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

TL;DR

This study investigates how the angular velocity of a circular disk propelled by symmetrically placed camphor pills depends on the number of pills and disk radius, revealing a bifurcation point where rotation ceases.

Contribution

It extends previous work by analyzing the bifurcation behavior and the dependence of angular velocity on pill density and disk size, supported by numerical modeling.

Findings

Angular velocity drops to zero after a critical number of pills.

Numerical model accurately predicts pill speed based on pill density.

Bifurcation analysis identifies conditions for transition between stationary and rotating states.

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.