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

Abstract

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·α is the most important parameter governing the onset of solutal-capillary convection, rather than Ma or α. 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.