Effect of disjoining pressure on the drainage and relaxation dynamics of liquid films with mobile interfaces

This work presents a generalized lubrication approximation of the drainage and relaxation of thin liquid films with tangentially mobile surfaces. The proposed model accounts for the dynamic effects and the role of surface forces of intermolecular origin. The van der Waals and hydrophobic attractive and the electrostatic and steric repulsive components of the disjoining pressure are included in the numerical calculations of the dynamics and relaxation of one-dimensional films. Different regimes of film drainage are discussed: regular and unstable mechanisms of thinning depending on the magnitude of the Reynolds number; pimple formation in the presence of large enough attractive surface forces; and stabilizing effects of the disjoining pressure repulsive components. In the case of relaxation, it is proven that the disturbances in the film thickness: decrease exponentially to the equilibrium state without taking into account the role of the disjoining pressure; increase very fast to the point of film rupture in the presence of attractive surface forces; oscillate with exponentially decreasing amplitudes towards the state of stable equilibrium when the electrostatic and steric repulsive forces are significant.