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

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.

9 pages, 8 figures

References in corpus (4)

• Self-motile colloidal particles: from directed propulsion to random walk
• Oscillatory Motion of a Camphor Grain in a One-Dimensional Finite Region
• Rotational motion of a droplet induced by interfacial tension
• General Criteria for Determining Rotation or Oscillation in a Two-dimensional Axisymmetric System

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