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

Abstract

Wave formation on a thin liquid layer used for de-icing air-plane wings is investigated by studying the stability of air flow 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 half a million), and the Reynolds number based on liquid depth and air viscosity is of the order of a few thousand in actual practice. 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, including the Froude number F representing the gravity effect and a parameter S representing the surface-tension effect. In the calculation, the wavenumber is not restricted in any way.The wavenumber of the waves that one expects to observe 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).