(112e) Hydrodynamic Memory and Quincke Rotation

Quincke rotation refers to the spontaneous rotational motion of an uncharged, solid, dielectric particle immersed in a viscous fluid under an external electric field, as observed by G. Quincke in 1896. The last decade has witnessed a resurgence of interest in this phenomenon, motivated by applications in colloidal directed assembly; droplet electro-hydrodynamics; active matter; and suspension rheology and conductivity. For example, Sherman and Swan (PRL, 2020) questioned what happens if a particle bears a net electric charge. They showed via explicit ion, Brownian dynamics simulations that the Quincke rotation couples with electrophoresis of the charged particle resulting in spontaneous propulsion in a direction perpendicular to the applied field and the angular velocity. They coined this as an "electrokinetic Magnus effect." That paper is just one of Jim’s wonderful scientific contributions that have taught me so much. Here, we re-analyze the rotation of an uncharged spherical particle. If the inertia of the particle and fluid are neglected, a single (pitchfork) bifurcation from a quiescent base state to steady rotation is predicted. However, previous experiments have observed a second bifurcation from steady rotation to chaos at sufficiently large field strengths. Exiting theories, which only account for the inertia of the particle, under-predict the threshold field strength for the onset of chaos. We show that accounting for the transient fluid inertia, or “hydrodynamic memory,” associated with the unsteady diffusion of momentum from the angularly accelerating particle leads to an increase in the computed field strength for the transition to chaos, in line with experiments. Analysis of the rotational dynamics within the chaotic regime will also be presented.