  Here we report a surface curvature-induced directional movement phenomenon,
based on molecular dynamics simulations, that a nanoscale water droplet at the
outer surface of a graphene cone always spontaneously moves toward the larger
end of the cone, and at the inner surface toward the smaller end. The analysis
on the van der Waals interaction potential between a single water molecule and
a curved graphene surface reveals that the curvature with its gradient does
generate the driving force resulting in the above directional motion.
Furthermore, we found that the direction of the above movement is independent
of the wettability, namely is regardless of either hydrophobic or hydrophilic
of the surface. However, the latter surface is in general leading to higher
motion speed than the former. The above results provide a basis for a better
understanding of many reported observations, and helping design of curved
surfaces with desired directional surface water transportation.
