An unbounded approach to microfluidics using the Rayleigh-Plateau instability of viscous threads directly drawn in a bath

We study the droplet-forming instability of a thin jet extruded from a nozzle moving horizontally below the surface of an isoviscous immiscible fluid bath. While this interfacial instability is a classic problem in fluid mechanics, it has never been studied in the context of the deposition of a thread into a reservoir, an open-sky version of microfluidics. As the nozzle translates through the reservoir, drops may form at the nozzle (dripping) or further downstream (jetting). We first focus on rectilinear printing paths and derive a scaling law to rationalize the transition between dripping and jetting. We then leverage the flexibility of our system and study the dynamics of breakup when printing sinusoidal paths. We unravel a methodology to control both the size of the drops formed by the instability and the distance that separates them.