Role of Surface Forces in the Stability of Evaporating Thin Liquid Films That Contain Surfactant Micelles

Abstract

We consider an evaporating liquid film which lies on a planar heated solid substrate. The film contains a dissolved surfactant at a high concentration, so that micellar aggregates exist in the bulk. Linear stability analysis of this system is performed by investigating the time evolution of the amplitude of fluctuation waves. The liquid-vapor interface is regarded as a two-dimensional continuum characterized by intrinsic viscosity, specific adsorption, and surface tension. The latter quantities depend on the instantaneous subsurface concentration of surfactant monomers (subject to fluctuation) and upon the temperature. At small Reynolds and large Peclet numbers, and for thin films, the lubrication approximation model can be applied to solve the hydrodynamic problem. In the balance of normal stress at the fluid interface, we account for the contribution of intermolecular forces. There are van der Waals, electrostatic, steric, and oscillatory structural interactions, which are described in terms of separate components of disjoining pressure. The oscillatory structural forces are due to the presence of surfactant micelles or other colloidal particles in the film. These forces turn out to have the highest magnitude, and are of great importance for the stability. We solve numerically the evolution equation for the fluctuation, thus finding the critical thickness of film rupture and the critical lateral wave number. The influence of the surfactant type and concentration and the relative significance of the particular interactions under different conditions are discussed in detail.