Abstract
We study the linear stability of a condensing thin liquid film of a binary vapor mixture by solving directly the bulk equations of the gas phase. The boundary layer of a finite depth is introduced above the liquid film, within which the variables are disturbed. The spatio-temporal evolution of the film thickness is described by the long-wave equation. The neutral stability condition predicts the existence of a critical thickness below which a flat film is stable due to the mass gain effect. However, if we consider the thickening of the liquid film by condensation, the relative neutral stability can be defined such that the growth rate of a disturbance is equal to that of the basic film thickness. The critical thickness and wavenumber obtained from the relative neutral stability condition significantly change from the original ones. Employing the asymptotic analysis for large wavenumbers, the critical thickness and wavenumber are numerically calculated for the water-ethanol system. Their dependence on the boundary layer depth, interface temperature and ambient vapor concentration is investigated. The results quite well agree with the experimental data not only qualitatively but also quantitatively.
