The growth of leading-edge distortions on a viscous sheet

The results of a set of experiments to determine some features of the undulations that develop on the leading edge of a sheet of fluid on an inclined plane are presented. A range of fluid viscosities, fluid volumes, and plate angles was used. In nearly all the cases, the observed disturbances had a triangular or sawtooth shape, with only a single example of a finger or parallel-sided shape appearing. The power-law exponents for the position down the plate of both the tips of the disturbances and their roots, that is, the points where they join the uniform sheet above them, were calculated from a series of photographs, and the corresponding wavelengths measured. The exponents are broadly in line with those that can be deduced from a simple model including viscosity, gravity, and volume flux, and ignoring all capillary effects. This conclusion suggests that the criterion for distinguishing the two types of disturbance does not depend on the global dynamics of the developing structures, and that a detailed analysis of the tip and root regions, where capillarity will be significant, is needed for further progress to be made.