  Earlier works found out spontaneous directional motion of liquid droplets on
hydrophilic conical surfaces, however, not hydrophobic case. Here we show that
droplets on any surface may take place spontaneous directional motion without
considering contact angle property. The driving force is found to be
proportional to the curvature gradient of the surface. Fast motion can be lead
at surfaces with small curvature radii. The above discovery can help to create
more effective transportation technology of droplets, and better understand
some observed natural phenomena.
