A nonlinear rupture theory of thin liquid films with soluble surfactant

The effects of soluble surfactant on the dynamic rupture of thin Liquid fil ms are investigated. A nonlinear coupling evolution equation is used to sim ulate the motion of thin liquid films on free surfaces. A generalized Frumk in model is adopted to simulate the adsorption/desorption kinetics of the s oluble surfactant between the surface and the bulk phases. Numerical simula tion results show that the liquid film system with soluble surfactant is mo re unstable than that with insoluble surfactant, Moreover, a generalized Fr umkin model is substituted for the Langmuir model to predict the instabilit y of liquid film with soluble surfactant. A numerical calculation using the generalized Frumkin model shows that the surfactant solubility increases a s the values of parameters of absorption/desorption rate constant (J), acti vation energy desorption (nu (d)), and bulk diffusion constant (D-1) increa se, which consequently causes the film system to become unstable. The surfa ctant solubility decreases as the rate of equilibrium (lambda) and interact ion among molecules (K) are increased, which therefore stabilizes the film system. On the other hand, an increase of relative surface concentration (t he index of a power law), beta>(*) over bar * (n), will initially result in a decrease of corresponding shear drag force as beta and n increase from 0 to 0.3 and 0.85, respectively. This will enhance the Marangoni effect. How ever, a further increase of beta and n to greater than 0.3 and 0.85, respec tively, will conversely result in an increase of the corresponding shear dr ag force. This will weaken the Marangoni effect and thus result in a reduct ion of interfacial stability. (C) 2000 Academic Press.