Three-dimensional internal flow evolution of an evaporating droplet and its role in particle deposition pattern

The internal flow within an evaporating sessile droplet is one of the driving mechanisms that lead to various particle deposition patterns seen in applications such as inkjet printing, surface patterning, and blood stain analysis. Despite decades of research, the causal link between droplet internal flow and particle deposition patterns has not been fully established. In this study, we employ a three-dimensional (3D) imaging technique based on digital inline holography to quantitatively assess the evolution of internal flow fields and particle migration in three distinct types of wetting droplets, namely water droplets, sucrose aqueous solution droplets, and sodium dodecylsulfate aqueous solution droplets, throughout their entire evaporation process. Our imaging reveals the three-stage evolution of the 3D internal flow regimes driven by changes in the relative importance of capillary flow, Marangoni flow, and droplet boundary movement during evaporation. Moreover, the migration of individual particles from their initial locations to deposition can be divided into five categories, with some particles depositing at the contact line and others inside the droplet. In particular, we observe the changing migration directions of particles due to competing Marangoni and capillary flows. We further develop an analytical model that predicts the droplet internal flow, deposition patterns, and determines the deposition mechanisms depending on their initial locations and evolving internal flow. The model, validated using different types of droplets from our experiment and the literature, can be further expanded to other Newtonian and non-Newtonian droplets, potentially serving as a real-time assessment tool for particle deposition in various applications.