Simultaneous thermal and surfactant-induced Marangoni effects in thin liquid films

The deformation of a thin liquid film in the presence of a surfactant monolayer, varying temperature distributions, and limited mass flux is considered. Use of lubrication theory yields a coupled pair of partial differential equations for the film height and surfactant surface monolayer concentration. The long-wave stability of the isothermal film is examined over a wide range of parameter values. It is shown that droplet patterns are obtained under certain thermal conditions for both an isothermal and nonisothermal underlying substrate. For the case of a localized thermal gradient initially imposed at the air-liquid interface, severe film thinning beneath the heat source was observed, which was not accompanied by droplet formation; pseudo steady states are observed in this case. In all situations the surfactant is found to rigidify the air-liquid interface, retarding thermally driven flow, while evaporation (condensation) acts to destabilize (stabilize) the film.     

Coating of an inclined plane in the presence of insoluble surfactant

We consider the flow of a thin liquid film coating an inclined plane in the presence of an insoluble surfactant. A fully non-linear two-dimensional system of governing equations is formulated using lubrication theory to describe the dynamics. Numerical simulations of this system highlight a fingering instability present at the main fluid front and elucidate the role of surfactant in the destabilizing mechanism. A full parametric study is undertaken which reveals the dependence of the fingering characteristics on system parameters. Numerical solutions at low angles of inclination are also obtained in order to illustrate the connection between gravitationally driven fingering and the instability induced by surfactant on a flat substrate. The similarities and differences between the destabilizing mechanisms in each case are discussed.     

A note on the coating of an inclined plane in the presence of soluble surfactant

We consider the flow of a thin liquid film coating an inclined plane in the presence of a soluble surfactant. A two-dimensional three-equation model is derived using lubrication theory in the rapid diffusion limit and then used to investigate the stability of the fluid height and the surfactant surface and bulk concentrations. We present solutions for an insoluble surfactant system, which are then contrasted with those obtained for a system containing a soluble surfactant; both transient growth and fully nonlinear two-dimensional simulation results are discussed. Our results indicate that the characteristics of the fingering phenomena which accompany the flow are altered by the effects of solubility. In particular, we find that these effects de-stabilise the system further over an intermediate range of surfactant solubility.