Droplet Tilings in Precessive Fields: Hysteresis, Elastic Defects, and Annealing

Two-component Marangoni contracted droplets can be arranged into arbitrary two-dimensional tiling patterns where they display rich dynamics due to vapor mediated long-range interactions. Recent work has characterized the centered hexagonal honeycomb lattice, showing it to be a highly frustrated system with many metastable states and relaxation occurring over multiple timescales [Molina et al., PNAS, 2021, 18, 34]. Here, we study this system under the influence of a rotating gravitational field. High amplitudes are able to completely disrupt droplet-droplet interactions, making it possible to identify a transition between field-dominated to interaction-dominated regimes. The system displays complex hysteresis behavior, the details of which are connected to the emergence of linear mesoscale structures. These mesoscale features display an elasticity that is governed by the balance between gravity and long-ranged vapor-mediated attractions. We find that disorder plays an important role in determining the dynamics of these features. Finally, we demonstrate the ability to anneal the system by progressively reducing the field amplitude, a process that reduces configurational energy compared to a rapid quench. The ability to manipulate vapor-mediated interactions in deliberately designed droplet tilings provides a novel platform for table-top explorations of multi-body interactions.