Stability of evaporating two-layered liquid film in the presence of surfactant - I. The equations of lubrication approximation

In this study we consider the stability of horizontal two-layered liquid film attached to a heated solid substrate. The film can contain surfactant that is soluble in both liquid phases. The evaporation of solvent from the upper film is also taken into account. Thus, the two-layered film can exhibit both thermocapillary and Marangoni instabilities coupled with the effect of solvent mass loss. The problem is solved in the framework of the lubrication approximation. We derive a system of partial differential equations describing the evolution of long-wave disturbances in the presence of surfactant and evaporation. Appropriate rescaling is proposed and a numerical analysis of the dimensionless groups for particular system of water-light oil film upon a horizontal PVC plate is performed. The model allows one to investigate the role of different factors on the film stability: the surfactant concentration and distribution coefficient, the critical concentrations of micellization, the surface viscosities, the adsorption isotherms of the surfactant at the liquid surfaces and the intensity of evaporation. Based on this model the full linear analysis of the stability is given in Part II [see Danov et al. (1997b) Chem. Engng Sci., submitted]. The non-linear effects are also taken into account in Part III [see Paunov et al. (1997) Chem. Engng Sci. submitted], where these effects are studied numerically for a particular case of PVC/tetrachlorethane/water/vapour system. (C) 1998 Elsevier Science Ltd. All rights reserved.