of the inversion as a function of the duration of the phase when the rotor is stopped. Moreover, the model allows to introduce the rotor asymmetry unavoidable in real experiments and study its influence on the studied phenomenon. Our numerical simulations have revealed that the probability of the inversion of rotational direction is determined by the competition among the transport of the camphor molecules by the flow, the intrinsic asymmetry of the rotor, and the noise amplitude.