Assessment of the film existence boundary position on an air streamed surface for a problem of airfoil icing

Within the framework of lubrication theory, numerical studies of thin film movement along the surface of a wing with the NACA0012 airfoil were carried out. The film is created by incoming drops of water and drifted by the external air flow. A model problem of one-dimensional film motion in the presence of a retarding longitudinal stress caused by disjoining pressure is considered. A cubic equation was obtained to determine the film thickness. If the contact angle exceeds a certain critical value, then the solution of this equation loses its physical meaning at some distance from the front critical point (the film thickness becomes negative). This means that the one-dimensional flow assumption is no longer satisfied. The maximum coordinate for existence a one-dimensional solution can be considered approximately as the beginning for the film disintegration into rivulets. Theoretical results are compared with the available experimental data.