Nonlinear rupture theory of a thin free liquid film with insoluble surfactant

Effects of insoluble surfactant on the dynamic rupture of a thin free film are investigated. The integral method is applied to derive the strong nonlinear evolution equations. Then the numerical method is used to analyze the nonlinear rupture process. The results show that the Marangoni effect due to the concentration gradient of insoluble surfactant delays the rupture process. Furthermore, the rupture time predicted by the evolution equations derived by the integral theory is always longer than that predicted by the evolution equations derived by the long-wave expansion method. Besides, it is shown that the stronger the Marangoni effect becomes, the larger the difference between the rupture time predicted by both above two models becomes.