A Nonlinear Rupture Theory of Thin Liquid Films with Soluble Surfactant

Abstract

The effects of soluble surfactant on the dynamic rupture of thin liquid films are investigated. A nonlinear coupling evolution equation is used to simulate the motion of thin liquid films on free surfaces. A generalized Frumkin model is adopted to simulate the adsorption/desorption kinetics of the soluble surfactant between the surface and the bulk phases. Numerical simulation results show that the liquid film system with soluble surfactant is more unstable than that with insoluble surfactant. Moreover, a generalized Frumkin model is substituted for the Langmuir model to predict the instability of liquid film with soluble surfactant. A numerical calculation using the generalized Frumkin model shows that the surfactant solubility increases as the values of parameters of absorption/desorption rate constant (J), activation energy desorption (νd), and bulk diffusion constant (D1) increase, which consequently causes the film system to become unstable. The surfactant solubility decreases as the rate of equilibrium (λ) and interaction among molecules (K) are increased, which therefore stabilizes the film system. On the other hand, an increase of relative surface concentration (the index of a power law), β(n), will initially result in a decrease of corresponding shear drag force as β and n increase from 0 to 0.3 and 0.85, respectively. This will enhance the Marangoni effect. However, a further increase of β and n to greater than 0.3 and 0.85, respectively, will conversely result in an increase of the corresponding shear drag force. This will weaken the Marangoni effect and thus result in a reduction of interfacial stability.