Rotating electrohydrodynamic flow in a suspended liquid film

The mathematical model of a rotating electrohydrodynamic flow in a thin suspended liquid film is proposed and studied. The motion is driven by the given difference of potentials in one direction and constant external electrical field $\vE_\text{out}$ in another direction in the plane of a film. To derive the model we employ the spatial averaging over the normal coordinate to a film that leads to the average Reynolds stress that is proportional to $|\vE_\text{out}|^3$. This stress generates tangential velocity in the vicinity of the edges of a film that, in turn, causes the rotational motion of a liquid. The proposed model is aimed to explain the experimental observations of the \emph{liquid film motor} (see arXiv:0805.0490v2).