# Relationship between the size of camphor-driven rotor and its angular velocity

## TL;DR

This study explores how the size of a camphor-driven rotor affects its steady angular velocity, revealing a maximum velocity at an optimal size and identifying a critical size below which rotation ceases.

## Contribution

The paper introduces a simple numerical model to analyze the relationship between rotor size and angular velocity, including the existence of a critical size for rotation.

## Key findings

- Angular velocity peaks at an optimal rotor size.
- Velocity decreases for larger rotor sizes beyond the peak.
- A critical rotor size exists below which rotation does not occur.

## Abstract

We consider a rotor made of two camphor disks glued below the ends of a plastic stripe. The disks are floating on a water surface and the plastic stripe does not touch the surface. The system can rotate around a vertical axis located at the center of the stripe. The disks dissipate camphor molecules. The driving momentum comes from the nonuniformity of surface tension resulting from inhomogeneous surface concentration of camphor molecules around the disks. We investigate the stationary angular velocity as a function of rotor radius $\ell$. For large $\ell$ the angular velocity decreases for increasing $\ell$. At a specific value of $\ell$ the angular velocity reaches its maximum and, for short $\ell$ it rapidly decreases. Such behaviour is confirmed by a simple numerical model. The model also predicts that there is a critical rotor size below which it does not rotate. Within the introduced model we analyze the type of this bifurcation.