Evaporation-driven solutal-Marangoni instability in a saline solution: Theoretical and numerical studies

The onset of solutal-capillary instability driven by evaporation through the solution-air interface is investigated theoretically and numerically in thin saline water. A scaling analysis shows that the development of the surface tension gradient is mainly driven by evaporative mass flux rather than evaporative heat flux, leading to the onset of solutal-capillary instability. The onset time of instability is theoretically analyzed through a linear stability analysis with newly derived stability equations that consider variations in the evaporative concentration, concluding that Ma center dot alpha is the most important parameter governing the onset of solutal-capillary convection, rather than Ma or alpha. Correspondingly, a nonlinear numerical simulation demonstrates that as evaporation proceeds, a nonvolatile salt accumulates near the evaporating interface and inhomogeneity of the concentration along the interface, which induces solutal-capillary motion, develops. The critical onset time determined from the linear stability analysis is in good agreement with the numerical simulation outcomes. The present theoretical and numerical study provides a better understanding of the evaporation-driven instability that develops in thin liquid films under the given temperature variation.