Shaping a Surface Microdroplet by Marangoni Forces along a Moving Contact Line of Four Immiscible Phases

The ability to transfer microdroplets between fluid phases offers numerous advantages in various fields, enabling better control, manipulation, and utilization of small volumes of fluids in pharmaceutical formulations, microfluidics, and lab-on-a-chip devices, single-cell analysis or droplet-based techniques for nanomaterial synthesis. This study focuses on the stability and morphology of a sessile oil microdroplet at the four-phase contact line of solid-water-oil-air during the droplet transfer from underwater to air. We observed a distinct transition in microdroplet dynamics, characterized by a shift from a scenario dominated by Marangoni forces to one dominated by capillary forces. In the regime dominated by Marangoni forces, the oil microdroplets spread in response to the contact between the water-air interface and the water-oil interface and the emergence of an oil concentration gradient along the water-air interface. The spreading distance along the four-phase contact line follows a power law relationship of $t^{3/4}$, reflecting the balance between Marangoni forces and viscous forces. On the other hand, in the capillarity-dominated regime, the oil microdroplets remain stable at the contact line and after being transferred into the air. We identify the crossover between these two regimes in the parameter space defined by three factors: the approaching velocity of the solid-water-air contact line ($v_{cl}$), the radius of the oil microdroplet ($r_o$), and the radius of the water drop ($r_w$). Furthermore, we demonstrate how to use the four-phase contact line for shaping oil microdroplets using a full liquid process by the contact line lithography. The findings in this study may be also applied to materials synthesis where nanoparticles, microspheres, or nanocapsules are produced by microdroplet-based techniques.