We extended a mathematical model for the drying of sessile droplets, based on the lubrication approximation, to binary mixture droplets. This extension is relevant for e.g. inkjet printing applications, where ink consisting of several components are used. The extension involves the generalization of an established vapor diffusion-limited evaporation model to multi-component mixtures. The different volatilities of the liquid components generate a composition gradient at the liquid-air interface. The model takes the composition-dependence of the mass density, viscosity, surface tension, mutual diffusion coefficient and thermodynamic activities into account. This leads to a variety of effects ranging from solutal Marangoni flow over deviations from the typical spherical cap shape to an entrapped residual amount of the more volatile component at later stages of the drying. These aspects are discussed in detail on the basis of the numerical results for water-glycerol and water-ethanol droplets. The results show good agreement with experimental findings. Finally, the accuracy of the lubrication approximation is assessed by comparison with a finite element method.
- Marangoni flow
- Lubrication approximation
- Multi-component flow
Diddens, C., Kuerten, J. G. M., van der Geld, C. W. M., & Wijshoff, H. M. A. (2017). Modeling the evaporation of sessile multi-component droplets. Journal of colloid and interface science, 487, 426-436. https://doi.org/10.1016/j.jcis.2016.10.030