Bifurcation in the angular velocity of a circular disk propelled by symmetrically distributed camphor pills

Abstract

We studied rotation of a disk propelled by a number of camphor pills symmetrically distributed at its edge. The disk was put on a water surface so that it could rotate around a vertical axis located at the disk center. In such a system, the driving torque originates from surface tension difference resulting from inhomogeneous surface concentration of camphor molecules released from the pills. Here we investigated the dependence of the stationary angular velocity on the disk radius and on the number of pills. The work extends our previous study on a linear rotor propelled by two camphor pills [Phys. Rev. E, 96, 012609 (2017)]. It was observed that the angular velocity dropped to zero after a critical number of pills was exceeded. Such behavior was confirmed by a numerical model of time evolution of the rotor. The model predicts that, for a fixed friction coefficient, the speed of pills can be accurately represented by a function of the linear number density of pills. We also present bifurcation analysis of the conditions at which the transition between a standing and a rotating disk appears.

arXiv comment14 pages, 8 figures

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Cited by in corpus (4)

• Spontaneous motion of a camphor particle with a triangular modification from a circle
• Imperfect bifurcation in the rotation of a propeller-shaped camphor rotor
• On a simple model that explains inversion of a self-propelled rotor under periodic stop and release operations
• Mathematical modeling for the synchronization of two interacting active rotors