Chapter 2: 2015 Problem 4: Liquid Film Motor

In this solution, we investigate the rotating of a polarized liquid film in an electric field. Ionic polarization model and Helmholtz-Smoluchowski slip condition are applied to describe the motion. We divide the film into two parts: boundary layer bearing polarization charge and inner part with no net charge. Theoretically, we solve the electric field and the charge distribution. We calculate the flow velocity near the boundary. In the experiment, by changing voltages and shape of the film, we verify the predictions for the relation between the rotating velocity and the parameters.