Evaporation of a binary mixture droplet with a slightly non-monotonic surface tension

Evaporating droplets consisting of a mixture of water and 1,2-hexanediol can be considered as an idealized model system for commercial ink used in water-based inkjet printing.

In these droplets, water evaporates - preferentially near the contact line - leaving behind the non-volatile 1,2-hexanediol.

With decreasing water concentration, the surface tension of this mixture initially strongly declines, giving rise to an axisymmetric Marangoni flow from the hexanediol-rich contact line along the liquid-gas interface to the water-rich top of the droplet.

However, in the limit of high hexanediol concentrations, the surface tension slightly increases again. This tiny increase of less than half a mN/m triggers the emergence of a reversed Marangoni flow in the rim region of the droplet, which breaks the azimuthal symmetry of the flow and composition field. When the hexanediol concentration near the contact line exceeds the critical composition with minimum surface tension, tiny spots of enhanced hexanediol concentrations appear at the contact line. Subsequently, the Marangoni dynamics leads to a coarsening of these spots until the entire droplet is covered and the flow ceases.

By means of experiments, three-dimensional finite element simulations and numerical azimuthal stability analysis, we investigate this intriguing phenomenon. Furthermore, we predict the wavelength of this remarkable and naively unexpected instability for any locally parabolic surface tension profile by means of a Marangoni number.