Application of the thin-film equations in modelling of Marangoni flow patterns amongst surfactant source and drain locations

Surfactants that are deposited at aqueous liquid films have the ability to generate surface tension gradients at the air-water interface, and thereby induce Marangoni flow. Combined with the production and depletion of surfactants at different locations of source and drains, out-of-equilibrium surface tension gradients can be sustained, resulting in Marangoni flow patterns that drive e.g., self-organization of amphiphile myelin assemblies. Here, a mathematical model based on the thin-film equations is proposed to simulate these flow patterns. The model equations are based on the surfactant source and drain concentrations, film-height and surfactant bulk concentration. We present a numerical scheme for approximating the model equations and discuss the numerically observed properties of the model.