Stationary waves on plane liquid sheets falling vertically

A theoretical and experimental investigation is carried out to study stationary waves on plane thin sheets of liquid (water) falling freely in still air in the presence of surface-active agents. Waves are produced experimentally by means of an obstacle, a very thin rod, placed normally through the sheet. Both sinuous and varicose waves are analysed. Theory predicts the fluid acceleration along the vertical direction to cause both the wavelength and the amplitude to decrease as the liquid falls. The angle between the tangent to the curve of constant phase of sinuous waves at the obstacle and the vertical direction, well recovered experimentally for pure water, is found to be practically unchanged when surfactants are added to the water. However, wave attenuation due to surface dissipation is evident. The observed wave patterns agree well with the numerical values computed by means of the method of characteristics.