A low-Reynolds-number actuator driven by instability: rotating or oscillating

Due to an electro-hydrodynamic instability, a dielectric spherical particle immersed in a dielectric viscous solvent can exhibit steady rotation spontaneously (Quincke rotation) in a uniform steady electric field of sufficient strength. The recent works [Zhu and Stone, Phys Rev Fluids, 4(6):061701, 2019; Zhu and Stone, J Fluid Mech, p 888, 2020; Han et al., Proc Natl Acad Sci USA, 118(29), 2021] have demonstrated using an elastic structure to tune that instability for generating self-oscillation via an elasto-electro-hydrodynamic instability. Inspired by these studies, here, we use simulations to conceive a low-Reynolds-number actuator made of a dielectric spherical particle attached to an anchor via a flexible filament. We show that the actuator displays multiple behaviors: stationary, two modes of steady rotation, and a self-oscillatory motion, depending on the ratio μ¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{\mu }$$\end{document} of the viscous over elastic forces, slenderness of the filament, and the strength of the electric field. The complex dependence is illustrated by bifurcation diagrams revealing multiple features of the dynamical system. We then develop a reduced-order model that captures the main features of the dynamics revealed by the full model. A linear stability analysis is also performed to predict the onset of instability of the model system, which agrees well with the numerical results.