Instability of a Liquid Film Flowing down an Inclined Plane

Abstract

The mechanism of the instability of a layer of liquid flowing down an inclined plane is studied. First, the instability of the flow with respect to Tollimen-Schlichting wave is investigated. The results obtained are then compared with the known results of the instability of the same flow with respect to surface wave formation. It is found that, for a given angle of inclination, there exists a critical wavelength of the surface wave. If the wavelengths of the free surface disturbances are shorter than this critical wavelength, the film can become unstable due to shear waves before it becomes unstable with respect to surface waves. On the other hand, if the wavelengths of the free surface disturbances are longer than this critical wavelength, then the film will always become unstable due to free surface disturbances.