Nonlinear Spreading Dynamics of a Localized Soluble Surfactant on a Thin Liquid Film

This paper focuses on the study of the spreading behavior of soluble surfactant in a thin liquid film system. For the convenience of numerical calculation, the system coordinate of the evolution equation is transformed. The generalized Frumkin model is used to simulate the adsorption/desorption process of soluble surfactant. Nonlinear coupling evolution equations are derived using the long-wave approximation and the cross-sectional averaging method. The spreading rate of a liquid film predicted by the generalized Frumkin model is faster than predicted by the Langmuir model. When the prediction using the generalized Frumkin model is performed at a smaller fi 8 (relative surface concentration), the effect of solubility of surfactant will be enhanced. Consequently, a small β will lead to the acceleration of spreading behavior; however, contrary results will come out while the value of β exceeds 2.0. The dimensionless bulk diffusion constant D₁ (the molecular interaction parameter, K and the activation energy of desorption, v_d) will enhance (weaken) the desorption of surfactant and decelerate (accelerate) the spreading rate of thin liquid film.