Taming elasto-electro-hydrodynamic instability for low-Reynolds-number propulsion

Several micro-organisms propel themselves by propagating oscillatory bending waves along their slender appendages, flagella and cilia. This self-organised oscillation results from the sliding forces powered by the dynein motor proteins. Such a sophisticated strategy may not be easily engineered to drive synthetic micro-robots. An oscillatory electric or magnetic field is commonly used to wiggle a polarized body with a flexible slender structure along which undulatory waves are propagated.

By employing the electro-hydrodynamic instability to actuate the undulation of an elastic filament, we propose a new strategy to drive the low-Reynolds-number synthetic swimmers based on a time-independent uniform electric field. We solve the coupled electro-hydrodynamic equations and Euler–Bernoulli equations for the elastic filament numerically. We demonstrate that in certain regimes, instability occurs through a pitchfork or Hopf bifurcation; in the latter case, the filament undergoes self-organised undulation resulting in locomotion. We perform a linear stability analysis incorporating elasto-hydrodynamic models and the predicted critical elastic numbers corresponding to the onset of instability agree well with the numerical counterparts.