We investigate the cyclical stick-slip motion of water nanodroplets on a hydrophilic
substrate viewed with and stimulated by a transmission electron microscope. Using
a continuum long wave theory, we show how the electrostatic stress imposed by nonuniform charge distribution causes a pinned convex drop to deform into a toroidal
shape, with the shape characterized by the competition between the electrostatic
stress and the surface tension of the drop, as well as the charge density distribution
which follows a Poisson equation. A horizontal gradient in the charge density creates
a lateral driving force, which when sufficiently large, overcomes the pinning induced
by surface heterogeneities in the substrate disjoining pressure, causing the drop to
slide on the substrate via a cyclical stick-slip motion. Our model predicts steplike dynamics in drop displacement and surface area jumps, qualitatively consistent
with experimental observations.