The stability of evaporating thin liquid films in the presence of surfactant. I. Lubrication approximation and linear analysis

Abstract

The dynamics of an evaporating wetting liquid film in the presence of dissolved surfactant is investigated. The solid substrate is planar and is subjected to heating. The liquid–vapor interface is a two-dimensional continuum characterized by specific adsorption, interfacial viscosity, and surface tension, which depend on the surfactant subsurface concentration and temperature. In the case of small density, viscosity, and thermal conductivity of the vapor phase (compared to the respective values for the liquid phase), at small Reynolds and large Peclet numbers and for thin films, the lubrication approximation model can be applied. The effect of the van der Waals disjoining pressure is taken into account. The appearing dimensionless groups, defined in terms of the real physical parameters, can vary by several orders of magnitude depending on the film initial thickness, temperature difference, and type of surfactants. The developed linear theory describes the competition among the various instabilities. The numerical solution of the evolution equation provides information about the critical film thickness, critical lateral wave number, and time for rupture. The influence of the interfacial mass loss due to evaporation, the van der Waals attraction, the Marangoni effects due to thermal and concentration gradients, and the interfacial viscous friction upon the critical film thickness is discussed.