Figure 1

Left: schematic view of a liquid-film motor. A suspended liquid film is under the action of two electrical forcing. The first field is due to a voltage difference \(V_{\text{ in }}\) that is applied to the conducting electrodes forming two lateral edges of the frame. The second force comes from an externally applied electric field \(\mathbf{E}_{\text{ex}}\), asymptotically parallel to the plane of the film. As a result of these applied fields, the liquid fluid will eventually flow rotationally. Right: An idealized symmetric geometry where the frame is replaced by a circular frame with radius R. In this case a potential distribution \(V_{\text{in}}(\psi )=-\frac{V_{\text{in}}}{2}\cos \psi\) is applied to the frame