Effect of Ionic Surfactants on the Film Drainage

The drainage of a partially mobile thin liquid film between two deformed gas bubbles is studied. The lubrication approximation and the assumption for small Peclet number are used to formulate the mathematical model of the problem. The mass balance equations for each of the species (ionic surfactant and background indifferent electrolyte) are simplified to an integral mass balance equations in the film. The material properties of the surfaces (surface viscosity, Gibbs elasticity, surface and/or bulk diffusivities, and surface electric potential) are taken into account in the tangential and normal stress balances. A simple analytical solution for a plane-parallel film is derived in the case of small deviations from equilibrium. The numerical analysis of the governing nonlinear equations shows the region of transition from partially mobile to immobile interfaces. A quantitative explanation of the following effects is proposed: (i) the increase of the surface mobility with the bulk and surface diffusivities; (ii) the role of the surface viscosity, compared to that of the Gibbs elasticity; (iii) the significant influence of the meniscus on the film drainage due to the increased hydrodynamic resistance; (iv) the effects of the surface potential and disjoining pressure. The model can be applied to explain the stability of foams in practical applications.