Air-damping effects on developing velocity profiles in flowing soap films

The continuously running gravity-driven soap-film tunnel is a device suitable for the study of two-dimensional flows. In this innovative device, the films start from a reservoir, run over a vertical wire frame and get pulled by the gravity force. Despite its simple design and successful applications in two-dimensional flows, its working mechanisms are not fully understood. In the present work, the laminar velocity profiles of freely suspended flowing soap films are examined theoretically and experimentally. A complete momentum integral analysis is performed including boundary layers developed within the channel on the film as well as beside the film in the air. The theoretical results are compared with the experimental measurements via laser Doppler velocimetry. Reasonable agreements are observed. Although the gravity force speeds up the film motion, the acceleration is significantly slowed down, but not completely, by the air friction. The growth of the boundary layers developed on the film is also damped by the air friction so that across the film channel the velocity profile is mostly uniform. Moreover, a saturated boundary layer thickness seemingly exists when the thinning due to acceleration and the thickening due to viscous diffusion are in balance.