Wave formation on a liquid layer for de-icing airplane wings

Wave formation on a thin liquid layer used for deicing aircraft wings is investigated by studying the stability of airflow over a liquid-coated flat plate at zero angle of incidence. The ratio of the viscosity of the liquid to that of air is very high (over 500,000), and the Reynolds number based on liquid depth and air viscosity is of the order of a few thousand. Under these circumstances the analysis gives two formulas, in closed form, for the growth rate and phase velocity of the waves in terms of the wavenumber and other relevant parameters. The expected wavenumber is that for which the growth rate is the maximum. The instability is one in which the viscosity difference between the two fluids (air and liquid) plays the dominant role, and is of the kind found by Yih (1967).