Experimental evidence for a short-wave global mode in film flow along periodic corrugations

The primary instability of liquid film flow along periodically corrugated substrates is studied experimentally. Two different wall shapes, of the same wavelength and height, are tested for a wide range of inclinations. It is found that, beyond a specific inclination, a new instability mode occurs before the classical, convective, long-wave one. This is a short, travelling wave, which is highly regular and persistently two-dimensional, and appears to be a global mode. The exact shape of the corrugations has a leading-order effect on the inclination at which the new mode appears and on its wavelength at inception. Compared with the behaviour of film flow on a flat substrate, the presently tested periodic walls are found to delay very significantly, but each one to a different extent, the onset of the primary instability. This delay increases with inclination, and presents a distinct discontinuity when transition from the long-to the short-wave mode takes place.