Rotating electrohydrodynamic flow in a suspended liquid film

TL;DR

This paper develops a mathematical model for rotating electrohydrodynamic flow in thin liquid films, explaining experimental liquid film motor behavior through averaged stress and velocity analysis.

Contribution

It introduces a novel spatially averaged model linking electric fields to rotational flow in liquid films, advancing understanding of liquid film motors.

Findings

Model predicts tangential velocity near film edges

Stress proportional to cube of external electric field magnitude

Explains experimental rotation phenomena in liquid film motors

Abstract

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).