The production of small fluid droplets relies on an instability of solutions to the Young-Laplace equation. We ask whether smaller droplets can be produced by changing the shape of the nozzle. At a given critical pressure, the circular nozzle actually produces the largest droplet. The droplet volume can be decreased by up to 18% using a triangular nozzle with stretched corners.

We report a regime of ion beam sputtering that occurs for sufficiently steep slopes. High slopes propagate over large distances without dissipating the steepest features. Both the propagation velocity and the dynamically selected slope are universal, independent of the details of the initial shape of the surface. The resulting behavior can be understood as the propagation of a shock front that self-selects a stable slope, as has been previously observed in thin-film fluid flows. Experiments confirm predictions of the theory. An important implication of the propagative behavior at high surface slopes is that a pattern can be fabricated at a large length scale and, through uniform ion irradiation, reduced to a smaller length scale while preserving, or even sharpening, the sharpest features.