Optical signatures of no-slip rotation in liquid films: Spiral fringes and frame permittivity effects

Since the discovery of controlled rotation in soap films under electric fields in 2009, the rotation of suspended liquid films has drawn attention across disciplines. While prior studies identified surface charge as a primary driver—particularly in polar liquids and liquid crystals—our work introduces a new influencing factor: the permittivity of the supporting frame. We show that the frame-to-film permittivity ratio governs the transition between slip and no-slip rotational modes. Using both Particle-Image Velocimetry (PIV) and visual inspection, we characterize these modes. Although PIV offers precise measurements, we demonstrate that the two rotational states can be visually distinguished through their color patterns. Films in no-slip rotation exhibit vivid, colored spiral fringe patterns, while slip modes display steady central patterns. These spiral fringes result from white light interference between the incident wave and the portion transmitted through the film and reflected back from the second surface. When the film’s thickness is below the temporal coherence length of white light, and its geometry resembles a hybrid lens–spiral-phase element, concentric fringes transform into dynamic, colored spirals. We propose that in the no-slip mode, the rotating film behaves as a lens-like spiral-phase object. The observed spiral pattern thus serves as both a qualitative signature and a physical indicator of the no-slip regime. This finding provides an accessible optical method for identifying rotational modes and offers new insights into the interplay between electromechanical forces, geometry, and optical behavior in thin liquid films.