Self Templating Assembly of Drop Lattices

We study the recursive Rayleigh-Plateau instability of neighboring viscous threads. We have recently found that the successive breakup of viscous threads deposited in an immiscible bath from a moving nozzle generates periodic drop patterns. In addition to the low-energy hexagonal lattice we report a variety of other non-hexagonal lattices obtained by adjusting nozzle translation speed and exploring diverse extrusion toolpaths, e.g. spirals. In order to elucidate this self-assembly mechanism, we study the instability of a single thread close to a periodic template. We find that the presence of a boundary drives the dynamics of the instability and affects the breakup pattern in a certain regime of parameters we will specify. We quantify the ``memory'' of the system, predicting when the patterns bear an imprint of the initial conditions or instead evolve towards universal solutions. We leverage this understanding to engineer the lattice morphology and characteristics.