Self-propagation of an electrode in leaky dielectrics and its possible relation to bacterial flagellar motors

In this letter, the origin of a force resulting in steady-state propagation of a spherical electrode in a leaky dielectric is explained and the force is calculated. The phenomenon of self-propagation begins from a perturbation in any direction resulting in the electrode motion in that direction. After that, the process sustains itself and a macroscopic electrode moves in the direction of the initial perturbation with a constant velocity U proportional to the potential difference ΔV applied to the system. Microscopic electrodes and bacterial flagellar motors should move with a velocity U∼ (ΔV)2. The predicted velocities agree fairly well with the experimental data.