The spreading of droplet take placed when the surfactant-laden thin liquid films in the preset film or solid substrate, which is remarkably changed with the interface variation of solutions by the effect of surfactant. The spreading of surfactant solutions demonstrates the complex fingering phenomena and Marangoni effect, with strong nonlinear characteristics.The spreading process of surfactant solutions is captured by the disjoining pressure when the film thickness is less than roughly 100nm. It plays an acceleration or delay role in the spreading with different disjoining pressure models. The disjoining pressure controls the stability and wettability of the liquid film, and influences the dry spots formation speed obviously.Firstly, a reasonable disjoining pressure model of non-uniform is suggested, combining the non-uniform spreading characteristic of surfactant solution by microscopic molecular dynamics, surface colloid chemistry and macro fluid dynamics. Secondly, the theoretical model and the nonlinear three evolution equations for the film thickness and surface and bulk surfactant concentrations are derived on the base of diffusion theory, boundary theory and lubrication theory. Lastly, the procedure of PDECOL is used to perform the numerical simulation of the evolution equations whenÎ = 0,Î =Î ( h) andÎ =Î ( h , hx , hxx), which using finite element for space discretization and Gear's method in time. Effects of several parameters as capillary parameter, kinetic parameter and surfactant solubility on the profile of film thickness and surfactant concentrations are examined. The paper has considered the different influence of surfactant concentration on intermolecular repulsive and attractive forces. Linear stability is investigated for the evolution equation with the non-modal theory method by calculating the disturbance energy growth ratio and transient energy growth ratio. It not only improves the basic theory in the field, but also promotes the application of surfactant solutions, and the further prospects are suggested. |