Dynamics of an evaporating thin film of polar liquid with solutocapillary Marangoni effect and capillary osmosis

The stability of the thin film of the polar liquid on the solid substrate with the hydrodynamic slip boundary condition is investigated in relation to the solutocapillary Marangoni effect. The solutocapillary Marangoni effect is driven by a surfactant changing the surface tension of the liquid. We hypothesize, that the bulk concentration of the surfactant changes linearly from the value on the solid-liquid interface to the value on the liquid-gas interface. The critical Marangoni numbers were found for various parameters responsible for solvent evaporation, surfactant diffusion, and surfactant solubility. We found, that only an anti-surfactant increasing the surface tension can destabilize the system under stated conditions and the adopted hypothesis. It was also observed, that the fluid slip along the substrate destabilizes the system slightly, and the diffusion along the liquid-gas interface stabilizes the film regarding the solutocapillary Marangoni effect.