Nonlinear rupture theory of a thin liquid film with insoluble surfactant

Effects of insoluble surfactant on the dynamic rupture of a thin liquid film coated on a flat plate are studied. The strong nonlinear evolution equations derived by the integral method are solved by numerical method. The results show that enhancing (weakening) the Marangoni effect (the surface diffusion effect) will delay the rupture process. Furthermore, the rupture time predicted by the integral theory is shorter than that predicted by the long-wave expansion method. In addition, the quantitative difference in the rupture time predicted by two models enlarges with the increase of Marangoni effect, however, without obvious change as the diffusion effect increases.