  Making liquid droplets move spontaneously on solid surfaces is a key
challenge in lab-on-chip and heat exchanger technologies. The best-known
mechanism, a wettability gradient, does not generally move droplets rapidly
enough and cannot drive droplets smaller than a critical size. Here we report
how a curvature gradient is particularly effective at accelerating small
droplets, and works for both hydrophilic and hydrophobic surfaces. Experiments
for water droplets on tapered surfaces with curvature radii in the
sub-millimeter range show a maximum speed of 0.28 m/s, two orders of magnitude
higher than obtained by wettability gradient. We show that the force exerted on
a droplet scales as the surface curvature gradient. Using molecular dynamics
simulations, we observe nanoscale droplets moving spontaneously at over 100 m/s
on tapered surfaces.
