Capillary flow mediated dynamics of liquid droplet generation from a yarn

The spontaneous capillary imbibition of liquids through the porous netwrok of a yarn is a well studied phenomena and finds its application in numerous industrial processes. Of late, threads/yarns have been used as microfluidic devices, under the name μ-TAD, to study biochemical reactions, mixing of reagents, or as smart bandages. Interestingly, we find that, such an spontaneous flow can also result in the formation of liquid droplets at the freely hanging end of a verticaly placed yarn. However, the dynamics of the liquid droplet formation from a yarn is substantially different than that of a solid non-wettable nozzle. In the former the droplet growth is observed in three distinct modes namely, "radial growth", "axial growth", and "motion" regime. Each of the aforementioned stages exhibit distinct contact line and interfacial dynamics as the droplet grow freely in the yarn. We explore with a range of liquid viscosity to show that these dynamics in each regime are universal and can be elucidated with the help of unified scaling laws. Further, critical droplet volumes for the "motion" stage can also be derived theoretically, which in turn determines the pinch-off liquid volume. Such an system can be exploited as a prototype for the development of porous, wettable nozzles in future.