Antiphase synchronization of electrically shaken conducting beads

Abstract

When a spherical conducting bead is placed in an electrode, it experiences an electric force. In a plane capacitor, it can undergo a periodic bouncing between the electrodes. Using a fast video camera, we measured the acceleration of the bead and the period of its motion as a function of the applied voltage. A mathematical model based on the hypothesis of electrostatic equilibrium is proposed to describe the dynamics of the system. We observe a stabilization of the trajectories: A bead bouncing between two electrodes tends to oscillate on a quasivertical trajectory, whatever its initial horizontal velocity. When two identical beads are placed together in a capacitor, they oscillate at the same frequency and an antiphase synchronization effect occurs. We propose a simple mechanism based on a Kuramoto-like model to explain it.