On the instabilities of vertical falling liquid films in the presence of surface-active solute

Abstract

A linear-stability analysis is performed on a vertical falling film with a surface-active solute. It is assumed in the present model that the surfactant is soluble and volatile. In addition to the surface wave mode and the ‘wall wave’ mode which originate from the gravity-driven flow of the falling film itself, a new mode of instability related to the Marangoni effect induced by surface tension gradients is found for low Reynolds numbers and for moderate- or short-wavelength disturbances. The new mode is thought to be analogous to the thermocapillary instability examined first by Pearson (1958). The Marangoni instability of large-wavelength disturbances, revealed by Goussis & Kelly (1990) in a study of a liquid layer heated from below, may be completely suppressed in the present system by the effect of surface-excess concentration of the surfactant. The influence of the desorption of the solute and of its adsorption at the gas-liquid interface is determined for both the surface wave mode and the new wave mode. Desorption of the surfactant is shown to be responsible for the Marangoni instability of the new mode.