  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.
