Investigation Of Effect Of Disjoining Pressure And Surface Viscosity On Film Drainage Process

Foam is one of the most common,but most difficult to understand and grasp the decentralized system of daily life.The drainage of vertical soap film is a simplified model of foam drainage.The stability of film drainage is a key to understand foam formation and foam stability.The type,structure and concentration of surfactants have important influence on the stability of foam drainage,but the mechanism is surprisingly not yet elucidated.Most studies in this field focus on the independent effect of disjoining pressure or surface viscosity,whereas the coupled effect of former and latter are not involved.In this study,a model of vertical film drainage is constructed based on fluid mechanics theory considering the coupled effects of surface viscosity and disjoining pressure dependent on the type and concentration of surfactant.The evolution equations including the film thickness and surfactants concentrations relating to the unsteady drainage process is derived.Numerical calculations are conducted to determine the influence of regularity and strength of the above factors on the film profile,lifetime,and length of black film.The coupled mechanism of above factors all related to surfactants is elucidated.The main contents of the paper are as following:(1)Lubrication theory is applied to derive a coupled equation set describing the evolution of the film thickness,surfactant concentration and surface velocity.The equation set is solved numerically by the FreeFem program based on finite element method.(2)For the drainage under the gravity of a vertical foam film containing insoluble surfactant,an improved concentration-dependent disjoining pressure model is formulated based on the published experimental results.The characteristics of film evolution under the disjoining pressure are simulated numerically.(3)A mathematical model is established to investigate the gravity-driven draining process of a vertical thin liquid film containing insoluble surfactants when considering the synergistic effects of surface viscosity and disjoining pressure.The features of film evolution under the constant and variable surface viscosity are examined.(4)The drainage of a vertical foam film containing insoluble surfactant is explored based on the consideration of the combined effect of the disjoining pressure and surface viscosity,and the dynamics of film evolution under the different initial surfactant concentration and gradient are revealed with simulation.