Wave growth on thin sheets of non-Newtonian liquids

Abstract

Abstract A linearized analysis has been employed to investigate wave growth on flat sheets of Newtonian and non-Newtonian liquids. Dispersive relations are obtained for both sinuous and dilational waves when the sheet is thin and the wavelengths are long compared to the sheet thickness. These relations yield the unexpected result, which is confirmed experimentally, that liquid viscosity has no effect on the initial wave growth of sinuous waves. They also predict instability for a much greater range of wave frequencies than those for the purely inviscid theory.