THE STABILITY OF EVAPORATING THIN LIQUID-FILMS IN THE PRESENCE OF SURFACTANT .1. LUBRICATION APPROXIMATION AND LINEAR-ANALYSIS

The dynamics of an evaporating wetting liquid film in the presence of dissolved surfactant is investigated. The solid substrate is planar an d is subjected to heating, The liquid-vapor interface is a two-dimensi onal continuum characterized by specific adsorption, interfacial visco sity, and surface tension, which depend on the surfactant subsurface c oncentration and temperature. In the case of small density, viscosity, and thermal conductivity of the vapor phase (compared to the respecti ve values for the liquid phase), at small Reynolds and large Peclet nu mbers and for thin films, the lubrication approximation model can be a pplied. The effect of the van der Waals disjoining pressure is taken i nto account. The appearing dimensionless groups, defined in terms of t he real physical parameters, can vary by several orders of magnitude d epending on the film initial thickness, temperature difference, and ty pe of surfactants. The developed linear theory describes the competiti on among the various instabilities. The numerical solution of the evol ution 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 attrac tion, the Marangoni effects due to thermal and concentration gradients , and the interfacial viscous friction upon the critical film thicknes s is discussed. (C) 1998 American Institute of Physics.