Dynamics of a Quincke-rotating colloid near a planar electrode

The Quincke effect is an electrohydrodynamic instability that gives rise to an electric torque on a dielectric particle in a uniform DC electric field above a critical field. In free space, a Hopf bifurcation at higher field strength results in unsteady, chaotic rotation due to particle inertia.

The presence of a nearby electrode couples rotation and translation. After the first bifurcation, the torque on a spherical colloid results in the particle steady rolling. However, we find that at high field strengths the chaotic dynamics is suppressed, and instead periodic, oscillatory back-and-forth rolling takes place. We model the Quincke effect when higher order multipoles (due to the images) are present, and analyze the effect of particle-electrode gap and particle inertia. The bifurcation diagram quantifies the transition from the steady rolling state to chaotic and periodic oscillations, and illustratse the effect of the particle-electrode gap on the periodic orbits.