  Mesoscopic hydrodynamic equations are solved to investigate the dynamics of
nanodroplets positioned near a topographic step of the supporting substrate.
Our results show that the dynamics depends on the characteristic length scales
of the system given by the height of the step and the size of the nanodroplets
as well as on the constituting substances of both the nanodroplets and the
substrate. The lateral motion of nanodroplets far from the step can be
described well in terms of a power law of the distance from the step. In
general the direction of the motion depends on the details of the effective
laterally varying intermolecular forces. But for nanodroplets positioned far
from the step it is solely given by the sign of the Hamaker constant of the
system. Moreover, our study reveals that the steps always act as a barrier for
transporting liquid droplets from one side of the step to the other.
