The Optimal Faucet

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.

Figure 1

Evolution of nozzle shape with threefold symmetry. (a) Initial nozzle: $\tilde{V}=1.00$; (b) $\tilde{V}=0.97$; (c) $\tilde{V}=0.88$; (d) $\tilde{V}=0.82$. $\tilde{V}$ is a normalized volume given by (9).

Figure 2

Sequence of iterations away from the circular nozzle with an initial threefold perturbation. The normalized critical volume given by (9) is shown in the bottom graph. The arrows indicate the corresponding shapes in Fig. 1.